Portfolio Optimization

This portfolio optimizer tool supports the following portfolio optimization strategies:

The optimization is based on the monthly return statistics of the selected portfolio assets for the given time period. The optimization result does not predict what allocation would perform best outside the given time period, and the actual performance of portfolios constructed using the optimized asset weights may vary from the given performance goal.

The required inputs for the optimization include the time range and the portfolio assets. Portfolio asset weights and constraints are optional. You can also use the Black-Litterman model based portfolio optimization, which allows the benchmark portfolio asset weights to be optimized based on investor's views.

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Asset Groups
Min. Weight
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Portfolio Optimization Results (Jan 2012 - Dec 2019)

Portfolio optimization results for risk parity. The possible range of expected annual portfolio returns for the given period is 3.92% to 15.31%. Refer to the efficient frontier section for additional details.

Portfolio Allocations

Risk Parity
Ticker Name Allocation
VTI Vanguard Total Stock Market ETF 13.92%
VXUS Vanguard Total International Stock ETF 11.79%
VNQ Vanguard Real Estate ETF 9.93%
BND Vanguard Total Bond Market ETF 64.37%
Save portfolio »

Portfolio Performance Summary

Portfolio performance statistics
MetricRisk Parity
Start Balance$10,000
End Balance$15,691
CAGR5.79%
Expected Return 5.90%
Stdev4.47%
Best Year15.32%
Worst Year-2.93%
Max. Drawdown -3.96%
Sharpe Ratio (ex-ante)1.17
Sharpe Ratio (ex-post)1.14
Sortino Ratio1.93
US Stock Market Correlation0.71
   
Notes on results:
  • Past performance is no guarantee of future results, which may vary. All use is subject to terms of service.
  • Investing involves risk, including possible loss of principal. The value of the investments and the income derived from them may fluctuate over time.
  • All portfolio returns presented are hypothetical and backtested. Hypothetical returns do not reflect trading costs, transaction fees, or taxes.
  • Portfolio optimization determines target weights for portfolio assets based on mathematical models that can use either historical or forecasted data as inputs. Optimization results are not guarantees of future performance.
  • The results are based on information from a variety of sources we consider reliable, but we do not represent that the information is accurate or complete.
  • The results do not constitute investment advice or recommendation, are provided solely for informational purposes, and are not an offer to buy or sell any securities.
  • The results are based on the total return of assets and assume that all received dividends and distributions are reinvested.
  • CAGR = Compound Annual Growth Rate
  • Stdev = Annualized standard deviation of monthly returns
  • Sharpe ratio is calculated and annualized from monthly excess returns over the risk free rate (3-month treasury bill)
  • Drawdowns are calculated based on monthly returns.
  • The backtested results assume monthly rebalancing of portfolio assets to match the specified allocation.
Efficient Frontier Assets
#AssetCAGRExpected Return*Standard DeviationSharpe Ratio*Min. WeightMax. Weight
1Vanguard Total Stock Market ETF (VTI)14.59%15.31%11.31%1.2940.00%100.00%
2Vanguard Total International Stock ETF (VXUS)7.07%7.90%12.57%0.5750.00%100.00%
3Vanguard Real Estate ETF (VNQ)10.47%11.47%13.62%0.7930.00%100.00%
4Vanguard Total Bond Market ETF (BND)2.73%2.78%3.10%0.6790.00%100.00%
*Expected return is annualized from historical monthly mean return. Ex ante Sharpe Ratio calculated using historical 3-month treasury bill returns as the risk-free rate (0.68% annualized).

