BTC-USD σ=0.0381, SOYB σ=0.0147, ρ=0.079. Min-variance weights: BTC-USD=0.109, SOYB=0.891.

Question:
Assets: BTC-USD, SOYB
BTC-USD: annualized_mean_return=0.6804, daily_std=0.0381
SOYB: annualized_mean_return=-0.0252, daily_std=0.0147
Minimum required portfolio return (annualized): 0.3972
Market regime: sideways

Compute portfolio weights (w_BTC-USD, w_SOYB) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BTC-USD=X.XXXX, w_SOYB=X.XXXX

Answer: w_BTC-USD=0.5986, w_SOYB=0.4014

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000216 - 0.000044) / (0.001451 + 0.000216 - 0.000088)
  Unconstrained: w_BTC-USD=0.1087
  After long-only clamp: w_BTC-USD=0.1087, w_SOYB=0.8913.


Question:
Assets: BTC-USD, LQD
BTC-USD: annualized_mean_return=2.0664, daily_std=0.0450
LQD: annualized_mean_return=0.0504, daily_std=0.0022
Minimum required portfolio return (annualized): 0.0511
Market regime: sideways

Compute portfolio weights (w_BTC-USD, w_LQD) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BTC-USD=X.XXXX, w_LQD=X.XXXX

Answer: w_BTC-USD=0.0008, w_LQD=0.9992

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000005 - 0.000003) / (0.002026 + 0.000005 - 0.000006)
  Unconstrained: w_BTC-USD=0.0008
  After long-only clamp: w_BTC-USD=0.0008, w_LQD=0.9992.


BNB-USD σ=0.0397, ICSH σ=0.0002, ρ=0.241. Min-variance weights: BNB-USD=0.000, ICSH=1.000.

Question:
Assets: BNB-USD, ICSH
BNB-USD: annualized_mean_return=2.2176, daily_std=0.0397
ICSH: annualized_mean_return=-0.0000, daily_std=0.0002
Minimum required portfolio return (annualized): 0.8328
Market regime: sideways

Compute portfolio weights (w_BNB-USD, w_ICSH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BNB-USD=X.XXXX, w_ICSH=X.XXXX

Answer: w_BNB-USD=0.3755, w_ICSH=0.6245

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000002) / (0.001578 + 0.000000 - 0.000004)
  Unconstrained: w_BNB-USD=-0.0012
  After long-only clamp: w_BNB-USD=0.0000, w_ICSH=1.0000.


Question:
Assets: DOT-USD, USMV
DOT-USD: annualized_mean_return=-1.0080, daily_std=0.0363
USMV: annualized_mean_return=-0.0504, daily_std=0.0107
Minimum required portfolio return (annualized): -0.5071
Market regime: sideways

Compute portfolio weights (w_DOT-USD, w_USMV) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_DOT-USD=X.XXXX, w_USMV=X.XXXX

Answer: w_DOT-USD=0.1014, w_USMV=0.8986

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000114 - -0.000040) / (0.001321 + 0.000114 - -0.000079)
  Unconstrained: w_DOT-USD=0.1013
  After long-only clamp: w_DOT-USD=0.1013, w_USMV=0.8987.


MATIC-USD σ=0.1198, GLD σ=0.0086, ρ=-0.098. Min-variance weights: MATIC-USD=0.012, GLD=0.988.

Question:
Assets: MATIC-USD, GLD
MATIC-USD: annualized_mean_return=6.6780, daily_std=0.1198
GLD: annualized_mean_return=-0.1260, daily_std=0.0086
Minimum required portfolio return (annualized): 4.8021
Market regime: sideways

Compute portfolio weights (w_MATIC-USD, w_GLD) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_MATIC-USD=X.XXXX, w_GLD=X.XXXX

Answer: w_MATIC-USD=0.7243, w_GLD=0.2757

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000075 - -0.000101) / (0.014347 + 0.000075 - -0.000203)
  Unconstrained: w_MATIC-USD=0.0120
  After long-only clamp: w_MATIC-USD=0.0120, w_GLD=0.9880.


Question:
Assets: BNB-USD, CORN
BNB-USD: annualized_mean_return=8.5932, daily_std=0.1088
CORN: annualized_mean_return=-0.1008, daily_std=0.0055
Minimum required portfolio return (annualized): -0.0306
Market regime: sideways

Compute portfolio weights (w_BNB-USD, w_CORN) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BNB-USD=X.XXXX, w_CORN=X.XXXX

Answer: w_BNB-USD=0.0139, w_CORN=0.9861

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000030 - -0.000138) / (0.011839 + 0.000030 - -0.000275)
  Unconstrained: w_BNB-USD=0.0138
  After long-only clamp: w_BNB-USD=0.0138, w_CORN=0.9862.


Question:
Assets: EWJ, VCIT
EWJ: annualized_mean_return=0.1512, daily_std=0.0070
VCIT: annualized_mean_return=-0.0252, daily_std=0.0016
Minimum required portfolio return (annualized): 0.0473
Market regime: sideways

Compute portfolio weights (w_EWJ, w_VCIT) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_EWJ=X.XXXX, w_VCIT=X.XXXX

Answer: w_EWJ=0.4110, w_VCIT=0.5890

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000002 - 0.000001) / (0.000049 + 0.000002 - 0.000002)
  Unconstrained: w_EWJ=0.0271
  After long-only clamp: w_EWJ=0.0271, w_VCIT=0.9729.


QUAL σ=0.0075, ETH-USD σ=0.0480, ρ=0.096. Min-variance weights: QUAL=0.991, ETH-USD=0.009.

Question:
Assets: QUAL, ETH-USD
QUAL: annualized_mean_return=0.1008, daily_std=0.0075
ETH-USD: annualized_mean_return=1.4868, daily_std=0.0480
Minimum required portfolio return (annualized): 0.1063
Market regime: sideways

Compute portfolio weights (w_QUAL, w_ETH-USD) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_QUAL=X.XXXX, w_ETH-USD=X.XXXX

Answer: w_QUAL=0.9910, w_ETH-USD=0.0090

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.002308 - 0.000035) / (0.000056 + 0.002308 - 0.000069)
  Unconstrained: w_QUAL=0.9908
  After long-only clamp: w_QUAL=0.9908, w_ETH-USD=0.0092.


ADA-USD σ=0.0624, SGOV σ=0.0001, ρ=0.120. Min-variance weights: ADA-USD=0.000, SGOV=1.000.

Question:
Assets: ADA-USD, SGOV
ADA-USD: annualized_mean_return=2.4444, daily_std=0.0624
SGOV: annualized_mean_return=0.0000, daily_std=0.0001
Minimum required portfolio return (annualized): 1.4231
Market regime: sideways

Compute portfolio weights (w_ADA-USD, w_SGOV) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_ADA-USD=X.XXXX, w_SGOV=X.XXXX

Answer: w_ADA-USD=0.5822, w_SGOV=0.4178

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000001) / (0.003900 + 0.000000 - 0.000001)
  Unconstrained: w_ADA-USD=-0.0001
  After long-only clamp: w_ADA-USD=0.0000, w_SGOV=1.0000.


Question:
Assets: EWJ, ICSH
EWJ: annualized_mean_return=-0.0000, daily_std=0.0112
ICSH: annualized_mean_return=0.0252, daily_std=0.0003
Minimum required portfolio return (annualized): 0.0208
Market regime: sideways

Compute portfolio weights (w_EWJ, w_ICSH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_EWJ=X.XXXX, w_ICSH=X.XXXX

Answer: w_EWJ=0.0007, w_ICSH=0.9993

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000126 + 0.000000 - 0.000000)
  Unconstrained: w_EWJ=0.0001
  After long-only clamp: w_EWJ=0.0001, w_ICSH=0.9999.


Question:
Assets: BTC-USD, ICSH
BTC-USD: annualized_mean_return=-0.9072, daily_std=0.0255
ICSH: annualized_mean_return=0.0252, daily_std=0.0002
Minimum required portfolio return (annualized): 0.0252
Market regime: sideways

Compute portfolio weights (w_BTC-USD, w_ICSH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BTC-USD=X.XXXX, w_ICSH=X.XXXX

Answer: w_BTC-USD=-0.0000, w_ICSH=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000651 + 0.000000 - -0.000000)
  Unconstrained: w_BTC-USD=0.0004
  After long-only clamp: w_BTC-USD=0.0004, w_ICSH=0.9996.


Question:
Assets: ACWI, ICSH
ACWI: annualized_mean_return=0.1512, daily_std=0.0072
ICSH: annualized_mean_return=0.0252, daily_std=0.0002
Minimum required portfolio return (annualized): 0.0253
Market regime: sideways

Compute portfolio weights (w_ACWI, w_ICSH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_ACWI=X.XXXX, w_ICSH=X.XXXX

Answer: w_ACWI=0.0009, w_ICSH=0.9991

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000052 + 0.000000 - -0.000000)
  Unconstrained: w_ACWI=0.0013
  After long-only clamp: w_ACWI=0.0013, w_ICSH=0.9987.


Question:
Assets: ^VIX, PPLT
^VIX: annualized_mean_return=0.6048, daily_std=0.0779
PPLT: annualized_mean_return=-0.3276, daily_std=0.0166
Minimum required portfolio return (annualized): -0.3021
Market regime: sideways

Compute portfolio weights (w_^VIX, w_PPLT) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_^VIX=X.XXXX, w_PPLT=X.XXXX

Answer: w_^VIX=0.0274, w_PPLT=0.9726

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000275 - 0.000107) / (0.006073 + 0.000275 - 0.000213)
  Unconstrained: w_^VIX=0.0274
  After long-only clamp: w_^VIX=0.0274, w_PPLT=0.9726.


Question:
Assets: XLK, IAU
XLK: annualized_mean_return=-0.0504, daily_std=0.0161
IAU: annualized_mean_return=0.0756, daily_std=0.0074
Minimum required portfolio return (annualized): 0.0698
Market regime: sideways

Compute portfolio weights (w_XLK, w_IAU) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLK=X.XXXX, w_IAU=X.XXXX

Answer: w_XLK=0.0460, w_IAU=0.9540

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000055 - -0.000000) / (0.000259 + 0.000055 - -0.000001)
  Unconstrained: w_XLK=0.1748
  After long-only clamp: w_XLK=0.1748, w_IAU=0.8252.


Question:
Assets: IWM, PDBC
IWM: annualized_mean_return=-0.3780, daily_std=0.0120
PDBC: annualized_mean_return=-0.7056, daily_std=0.0099
Minimum required portfolio return (annualized): -0.6067
Market regime: sideways

Compute portfolio weights (w_IWM, w_PDBC) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_IWM=X.XXXX, w_PDBC=X.XXXX

Answer: w_IWM=0.4016, w_PDBC=0.5984

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000097 - 0.000002) / (0.000144 + 0.000097 - 0.000003)
  Unconstrained: w_IWM=0.4018
  After long-only clamp: w_IWM=0.4018, w_PDBC=0.5982.


Question:
Assets: MTUM, LQD
MTUM: annualized_mean_return=0.3024, daily_std=0.0088
LQD: annualized_mean_return=-0.0504, daily_std=0.0027
Minimum required portfolio return (annualized): 0.0609
Market regime: sideways

Compute portfolio weights (w_MTUM, w_LQD) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_MTUM=X.XXXX, w_LQD=X.XXXX

Answer: w_MTUM=0.3155, w_LQD=0.6845

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000007 - -0.000001) / (0.000078 + 0.000007 - -0.000003)
  Unconstrained: w_MTUM=0.0962
  After long-only clamp: w_MTUM=0.0962, w_LQD=0.9038.


BTC-USD σ=0.0204, VCIT σ=0.0035, ρ=0.000. Min-variance weights: BTC-USD=0.028, VCIT=0.972.

