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
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Portfolio Optimization Results (Jan 2012 - Mar 2021) Save

Portfolio optimization results for risk parity. The possible range of expected annual portfolio returns for the given period is 3.46% to 16.70%. Refer to the efficient frontier section for additional details.

Portfolio Allocations

Risk Parity
Ticker Name Allocation
VTI Vanguard Total Stock Market ETF 12.30%
VXUS Vanguard Total International Stock ETF 11.44%
VNQ Vanguard Real Estate ETF 9.97%
BND Vanguard Total Bond Market ETF 66.28%
Save portfolio »

Portfolio Performance Summary

Portfolio performance statistics
MetricRisk Parity
Start Balance$10,000
End Balance$16,798
CAGR5.77%
Expected Return 5.91%
Stdev5.28%
Best Year14.93%
Worst Year-2.80%
Max. Drawdown -7.70%
Sharpe Ratio (ex-ante)1.00
Sharpe Ratio (ex-post)0.97
Sortino Ratio1.56
US Stock Market Correlation0.78
   

Trailing Returns

Trailing Returns
NameAnnualized ReturnAnnualized Volatility
3 MonthYTD1 year3 year5 yearFull3 year5 year
Risk Parity-0.28%-0.28%16.59%7.39%6.05%5.77%6.98%5.85%
Trailing annualized return and volatility are for full months ending in March 2021 excluding portfolio cashflows.
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.
  • The annual results for 2021 are based on full calendar months from January to March
  • 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 ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1Vanguard Total Stock Market ETF (VTI)15.64%16.70%13.67%1.1760.00%100.00%
2Vanguard Total International Stock ETF (VXUS)7.76%8.88%14.40%0.5730.00%100.00%
3Vanguard Real Estate ETF (VNQ)9.42%10.71%15.32%0.6580.00%100.00%
4Vanguard Total Bond Market ETF (BND)2.77%2.83%3.33%0.6580.00%100.00%
Results based on historical returns. Ex ante Sharpe Ratio calculated using 3-month treasury bill returns as the risk-free rate (0.63% annualized).