Monthly Correlations

Efficient Frontier Asset Correlations
NameTickerVTIVXUSVNQBND
Vanguard Total Stock Market ETFVTI1.000.810.48-0.12
Vanguard Total International Stock ETFVXUS0.811.000.410.03
Vanguard Real Estate ETFVNQ0.480.411.000.49
Vanguard Total Bond Market ETFBND-0.120.030.491.00
Based on monthly returns from Jan 2012 to Dec 2019
Efficient Frontier Assets
#VTIVXUSVNQBNDExpected Return*Standard Deviation*Sharpe Ratio*
19.54%0.00%0.00%90.46%3.92%2.88%1.127
210.45%0.00%0.00%89.55%4.03%2.88%1.165
311.37%0.00%0.00%88.63%4.14%2.88%1.200
412.28%0.00%0.00%87.72%4.25%2.90%1.234
513.19%0.00%0.00%86.81%4.36%2.91%1.265
614.11%0.00%0.00%85.89%4.47%2.93%1.295
715.02%0.00%0.00%84.98%4.58%2.95%1.322
815.93%0.00%0.00%84.07%4.69%2.98%1.347
916.85%0.00%0.00%83.15%4.80%3.01%1.370
1017.76%0.00%0.00%82.24%4.91%3.04%1.391
1118.68%0.00%0.00%81.32%5.02%3.08%1.410
1219.59%0.00%0.00%80.41%5.13%3.12%1.427
1320.50%0.00%0.00%79.50%5.24%3.17%1.442
1421.42%0.00%0.00%78.58%5.35%3.22%1.455
1522.33%0.00%0.00%77.67%5.46%3.27%1.466
1623.24%0.00%0.00%76.76%5.58%3.32%1.476
1724.16%0.00%0.00%75.84%5.69%3.38%1.484
1825.07%0.00%0.00%74.93%5.80%3.44%1.491
1925.99%0.00%0.00%74.01%5.91%3.50%1.497
2026.90%0.00%0.00%73.10%6.02%3.56%1.501
2127.81%0.00%0.00%72.19%6.13%3.63%1.505
2228.73%0.00%0.00%71.27%6.24%3.70%1.507
2329.64%0.00%0.00%70.36%6.36%3.77%1.509
2430.55%0.00%0.00%69.45%6.47%3.84%1.510
2531.47%0.00%0.00%68.53%6.58%3.91%1.510
2632.38%0.00%0.00%67.62%6.69%3.99%1.509
2733.30%0.00%0.00%66.70%6.81%4.07%1.508
2834.21%0.00%0.00%65.79%6.92%4.14%1.507
2935.12%0.00%0.00%64.88%7.03%4.22%1.505
3036.04%0.00%0.00%63.96%7.14%4.31%1.502
3136.95%0.00%0.00%63.05%7.26%4.39%1.500
3237.86%0.00%0.00%62.14%7.37%4.47%1.497
3338.78%0.00%0.00%61.22%7.48%4.56%1.494
3439.69%0.00%0.00%60.31%7.60%4.64%1.490
3540.61%0.00%0.00%59.39%7.71%4.73%1.487
3641.52%0.00%0.00%58.48%7.82%4.82%1.483
3742.43%0.00%0.00%57.57%7.94%4.91%1.479
3843.35%0.00%0.00%56.65%8.05%5.00%1.475
3944.26%0.00%0.00%55.74%8.16%5.09%1.471
4045.17%0.00%0.00%54.83%8.28%5.18%1.467
4146.09%0.00%0.00%53.91%8.39%5.27%1.463
4247.00%0.00%0.00%53.00%8.51%5.37%1.459
4347.92%0.00%0.00%52.08%8.62%5.46%1.455
4448.83%0.00%0.00%51.17%8.73%5.55%1.451
4549.74%0.00%0.00%50.26%8.85%5.65%1.447
4650.66%0.00%0.00%49.34%8.96%5.74%1.443
4751.57%0.00%0.00%48.43%9.08%5.84%1.439
4852.48%0.00%0.00%47.52%9.19%5.94%1.435
4953.40%0.00%0.00%46.60%9.31%6.03%1.431
5054.31%0.00%0.00%45.69%9.42%6.13%1.427
5155.23%0.00%0.00%44.77%9.54%6.23%1.423
5256.14%0.00%0.00%43.86%9.65%6.33%1.419
5357.05%0.00%0.00%42.95%9.77%6.43%1.415
5457.90%0.00%0.09%42.01%9.88%6.52%1.411