Question:
Assets: BTC-USD, VCIT
BTC-USD: annualized_mean_return=0.9324, daily_std=0.0204
VCIT: annualized_mean_return=-0.1260, daily_std=0.0035
Minimum required portfolio return (annualized): -0.1052
Market regime: sideways

Compute portfolio weights (w_BTC-USD, w_VCIT) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BTC-USD=X.XXXX, w_VCIT=X.XXXX

Answer: w_BTC-USD=0.0283, w_VCIT=0.9717

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000012 - 0.000000) / (0.000417 + 0.000012 - 0.000000)
  Unconstrained: w_BTC-USD=0.0283
  After long-only clamp: w_BTC-USD=0.0283, w_VCIT=0.9717.


Question:
Assets: XLU, HAUZ
XLU: annualized_mean_return=-0.1008, daily_std=0.0102
HAUZ: annualized_mean_return=0.1260, daily_std=0.0096
Minimum required portfolio return (annualized): 0.0438
Market regime: sideways

Compute portfolio weights (w_XLU, w_HAUZ) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLU=X.XXXX, w_HAUZ=X.XXXX

Answer: w_XLU=0.3624, w_HAUZ=0.6376

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000093 - 0.000011) / (0.000105 + 0.000093 - 0.000022)
  Unconstrained: w_XLU=0.4663
  After long-only clamp: w_XLU=0.4663, w_HAUZ=0.5337.


Question:
Assets: XLB, ICSH
XLB: annualized_mean_return=0.0000, daily_std=0.0121
ICSH: annualized_mean_return=0.0252, daily_std=0.0003
Minimum required portfolio return (annualized): 0.0164
Market regime: sideways

Compute portfolio weights (w_XLB, w_ICSH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLB=X.XXXX, w_ICSH=X.XXXX

Answer: w_XLB=0.0005, w_ICSH=0.9995

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000146 + 0.000000 - -0.000000)
  Unconstrained: w_XLB=0.0014
  After long-only clamp: w_XLB=0.0014, w_ICSH=0.9986.


Question:
Assets: XLI, ICSH
XLI: annualized_mean_return=0.2772, daily_std=0.0058
ICSH: annualized_mean_return=0.0000, daily_std=0.0003
Minimum required portfolio return (annualized): 0.1142
Market regime: sideways

Compute portfolio weights (w_XLI, w_ICSH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLI=X.XXXX, w_ICSH=X.XXXX

Answer: w_XLI=0.4120, w_ICSH=0.5880

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000034 + 0.000000 - 0.000000)
  Unconstrained: w_XLI=-0.0008
  After long-only clamp: w_XLI=0.0000, w_ICSH=1.0000.


Question:
Assets: XLF, LQD
XLF: annualized_mean_return=0.5040, daily_std=0.0083
LQD: annualized_mean_return=0.0000, daily_std=0.0038
Minimum required portfolio return (annualized): 0.1196
Market regime: sideways

Compute portfolio weights (w_XLF, w_LQD) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLF=X.XXXX, w_LQD=X.XXXX

Answer: w_XLF=0.2398, w_LQD=0.7602

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000014 - -0.000011) / (0.000069 + 0.000014 - -0.000021)
  Unconstrained: w_XLF=0.2382
  After long-only clamp: w_XLF=0.2382, w_LQD=0.7618.


Question:
Assets: VEA, REZ
VEA: annualized_mean_return=0.3276, daily_std=0.0049
REZ: annualized_mean_return=0.1512, daily_std=0.0081
Minimum required portfolio return (annualized): 0.3082
Market regime: sideways

Compute portfolio weights (w_VEA, w_REZ) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_VEA=X.XXXX, w_REZ=X.XXXX

Answer: w_VEA=0.8900, w_REZ=0.1100

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000066 - 0.000007) / (0.000024 + 0.000066 - 0.000013)
  Unconstrained: w_VEA=0.7751
  After long-only clamp: w_VEA=0.7751, w_REZ=0.2249.


Question:
Assets: XLI, IGOV
XLI: annualized_mean_return=-0.4536, daily_std=0.0114
IGOV: annualized_mean_return=-0.1260, daily_std=0.0034
Minimum required portfolio return (annualized): -0.1411
Market regime: sideways

Compute portfolio weights (w_XLI, w_IGOV) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLI=X.XXXX, w_IGOV=X.XXXX

Answer: w_XLI=0.0461, w_IGOV=0.9539

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000011 - 0.000000) / (0.000129 + 0.000011 - 0.000000)
  Unconstrained: w_XLI=0.0802
  After long-only clamp: w_XLI=0.0802, w_IGOV=0.9198.


Question:
Assets: XLB, DBA
XLB: annualized_mean_return=0.2268, daily_std=0.0134
DBA: annualized_mean_return=0.3780, daily_std=0.0072
Minimum required portfolio return (annualized): 0.3720
Market regime: sideways

Compute portfolio weights (w_XLB, w_DBA) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLB=X.XXXX, w_DBA=X.XXXX

Answer: w_XLB=0.0397, w_DBA=0.9603

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000051 - 0.000016) / (0.000179 + 0.000051 - 0.000032)
  Unconstrained: w_XLB=0.1765
  After long-only clamp: w_XLB=0.1765, w_DBA=0.8235.


Question:
Assets: VLUE, CORN
VLUE: annualized_mean_return=-0.0252, daily_std=0.0122
CORN: annualized_mean_return=0.1512, daily_std=0.0124
Minimum required portfolio return (annualized): 0.0949
Market regime: sideways

Compute portfolio weights (w_VLUE, w_CORN) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_VLUE=X.XXXX, w_CORN=X.XXXX

Answer: w_VLUE=0.3192, w_CORN=0.6808

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000154 - -0.000012) / (0.000149 + 0.000154 - -0.000024)
  Unconstrained: w_VLUE=0.5073
  After long-only clamp: w_VLUE=0.5073, w_CORN=0.4927.


AVAX-USD σ=0.0897, BIL σ=0.0001, ρ=0.180. Min-variance weights: AVAX-USD=0.000, BIL=1.000.

Question:
Assets: AVAX-USD, BIL
AVAX-USD: annualized_mean_return=2.4696, daily_std=0.0897
BIL: annualized_mean_return=-0.0000, daily_std=0.0001
Minimum required portfolio return (annualized): -0.0000
Market regime: sideways

Compute portfolio weights (w_AVAX-USD, w_BIL) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_AVAX-USD=X.XXXX, w_BIL=X.XXXX

Answer: w_AVAX-USD=0.0000, w_BIL=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000002) / (0.008038 + 0.000000 - 0.000003)
  Unconstrained: w_AVAX-USD=-0.0002
  After long-only clamp: w_AVAX-USD=0.0000, w_BIL=1.0000.


Question:
Assets: VTI, HYG
VTI: annualized_mean_return=0.0504, daily_std=0.0098
HYG: annualized_mean_return=0.0000, daily_std=0.0024
Minimum required portfolio return (annualized): 0.0318
Market regime: sideways

Compute portfolio weights (w_VTI, w_HYG) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_VTI=X.XXXX, w_HYG=X.XXXX

Answer: w_VTI=0.6310, w_HYG=0.3690

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000006 - -0.000007) / (0.000097 + 0.000006 - -0.000014)
  Unconstrained: w_VTI=0.1101
  After long-only clamp: w_VTI=0.1101, w_HYG=0.8899.


Question:
Assets: ^VIX, PALL
^VIX: annualized_mean_return=0.6552, daily_std=0.0679
PALL: annualized_mean_return=0.5544, daily_std=0.0181
Minimum required portfolio return (annualized): 0.5597
Market regime: sideways

Compute portfolio weights (w_^VIX, w_PALL) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_^VIX=X.XXXX, w_PALL=X.XXXX

Answer: w_^VIX=0.1052, w_PALL=0.8948

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000329 - -0.000241) / (0.004604 + 0.000329 - -0.000482)
  Unconstrained: w_^VIX=0.1052
  After long-only clamp: w_^VIX=0.1052, w_PALL=0.8948.


ADA-USD σ=0.0624, PALL σ=0.0197, ρ=0.012. Min-variance weights: ADA-USD=0.088, PALL=0.912.

Question:
Assets: ADA-USD, PALL
ADA-USD: annualized_mean_return=3.0744, daily_std=0.0624
PALL: annualized_mean_return=-0.0252, daily_std=0.0197
Minimum required portfolio return (annualized): 1.7917
Market regime: sideways

Compute portfolio weights (w_ADA-USD, w_PALL) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_ADA-USD=X.XXXX, w_PALL=X.XXXX

Answer: w_ADA-USD=0.5862, w_PALL=0.4138

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000390 - 0.000015) / (0.003890 + 0.000390 - 0.000029)
  Unconstrained: w_ADA-USD=0.0882
  After long-only clamp: w_ADA-USD=0.0882, w_PALL=0.9118.


Question:
Assets: FXI, BNO
FXI: annualized_mean_return=0.6048, daily_std=0.0078
BNO: annualized_mean_return=-0.5292, daily_std=0.0135
Minimum required portfolio return (annualized): -0.1508
Market regime: sideways

Compute portfolio weights (w_FXI, w_BNO) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_FXI=X.XXXX, w_BNO=X.XXXX

Answer: w_FXI=0.7822, w_BNO=0.2178

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000181 - 0.000015) / (0.000061 + 0.000181 - 0.000030)
  Unconstrained: w_FXI=0.7816
  After long-only clamp: w_FXI=0.7816, w_BNO=0.2184.


ADA-USD σ=0.0438, VNQI σ=0.0110, ρ=0.128. Min-variance weights: ADA-USD=0.031, VNQI=0.969.

Question:
Assets: ADA-USD, VNQI
ADA-USD: annualized_mean_return=0.6552, daily_std=0.0438
VNQI: annualized_mean_return=0.3276, daily_std=0.0110
Minimum required portfolio return (annualized): 0.5826
Market regime: sideways

Compute portfolio weights (w_ADA-USD, w_VNQI) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_ADA-USD=X.XXXX, w_VNQI=X.XXXX

Answer: w_ADA-USD=0.7784, w_VNQI=0.2216

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000121 - 0.000062) / (0.001919 + 0.000121 - 0.000123)
  Unconstrained: w_ADA-USD=0.0311
  After long-only clamp: w_ADA-USD=0.0311, w_VNQI=0.9689.


Question:
Assets: XLB, ICSH
XLB: annualized_mean_return=0.2520, daily_std=0.0122
ICSH: annualized_mean_return=0.0252, daily_std=0.0002
Minimum required portfolio return (annualized): 0.0253
Market regime: sideways

Compute portfolio weights (w_XLB, w_ICSH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLB=X.XXXX, w_ICSH=X.XXXX

Answer: w_XLB=0.0004, w_ICSH=0.9996

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000150 + 0.000000 - -0.000000)
  Unconstrained: w_XLB=0.0011
  After long-only clamp: w_XLB=0.0011, w_ICSH=0.9989.


Question:
Assets: XLU, ICSH
XLU: annualized_mean_return=0.2016, daily_std=0.0080
ICSH: annualized_mean_return=0.0000, daily_std=0.0008
Minimum required portfolio return (annualized): 0.1012
Market regime: sideways

Compute portfolio weights (w_XLU, w_ICSH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLU=X.XXXX, w_ICSH=X.XXXX

Answer: w_XLU=0.5020, w_ICSH=0.4980

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000001 - -0.000000) / (0.000064 + 0.000001 - -0.000000)
  Unconstrained: w_XLU=0.0108
  After long-only clamp: w_XLU=0.0108, w_ICSH=0.9892.


Question:
Assets: XLF, IEF
XLF: annualized_mean_return=-0.0504, daily_std=0.0115
IEF: annualized_mean_return=0.2772, daily_std=0.0033
Minimum required portfolio return (annualized): 0.0873
Market regime: sideways

Compute portfolio weights (w_XLF, w_IEF) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLF=X.XXXX, w_IEF=X.XXXX

Answer: w_XLF=0.1585, w_IEF=0.8415

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000011 - -0.000017) / (0.000133 + 0.000011 - -0.000034)
  Unconstrained: w_XLF=0.1586
  After long-only clamp: w_XLF=0.1586, w_IEF=0.8414.


