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 - Aug 2020)

Portfolio optimization results for risk parity. The possible range of expected annual portfolio returns for the given period is 3.99% to 15.59%. Refer to the efficient frontier section for additional details.

Portfolio Allocations

Risk Parity
Ticker Name Allocation
VTI Vanguard Total Stock Market ETF 12.53%
VXUS Vanguard Total International Stock ETF 11.62%
VNQ Vanguard Real Estate ETF 9.81%
BND Vanguard Total Bond Market ETF 66.04%
Save portfolio »

Portfolio Performance Summary

Portfolio performance statistics
MetricRisk Parity
Start Balance$10,000
End Balance$16,214
CAGR5.74%
Expected Return 5.88%
Stdev5.20%
Best Year14.97%
Worst Year-2.83%
Max. Drawdown -7.75%
Sharpe Ratio (ex-ante)1.00
Sharpe Ratio (ex-post)0.97
Sortino Ratio1.50
US Stock Market Correlation0.77
   

Trailing Returns

Trailing Returns
Name3 MonthYTD1 year3 year5 yearFull
Risk Parity4.88%4.78%7.58%6.08%6.18%5.74%
Trailing returns are for full months ending in August 2020 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 2020 are based on full calendar months from January to August
  • 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)14.57%15.60%13.41%1.1130.00%100.00%
2Vanguard Total International Stock ETF (VXUS)6.11%7.18%14.12%0.4610.00%100.00%
3Vanguard Real Estate ETF (VNQ)8.25%9.53%15.33%0.5780.00%100.00%
4Vanguard Total Bond Market ETF (BND)3.32%3.37%3.30%0.8190.00%100.00%
Results based on historical returns. Ex ante Sharpe Ratio calculated using 3-month treasury bill returns as the risk-free rate (0.67% annualized).