Asset Correlations

Efficient Frontier Asset Correlations
NameTickerVTIVXUSVNQBND
Vanguard Total Stock Market ETFVTI1.000.860.630.04
Vanguard Total International Stock ETFVXUS0.861.000.580.11
Vanguard Real Estate ETFVNQ0.630.581.000.46
Vanguard Total Bond Market ETFBND0.040.110.461.00
Based on monthly returns from Jan 2012 to Mar 2021
Efficient Frontier Assets
#VTIVXUSVNQBNDExpected Return*Standard Deviation*Sharpe Ratio*
14.86%0.00%0.00%95.14%3.46%3.26%0.867
25.82%0.00%0.00%94.18%3.59%3.27%0.905
36.79%0.00%0.00%93.21%3.72%3.27%0.942
47.75%0.00%0.00%92.25%3.84%3.29%0.976
58.71%0.00%0.00%91.29%3.97%3.31%1.009
69.67%0.00%0.00%90.33%4.10%3.33%1.040
710.63%0.00%0.00%89.37%4.23%3.36%1.069
811.59%0.00%0.00%88.41%4.35%3.40%1.095
912.55%0.00%0.00%87.45%4.48%3.44%1.120
1013.51%0.00%0.00%86.49%4.61%3.48%1.142
1114.47%0.00%0.00%85.53%4.74%3.53%1.163
1215.43%0.00%0.00%84.57%4.86%3.58%1.181
1316.40%0.00%0.00%83.60%4.99%3.64%1.198
1417.36%0.00%0.00%82.64%5.12%3.70%1.213
1518.32%0.00%0.00%81.68%5.25%3.76%1.226
1619.28%0.00%0.00%80.72%5.38%3.83%1.238
1720.24%0.00%0.00%79.76%5.51%3.91%1.248
1821.20%0.00%0.00%78.80%5.63%3.98%1.257
1922.16%0.00%0.00%77.84%5.76%4.06%1.264
2023.12%0.00%0.00%76.88%5.89%4.14%1.271
2124.08%0.00%0.00%75.92%6.02%4.22%1.276
2225.04%0.00%0.00%74.96%6.15%4.31%1.280
2326.01%0.00%0.00%73.99%6.28%4.40%1.284
2426.97%0.00%0.00%73.03%6.41%4.49%1.287
2527.93%0.00%0.00%72.07%6.54%4.58%1.289
2628.89%0.00%0.00%71.11%6.67%4.68%1.291
2729.85%0.00%0.00%70.15%6.80%4.77%1.292
2830.81%0.00%0.00%69.19%6.93%4.87%1.292
2931.77%0.00%0.00%68.23%7.06%4.97%1.292
3032.73%0.00%0.00%67.27%7.19%5.08%1.292
3133.69%0.00%0.00%66.31%7.32%5.18%1.292
3234.65%0.00%0.00%65.35%7.45%5.28%1.291
3335.61%0.00%0.00%64.39%7.58%5.39%1.290
3436.58%0.00%0.00%63.42%7.72%5.50%1.288
3537.54%0.00%0.00%62.46%7.85%5.61%1.287
3638.50%0.00%0.00%61.50%7.98%5.72%1.285
3739.46%0.00%0.00%60.54%8.11%5.83%1.283
3840.42%0.00%0.00%59.58%8.24%5.94%1.282
3941.38%0.00%0.00%58.62%8.37%6.05%1.280
4042.34%0.00%0.00%57.66%8.51%6.16%1.277
4143.30%0.00%0.00%56.70%8.64%6.28%1.275
4244.26%0.00%0.00%55.74%8.77%6.39%1.273
4345.22%0.00%0.00%54.78%8.90%6.51%1.271
4446.19%0.00%0.00%53.81%9.04%6.62%1.269
4547.15%0.00%0.00%52.85%9.17%6.74%1.266
4648.11%0.00%0.00%51.89%9.30%6.86%1.264
4749.07%0.00%0.00%50.93%9.43%6.98%1.262
4850.03%0.00%0.00%49.97%9.57%7.10%1.259
4950.99%0.00%0.00%49.01%9.70%7.21%1.257
5051.95%0.00%0.00%48.05%9.83%7.33%1.255
5152.91%0.00%0.00%47.09%9.97%7.45%1.252
5253.87%0.00%0.00%46.13%10.10%7.58%1.250
5354.83%0.00%0.00%45.17%10.24%7.70%1.248
5455.80%0.00%0.00%44.20%10.37%7.82%1.245
5556.76%0.00%0.00%43.24%10.50%7.94%1.243
5657.72%0.00%0.00%42.28%10.64%8.06%1.241
5758.68%0.00%0.00%41.32%10.77%8.19%1.239
5859.64%0.00%0.00%40.36%10.91%8.31%1.237
5960.60%0.00%0.00%39.40%11.04%8.43%1.235
6061.56%0.00%0.00%38.44%11.18%8.56%1.233
6162.52%0.00%0.00%37.48%11.31%8.68%1.230
6263.48%0.00%0.00%36.52%11.45%8.80%1.228
6364.44%0.00%0.00%35.56%11.58%8.93%1.226
6465.40%0.00%0.00%34.60%11.72%9.05%1.225