Question:
Assets: XLK, WEAT
XLK: annualized_mean_return=0.2520, daily_std=0.0071
WEAT: annualized_mean_return=0.3024, daily_std=0.0165
Minimum required portfolio return (annualized): 0.2898
Market regime: sideways

Compute portfolio weights (w_XLK, w_WEAT) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLK=X.XXXX, w_WEAT=X.XXXX

Answer: w_XLK=0.2500, w_WEAT=0.7500

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000273 - -0.000010) / (0.000051 + 0.000273 - -0.000021)
  Unconstrained: w_XLK=0.8227
  After long-only clamp: w_XLK=0.8227, w_WEAT=0.1773.


Question:
Assets: ETH-USD, HAUZ
ETH-USD: annualized_mean_return=-2.8980, daily_std=0.0556
HAUZ: annualized_mean_return=-0.7308, daily_std=0.0114
Minimum required portfolio return (annualized): -1.5414
Market regime: sideways

Compute portfolio weights (w_ETH-USD, w_HAUZ) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_ETH-USD=X.XXXX, w_HAUZ=X.XXXX

Answer: w_ETH-USD=0.0648, w_HAUZ=0.9352

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000131 - -0.000090) / (0.003091 + 0.000131 - -0.000180)
  Unconstrained: w_ETH-USD=0.0649
  After long-only clamp: w_ETH-USD=0.0649, w_HAUZ=0.9351.


Question:
Assets: BTC-USD, UNG
BTC-USD: annualized_mean_return=0.6804, daily_std=0.0308
UNG: annualized_mean_return=-0.0000, daily_std=0.0110
Minimum required portfolio return (annualized): 0.4331
Market regime: sideways

Compute portfolio weights (w_BTC-USD, w_UNG) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BTC-USD=X.XXXX, w_UNG=X.XXXX

Answer: w_BTC-USD=0.6365, w_UNG=0.3635

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000121 - -0.000110) / (0.000947 + 0.000121 - -0.000219)
  Unconstrained: w_BTC-USD=0.1792
  After long-only clamp: w_BTC-USD=0.1792, w_UNG=0.8208.


Question:
Assets: XLI, SGOV
XLI: annualized_mean_return=0.0756, daily_std=0.0090
SGOV: annualized_mean_return=0.0000, daily_std=0.0001
Minimum required portfolio return (annualized): -0.0000
Market regime: sideways

Compute portfolio weights (w_XLI, w_SGOV) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLI=X.XXXX, w_SGOV=X.XXXX

Answer: w_XLI=0.0001, w_SGOV=0.9999

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000081 + 0.000000 - 0.000000)
  Unconstrained: w_XLI=-0.0016
  After long-only clamp: w_XLI=0.0000, w_SGOV=1.0000.


BNB-USD σ=0.0405, CORN σ=0.0092, ρ=0.021. Min-variance weights: BNB-USD=0.045, CORN=0.955.

Question:
Assets: BNB-USD, CORN
BNB-USD: annualized_mean_return=-2.4192, daily_std=0.0405
CORN: annualized_mean_return=0.0504, daily_std=0.0092
Minimum required portfolio return (annualized): 0.0202
Market regime: sideways

Compute portfolio weights (w_BNB-USD, w_CORN) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BNB-USD=X.XXXX, w_CORN=X.XXXX

Answer: w_BNB-USD=0.0122, w_CORN=0.9878

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000085 - 0.000008) / (0.001642 + 0.000085 - 0.000015)
  Unconstrained: w_BNB-USD=0.0449
  After long-only clamp: w_BNB-USD=0.0449, w_CORN=0.9551.


Question:
Assets: IVV, IEF
IVV: annualized_mean_return=0.1260, daily_std=0.0045
IEF: annualized_mean_return=0.1260, daily_std=0.0026
Minimum required portfolio return (annualized): 0.1260
Market regime: sideways

Compute portfolio weights (w_IVV, w_IEF) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_IVV=X.XXXX, w_IEF=X.XXXX

Answer: w_IVV=0.2659, w_IEF=0.7341

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000007 - -0.000001) / (0.000020 + 0.000007 - -0.000001)
  Unconstrained: w_IVV=0.2607
  After long-only clamp: w_IVV=0.2607, w_IEF=0.7393.


Question:
Assets: IWM, SGOV
IWM: annualized_mean_return=-0.1008, daily_std=0.0141
SGOV: annualized_mean_return=0.0000, daily_std=0.0001
Minimum required portfolio return (annualized): -0.0308
Market regime: sideways

Compute portfolio weights (w_IWM, w_SGOV) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_IWM=X.XXXX, w_SGOV=X.XXXX

Answer: w_IWM=0.0000, w_SGOV=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000197 + 0.000000 - -0.000000)
  Unconstrained: w_IWM=0.0005
  After long-only clamp: w_IWM=0.0005, w_SGOV=0.9995.


Question:
Assets: VTI, SGOV
VTI: annualized_mean_return=0.0252, daily_std=0.0093
SGOV: annualized_mean_return=0.0000, daily_std=0.0001
Minimum required portfolio return (annualized): -0.0001
Market regime: sideways

Compute portfolio weights (w_VTI, w_SGOV) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_VTI=X.XXXX, w_SGOV=X.XXXX

Answer: w_VTI=0.0000, w_SGOV=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000087 + 0.000000 - -0.000000)
  Unconstrained: w_VTI=0.0003
  After long-only clamp: w_VTI=0.0003, w_SGOV=0.9997.


Question:
Assets: XLB, ICSH
XLB: annualized_mean_return=0.4032, daily_std=0.0121
ICSH: annualized_mean_return=0.0000, daily_std=0.0002
Minimum required portfolio return (annualized): 0.1301
Market regime: sideways

Compute portfolio weights (w_XLB, w_ICSH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLB=X.XXXX, w_ICSH=X.XXXX

Answer: w_XLB=0.3227, w_ICSH=0.6773

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000147 + 0.000000 - -0.000000)
  Unconstrained: w_XLB=0.0014
  After long-only clamp: w_XLB=0.0014, w_ICSH=0.9986.


Question:
Assets: BNB-USD, IAU
BNB-USD: annualized_mean_return=0.0252, daily_std=0.0370
IAU: annualized_mean_return=-0.0756, daily_std=0.0068
Minimum required portfolio return (annualized): -0.0711
Market regime: sideways

Compute portfolio weights (w_BNB-USD, w_IAU) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BNB-USD=X.XXXX, w_IAU=X.XXXX

Answer: w_BNB-USD=0.0641, w_IAU=0.9359

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000046 - -0.000051) / (0.001367 + 0.000046 - -0.000103)
  Unconstrained: w_BNB-USD=0.0642
  After long-only clamp: w_BNB-USD=0.0642, w_IAU=0.9358.


LINK-USD σ=0.0799, BIL σ=0.0001, ρ=0.248. Min-variance weights: LINK-USD=0.000, BIL=1.000.

Question:
Assets: LINK-USD, BIL
LINK-USD: annualized_mean_return=-0.4536, daily_std=0.0799
BIL: annualized_mean_return=-0.0000, daily_std=0.0001
Minimum required portfolio return (annualized): -0.2282
Market regime: sideways

Compute portfolio weights (w_LINK-USD, w_BIL) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_LINK-USD=X.XXXX, w_BIL=X.XXXX

Answer: w_LINK-USD=0.0000, w_BIL=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000002) / (0.006382 + 0.000000 - 0.000004)
  Unconstrained: w_LINK-USD=-0.0003
  After long-only clamp: w_LINK-USD=0.0000, w_BIL=1.0000.


MATIC-USD σ=0.0485, IAU σ=0.0083, ρ=-0.193. Min-variance weights: MATIC-USD=0.057, IAU=0.943.

Question:
Assets: MATIC-USD, IAU
MATIC-USD: annualized_mean_return=0.8568, daily_std=0.0485
IAU: annualized_mean_return=-0.1260, daily_std=0.0083
Minimum required portfolio return (annualized): 0.2400
Market regime: sideways

Compute portfolio weights (w_MATIC-USD, w_IAU) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_MATIC-USD=X.XXXX, w_IAU=X.XXXX

Answer: w_MATIC-USD=0.3724, w_IAU=0.6276

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000068 - -0.000077) / (0.002348 + 0.000068 - -0.000155)
  Unconstrained: w_MATIC-USD=0.0567
  After long-only clamp: w_MATIC-USD=0.0567, w_IAU=0.9433.


Question:
Assets: ETH-USD, SGOV
ETH-USD: annualized_mean_return=1.2852, daily_std=0.0461
SGOV: annualized_mean_return=0.0000, daily_std=0.0001
Minimum required portfolio return (annualized): -0.0001
Market regime: sideways

Compute portfolio weights (w_ETH-USD, w_SGOV) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_ETH-USD=X.XXXX, w_SGOV=X.XXXX

Answer: w_ETH-USD=0.0000, w_SGOV=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.002128 + 0.000000 - -0.000001)
  Unconstrained: w_ETH-USD=0.0002
  After long-only clamp: w_ETH-USD=0.0002, w_SGOV=0.9998.


Question:
Assets: XLI, ITB
XLI: annualized_mean_return=-0.4284, daily_std=0.0105
ITB: annualized_mean_return=-0.5544, daily_std=0.0160
Minimum required portfolio return (annualized): -0.4891
Market regime: sideways

Compute portfolio weights (w_XLI, w_ITB) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLI=X.XXXX, w_ITB=X.XXXX

Answer: w_XLI=1.0000, w_ITB=0.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000256 - 0.000146) / (0.000110 + 0.000256 - 0.000292)
  Unconstrained: w_XLI=1.4906
  After long-only clamp: w_XLI=1.0000, w_ITB=0.0000.


Question:
Assets: EFA, ICSH
EFA: annualized_mean_return=-0.5040, daily_std=0.0109
ICSH: annualized_mean_return=0.0252, daily_std=0.0003
Minimum required portfolio return (annualized): 0.0165
Market regime: sideways

Compute portfolio weights (w_EFA, w_ICSH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_EFA=X.XXXX, w_ICSH=X.XXXX

Answer: w_EFA=0.0007, w_ICSH=0.9993

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000118 + 0.000000 - -0.000001)
  Unconstrained: w_EFA=0.0045
  After long-only clamp: w_EFA=0.0045, w_ICSH=0.9955.


Question:
Assets: SOL-USD, IYR
SOL-USD: annualized_mean_return=0.2016, daily_std=0.0365
IYR: annualized_mean_return=-0.7308, daily_std=0.0155
Minimum required portfolio return (annualized): -0.2076
Market regime: sideways

Compute portfolio weights (w_SOL-USD, w_IYR) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_SOL-USD=X.XXXX, w_IYR=X.XXXX

Answer: w_SOL-USD=0.5611, w_IYR=0.4389

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000239 - 0.000017) / (0.001331 + 0.000239 - 0.000034)
  Unconstrained: w_SOL-USD=0.1445
  After long-only clamp: w_SOL-USD=0.1445, w_IYR=0.8555.


Question:
Assets: VTI, DBB
VTI: annualized_mean_return=0.1764, daily_std=0.0046
DBB: annualized_mean_return=-0.1764, daily_std=0.0117
Minimum required portfolio return (annualized): 0.0079
Market regime: sideways

Compute portfolio weights (w_VTI, w_DBB) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_VTI=X.XXXX, w_DBB=X.XXXX

Answer: w_VTI=0.8888, w_DBB=0.1112

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000138 - 0.000004) / (0.000021 + 0.000138 - 0.000009)
  Unconstrained: w_VTI=0.8906
  After long-only clamp: w_VTI=0.8906, w_DBB=0.1094.