Asset Correlations

Efficient Frontier Asset Correlations
NameTickerVTIVXUSVNQBND
Vanguard Total Stock Market ETFVTI1.000.850.610.02
Vanguard Total International Stock ETFVXUS0.851.000.560.10
Vanguard Real Estate ETFVNQ0.610.561.000.49
Vanguard Total Bond Market ETFBND0.020.100.491.00
Based on provided custom correlation matrix
Efficient Frontier Assets
#VTIVXUSVNQBNDExpected Return*Standard Deviation*Sharpe Ratio*
15.36%0.00%0.00%94.64%3.99%3.21%1.034
26.31%0.00%0.00%93.69%4.11%3.22%1.068
37.27%0.00%0.00%92.73%4.22%3.22%1.100
48.22%0.00%0.00%91.78%4.33%3.24%1.130
59.18%0.00%0.00%90.82%4.44%3.26%1.158
610.14%0.00%0.00%89.86%4.55%3.28%1.184
711.09%0.00%0.00%88.91%4.67%3.31%1.207
812.05%0.00%0.00%87.95%4.78%3.34%1.229
913.00%0.00%0.00%87.00%4.89%3.38%1.248
1013.96%0.00%0.00%86.04%5.00%3.43%1.265
1114.92%0.00%0.00%85.08%5.12%3.47%1.280
1215.87%0.00%0.00%84.13%5.23%3.52%1.293
1316.83%0.00%0.00%83.17%5.34%3.58%1.305
1417.78%0.00%0.00%82.22%5.45%3.64%1.314
1518.74%0.00%0.00%81.26%5.57%3.70%1.322
1619.70%0.00%0.00%80.30%5.68%3.77%1.329
1720.65%0.00%0.00%79.35%5.79%3.84%1.334
1821.61%0.00%0.00%78.39%5.91%3.92%1.338
1922.56%0.00%0.00%77.44%6.02%3.99%1.340
2023.52%0.00%0.00%76.48%6.13%4.07%1.342
2124.48%0.00%0.00%75.52%6.25%4.15%1.343
2225.43%0.00%0.00%74.57%6.36%4.24%1.343
2326.39%0.00%0.00%73.61%6.48%4.32%1.343
2427.34%0.00%0.00%72.66%6.59%4.41%1.341
2528.30%0.00%0.00%71.70%6.70%4.51%1.340
2629.26%0.00%0.00%70.74%6.82%4.60%1.337
2730.21%0.00%0.00%69.79%6.93%4.69%1.335
2831.17%0.00%0.00%68.83%7.05%4.79%1.332
2932.12%0.00%0.00%67.88%7.16%4.89%1.328
3033.08%0.00%0.00%66.92%7.28%4.99%1.325
3134.04%0.00%0.00%65.96%7.39%5.09%1.321
3234.99%0.00%0.00%65.01%7.51%5.19%1.317
3335.95%0.00%0.00%64.05%7.62%5.30%1.313
3436.90%0.00%0.00%63.10%7.74%5.40%1.309
3537.86%0.00%0.00%62.14%7.85%5.51%1.304
3638.82%0.00%0.00%61.18%7.97%5.61%1.300
3739.77%0.00%0.00%60.23%8.08%5.72%1.295
3840.73%0.00%0.00%59.27%8.20%5.83%1.291
3941.68%0.00%0.00%58.32%8.32%5.94%1.287
4042.64%0.00%0.00%57.36%8.43%6.05%1.282
4143.60%0.00%0.00%56.40%8.55%6.17%1.278
4244.55%0.00%0.00%55.45%8.66%6.28%1.273
4345.51%0.00%0.00%54.49%8.78%6.39%1.269
4446.46%0.00%0.00%53.54%8.90%6.51%1.265
4547.42%0.00%0.00%52.58%9.01%6.62%1.260
4648.38%0.00%0.00%51.62%9.13%6.74%1.256
4749.33%0.00%0.00%50.67%9.25%6.85%1.252
4850.29%0.00%0.00%49.71%9.36%6.97%1.248
4951.24%0.00%0.00%48.76%9.48%7.08%1.243
5052.20%0.00%0.00%47.80%9.60%7.20%1.239
5153.16%0.00%0.00%46.84%9.71%7.32%1.235
5254.11%0.00%0.00%45.89%9.83%7.44%1.232
5355.07%0.00%0.00%44.93%9.95%7.56%1.228
5456.02%0.00%0.00%43.98%10.07%7.68%1.224
5556.98%0.00%0.00%43.02%10.18%7.80%1.220
5657.94%0.00%0.00%42.06%10.30%7.92%1.217
5758.89%0.00%0.00%41.11%10.42%8.04%1.213
5859.85%0.00%0.00%40.15%10.54%8.16%1.210
5960.80%0.00%0.00%39.20%10.65%8.28%1.206
6061.76%0.00%0.00%38.24%10.77%8.40%1.203
6162.72%0.00%0.00%37.28%10.89%8.52%1.200
6263.67%0.00%0.00%36.33%11.01%8.64%1.196
6364.63%0.00%0.00%35.37%11.13%8.77%1.193
6465.58%0.00%0.00%34.42%11.25%8.89%1.190
6566.54%0.00%0.00%33.46%11.37%9.01%1.187
6667.50%0.00%0.00%32.50%11.48%9.13%1.184
6768.45%0.00%0.00%31.55%11.60%9.26%1.181
6869.41%0.00%0.00%30.59%11.72%9.38%1.178
6970.36%0.00%0.00%29.64%11.84%9.50%1.176
7071.32%0.00%0.00%28.68%11.96%9.63%1.173
7172.28%0.00%0.00%27.72%12.08%9.75%1.170
7273.23%0.00%0.00%26.77%12.20%9.88%1.167