5558.64%0.00%0.34%41.02%10.00%6.62%1.408
5659.38%0.00%0.59%40.03%10.11%6.72%1.404
5760.12%0.00%0.84%39.04%10.23%6.82%1.401
5860.86%0.00%1.09%38.06%10.35%6.92%1.397
5961.59%0.00%1.34%37.07%10.46%7.02%1.394
6062.33%0.00%1.59%36.08%10.58%7.12%1.390
6163.07%0.00%1.84%35.09%10.69%7.22%1.387
6263.81%0.00%2.09%34.11%10.81%7.32%1.384
6364.55%0.00%2.34%33.12%10.93%7.42%1.381
6465.28%0.00%2.59%32.13%11.04%7.53%1.378
6566.02%0.00%2.84%31.14%11.16%7.63%1.375
6666.76%0.00%3.09%30.15%11.28%7.73%1.372
6767.50%0.00%3.34%29.17%11.39%7.83%1.369
6868.24%0.00%3.58%28.18%11.51%7.93%1.366
6968.97%0.00%3.83%27.19%11.63%8.03%1.364
7069.71%0.00%4.08%26.20%11.75%8.13%1.361
7170.45%0.00%4.33%25.22%11.86%8.24%1.358
7271.19%0.00%4.58%24.23%11.98%8.34%1.356
7371.93%0.00%4.83%23.24%12.10%8.44%1.353
7472.66%0.00%5.08%22.25%12.22%8.54%1.351
7573.40%0.00%5.33%21.27%12.33%8.65%1.348
7674.14%0.00%5.58%20.28%12.45%8.75%1.346
7774.88%0.00%5.83%19.29%12.57%8.85%1.344
7875.62%0.00%6.08%18.30%12.69%8.95%1.342
7976.35%0.00%6.33%17.32%12.81%9.06%1.339
8077.09%0.00%6.58%16.33%12.92%9.16%1.337
8177.83%0.00%6.83%15.34%13.04%9.26%1.335
8278.57%0.00%7.08%14.35%13.16%9.37%1.333
8379.30%0.00%7.33%13.37%13.28%9.47%1.331
8480.04%0.00%7.58%12.38%13.40%9.57%1.329
8580.78%0.00%7.83%11.39%13.52%9.67%1.327
8681.52%0.00%8.08%10.40%13.64%9.78%1.325
8782.26%0.00%8.33%9.42%13.75%9.88%1.324
8882.99%0.00%8.58%8.43%13.87%9.98%1.322
8983.73%0.00%8.83%7.44%13.99%10.09%1.320
9084.47%0.00%9.08%6.45%14.11%10.19%1.318
9185.21%0.00%9.33%5.47%14.23%10.30%1.317
9285.95%0.00%9.58%4.48%14.35%10.40%1.315
9386.68%0.00%9.83%3.49%14.47%10.50%1.314
9487.42%0.00%10.08%2.50%14.59%10.61%1.312
9588.16%0.00%10.32%1.51%14.71%10.71%1.310
9688.90%0.00%10.57%0.53%14.83%10.82%1.309
9790.73%0.00%9.27%0.00%14.95%10.92%1.307
9893.82%0.00%6.18%0.00%15.07%11.04%1.304
9996.91%0.00%3.09%0.00%15.19%11.17%1.300
100100.00%0.00%0.00%0.00%15.31%11.31%1.294
*Ex-ante values shown for portfolio return and volatility. Ex ante Sharpe Ratio calculated using historical 3-month treasury bill returns as the risk-free rate (0.68% annualized).
Annual returns for the configured portfolios
YearInflationRisk Parity ReturnRisk Parity BalanceVanguard Total Stock Market ETF (VTI)Vanguard Total International Stock ETF (VXUS)Vanguard Real Estate ETF (VNQ)Vanguard Total Bond Market ETF (BND)
20121.74%8.32%$10,83216.45%18.61%17.63%3.16%
20131.50%4.77%$11,34933.45%14.61%2.31%-2.10%
20140.76%7.79%$12,23312.54%-4.74%30.36%5.82%
20150.73%0.41%$12,2830.36%-4.19%2.42%0.56%
20162.07%5.00%$12,89712.83%4.81%8.60%2.52%