MATIC-USD σ=0.0944, REZ σ=0.0081, ρ=0.096. Min-variance weights: MATIC-USD=0.000, REZ=1.000.

Question:
Assets: MATIC-USD, REZ
MATIC-USD: annualized_mean_return=3.5280, daily_std=0.0944
REZ: annualized_mean_return=-0.2520, daily_std=0.0081
Minimum required portfolio return (annualized): 1.7015
Market regime: sideways

Compute portfolio weights (w_MATIC-USD, w_REZ) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_MATIC-USD=X.XXXX, w_REZ=X.XXXX

Answer: w_MATIC-USD=0.5168, w_REZ=0.4832

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000066 - 0.000074) / (0.008908 + 0.000066 - 0.000148)
  Unconstrained: w_MATIC-USD=-0.0009
  After long-only clamp: w_MATIC-USD=0.0000, w_REZ=1.0000.


MATIC-USD σ=0.0409, PALL σ=0.0208, ρ=-0.180. Min-variance weights: MATIC-USD=0.243, PALL=0.757.

Question:
Assets: MATIC-USD, PALL
MATIC-USD: annualized_mean_return=-0.7812, daily_std=0.0409
PALL: annualized_mean_return=0.7560, daily_std=0.0208
Minimum required portfolio return (annualized): 0.0562
Market regime: sideways

Compute portfolio weights (w_MATIC-USD, w_PALL) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_MATIC-USD=X.XXXX, w_PALL=X.XXXX

Answer: w_MATIC-USD=0.2426, w_PALL=0.7574

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000432 - -0.000153) / (0.001673 + 0.000432 - -0.000306)
  Unconstrained: w_MATIC-USD=0.2426
  After long-only clamp: w_MATIC-USD=0.2426, w_PALL=0.7574.


Question:
Assets: EWJ, GLD
EWJ: annualized_mean_return=-0.0252, daily_std=0.0092
GLD: annualized_mean_return=0.1764, daily_std=0.0078
Minimum required portfolio return (annualized): 0.1605
Market regime: sideways

Compute portfolio weights (w_EWJ, w_GLD) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_EWJ=X.XXXX, w_GLD=X.XXXX

Answer: w_EWJ=0.0789, w_GLD=0.9211

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000061 - 0.000019) / (0.000085 + 0.000061 - 0.000039)
  Unconstrained: w_EWJ=0.3908
  After long-only clamp: w_EWJ=0.3908, w_GLD=0.6092.


Question:
Assets: XLK, PPLT
XLK: annualized_mean_return=-0.1512, daily_std=0.0147
PPLT: annualized_mean_return=-0.3276, daily_std=0.0133
Minimum required portfolio return (annualized): -0.2769
Market regime: sideways

Compute portfolio weights (w_XLK, w_PPLT) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLK=X.XXXX, w_PPLT=X.XXXX

Answer: w_XLK=0.4143, w_PPLT=0.5857

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000176 - 0.000081) / (0.000216 + 0.000176 - 0.000162)
  Unconstrained: w_XLK=0.4143
  After long-only clamp: w_XLK=0.4143, w_PPLT=0.5857.


Question:
Assets: XLI, VNQ
XLI: annualized_mean_return=0.4032, daily_std=0.0052
VNQ: annualized_mean_return=0.0504, daily_std=0.0051
Minimum required portfolio return (annualized): 0.2951
Market regime: sideways

Compute portfolio weights (w_XLI, w_VNQ) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLI=X.XXXX, w_VNQ=X.XXXX

Answer: w_XLI=0.6936, w_VNQ=0.3064

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000026 - 0.000002) / (0.000027 + 0.000026 - 0.000004)
  Unconstrained: w_XLI=0.4883
  After long-only clamp: w_XLI=0.4883, w_VNQ=0.5117.


Question:
Assets: EWJ, TLH
EWJ: annualized_mean_return=-0.1260, daily_std=0.0100
TLH: annualized_mean_return=-0.0252, daily_std=0.0041
Minimum required portfolio return (annualized): -0.0347
Market regime: sideways

Compute portfolio weights (w_EWJ, w_TLH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_EWJ=X.XXXX, w_TLH=X.XXXX

Answer: w_EWJ=0.0942, w_TLH=0.9058

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000017 - -0.000012) / (0.000100 + 0.000017 - -0.000023)
  Unconstrained: w_EWJ=0.2047
  After long-only clamp: w_EWJ=0.2047, w_TLH=0.7953.


Question:
Assets: XLV, STIP
XLV: annualized_mean_return=-0.0504, daily_std=0.0114
STIP: annualized_mean_return=0.0756, daily_std=0.0009
Minimum required portfolio return (annualized): 0.0741
Market regime: sideways

Compute portfolio weights (w_XLV, w_STIP) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLV=X.XXXX, w_STIP=X.XXXX

Answer: w_XLV=0.0000, w_STIP=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000001 - 0.000001) / (0.000130 + 0.000001 - 0.000003)
  Unconstrained: w_XLV=-0.0047
  After long-only clamp: w_XLV=0.0000, w_STIP=1.0000.


Question:
Assets: XLK, IEF
XLK: annualized_mean_return=0.3276, daily_std=0.0089
IEF: annualized_mean_return=-0.0252, daily_std=0.0034
Minimum required portfolio return (annualized): 0.0141
Market regime: sideways

Compute portfolio weights (w_XLK, w_IEF) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLK=X.XXXX, w_IEF=X.XXXX

Answer: w_XLK=0.1289, w_IEF=0.8711

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000012 - -0.000000) / (0.000079 + 0.000012 - -0.000000)
  Unconstrained: w_XLK=0.1304
  After long-only clamp: w_XLK=0.1304, w_IEF=0.8696.


Question:
Assets: DOT-USD, HYG
DOT-USD: annualized_mean_return=-0.3780, daily_std=0.0385
HYG: annualized_mean_return=0.1008, daily_std=0.0078
Minimum required portfolio return (annualized): 0.0755
Market regime: sideways

Compute portfolio weights (w_DOT-USD, w_HYG) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_DOT-USD=X.XXXX, w_HYG=X.XXXX

Answer: w_DOT-USD=0.0528, w_HYG=0.9472

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000061 - -0.000068) / (0.001479 + 0.000061 - -0.000135)
  Unconstrained: w_DOT-USD=0.0766
  After long-only clamp: w_DOT-USD=0.0766, w_HYG=0.9234.


Question:
Assets: QUAL, PPLT
QUAL: annualized_mean_return=0.0252, daily_std=0.0049
PPLT: annualized_mean_return=0.1512, daily_std=0.0088
Minimum required portfolio return (annualized): 0.0569
Market regime: sideways

Compute portfolio weights (w_QUAL, w_PPLT) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_QUAL=X.XXXX, w_PPLT=X.XXXX

Answer: w_QUAL=0.7464, w_PPLT=0.2536

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000077 - -0.000003) / (0.000024 + 0.000077 - -0.000006)
  Unconstrained: w_QUAL=0.7474
  After long-only clamp: w_QUAL=0.7474, w_PPLT=0.2526.


Question:
Assets: ACWI, DBA
ACWI: annualized_mean_return=0.2520, daily_std=0.0062
DBA: annualized_mean_return=0.0252, daily_std=0.0062
Minimum required portfolio return (annualized): 0.1993
Market regime: sideways

Compute portfolio weights (w_ACWI, w_DBA) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_ACWI=X.XXXX, w_DBA=X.XXXX

Answer: w_ACWI=0.7676, w_DBA=0.2324

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000038 - 0.000004) / (0.000039 + 0.000038 - 0.000007)
  Unconstrained: w_ACWI=0.4950
  After long-only clamp: w_ACWI=0.4950, w_DBA=0.5050.


AVAX-USD σ=0.0780, IEF σ=0.0036, ρ=0.097. Min-variance weights: AVAX-USD=0.000, IEF=1.000.

Question:
Assets: AVAX-USD, IEF
AVAX-USD: annualized_mean_return=1.8900, daily_std=0.0780
IEF: annualized_mean_return=-0.0252, daily_std=0.0036
Minimum required portfolio return (annualized): -0.0252
Market regime: sideways

Compute portfolio weights (w_AVAX-USD, w_IEF) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_AVAX-USD=X.XXXX, w_IEF=X.XXXX

Answer: w_AVAX-USD=0.0000, w_IEF=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000013 - 0.000027) / (0.006079 + 0.000013 - 0.000054)
  Unconstrained: w_AVAX-USD=-0.0024
  After long-only clamp: w_AVAX-USD=0.0000, w_IEF=1.0000.


Question:
Assets: XLV, PDBC
XLV: annualized_mean_return=0.1512, daily_std=0.0098
PDBC: annualized_mean_return=0.1008, daily_std=0.0102
Minimum required portfolio return (annualized): 0.1429
Market regime: sideways

Compute portfolio weights (w_XLV, w_PDBC) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLV=X.XXXX, w_PDBC=X.XXXX

Answer: w_XLV=0.8353, w_PDBC=0.1647

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000105 - 0.000050) / (0.000096 + 0.000105 - 0.000100)
  Unconstrained: w_XLV=0.5410
  After long-only clamp: w_XLV=0.5410, w_PDBC=0.4590.


Question:
Assets: ADA-USD, IYR
ADA-USD: annualized_mean_return=6.0228, daily_std=0.0805
IYR: annualized_mean_return=0.1260, daily_std=0.0100
Minimum required portfolio return (annualized): 0.1260
Market regime: sideways

Compute portfolio weights (w_ADA-USD, w_IYR) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_ADA-USD=X.XXXX, w_IYR=X.XXXX

Answer: w_ADA-USD=0.0000, w_IYR=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000100 - 0.000111) / (0.006486 + 0.000100 - 0.000222)
  Unconstrained: w_ADA-USD=-0.0017
  After long-only clamp: w_ADA-USD=0.0000, w_IYR=1.0000.


Question:
Assets: XLB, DBC
XLB: annualized_mean_return=-0.2268, daily_std=0.0137
DBC: annualized_mean_return=-0.0252, daily_std=0.0106
Minimum required portfolio return (annualized): -0.0612
Market regime: sideways

Compute portfolio weights (w_XLB, w_DBC) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLB=X.XXXX, w_DBC=X.XXXX

Answer: w_XLB=0.1786, w_DBC=0.8214

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000113 - 0.000014) / (0.000187 + 0.000113 - 0.000028)
  Unconstrained: w_XLB=0.3646
  After long-only clamp: w_XLB=0.3646, w_DBC=0.6354.


Question:
Assets: MTUM, HAUZ
MTUM: annualized_mean_return=-0.2016, daily_std=0.0158
HAUZ: annualized_mean_return=0.2268, daily_std=0.0100
Minimum required portfolio return (annualized): 0.0747
Market regime: sideways

Compute portfolio weights (w_MTUM, w_HAUZ) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_MTUM=X.XXXX, w_HAUZ=X.XXXX

Answer: w_MTUM=0.0275, w_HAUZ=0.9725

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000099 - 0.000095) / (0.000249 + 0.000099 - 0.000190)
  Unconstrained: w_MTUM=0.0275
  After long-only clamp: w_MTUM=0.0275, w_HAUZ=0.9725.


Question:
Assets: XLU, LQD
XLU: annualized_mean_return=0.1764, daily_std=0.0057
LQD: annualized_mean_return=0.0252, daily_std=0.0022
Minimum required portfolio return (annualized): 0.0474
Market regime: sideways

Compute portfolio weights (w_XLU, w_LQD) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLU=X.XXXX, w_LQD=X.XXXX

Answer: w_XLU=0.1705, w_LQD=0.8295

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000005 - -0.000002) / (0.000032 + 0.000005 - -0.000003)
  Unconstrained: w_XLU=0.1659
  After long-only clamp: w_XLU=0.1659, w_LQD=0.8341.