7374.19%0.00%0.00%25.81%12.32%10.00%1.165
7475.14%0.00%0.00%24.86%12.44%10.12%1.162
7576.10%0.00%0.00%23.90%12.56%10.25%1.160
7677.06%0.00%0.00%22.94%12.68%10.37%1.158
7778.01%0.00%0.00%21.99%12.80%10.50%1.155
7878.97%0.00%0.00%21.03%12.92%10.63%1.153
7979.92%0.00%0.00%20.08%13.04%10.75%1.151
8080.88%0.00%0.00%19.12%13.16%10.88%1.148
8181.84%0.00%0.00%18.16%13.28%11.00%1.146
8282.79%0.00%0.00%17.21%13.40%11.13%1.144
8383.75%0.00%0.00%16.25%13.52%11.25%1.142
8484.70%0.00%0.00%15.30%13.64%11.38%1.140
8585.66%0.00%0.00%14.34%13.77%11.51%1.138
8686.62%0.00%0.00%13.38%13.89%11.63%1.136
8787.57%0.00%0.00%12.43%14.01%11.76%1.134
8888.53%0.00%0.00%11.47%14.13%11.89%1.132
8989.48%0.00%0.00%10.52%14.25%12.01%1.131
9090.44%0.00%0.00%9.56%14.37%12.14%1.129
9191.40%0.00%0.00%8.60%14.49%12.27%1.127
9292.35%0.00%0.00%7.65%14.62%12.39%1.125
9393.31%0.00%0.00%6.69%14.74%12.52%1.124
9494.26%0.00%0.00%5.74%14.86%12.65%1.122
9595.22%0.00%0.00%4.78%14.98%12.77%1.120
9696.18%0.00%0.00%3.82%15.11%12.90%1.119
9797.13%0.00%0.00%2.87%15.23%13.03%1.117
9898.09%0.00%0.00%1.91%15.35%13.16%1.116
9999.04%0.00%0.00%0.96%15.47%13.28%1.114
100100.00%0.00%0.00%0.00%15.60%13.41%1.113
*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 (0.67% 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%8.09%$10,80916.45%18.61%17.63%3.16%
20131.50%4.28%$11,27233.45%14.61%2.31%-2.10%
20140.76%7.68%$12,13912.54%-4.74%30.36%5.82%
20150.73%0.41%$12,1880.36%-4.19%2.42%0.56%
20162.07%4.84%$12,77812.83%4.81%8.60%2.52%
20172.11%8.41%$13,85221.21%27.45%4.91%3.57%
20181.91%-2.83%$13,460-5.21%-14.43%-6.02%-0.12%
20192.29%14.97%$15,47530.67%21.75%28.87%8.83%
20200.83%4.78%$16,2149.35%-3.20%-10.37%6.96%
Annual returns for 2020 are based on partial year data
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)
201212.53%$10,2535.07%7.33%6.38%0.63%
201220.97%$10,3534.22%4.56%-1.15%0.04%
201230.49%$10,4043.06%-0.54%5.19%-0.51%
201240.69%$10,476-0.64%-2.08%2.86%1.10%
20125-1.86%$10,280-6.23%-10.83%-4.51%0.93%
201261.79%$10,4644.05%5.97%5.52%0.07%
201271.15%$10,5850.88%0.31%2.00%1.23%
201280.75%$10,6642.70%2.60%-0.01%0.16%
201290.65%$10,7332.49%3.41%-1.86%0.18%
201210-0.29%$10,702-1.81%0.81%-0.91%-0.10%
2012110.49%$10,7540.77%2.06%-0.26%0.27%
2012120.51%$10,8091.29%4.88%3.72%-0.88%
201310.87%$10,9035.42%2.40%3.74%-0.69%
201320.50%$10,9581.28%-1.14%1.22%0.54%
201330.94%$11,0613.95%0.93%2.87%0.08%
201341.94%$11,2751.61%3.50%6.73%1.01%
20135-1.94%$11,0572.44%-3.30%-5.98%-1.93%
20136-1.88%$10,849-1.43%-3.57%-1.98%-1.65%
201371.60%$11,0225.75%4.62%0.90%0.38%
20138-1.86%$10,818-3.03%-1.95%-6.98%-0.86%
201392.44%$11,0823.90%7.51%3.49%1.11%
2013101.97%$11,3004.27%3.67%4.52%0.86%
201311-0.35%$11,2602.70%0.13%-5.25%-0.29%
2013120.11%$11,2722.73%1.52%0.10%-0.64%
201410.42%$11,319-3.17%-5.40%4.28%1.55%
201422.07%$11,5534.87%5.59%5.07%0.47%
201430.06%$11,5600.51%0.49%0.49%-0.17%
201441.01%$11,6760.06%1.26%3.29%0.80%
201451.42%$11,8422.10%1.93%2.40%1.05%
201460.72%$11,9262.62%1.89%1.13%0.08%
20147-0.63%$11,852-1.99%-1.73%0.08%-0.28%
201481.71%$12,0544.15%1.16%3.04%1.14%
20149-1.81%$11,835-2.10%-5.01%-6.04%-0.57%
2014101.79%$12,0472.75%-0.08%9.94%0.72%
2014111.00%$12,1672.48%-0.51%2.00%0.83%
201412-0.23%$12,139-0.04%-3.87%1.88%0.06%
201511.95%$12,375-2.74%0.27%6.85%2.40%
201520.17%$12,3965.74%5.78%-3.67%-1.31%