20172.11%8.68%$14,01721.21%27.45%4.91%3.57%
20181.91%-2.93%$13,607-5.21%-14.43%-6.02%-0.12%
20192.29%15.32%$15,69130.67%21.75%28.87%8.83%
Monthly returns for the configured portfolios
YearMonthRisk Parity ReturnRisk Parity BalanceVanguard Total Stock Market ETF (VTI)Vanguard Total International Stock ETF (VXUS)Vanguard Real Estate ETF (VNQ)Vanguard Total Bond Market ETF (BND)
201212.61%$10,2615.07%7.33%6.38%0.63%
201221.04%$10,3684.22%4.56%-1.15%0.04%
201230.55%$10,4253.06%-0.54%5.19%-0.51%
201240.66%$10,493-0.64%-2.08%2.86%1.10%
20125-1.99%$10,285-6.23%-10.83%-4.51%0.93%
201261.86%$10,4764.05%5.97%5.52%0.07%
201271.15%$10,5960.88%0.31%2.00%1.23%
201280.78%$10,6792.70%2.60%-0.01%0.16%
201290.68%$10,7522.49%3.41%-1.86%0.18%
201210-0.31%$10,719-1.81%0.81%-0.91%-0.10%
2012110.50%$10,7720.77%2.06%-0.26%0.27%
2012120.56%$10,8321.29%4.88%3.72%-0.88%
201310.96%$10,9375.42%2.40%3.74%-0.69%
201320.51%$10,9921.28%-1.14%1.22%0.54%
201330.99%$11,1023.95%0.93%2.87%0.08%
201341.96%$11,3191.61%3.50%6.73%1.01%
20135-1.88%$11,1062.44%-3.30%-5.98%-1.93%
20136-1.88%$10,898-1.43%-3.57%-1.98%-1.65%
201371.68%$11,0815.75%4.62%0.90%0.38%
20138-1.90%$10,871-3.03%-1.95%-6.98%-0.86%
201392.49%$11,1413.90%7.51%3.49%1.11%
2013102.03%$11,3674.27%3.67%4.52%0.86%
201311-0.32%$11,3312.70%0.13%-5.25%-0.29%
2013120.16%$11,3492.73%1.52%0.10%-0.64%
201410.34%$11,388-3.17%-5.40%4.28%1.55%
201422.14%$11,6324.87%5.59%5.07%0.47%
201430.07%$11,6400.51%0.49%0.49%-0.17%
201441.00%$11,7560.06%1.26%3.29%0.80%
201451.44%$11,9252.10%1.93%2.40%1.05%
201460.75%$12,0152.62%1.89%1.13%0.08%
20147-0.65%$11,937-1.99%-1.73%0.08%-0.28%
201481.75%$12,1464.15%1.16%3.04%1.14%
20149-1.85%$11,921-2.10%-5.01%-6.04%-0.57%
2014101.82%$12,1392.75%-0.08%9.94%0.72%
2014111.02%$12,2622.48%-0.51%2.00%0.83%
201412-0.24%$12,233-0.04%-3.87%1.88%0.06%
201511.88%$12,463-2.74%0.27%6.85%2.40%
201520.27%$12,4975.74%5.78%-3.67%-1.31%
201530.19%$12,521-1.16%-1.49%1.74%0.55%
20154-0.14%$12,5030.62%4.81%-5.85%-0.32%
20155-0.28%$12,4691.30%-0.91%-0.30%-0.50%
20156-1.73%$12,253-1.67%-2.73%-4.68%-1.11%
201571.31%$12,4131.70%-0.56%5.77%0.88%
20158-2.51%$12,102-6.09%-7.43%-6.29%-0.25%
20159-0.04%$12,097-2.92%-3.85%3.05%0.81%
2015102.43%$12,3917.91%6.25%5.76%0.03%
201511-0.39%$12,3430.60%-1.32%-0.63%-0.39%
201512-0.49%$12,283-2.13%-2.17%1.82%-0.18%
20161-1.01%$12,160-5.72%-5.45%-3.44%1.20%
201620.22%$12,186-0.01%-2.46%-0.36%0.85%
201633.58%$12,6237.11%8.33%10.48%0.88%
201640.37%$12,6700.66%2.16%-2.35%0.40%
201650.34%$12,7131.73%-0.98%2.25%-0.01%
201661.92%$12,9570.27%-0.90%6.92%2.02%
201671.89%$13,2033.98%4.52%4.26%0.60%