Question:
Assets: XLF, TIP
XLF: annualized_mean_return=0.1008, daily_std=0.0120
TIP: annualized_mean_return=0.0756, daily_std=0.0012
Minimum required portfolio return (annualized): 0.0873
Market regime: sideways

Compute portfolio weights (w_XLF, w_TIP) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLF=X.XXXX, w_TIP=X.XXXX

Answer: w_XLF=0.4643, w_TIP=0.5357

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000002 - 0.000000) / (0.000144 + 0.000002 - 0.000000)
  Unconstrained: w_XLF=0.0087
  After long-only clamp: w_XLF=0.0087, w_TIP=0.9913.


Question:
Assets: MTUM, TLT
MTUM: annualized_mean_return=0.1008, daily_std=0.0147
TLT: annualized_mean_return=0.0504, daily_std=0.0057
Minimum required portfolio return (annualized): 0.0562
Market regime: sideways

Compute portfolio weights (w_MTUM, w_TLT) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_MTUM=X.XXXX, w_TLT=X.XXXX

Answer: w_MTUM=0.1333, w_TLT=0.8667

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000032 - -0.000001) / (0.000215 + 0.000032 - -0.000003)
  Unconstrained: w_MTUM=0.1345
  After long-only clamp: w_MTUM=0.1345, w_TLT=0.8655.


Question:
Assets: XLB, PPLT
XLB: annualized_mean_return=0.2520, daily_std=0.0094
PPLT: annualized_mean_return=-0.3024, daily_std=0.0162
Minimum required portfolio return (annualized): 0.2020
Market regime: sideways

Compute portfolio weights (w_XLB, w_PPLT) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLB=X.XXXX, w_PPLT=X.XXXX

Answer: w_XLB=0.9098, w_PPLT=0.0902

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000262 - 0.000041) / (0.000089 + 0.000262 - 0.000083)
  Unconstrained: w_XLB=0.8217
  After long-only clamp: w_XLB=0.8217, w_PPLT=0.1783.


Question:
Assets: ETH-USD, BNO
ETH-USD: annualized_mean_return=-1.2096, daily_std=0.0394
BNO: annualized_mean_return=-0.0252, daily_std=0.0242
Minimum required portfolio return (annualized): -0.5456
Market regime: sideways

Compute portfolio weights (w_ETH-USD, w_BNO) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_ETH-USD=X.XXXX, w_BNO=X.XXXX

Answer: w_ETH-USD=0.3046, w_BNO=0.6954

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000586 - -0.000164) / (0.001549 + 0.000586 - -0.000329)
  Unconstrained: w_ETH-USD=0.3046
  After long-only clamp: w_ETH-USD=0.3046, w_BNO=0.6954.


Question:
Assets: BTC-USD, SHV
BTC-USD: annualized_mean_return=-0.3780, daily_std=0.0342
SHV: annualized_mean_return=-0.0000, daily_std=0.0001
Minimum required portfolio return (annualized): -0.1526
Market regime: sideways

Compute portfolio weights (w_BTC-USD, w_SHV) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BTC-USD=X.XXXX, w_SHV=X.XXXX

Answer: w_BTC-USD=0.0000, w_SHV=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000001) / (0.001170 + 0.000000 - 0.000002)
  Unconstrained: w_BTC-USD=-0.0007
  After long-only clamp: w_BTC-USD=0.0000, w_SHV=1.0000.


Question:
Assets: BTC-USD, TLT
BTC-USD: annualized_mean_return=-0.3276, daily_std=0.0230
TLT: annualized_mean_return=-0.1512, daily_std=0.0068
Minimum required portfolio return (annualized): -0.2297
Market regime: sideways

Compute portfolio weights (w_BTC-USD, w_TLT) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BTC-USD=X.XXXX, w_TLT=X.XXXX

Answer: w_BTC-USD=0.0936, w_TLT=0.9064

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000046 - -0.000009) / (0.000528 + 0.000046 - -0.000019)
  Unconstrained: w_BTC-USD=0.0941
  After long-only clamp: w_BTC-USD=0.0941, w_TLT=0.9059.


Question:
Assets: XLU, STIP
XLU: annualized_mean_return=0.1512, daily_std=0.0117
STIP: annualized_mean_return=-0.0252, daily_std=0.0011
Minimum required portfolio return (annualized): 0.0774
Market regime: sideways

Compute portfolio weights (w_XLU, w_STIP) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLU=X.XXXX, w_STIP=X.XXXX

Answer: w_XLU=0.5816, w_STIP=0.4184

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000001 - 0.000003) / (0.000136 + 0.000001 - 0.000005)
  Unconstrained: w_XLU=-0.0095
  After long-only clamp: w_XLU=0.0000, w_STIP=1.0000.


Question:
Assets: XLY, BIL
XLY: annualized_mean_return=-0.5040, daily_std=0.0188
BIL: annualized_mean_return=0.0252, daily_std=0.0002
Minimum required portfolio return (annualized): -0.0027
Market regime: sideways

Compute portfolio weights (w_XLY, w_BIL) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLY=X.XXXX, w_BIL=X.XXXX

Answer: w_XLY=0.0001, w_BIL=0.9999

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000353 + 0.000000 - 0.000000)
  Unconstrained: w_XLY=-0.0004
  After long-only clamp: w_XLY=0.0000, w_BIL=1.0000.


Question:
Assets: XLU, EMB
XLU: annualized_mean_return=0.2268, daily_std=0.0098
EMB: annualized_mean_return=-0.0504, daily_std=0.0037
Minimum required portfolio return (annualized): 0.1163
Market regime: sideways

Compute portfolio weights (w_XLU, w_EMB) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLU=X.XXXX, w_EMB=X.XXXX

Answer: w_XLU=0.6014, w_EMB=0.3986

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000013 - 0.000002) / (0.000096 + 0.000013 - 0.000004)
  Unconstrained: w_XLU=0.1095
  After long-only clamp: w_XLU=0.1095, w_EMB=0.8905.


Question:
Assets: DOT-USD, XHB
DOT-USD: annualized_mean_return=1.5120, daily_std=0.0462
XHB: annualized_mean_return=0.4788, daily_std=0.0162
Minimum required portfolio return (annualized): 0.5937
Market regime: sideways

Compute portfolio weights (w_DOT-USD, w_XHB) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_DOT-USD=X.XXXX, w_XHB=X.XXXX

Answer: w_DOT-USD=0.1181, w_XHB=0.8819

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000263 - -0.000027) / (0.002138 + 0.000263 - -0.000055)
  Unconstrained: w_DOT-USD=0.1182
  After long-only clamp: w_DOT-USD=0.1182, w_XHB=0.8818.


Question:
Assets: BTC-USD, EMB
BTC-USD: annualized_mean_return=0.4788, daily_std=0.0370
EMB: annualized_mean_return=-0.0000, daily_std=0.0061
Minimum required portfolio return (annualized): 0.1665
Market regime: sideways

Compute portfolio weights (w_BTC-USD, w_EMB) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BTC-USD=X.XXXX, w_EMB=X.XXXX

Answer: w_BTC-USD=0.3477, w_EMB=0.6523

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000037 - -0.000011) / (0.001366 + 0.000037 - -0.000022)
  Unconstrained: w_BTC-USD=0.0340
  After long-only clamp: w_BTC-USD=0.0340, w_EMB=0.9660.


Question:
Assets: BNB-USD, BNDX
BNB-USD: annualized_mean_return=5.0652, daily_std=0.0709
BNDX: annualized_mean_return=-0.0504, daily_std=0.0024
Minimum required portfolio return (annualized): -0.0407
Market regime: sideways

Compute portfolio weights (w_BNB-USD, w_BNDX) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BNB-USD=X.XXXX, w_BNDX=X.XXXX

Answer: w_BNB-USD=0.0037, w_BNDX=0.9963

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000006 - -0.000013) / (0.005020 + 0.000006 - -0.000025)
  Unconstrained: w_BNB-USD=0.0036
  After long-only clamp: w_BNB-USD=0.0036, w_BNDX=0.9964.


Question:
Assets: MTUM, BIL
MTUM: annualized_mean_return=-0.2268, daily_std=0.0129
BIL: annualized_mean_return=-0.0000, daily_std=0.0002
Minimum required portfolio return (annualized): 0.0000
Market regime: sideways

Compute portfolio weights (w_MTUM, w_BIL) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_MTUM=X.XXXX, w_BIL=X.XXXX

Answer: w_MTUM=-0.0000, w_BIL=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000167 + 0.000000 - 0.000000)
  Unconstrained: w_MTUM=-0.0012
  After long-only clamp: w_MTUM=0.0000, w_BIL=1.0000.


AVAX-USD σ=0.0500, SGOV σ=0.0001, ρ=-0.135. Min-variance weights: AVAX-USD=0.000, SGOV=1.000.

Question:
Assets: AVAX-USD, SGOV
AVAX-USD: annualized_mean_return=-0.9324, daily_std=0.0500
SGOV: annualized_mean_return=0.0252, daily_std=0.0001
Minimum required portfolio return (annualized): -0.0513
Market regime: sideways

Compute portfolio weights (w_AVAX-USD, w_SGOV) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_AVAX-USD=X.XXXX, w_SGOV=X.XXXX

Answer: w_AVAX-USD=0.0004, w_SGOV=0.9996

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000001) / (0.002502 + 0.000000 - -0.000002)
  Unconstrained: w_AVAX-USD=0.0004
  After long-only clamp: w_AVAX-USD=0.0004, w_SGOV=0.9996.


Question:
Assets: USMV, XHB
USMV: annualized_mean_return=-0.0504, daily_std=0.0059
XHB: annualized_mean_return=0.0252, daily_std=0.0087
Minimum required portfolio return (annualized): -0.0103
Market regime: sideways

Compute portfolio weights (w_USMV, w_XHB) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_USMV=X.XXXX, w_XHB=X.XXXX

Answer: w_USMV=0.4696, w_XHB=0.5304

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000076 - 0.000036) / (0.000035 + 0.000076 - 0.000073)
  Unconstrained: w_USMV=1.0370
  After long-only clamp: w_USMV=1.0000, w_XHB=0.0000.


Question:
Assets: BNB-USD, EFA
BNB-USD: annualized_mean_return=0.8820, daily_std=0.0227
EFA: annualized_mean_return=-0.4284, daily_std=0.0138
Minimum required portfolio return (annualized): -0.2769
Market regime: sideways

Compute portfolio weights (w_BNB-USD, w_EFA) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BNB-USD=X.XXXX, w_EFA=X.XXXX

Answer: w_BNB-USD=0.2699, w_EFA=0.7301

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000189 - -0.000002) / (0.000515 + 0.000189 - -0.000005)
  Unconstrained: w_BNB-USD=0.2701
  After long-only clamp: w_BNB-USD=0.2701, w_EFA=0.7299.


Question:
Assets: XRP-USD, BNO
XRP-USD: annualized_mean_return=1.5624, daily_std=0.0459
BNO: annualized_mean_return=-0.0504, daily_std=0.0235
Minimum required portfolio return (annualized): 0.5305
Market regime: sideways

Compute portfolio weights (w_XRP-USD, w_BNO) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XRP-USD=X.XXXX, w_BNO=X.XXXX

Answer: w_XRP-USD=0.3602, w_BNO=0.6398

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000550 - 0.000099) / (0.002107 + 0.000550 - 0.000198)
  Unconstrained: w_XRP-USD=0.1835
  After long-only clamp: w_XRP-USD=0.1835, w_BNO=0.8165.


Question:
Assets: BTC-USD, SHV
BTC-USD: annualized_mean_return=-2.3688, daily_std=0.0419
SHV: annualized_mean_return=0.0000, daily_std=0.0002
Minimum required portfolio return (annualized): -1.2999
Market regime: sideways

Compute portfolio weights (w_BTC-USD, w_SHV) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BTC-USD=X.XXXX, w_SHV=X.XXXX

Answer: w_BTC-USD=0.0000, w_SHV=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000001) / (0.001757 + 0.000000 - 0.000003)
  Unconstrained: w_BTC-USD=-0.0008
  After long-only clamp: w_BTC-USD=0.0000, w_SHV=1.0000.