6566.37%0.00%0.00%33.63%11.86%9.18%1.223
6667.33%0.00%0.00%32.67%11.99%9.30%1.221
6768.29%0.00%0.00%31.71%12.13%9.43%1.219
6869.25%0.00%0.00%30.75%12.26%9.56%1.217
6970.21%0.00%0.00%29.79%12.40%9.68%1.215
7071.17%0.00%0.00%28.83%12.54%9.81%1.214
7172.13%0.00%0.00%27.87%12.67%9.93%1.212
7273.09%0.00%0.00%26.91%12.81%10.06%1.210
7374.05%0.00%0.00%25.95%12.95%10.19%1.209
7475.01%0.00%0.00%24.99%13.08%10.32%1.207
7575.98%0.00%0.00%24.02%13.22%10.44%1.205
7676.94%0.00%0.00%23.06%13.36%10.57%1.204
7777.90%0.00%0.00%22.10%13.50%10.70%1.202
7878.86%0.00%0.00%21.14%13.63%10.83%1.201
7979.82%0.00%0.00%20.18%13.77%10.95%1.200
8080.78%0.00%0.00%19.22%13.91%11.08%1.198
8181.74%0.00%0.00%18.26%14.05%11.21%1.197
8282.70%0.00%0.00%17.30%14.19%11.34%1.195
8383.66%0.00%0.00%16.34%14.33%11.47%1.194
8484.62%0.00%0.00%15.38%14.46%11.59%1.193
8585.59%0.00%0.00%14.41%14.60%11.72%1.192
8686.55%0.00%0.00%13.45%14.74%11.85%1.190
8787.51%0.00%0.00%12.49%14.88%11.98%1.189
8888.47%0.00%0.00%11.53%15.02%12.11%1.188
8989.43%0.00%0.00%10.57%15.16%12.24%1.187
9090.39%0.00%0.00%9.61%15.30%12.37%1.186
9191.35%0.00%0.00%8.65%15.44%12.50%1.185
9292.31%0.00%0.00%7.69%15.58%12.63%1.184
9393.27%0.00%0.00%6.73%15.72%12.76%1.183
9494.23%0.00%0.00%5.77%15.86%12.89%1.182
9595.20%0.00%0.00%4.80%16.00%13.02%1.181
9696.16%0.00%0.00%3.84%16.14%13.15%1.180
9797.12%0.00%0.00%2.88%16.28%13.28%1.179
9898.08%0.00%0.00%1.92%16.42%13.41%1.178
9999.04%0.00%0.00%0.96%16.56%13.54%1.177
100100.00%0.00%0.00%0.00%16.70%13.67%1.176
*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 (0.63% 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%8.06%$10,80616.45%18.61%17.63%3.16%
20131.50%4.19%$11,25833.45%14.61%2.31%-2.10%
20140.76%7.73%$12,12812.54%-4.74%30.36%5.82%
20150.73%0.42%$12,1790.36%-4.19%2.42%0.56%
20162.07%4.82%$12,76712.83%4.81%8.60%2.52%
20172.11%8.33%$13,83021.21%27.45%4.91%3.57%
20181.91%-2.80%$13,442-5.21%-14.43%-6.02%-0.12%
20192.29%14.93%$15,44930.67%21.75%28.87%8.83%
20201.36%9.04%$16,84521.03%10.69%-4.68%7.71%
20210.98%-0.28%$16,7986.54%4.48%8.79%-3.64%
Annual return for 2021 is from 01/01/2021 to 03/31/2021
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)
201212.52%$10,2525.07%7.33%6.38%0.63%
201220.95%$10,3504.22%4.56%-1.15%0.04%
201230.50%$10,4013.06%-0.54%5.19%-0.51%
201240.70%$10,474-0.64%-2.08%2.86%1.10%
20125-1.84%$10,281-6.23%-10.83%-4.51%0.93%
201261.78%$10,4644.05%5.97%5.52%0.07%
201271.16%$10,5850.88%0.31%2.00%1.23%
201280.73%$10,6632.70%2.60%-0.01%0.16%
201290.63%$10,7302.49%3.41%-1.86%0.18%
201210-0.29%$10,700-1.81%0.81%-0.91%-0.10%
2012110.48%$10,7510.77%2.06%-0.26%0.27%
2012120.51%$10,8061.29%4.88%3.72%-0.88%
201310.86%$10,8985.42%2.40%3.74%-0.69%
201320.50%$10,9531.28%-1.14%1.22%0.54%
201330.93%$11,0553.95%0.93%2.87%0.08%
201341.94%$11,2701.61%3.50%6.73%1.01%
20135-1.95%$11,0502.44%-3.30%-5.98%-1.93%
20136-1.87%$10,843-1.43%-3.57%-1.98%-1.65%
201371.58%$11,0145.75%4.62%0.90%0.38%
20138-1.86%$10,809-3.03%-1.95%-6.98%-0.86%
201392.43%$11,0723.90%7.51%3.49%1.11%