20168-0.49%$13,1380.21%0.45%-3.76%-0.31%
201690.12%$13,1540.21%1.70%-1.82%0.11%
201610-1.70%$12,930-2.19%-1.91%-5.74%-0.94%
201611-1.43%$12,7444.49%-2.01%-1.68%-2.57%
2016121.20%$12,8971.98%1.96%4.82%0.33%
201710.84%$13,0051.86%4.08%-0.19%0.19%
201721.42%$13,1893.69%1.34%3.51%0.62%
201730.10%$13,2020.06%3.00%-2.42%-0.04%
201740.93%$13,3241.06%2.05%0.24%0.80%
201750.87%$13,4411.01%2.96%-0.72%0.71%
201760.46%$13,5030.95%0.63%2.23%0.05%
201771.04%$13,6431.88%3.37%1.24%0.40%
201780.61%$13,7270.15%0.54%-0.26%0.86%
201790.25%$13,7612.44%1.88%-0.11%-0.47%
2017100.42%$13,8182.17%2.03%-1.07%-0.03%
2017110.69%$13,9143.03%0.63%2.66%-0.11%
2017120.74%$14,0171.16%2.07%-0.14%0.54%
201810.18%$14,0425.23%5.72%-4.25%-1.24%
20182-2.57%$13,681-3.76%-5.24%-7.68%-1.04%
201830.51%$13,751-1.95%-0.38%3.88%0.69%
20184-0.35%$13,7030.45%0.46%0.82%-0.85%
201850.99%$13,8392.72%-1.64%3.68%0.68%
201860.24%$13,8710.70%-2.14%4.20%-0.04%
201870.80%$13,9823.32%2.55%0.60%-0.04%
201880.88%$14,1053.43%-2.40%2.58%0.67%
20189-0.56%$14,0260.20%0.21%-2.64%-0.55%
201810-2.88%$13,622-7.41%-8.56%-2.93%-0.86%
2018111.35%$13,8062.01%1.68%4.67%0.64%
201812-1.44%$13,607-9.16%-4.93%-7.96%1.87%
201913.98%$14,1498.54%7.67%11.85%1.11%
201920.70%$14,2483.56%1.63%0.70%-0.09%
201931.95%$14,5261.42%0.77%4.21%1.94%
201940.84%$14,6493.93%2.77%-0.16%-0.02%
20195-0.35%$14,598-6.45%-5.42%0.14%1.83%
201962.62%$14,9807.08%5.77%1.54%1.25%
201970.23%$15,0141.41%-1.99%1.70%0.15%
201981.61%$15,256-2.08%-2.17%3.75%2.77%
201990.40%$15,3161.78%2.73%1.93%-0.57%
2019101.01%$15,4712.11%3.43%1.13%0.31%
2019110.49%$15,5463.79%0.99%-1.30%-0.04%
2019120.93%$15,6912.80%4.38%0.76%-0.07%
Portfolio return and risk metrics
MetricRisk Parity
Arithmetic Mean (monthly)0.48%
Arithmetic Mean (annualized)5.90%
Geometric Mean (monthly)0.47%
Geometric Mean (annualized)5.79%
Volatility (monthly)1.29%
Volatility (annualized)4.47%
Downside Deviation (monthly)0.74%
Max. Drawdown-3.96%
US Market Correlation0.71
Beta(*)0.28
Alpha (annualized)1.75%
R250.02%
Sharpe Ratio1.14
Sortino Ratio1.93
Treynor Ratio (%)18.07
Calmar Ratio1.91
Active Return-8.67%
Tracking Error8.69%
Information Ratio-1.00
Skewness-0.30
Excess Kurtosis0.59
Historical Value-at-Risk (5%)-1.91%
Analytical Value-at-Risk (5%)-1.63%
Conditional Value-at-Risk (5%)-2.49%
Upside Capture Ratio (%)31.66
Downside Capture Ratio (%)24.70
Safe Withdrawal Rate14.91%
Perpetual Withdrawal Rate3.93%
Positive Periods70 out of 96 (72.92%)
Gain/Loss Ratio0.95
* US stock market is used as the benchmark for calculations. Value-at-risk metrics are based on monthly values.