Question:
Assets: XLK, HYG
XLK: annualized_mean_return=0.7308, daily_std=0.0150
HYG: annualized_mean_return=0.2520, daily_std=0.0046
Minimum required portfolio return (annualized): 0.2535
Market regime: sideways

Compute portfolio weights (w_XLK, w_HYG) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLK=X.XXXX, w_HYG=X.XXXX

Answer: w_XLK=0.0046, w_HYG=0.9954

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000021 - 0.000020) / (0.000225 + 0.000021 - 0.000040)
  Unconstrained: w_XLK=0.0047
  After long-only clamp: w_XLK=0.0047, w_HYG=0.9953.


Question:
Assets: EEM, SGOV
EEM: annualized_mean_return=-0.4032, daily_std=0.0107
SGOV: annualized_mean_return=0.0000, daily_std=0.0001
Minimum required portfolio return (annualized): 0.0000
Market regime: sideways

Compute portfolio weights (w_EEM, w_SGOV) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_EEM=X.XXXX, w_SGOV=X.XXXX

Answer: w_EEM=-0.0000, w_SGOV=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000115 + 0.000000 - 0.000000)
  Unconstrained: w_EEM=-0.0005
  After long-only clamp: w_EEM=0.0000, w_SGOV=1.0000.


Question:
Assets: FXI, UNG
FXI: annualized_mean_return=0.3276, daily_std=0.0111
UNG: annualized_mean_return=0.4788, daily_std=0.0356
Minimum required portfolio return (annualized): 0.3288
Market regime: sideways

Compute portfolio weights (w_FXI, w_UNG) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_FXI=X.XXXX, w_UNG=X.XXXX

Answer: w_FXI=0.9869, w_UNG=0.0131

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.001265 - 0.000108) / (0.000123 + 0.001265 - 0.000217)
  Unconstrained: w_FXI=0.9871
  After long-only clamp: w_FXI=0.9871, w_UNG=0.0129.


Question:
Assets: BTC-USD, VCIT
BTC-USD: annualized_mean_return=1.6632, daily_std=0.0450
VCIT: annualized_mean_return=0.0252, daily_std=0.0019
Minimum required portfolio return (annualized): 1.0490
Market regime: sideways

Compute portfolio weights (w_BTC-USD, w_VCIT) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BTC-USD=X.XXXX, w_VCIT=X.XXXX

Answer: w_BTC-USD=0.6250, w_VCIT=0.3750

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000004 - -0.000014) / (0.002026 + 0.000004 - -0.000029)
  Unconstrained: w_BTC-USD=0.0087
  After long-only clamp: w_BTC-USD=0.0087, w_VCIT=0.9913.


Question:
Assets: XLE, XHB
XLE: annualized_mean_return=0.3528, daily_std=0.0065
XHB: annualized_mean_return=0.4536, daily_std=0.0068
Minimum required portfolio return (annualized): 0.3915
Market regime: sideways

Compute portfolio weights (w_XLE, w_XHB) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLE=X.XXXX, w_XHB=X.XXXX

Answer: w_XLE=0.5227, w_XHB=0.4773

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000047 - 0.000001) / (0.000043 + 0.000047 - 0.000002)
  Unconstrained: w_XLE=0.5227
  After long-only clamp: w_XLE=0.5227, w_XHB=0.4773.


Question:
Assets: USMV, TIP
USMV: annualized_mean_return=-0.1512, daily_std=0.0072
TIP: annualized_mean_return=0.0000, daily_std=0.0015
Minimum required portfolio return (annualized): -0.0007
Market regime: sideways

Compute portfolio weights (w_USMV, w_TIP) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_USMV=X.XXXX, w_TIP=X.XXXX

Answer: w_USMV=0.0046, w_TIP=0.9954

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000002 - 0.000002) / (0.000051 + 0.000002 - 0.000005)
  Unconstrained: w_USMV=-0.0021
  After long-only clamp: w_USMV=0.0000, w_TIP=1.0000.


Question:
Assets: FXI, USO
FXI: annualized_mean_return=0.3780, daily_std=0.0228
USO: annualized_mean_return=-0.0000, daily_std=0.0266
Minimum required portfolio return (annualized): 0.2888
Market regime: sideways

Compute portfolio weights (w_FXI, w_USO) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_FXI=X.XXXX, w_USO=X.XXXX

Answer: w_FXI=0.7640, w_USO=0.2360

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000709 - 0.000105) / (0.000520 + 0.000709 - 0.000210)
  Unconstrained: w_FXI=0.5923
  After long-only clamp: w_FXI=0.5923, w_USO=0.4077.


Question:
Assets: ETH-USD, DBC
ETH-USD: annualized_mean_return=-0.6804, daily_std=0.0357
DBC: annualized_mean_return=-0.1764, daily_std=0.0144
Minimum required portfolio return (annualized): -0.2629
Market regime: sideways

Compute portfolio weights (w_ETH-USD, w_DBC) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_ETH-USD=X.XXXX, w_DBC=X.XXXX

Answer: w_ETH-USD=0.1334, w_DBC=0.8666

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000207 - 0.000013) / (0.001274 + 0.000207 - 0.000027)
  Unconstrained: w_ETH-USD=0.1333
  After long-only clamp: w_ETH-USD=0.1333, w_DBC=0.8667.


Question:
Assets: XLRE, VNQI
XLRE: annualized_mean_return=0.5040, daily_std=0.0077
VNQI: annualized_mean_return=0.1512, daily_std=0.0068
Minimum required portfolio return (annualized): 0.3672
Market regime: sideways

Compute portfolio weights (w_XLRE, w_VNQI) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLRE=X.XXXX, w_VNQI=X.XXXX

Answer: w_XLRE=0.6122, w_VNQI=0.3878

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000046 - 0.000034) / (0.000059 + 0.000046 - 0.000067)
  Unconstrained: w_XLRE=0.3319
  After long-only clamp: w_XLRE=0.3319, w_VNQI=0.6681.


Question:
Assets: QUAL, VNQI
QUAL: annualized_mean_return=0.3276, daily_std=0.0191
VNQI: annualized_mean_return=0.4536, daily_std=0.0168
Minimum required portfolio return (annualized): 0.3734
Market regime: sideways

Compute portfolio weights (w_QUAL, w_VNQI) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_QUAL=X.XXXX, w_VNQI=X.XXXX

Answer: w_QUAL=0.2109, w_VNQI=0.7891

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000281 - 0.000250) / (0.000367 + 0.000281 - 0.000501)
  Unconstrained: w_QUAL=0.2092
  After long-only clamp: w_QUAL=0.2092, w_VNQI=0.7908.


Question:
Assets: QUAL, ICSH
QUAL: annualized_mean_return=0.1764, daily_std=0.0086
ICSH: annualized_mean_return=0.0252, daily_std=0.0003
Minimum required portfolio return (annualized): 0.0253
Market regime: sideways

Compute portfolio weights (w_QUAL, w_ICSH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_QUAL=X.XXXX, w_ICSH=X.XXXX

Answer: w_QUAL=0.0011, w_ICSH=0.9989

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000075 + 0.000000 - -0.000001)
  Unconstrained: w_QUAL=0.0053
  After long-only clamp: w_QUAL=0.0053, w_ICSH=0.9947.


MATIC-USD σ=0.0777, PPLT σ=0.0194, ρ=-0.118. Min-variance weights: MATIC-USD=0.082, PPLT=0.918.

Question:
Assets: MATIC-USD, PPLT
MATIC-USD: annualized_mean_return=1.3860, daily_std=0.0777
PPLT: annualized_mean_return=0.6048, daily_std=0.0194
Minimum required portfolio return (annualized): 1.0770
Market regime: sideways

Compute portfolio weights (w_MATIC-USD, w_PPLT) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_MATIC-USD=X.XXXX, w_PPLT=X.XXXX

Answer: w_MATIC-USD=0.6045, w_PPLT=0.3955

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000375 - -0.000177) / (0.006033 + 0.000375 - -0.000354)
  Unconstrained: w_MATIC-USD=0.0816
  After long-only clamp: w_MATIC-USD=0.0816, w_PPLT=0.9184.


Question:
Assets: IWM, XRP-USD
IWM: annualized_mean_return=0.9828, daily_std=0.0122
XRP-USD: annualized_mean_return=1.5120, daily_std=0.1000
Minimum required portfolio return (annualized): 0.9898
Market regime: sideways

Compute portfolio weights (w_IWM, w_XRP-USD) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_IWM=X.XXXX, w_XRP-USD=X.XXXX

Answer: w_IWM=0.9749, w_XRP-USD=0.0251

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.009993 - -0.000111) / (0.000150 + 0.009993 - -0.000222)
  Unconstrained: w_IWM=0.9749
  After long-only clamp: w_IWM=0.9749, w_XRP-USD=0.0251.


Question:
Assets: ACWI, REZ
ACWI: annualized_mean_return=0.2016, daily_std=0.0051
REZ: annualized_mean_return=-0.0252, daily_std=0.0088
Minimum required portfolio return (annualized): 0.1741
Market regime: sideways

Compute portfolio weights (w_ACWI, w_REZ) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_ACWI=X.XXXX, w_REZ=X.XXXX

Answer: w_ACWI=0.8787, w_REZ=0.1213

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000078 - -0.000003) / (0.000026 + 0.000078 - -0.000006)
  Unconstrained: w_ACWI=0.7368
  After long-only clamp: w_ACWI=0.7368, w_REZ=0.2632.


Question:
Assets: EEM, DBC
EEM: annualized_mean_return=0.1008, daily_std=0.0135
DBC: annualized_mean_return=-0.3276, daily_std=0.0142
Minimum required portfolio return (annualized): -0.2064
Market regime: sideways

Compute portfolio weights (w_EEM, w_DBC) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_EEM=X.XXXX, w_DBC=X.XXXX

Answer: w_EEM=0.5310, w_DBC=0.4690

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000200 - 0.000042) / (0.000182 + 0.000200 - 0.000083)
  Unconstrained: w_EEM=0.5309
  After long-only clamp: w_EEM=0.5309, w_DBC=0.4691.


Question:
Assets: XLY, EMB
XLY: annualized_mean_return=0.1512, daily_std=0.0110
EMB: annualized_mean_return=0.0504, daily_std=0.0040
Minimum required portfolio return (annualized): 0.0937
Market regime: sideways

Compute portfolio weights (w_XLY, w_EMB) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLY=X.XXXX, w_EMB=X.XXXX

Answer: w_XLY=0.4296, w_EMB=0.5704

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000016 - 0.000012) / (0.000121 + 0.000016 - 0.000024)
  Unconstrained: w_XLY=0.0370
  After long-only clamp: w_XLY=0.0370, w_EMB=0.9630.


Question:
Assets: EWJ, IYR
EWJ: annualized_mean_return=0.0504, daily_std=0.0071
IYR: annualized_mean_return=0.0252, daily_std=0.0101
Minimum required portfolio return (annualized): 0.0361
Market regime: sideways

Compute portfolio weights (w_EWJ, w_IYR) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_EWJ=X.XXXX, w_IYR=X.XXXX

Answer: w_EWJ=0.7329, w_IYR=0.2671

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000102 - 0.000021) / (0.000051 + 0.000102 - 0.000042)
  Unconstrained: w_EWJ=0.7326
  After long-only clamp: w_EWJ=0.7326, w_IYR=0.2674.


LINK-USD σ=0.0424, ICSH σ=0.0002, ρ=0.256. Min-variance weights: LINK-USD=0.000, ICSH=1.000.