2013101.96%$11,2894.27%3.67%4.52%0.86%
201311-0.37%$11,2472.70%0.13%-5.25%-0.29%
2013120.10%$11,2582.73%1.52%0.10%-0.64%
201410.45%$11,308-3.17%-5.40%4.28%1.55%
201422.05%$11,5414.87%5.59%5.07%0.47%
201430.05%$11,5470.51%0.49%0.49%-0.17%
201441.01%$11,6640.06%1.26%3.29%0.80%
201451.42%$11,8292.10%1.93%2.40%1.05%
201460.71%$11,9132.62%1.89%1.13%0.08%
20147-0.62%$11,839-1.99%-1.73%0.08%-0.28%
201481.70%$12,0414.15%1.16%3.04%1.14%
20149-1.81%$11,822-2.10%-5.01%-6.04%-0.57%
2014101.80%$12,0352.75%-0.08%9.94%0.72%
2014111.00%$12,1552.48%-0.51%2.00%0.83%
201412-0.22%$12,128-0.04%-3.87%1.88%0.06%
201511.97%$12,367-2.74%0.27%6.85%2.40%
201520.13%$12,3845.74%5.78%-3.67%-1.31%
201530.22%$12,412-1.16%-1.49%1.74%0.55%
20154-0.17%$12,3900.62%4.81%-5.85%-0.32%
20155-0.30%$12,3531.30%-0.91%-0.30%-0.50%
20156-1.72%$12,140-1.67%-2.73%-4.68%-1.11%
201571.30%$12,2981.70%-0.56%5.77%0.88%
20158-2.39%$12,004-6.09%-7.43%-6.29%-0.25%
201590.04%$12,009-2.92%-3.85%3.05%0.81%
2015102.28%$12,2837.91%6.25%5.76%0.03%
201511-0.40%$12,2340.60%-1.32%-0.63%-0.39%
201512-0.45%$12,179-2.13%-2.17%1.82%-0.18%
20161-0.87%$12,073-5.72%-5.45%-3.44%1.20%
201620.25%$12,102-0.01%-2.46%-0.36%0.85%
201633.46%$12,5217.11%8.33%10.48%0.88%
201640.36%$12,5660.66%2.16%-2.35%0.40%
201650.32%$12,6071.73%-0.98%2.25%-0.01%
201661.96%$12,8540.27%-0.90%6.92%2.02%
201671.83%$13,0893.98%4.52%4.26%0.60%
20168-0.51%$13,0220.21%0.45%-3.76%-0.31%
201690.11%$13,0370.21%1.70%-1.82%0.11%
201610-1.68%$12,818-2.19%-1.91%-5.74%-0.94%
201611-1.55%$12,6194.49%-2.01%-1.68%-2.57%
2016121.17%$12,7671.98%1.96%4.82%0.33%
201710.80%$12,8691.86%4.08%-0.19%0.19%
201721.37%$13,0443.69%1.34%3.51%0.62%
201730.08%$13,0550.06%3.00%-2.42%-0.04%
201740.92%$13,1751.06%2.05%0.24%0.80%
201750.86%$13,2881.01%2.96%-0.72%0.71%
201760.45%$13,3480.95%0.63%2.23%0.05%
201771.01%$13,4821.88%3.37%1.24%0.40%
201780.62%$13,5660.15%0.54%-0.26%0.86%
201790.19%$13,5922.44%1.88%-0.11%-0.47%
2017100.37%$13,6432.17%2.03%-1.07%-0.03%
2017110.64%$13,7303.03%0.63%2.66%-0.11%
2017120.72%$13,8301.16%2.07%-0.14%0.54%
201810.05%$13,8375.23%5.72%-4.25%-1.24%
20182-2.51%$13,489-3.76%-5.24%-7.68%-1.04%
201830.56%$13,564-1.95%-0.38%3.88%0.69%
20184-0.38%$13,5130.45%0.46%0.82%-0.85%
201850.97%$13,6442.72%-1.64%3.68%0.68%
201860.23%$13,6760.70%-2.14%4.20%-0.04%
201870.74%$13,7763.32%2.55%0.60%-0.04%
201880.85%$13,8933.43%-2.40%2.58%0.67%
20189-0.58%$13,8130.20%0.21%-2.64%-0.55%
201810-2.75%$13,433-7.41%-8.56%-2.93%-0.86%
2018111.33%$13,6112.01%1.68%4.67%0.64%
201812-1.24%$13,442-9.16%-4.93%-7.96%1.87%
201913.85%$13,9598.54%7.67%11.85%1.11%
201920.63%$14,0483.56%1.63%0.70%-0.09%
201931.97%$14,3241.42%0.77%4.21%1.94%
201940.77%$14,4343.93%2.77%-0.16%-0.02%
20195-0.19%$14,407-6.45%-5.42%0.14%1.83%
201962.51%$14,7697.08%5.77%1.54%1.25%
201970.22%$14,8001.41%-1.99%1.70%0.15%
201981.70%$15,053-2.08%-2.17%3.75%2.77%
201990.35%$15,1051.78%2.73%1.93%-0.57%
2019100.97%$15,2512.11%3.43%1.13%0.31%
2019110.42%$15,3163.79%0.99%-1.30%-0.04%
2019120.87%$15,4492.80%4.38%0.76%-0.07%