Drawdowns for Risk Parity

Drawdowns for Risk Parity (worst 10)
RankStartEndLengthRecovery ByRecovery TimeUnderwater PeriodDrawdown
1May 2013Aug 20134 monthsOct 20132 months6 months-3.96%
2Sep 2018Dec 20184 monthsJan 20191 month5 months-3.53%
3Aug 2016Nov 20164 monthsApr 20175 months9 months-3.48%
4Apr 2015Sep 20156 monthsMar 20166 months1 year-3.38%
5Feb 2018Feb 20181 monthAug 20186 months7 months-2.57%
6May 2012May 20121 monthJul 20122 months3 months-1.99%
7Sep 2014Sep 20141 monthNov 20142 months3 months-1.85%
8Jul 2014Jul 20141 monthAug 20141 month2 months-0.65%
9May 2019May 20191 monthJun 20191 month2 months-0.35%
10Nov 2013Nov 20131 monthJan 20142 months3 months-0.32%
Worst 10 drawdowns included above

Portfolio Assets

Performance statistics for portfolio components
TickerNameCAGRStdevBest YearWorst YearMax. DrawdownSharpe RatioSortino RatioUS Mkt Correlation
VTIVanguard Total Stock Market ETF14.59%11.31%33.45%-5.21%-14.20%1.211.971.00
VXUSVanguard Total International Stock ETF7.07%12.57%27.45%-14.43%-20.26%0.550.840.80
VNQVanguard Real Estate ETF10.47%13.62%30.36%-6.02%-14.88%0.751.250.48
BNDVanguard Total Bond Market ETF2.73%3.10%8.83%-2.10%-4.01%0.671.11-0.13

Monthly Correlations

Correlations for the portfolio assets
TickerNameVTIVXUSVNQBNDRisk Parity
VTIVanguard Total Stock Market ETF-0.810.48-0.120.71
VXUSVanguard Total International Stock ETF0.81-0.410.030.75
VNQVanguard Real Estate ETF0.480.41-0.490.83
BNDVanguard Total Bond Market ETF-0.120.030.49-0.56

Portfolio Risk Decomposition

Portfolio risk decomposition
TickerNameRisk Parity
VTIVanguard Total Stock Market ETF25.00%
VXUSVanguard Total International Stock ETF25.00%
VNQVanguard Real Estate ETF25.00%
BNDVanguard Total Bond Market ETF25.00%

Annual Asset Returns

Rolling returns summary
Roll PeriodAverageHighLow
1 year5.92%15.32%-2.93%
3 years5.07%6.95%3.47%
5 years4.83%5.29%3.70%
7 years4.97%5.44%4.50%
Result statistics are based on annualized rolling returns over full calendar year periods