Question:
Assets: LINK-USD, ICSH
LINK-USD: annualized_mean_return=2.2428, daily_std=0.0424
ICSH: annualized_mean_return=0.0252, daily_std=0.0002
Minimum required portfolio return (annualized): 1.1222
Market regime: sideways

Compute portfolio weights (w_LINK-USD, w_ICSH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_LINK-USD=X.XXXX, w_ICSH=X.XXXX

Answer: w_LINK-USD=0.4947, w_ICSH=0.5053

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000003) / (0.001797 + 0.000000 - 0.000005)
  Unconstrained: w_LINK-USD=-0.0014
  After long-only clamp: w_LINK-USD=0.0000, w_ICSH=1.0000.


Question:
Assets: EFA, LINK-USD
EFA: annualized_mean_return=0.0756, daily_std=0.0071
LINK-USD: annualized_mean_return=7.0812, daily_std=0.0838
Minimum required portfolio return (annualized): 0.1392
Market regime: sideways

Compute portfolio weights (w_EFA, w_LINK-USD) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_EFA=X.XXXX, w_LINK-USD=X.XXXX

Answer: w_EFA=0.9857, w_LINK-USD=0.0143

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.007015 - -0.000052) / (0.000051 + 0.007015 - -0.000104)
  Unconstrained: w_EFA=0.9857
  After long-only clamp: w_EFA=0.9857, w_LINK-USD=0.0143.


Question:
Assets: ^VIX, HAUZ
^VIX: annualized_mean_return=-0.9072, daily_std=0.1079
HAUZ: annualized_mean_return=-0.2268, daily_std=0.0198
Minimum required portfolio return (annualized): -0.2712
Market regime: sideways

Compute portfolio weights (w_^VIX, w_HAUZ) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_^VIX=X.XXXX, w_HAUZ=X.XXXX

Answer: w_^VIX=0.0653, w_HAUZ=0.9347

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000391 - -0.001300) / (0.011638 + 0.000391 - -0.002601)
  Unconstrained: w_^VIX=0.1156
  After long-only clamp: w_^VIX=0.1156, w_HAUZ=0.8844.


Question:
Assets: VLUE, DBB
VLUE: annualized_mean_return=-0.4284, daily_std=0.0146
DBB: annualized_mean_return=-0.1260, daily_std=0.0095
Minimum required portfolio return (annualized): -0.2747
Market regime: sideways

Compute portfolio weights (w_VLUE, w_DBB) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_VLUE=X.XXXX, w_DBB=X.XXXX

Answer: w_VLUE=0.3022, w_DBB=0.6978

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000091 - -0.000002) / (0.000212 + 0.000091 - -0.000003)
  Unconstrained: w_VLUE=0.3015
  After long-only clamp: w_VLUE=0.3015, w_DBB=0.6985.


Question:
Assets: EFA, BIL
EFA: annualized_mean_return=0.6048, daily_std=0.0100
BIL: annualized_mean_return=0.0000, daily_std=0.0001
Minimum required portfolio return (annualized): 0.1823
Market regime: sideways

Compute portfolio weights (w_EFA, w_BIL) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_EFA=X.XXXX, w_BIL=X.XXXX

Answer: w_EFA=0.3014, w_BIL=0.6986

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000101 + 0.000000 - 0.000000)
  Unconstrained: w_EFA=-0.0007
  After long-only clamp: w_EFA=0.0000, w_BIL=1.0000.


DOT-USD σ=0.0936, VCIT σ=0.0021, ρ=0.032. Min-variance weights: DOT-USD=0.000, VCIT=1.000.

Question:
Assets: DOT-USD, VCIT
DOT-USD: annualized_mean_return=-0.6300, daily_std=0.0936
VCIT: annualized_mean_return=0.1512, daily_std=0.0021
Minimum required portfolio return (annualized): -0.0062
Market regime: sideways

Compute portfolio weights (w_DOT-USD, w_VCIT) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_DOT-USD=X.XXXX, w_VCIT=X.XXXX

Answer: w_DOT-USD=0.0000, w_VCIT=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000005 - 0.000007) / (0.008767 + 0.000005 - 0.000013)
  Unconstrained: w_DOT-USD=-0.0002
  After long-only clamp: w_DOT-USD=0.0000, w_VCIT=1.0000.


Question:
Assets: ACWI, ICSH
ACWI: annualized_mean_return=0.0504, daily_std=0.0091
ICSH: annualized_mean_return=0.0000, daily_std=0.0002
Minimum required portfolio return (annualized): 0.0381
Market regime: sideways

Compute portfolio weights (w_ACWI, w_ICSH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_ACWI=X.XXXX, w_ICSH=X.XXXX

Answer: w_ACWI=0.7560, w_ICSH=0.2440

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000084 + 0.000000 - 0.000000)
  Unconstrained: w_ACWI=-0.0023
  After long-only clamp: w_ACWI=0.0000, w_ICSH=1.0000.


LINK-USD σ=0.0793, BIL σ=0.0001, ρ=0.084. Min-variance weights: LINK-USD=0.000, BIL=1.000.

Question:
Assets: LINK-USD, BIL
LINK-USD: annualized_mean_return=4.5108, daily_std=0.0793
BIL: annualized_mean_return=-0.0000, daily_std=0.0001
Minimum required portfolio return (annualized): -0.0000
Market regime: sideways

Compute portfolio weights (w_LINK-USD, w_BIL) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_LINK-USD=X.XXXX, w_BIL=X.XXXX

Answer: w_LINK-USD=0.0000, w_BIL=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000001) / (0.006282 + 0.000000 - 0.000001)
  Unconstrained: w_LINK-USD=-0.0001
  After long-only clamp: w_LINK-USD=0.0000, w_BIL=1.0000.


Question:
Assets: BTC-USD, IAU
BTC-USD: annualized_mean_return=-1.6884, daily_std=0.0273
IAU: annualized_mean_return=0.1008, daily_std=0.0056
Minimum required portfolio return (annualized): 0.0670
Market regime: sideways

Compute portfolio weights (w_BTC-USD, w_IAU) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BTC-USD=X.XXXX, w_IAU=X.XXXX

Answer: w_BTC-USD=0.0189, w_IAU=0.9811

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000032 - 0.000006) / (0.000745 + 0.000032 - 0.000013)
  Unconstrained: w_BTC-USD=0.0334
  After long-only clamp: w_BTC-USD=0.0334, w_IAU=0.9666.


Question:
Assets: IVV, BIL
IVV: annualized_mean_return=-0.0504, daily_std=0.0139
BIL: annualized_mean_return=-0.0000, daily_std=0.0001
Minimum required portfolio return (annualized): -0.0016
Market regime: sideways

Compute portfolio weights (w_IVV, w_BIL) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_IVV=X.XXXX, w_BIL=X.XXXX

Answer: w_IVV=0.0001, w_BIL=0.9999

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000194 + 0.000000 - 0.000001)
  Unconstrained: w_IVV=-0.0013
  After long-only clamp: w_IVV=0.0000, w_BIL=1.0000.


Question:
Assets: IVV, REZ
IVV: annualized_mean_return=0.1008, daily_std=0.0119
REZ: annualized_mean_return=0.3024, daily_std=0.0133
Minimum required portfolio return (annualized): 0.2682
Market regime: sideways

Compute portfolio weights (w_IVV, w_REZ) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_IVV=X.XXXX, w_REZ=X.XXXX

Answer: w_IVV=0.1696, w_REZ=0.8304

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000178 - 0.000114) / (0.000142 + 0.000178 - 0.000229)
  Unconstrained: w_IVV=0.6996
  After long-only clamp: w_IVV=0.6996, w_REZ=0.3004.


Question:
Assets: XLF, EMB
XLF: annualized_mean_return=-0.6804, daily_std=0.0154
EMB: annualized_mean_return=-0.0252, daily_std=0.0043
Minimum required portfolio return (annualized): -0.1434
Market regime: sideways

Compute portfolio weights (w_XLF, w_EMB) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLF=X.XXXX, w_EMB=X.XXXX

Answer: w_XLF=0.0331, w_EMB=0.9669

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000019 - 0.000011) / (0.000238 + 0.000019 - 0.000021)
  Unconstrained: w_XLF=0.0350
  After long-only clamp: w_XLF=0.0350, w_EMB=0.9650.


Question:
Assets: XRP-USD, EMB
XRP-USD: annualized_mean_return=-2.1672, daily_std=0.0675
EMB: annualized_mean_return=-0.0504, daily_std=0.0037
Minimum required portfolio return (annualized): -0.3810
Market regime: sideways

Compute portfolio weights (w_XRP-USD, w_EMB) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XRP-USD=X.XXXX, w_EMB=X.XXXX

Answer: w_XRP-USD=0.0085, w_EMB=0.9915

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000013 - -0.000026) / (0.004551 + 0.000013 - -0.000051)
  Unconstrained: w_XRP-USD=0.0084
  After long-only clamp: w_XRP-USD=0.0084, w_EMB=0.9916.


LINK-USD σ=0.0412, DBB σ=0.0082, ρ=0.026. Min-variance weights: LINK-USD=0.033, DBB=0.967.

Question:
Assets: LINK-USD, DBB
LINK-USD: annualized_mean_return=1.5624, daily_std=0.0412
DBB: annualized_mean_return=-0.2520, daily_std=0.0082
Minimum required portfolio return (annualized): 0.7354
Market regime: sideways

Compute portfolio weights (w_LINK-USD, w_DBB) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_LINK-USD=X.XXXX, w_DBB=X.XXXX

Answer: w_LINK-USD=0.5442, w_DBB=0.4558

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000067 - 0.000009) / (0.001700 + 0.000067 - 0.000018)
  Unconstrained: w_LINK-USD=0.0331
  After long-only clamp: w_LINK-USD=0.0331, w_DBB=0.9669.


Question:
Assets: QUAL, REZ
QUAL: annualized_mean_return=0.0000, daily_std=0.0127
REZ: annualized_mean_return=0.2268, daily_std=0.0115
Minimum required portfolio return (annualized): 0.0977
Market regime: sideways

Compute portfolio weights (w_QUAL, w_REZ) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_QUAL=X.XXXX, w_REZ=X.XXXX

Answer: w_QUAL=0.3157, w_REZ=0.6843

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000133 - 0.000109) / (0.000162 + 0.000133 - 0.000217)
  Unconstrained: w_QUAL=0.3171
  After long-only clamp: w_QUAL=0.3171, w_REZ=0.6829.


MATIC-USD σ=0.0804, PPLT σ=0.0170, ρ=0.255. Min-variance weights: MATIC-USD=0.000, PPLT=1.000.

Question:
Assets: MATIC-USD, PPLT
MATIC-USD: annualized_mean_return=2.4696, daily_std=0.0804
PPLT: annualized_mean_return=-0.1512, daily_std=0.0170
Minimum required portfolio return (annualized): 0.8798
Market regime: sideways

Compute portfolio weights (w_MATIC-USD, w_PPLT) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_MATIC-USD=X.XXXX, w_PPLT=X.XXXX

Answer: w_MATIC-USD=0.3934, w_PPLT=0.6066

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000289 - 0.000348) / (0.006459 + 0.000289 - 0.000696)
  Unconstrained: w_MATIC-USD=-0.0097
  After long-only clamp: w_MATIC-USD=0.0000, w_PPLT=1.0000.


Question:
Assets: BTC-USD, ICSH
BTC-USD: annualized_mean_return=-0.0252, daily_std=0.0277
ICSH: annualized_mean_return=0.0252, daily_std=0.0004
Minimum required portfolio return (annualized): -0.0037
Market regime: sideways

Compute portfolio weights (w_BTC-USD, w_ICSH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BTC-USD=X.XXXX, w_ICSH=X.XXXX

Answer: w_BTC-USD=0.0015, w_ICSH=0.9985

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000001) / (0.000770 + 0.000000 - -0.000002)
  Unconstrained: w_BTC-USD=0.0011
  After long-only clamp: w_BTC-USD=0.0011, w_ICSH=0.9989.