202011.04%$15,610-0.06%-3.39%1.23%1.98%
20202-1.33%$15,401-8.00%-6.60%-7.03%1.67%
20203-6.45%$14,407-13.91%-16.26%-19.42%-1.43%
202045.21%$15,15813.13%7.60%8.96%2.76%
202051.85%$15,4385.40%5.01%1.73%0.67%
202061.45%$15,6632.29%4.24%2.41%0.67%
202072.51%$16,0565.74%4.15%3.64%1.45%
202080.80%$16,1847.10%4.43%0.44%-0.94%
20209-0.98%$16,026-3.54%-1.82%-2.68%-0.10%
202010-1.17%$15,838-1.95%-2.30%-3.00%-0.56%
2020114.66%$16,57711.80%12.62%9.67%1.21%
2020121.62%$16,8454.68%5.86%2.72%0.15%
20211-0.58%$16,748-0.33%0.25%0.04%-0.86%
20212-0.03%$16,7423.14%2.30%3.43%-1.55%
202130.33%$16,7983.65%1.87%5.15%-1.27%
Portfolio return and risk metrics
MetricRisk Parity
Arithmetic Mean (monthly)0.48%
Arithmetic Mean (annualized)5.91%
Geometric Mean (monthly)0.47%
Geometric Mean (annualized)5.77%
Volatility (monthly)1.52%
Volatility (annualized)5.28%
Downside Deviation (monthly)0.93%
Max. Drawdown-7.70%
US Market Correlation0.78
Beta(*)0.30
Alpha (annualized)1.08%
R261.51%
Sharpe Ratio0.97
Sortino Ratio1.56
Treynor Ratio (%)16.92
Calmar Ratio0.96
Active Return-9.73%
Tracking Error10.07%
Information Ratio-0.97
Skewness-0.57
Excess Kurtosis3.97
Historical Value-at-Risk (5%)-1.87%
Analytical Value-at-Risk (5%)-2.02%
Conditional Value-at-Risk (5%)-2.99%
Upside Capture Ratio (%)29.80
Downside Capture Ratio (%)25.81
Safe Withdrawal Rate13.41%
Perpetual Withdrawal Rate3.98%
Positive Periods80 out of 111 (72.07%)
Gain/Loss Ratio0.92
* 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
1Feb 2020Mar 20202 monthsJun 20203 months5 months-7.70%
2May 2013Aug 20134 monthsOct 20132 months6 months-4.09%
3Aug 2016Nov 20164 monthsApr 20175 months9 months-3.59%
4Sep 2018Oct 20182 monthsJan 20193 months5 months-3.31%
5Apr 2015Aug 20155 monthsMar 20167 months1 year-3.28%
6Feb 2018Feb 20181 monthAug 20186 months7 months-2.51%
7Sep 2020Oct 20202 monthsNov 20201 month3 months-2.14%
8May 2012May 20121 monthJul 20122 months3 months-1.84%
9Sep 2014Sep 20141 monthNov 20142 months3 months-1.81%
10Jul 2014Jul 20141 monthAug 20141 month2 months-0.62%
Worst 10 drawdowns included above

Portfolio Assets

Performance statistics for portfolio components
TickerNameCAGRStdevBest YearWorst YearMax. DrawdownSharpe RatioSortino RatioUS Mkt Correlation
VTIVanguard Total Stock Market ETF15.64%13.67%33.45%-5.21%-20.84%1.091.761.00
VXUSVanguard Total International Stock ETF7.76%14.40%27.45%-14.43%-25.54%0.550.810.86
VNQVanguard Real Estate ETF9.42%15.32%30.36%-6.02%-25.08%0.630.930.63
BNDVanguard Total Bond Market ETF2.77%3.33%8.83%-3.64%-4.01%0.651.090.04

Monthly Correlations

Correlations for the portfolio assets
TickerNameVTIVXUSVNQBNDRisk Parity
VTIVanguard Total Stock Market ETF1.000.860.630.040.79
VXUSVanguard Total International Stock ETF0.861.000.580.110.80
VNQVanguard Real Estate ETF0.630.581.000.460.86
BNDVanguard Total Bond Market ETF0.040.110.461.000.60

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 year5.41%16.59%-2.80%
3 years4.86%7.47%2.89%
5 years4.82%6.76%3.03%
7 years5.08%5.94%3.86%