LINK-USD σ=0.0626, HAUZ σ=0.0087, ρ=-0.105. Min-variance weights: LINK-USD=0.032, HAUZ=0.968.

Question:
Assets: LINK-USD, HAUZ
LINK-USD: annualized_mean_return=0.2016, daily_std=0.0626
HAUZ: annualized_mean_return=0.2268, daily_std=0.0087
Minimum required portfolio return (annualized): 0.2265
Market regime: sideways

Compute portfolio weights (w_LINK-USD, w_HAUZ) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_LINK-USD=X.XXXX, w_HAUZ=X.XXXX

Answer: w_LINK-USD=0.0119, w_HAUZ=0.9881

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000075 - -0.000057) / (0.003918 + 0.000075 - -0.000113)
  Unconstrained: w_LINK-USD=0.0321
  After long-only clamp: w_LINK-USD=0.0321, w_HAUZ=0.9679.


LINK-USD σ=0.0685, BIL σ=0.0001, ρ=0.010. Min-variance weights: LINK-USD=0.000, BIL=1.000.

Question:
Assets: LINK-USD, BIL
LINK-USD: annualized_mean_return=1.4868, daily_std=0.0685
BIL: annualized_mean_return=0.0252, daily_std=0.0001
Minimum required portfolio return (annualized): 0.0252
Market regime: sideways

Compute portfolio weights (w_LINK-USD, w_BIL) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_LINK-USD=X.XXXX, w_BIL=X.XXXX

Answer: w_LINK-USD=0.0000, w_BIL=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.004688 + 0.000000 - 0.000000)
  Unconstrained: w_LINK-USD=-0.0000
  After long-only clamp: w_LINK-USD=0.0000, w_BIL=1.0000.


Question:
Assets: IWM, SCHP
IWM: annualized_mean_return=-0.4788, daily_std=0.0191
SCHP: annualized_mean_return=-0.1008, daily_std=0.0054
Minimum required portfolio return (annualized): -0.1094
Market regime: sideways

Compute portfolio weights (w_IWM, w_SCHP) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_IWM=X.XXXX, w_SCHP=X.XXXX

Answer: w_IWM=0.0228, w_SCHP=0.9772

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000029 - -0.000001) / (0.000363 + 0.000029 - -0.000002)
  Unconstrained: w_IWM=0.0755
  After long-only clamp: w_IWM=0.0755, w_SCHP=0.9245.


Question:
Assets: VLUE, PDBC
VLUE: annualized_mean_return=-0.2772, daily_std=0.0130
PDBC: annualized_mean_return=0.0252, daily_std=0.0108
Minimum required portfolio return (annualized): -0.0486
Market regime: sideways

Compute portfolio weights (w_VLUE, w_PDBC) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_VLUE=X.XXXX, w_PDBC=X.XXXX

Answer: w_VLUE=0.2440, w_PDBC=0.7560

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000116 - 0.000008) / (0.000170 + 0.000116 - 0.000017)
  Unconstrained: w_VLUE=0.3996
  After long-only clamp: w_VLUE=0.3996, w_PDBC=0.6004.


Question:
Assets: XLK, BIL
XLK: annualized_mean_return=0.5796, daily_std=0.0075
BIL: annualized_mean_return=-0.0000, daily_std=0.0001
Minimum required portfolio return (annualized): 0.0001
Market regime: sideways

Compute portfolio weights (w_XLK, w_BIL) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLK=X.XXXX, w_BIL=X.XXXX

Answer: w_XLK=0.0001, w_BIL=0.9999

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000057 + 0.000000 - -0.000000)
  Unconstrained: w_XLK=0.0035
  After long-only clamp: w_XLK=0.0035, w_BIL=0.9965.


Question:
Assets: QQQ, ADA-USD
QQQ: annualized_mean_return=0.5292, daily_std=0.0161
ADA-USD: annualized_mean_return=-0.5292, daily_std=0.0515
Minimum required portfolio return (annualized): 0.3013
Market regime: sideways

Compute portfolio weights (w_QQQ, w_ADA-USD) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_QQQ=X.XXXX, w_ADA-USD=X.XXXX

Answer: w_QQQ=0.8976, w_ADA-USD=0.1024

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.002656 - -0.000048) / (0.000260 + 0.002656 - -0.000096)
  Unconstrained: w_QQQ=0.8976
  After long-only clamp: w_QQQ=0.8976, w_ADA-USD=0.1024.


Question:
Assets: XLF, SCHH
XLF: annualized_mean_return=-0.0756, daily_std=0.0131
SCHH: annualized_mean_return=0.2268, daily_std=0.0120
Minimum required portfolio return (annualized): 0.1905
Market regime: sideways

Compute portfolio weights (w_XLF, w_SCHH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLF=X.XXXX, w_SCHH=X.XXXX

Answer: w_XLF=0.1200, w_SCHH=0.8800

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000144 - 0.000066) / (0.000172 + 0.000144 - 0.000132)
  Unconstrained: w_XLF=0.4248
  After long-only clamp: w_XLF=0.4248, w_SCHH=0.5752.


Question:
Assets: ETH-USD, LQD
ETH-USD: annualized_mean_return=-0.7308, daily_std=0.0426
LQD: annualized_mean_return=-0.2772, daily_std=0.0075
Minimum required portfolio return (annualized): -0.5190
Market regime: sideways

Compute portfolio weights (w_ETH-USD, w_LQD) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_ETH-USD=X.XXXX, w_LQD=X.XXXX

Answer: w_ETH-USD=0.0810, w_LQD=0.9190

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000056 - -0.000114) / (0.001816 + 0.000056 - -0.000227)
  Unconstrained: w_ETH-USD=0.0808
  After long-only clamp: w_ETH-USD=0.0808, w_LQD=0.9192.


Question:
Assets: BTC-USD, VNQI
BTC-USD: annualized_mean_return=-0.4284, daily_std=0.0314
VNQI: annualized_mean_return=0.1008, daily_std=0.0142
Minimum required portfolio return (annualized): 0.0151
Market regime: sideways

Compute portfolio weights (w_BTC-USD, w_VNQI) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BTC-USD=X.XXXX, w_VNQI=X.XXXX

Answer: w_BTC-USD=0.1619, w_VNQI=0.8381

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000202 - -0.000103) / (0.000988 + 0.000202 - -0.000207)
  Unconstrained: w_BTC-USD=0.2186
  After long-only clamp: w_BTC-USD=0.2186, w_VNQI=0.7814.


Question:
Assets: XLI, SOYB
XLI: annualized_mean_return=0.4284, daily_std=0.0129
SOYB: annualized_mean_return=0.4536, daily_std=0.0079
Minimum required portfolio return (annualized): 0.4453
Market regime: sideways

Compute portfolio weights (w_XLI, w_SOYB) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLI=X.XXXX, w_SOYB=X.XXXX

Answer: w_XLI=0.2405, w_SOYB=0.7595

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000063 - 0.000014) / (0.000167 + 0.000063 - 0.000029)
  Unconstrained: w_XLI=0.2392
  After long-only clamp: w_XLI=0.2392, w_SOYB=0.7608.


Question:
Assets: XLU, VCIT
XLU: annualized_mean_return=0.0252, daily_std=0.0223
VCIT: annualized_mean_return=0.2772, daily_std=0.0048
Minimum required portfolio return (annualized): 0.2740
Market regime: sideways

Compute portfolio weights (w_XLU, w_VCIT) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLU=X.XXXX, w_VCIT=X.XXXX

Answer: w_XLU=0.0127, w_VCIT=0.9873

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000023 - 0.000000) / (0.000499 + 0.000023 - 0.000000)
  Unconstrained: w_XLU=0.0443
  After long-only clamp: w_XLU=0.0443, w_VCIT=0.9557.


BTC-USD σ=0.0277, CPER σ=0.0097, ρ=0.232. Min-variance weights: BTC-USD=0.042, CPER=0.958.

Question:
Assets: BTC-USD, CPER
BTC-USD: annualized_mean_return=-0.0252, daily_std=0.0277
CPER: annualized_mean_return=-0.1764, daily_std=0.0097
Minimum required portfolio return (annualized): -0.1711
Market regime: sideways

Compute portfolio weights (w_BTC-USD, w_CPER) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BTC-USD=X.XXXX, w_CPER=X.XXXX

Answer: w_BTC-USD=0.0426, w_CPER=0.9574

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000093 - 0.000062) / (0.000769 + 0.000093 - 0.000124)
  Unconstrained: w_BTC-USD=0.0424
  After long-only clamp: w_BTC-USD=0.0424, w_CPER=0.9576.


Question:
Assets: BTC-USD, EMB
BTC-USD: annualized_mean_return=-0.6300, daily_std=0.0410
EMB: annualized_mean_return=0.2016, daily_std=0.0039
Minimum required portfolio return (annualized): 0.1946
Market regime: sideways

Compute portfolio weights (w_BTC-USD, w_EMB) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BTC-USD=X.XXXX, w_EMB=X.XXXX

Answer: w_BTC-USD=0.0000, w_EMB=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000015 - 0.000025) / (0.001684 + 0.000015 - 0.000050)
  Unconstrained: w_BTC-USD=-0.0061
  After long-only clamp: w_BTC-USD=0.0000, w_EMB=1.0000.


Question:
Assets: XLI, DBC
XLI: annualized_mean_return=-0.4536, daily_std=0.0101
DBC: annualized_mean_return=-0.7812, daily_std=0.0111
Minimum required portfolio return (annualized): -0.6153
Market regime: sideways

Compute portfolio weights (w_XLI, w_DBC) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLI=X.XXXX, w_DBC=X.XXXX

Answer: w_XLI=0.5497, w_DBC=0.4503

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000123 - 0.000007) / (0.000102 + 0.000123 - 0.000014)
  Unconstrained: w_XLI=0.5496
  After long-only clamp: w_XLI=0.5496, w_DBC=0.4504.


Question:
Assets: ^VIX, JNK
^VIX: annualized_mean_return=0.0252, daily_std=0.0642
JNK: annualized_mean_return=0.1764, daily_std=0.0032
Minimum required portfolio return (annualized): 0.1753
Market regime: sideways

Compute portfolio weights (w_^VIX, w_JNK) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_^VIX=X.XXXX, w_JNK=X.XXXX

Answer: w_^VIX=0.0073, w_JNK=0.9927

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000010 - -0.000078) / (0.004125 + 0.000010 - -0.000157)
  Unconstrained: w_^VIX=0.0207
  After long-only clamp: w_^VIX=0.0207, w_JNK=0.9793.


Question:
Assets: VEA, TLT
VEA: annualized_mean_return=0.2520, daily_std=0.0041
TLT: annualized_mean_return=0.0504, daily_std=0.0061
Minimum required portfolio return (annualized): 0.1481
Market regime: sideways

Compute portfolio weights (w_VEA, w_TLT) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_VEA=X.XXXX, w_TLT=X.XXXX

Answer: w_VEA=0.6561, w_TLT=0.3439

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000038 - -0.000006) / (0.000017 + 0.000038 - -0.000012)
  Unconstrained: w_VEA=0.6561
  After long-only clamp: w_VEA=0.6561, w_TLT=0.3439.


Question:
Assets: EEM, SCHP
EEM: annualized_mean_return=-0.1512, daily_std=0.0102
SCHP: annualized_mean_return=0.0000, daily_std=0.0030
Minimum required portfolio return (annualized): -0.0103
Market regime: sideways

Compute portfolio weights (w_EEM, w_SCHP) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_EEM=X.XXXX, w_SCHP=X.XXXX

Answer: w_EEM=0.0681, w_SCHP=0.9319

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000009 - -0.000002) / (0.000103 + 0.000009 - -0.000003)
  Unconstrained: w_EEM=0.0922
  After long-only clamp: w_EEM=0.0922, w_SCHP=0.9078.