201530.21%$12,422-1.16%-1.49%1.74%0.55%
20154-0.15%$12,4030.62%4.81%-5.85%-0.32%
20155-0.30%$12,3661.30%-0.91%-0.30%-0.50%
20156-1.72%$12,153-1.67%-2.73%-4.68%-1.11%
201571.30%$12,3111.70%-0.56%5.77%0.88%
20158-2.41%$12,014-6.09%-7.43%-6.29%-0.25%
201590.02%$12,017-2.92%-3.85%3.05%0.81%
2015102.30%$12,2937.91%6.25%5.76%0.03%
201511-0.40%$12,2440.60%-1.32%-0.63%-0.39%
201512-0.46%$12,188-2.13%-2.17%1.82%-0.18%
20161-0.89%$12,079-5.72%-5.45%-3.44%1.20%
201620.24%$12,108-0.01%-2.46%-0.36%0.85%
201633.47%$12,5287.11%8.33%10.48%0.88%
201640.37%$12,5750.66%2.16%-2.35%0.40%
201650.32%$12,6151.73%-0.98%2.25%-0.01%
201661.94%$12,8600.27%-0.90%6.92%2.02%
201671.84%$13,0963.98%4.52%4.26%0.60%
20168-0.50%$13,0310.21%0.45%-3.76%-0.31%
201690.12%$13,0470.21%1.70%-1.82%0.11%
201610-1.68%$12,827-2.19%-1.91%-5.74%-0.94%
201611-1.53%$12,6314.49%-2.01%-1.68%-2.57%
2016121.17%$12,7781.98%1.96%4.82%0.33%
201710.81%$12,8821.86%4.08%-0.19%0.19%
201721.37%$13,0583.69%1.34%3.51%0.62%
201730.09%$13,0700.06%3.00%-2.42%-0.04%
201740.92%$13,1901.06%2.05%0.24%0.80%
201750.87%$13,3051.01%2.96%-0.72%0.71%
201760.44%$13,3640.95%0.63%2.23%0.05%
201771.02%$13,5001.88%3.37%1.24%0.40%
201780.62%$13,5840.15%0.54%-0.26%0.86%
201790.20%$13,6122.44%1.88%-0.11%-0.47%
2017100.38%$13,6642.17%2.03%-1.07%-0.03%
2017110.64%$13,7523.03%0.63%2.66%-0.11%
2017120.73%$13,8521.16%2.07%-0.14%0.54%
201810.09%$13,8645.23%5.72%-4.25%-1.24%
20182-2.52%$13,515-3.76%-5.24%-7.68%-1.04%
201830.54%$13,589-1.95%-0.38%3.88%0.69%
20184-0.37%$13,5380.45%0.46%0.82%-0.85%
201850.96%$13,6682.72%-1.64%3.68%0.68%
201860.22%$13,6990.70%-2.14%4.20%-0.04%
201870.75%$13,8013.32%2.55%0.60%-0.04%
201880.85%$13,9183.43%-2.40%2.58%0.67%
20189-0.57%$13,8380.20%0.21%-2.64%-0.55%
201810-2.78%$13,454-7.41%-8.56%-2.93%-0.86%
2018111.33%$13,6322.01%1.68%4.67%0.64%
201812-1.26%$13,460-9.16%-4.93%-7.96%1.87%
201913.86%$13,9798.54%7.67%11.85%1.11%
201920.64%$14,0693.56%1.63%0.70%-0.09%
201931.96%$14,3451.42%0.77%4.21%1.94%
201940.78%$14,4573.93%2.77%-0.16%-0.02%
20195-0.22%$14,426-6.45%-5.42%0.14%1.83%
201962.53%$14,7917.08%5.77%1.54%1.25%
201970.21%$14,8221.41%-1.99%1.70%0.15%
201981.68%$15,072-2.08%-2.17%3.75%2.77%
201990.35%$15,1251.78%2.73%1.93%-0.57%
2019100.98%$15,2732.11%3.43%1.13%0.31%
2019110.43%$15,3393.79%0.99%-1.30%-0.04%
2019120.89%$15,4752.80%4.38%0.76%-0.07%
202011.03%$15,634-0.06%-3.39%1.23%1.98%
20202-1.36%$15,422-8.00%-6.60%-7.03%1.67%
20203-6.48%$14,423-13.91%-16.26%-19.42%-1.43%
202045.23%$15,17713.13%7.60%8.96%2.76%
202051.87%$15,4615.40%5.01%1.73%0.67%
202061.46%$15,6862.29%4.24%2.41%0.67%
202072.52%$16,0815.74%4.15%3.64%1.45%
202080.83%$16,2147.10%4.43%0.44%-0.94%
Portfolio return and risk metrics
MetricRisk Parity
Arithmetic Mean (monthly)0.48%
Arithmetic Mean (annualized)5.88%
Geometric Mean (monthly)0.47%
Geometric Mean (annualized)5.74%
Volatility (monthly)1.50%
Volatility (annualized)5.20%
Downside Deviation (monthly)0.95%
Max. Drawdown-7.75%
US Market Correlation0.77
Beta(*)0.30
Alpha (annualized)1.38%
R259.52%
Sharpe Ratio0.97
Sortino Ratio1.50
Treynor Ratio (%)16.86
Calmar Ratio0.78
Active Return-8.72%
Tracking Error9.93%
Information Ratio-0.88
Skewness-0.83
Excess Kurtosis4.41
Historical Value-at-Risk (5%)-1.92%
Analytical Value-at-Risk (5%)-1.98%
Conditional Value-at-Risk (5%)-3.22%
Upside Capture Ratio (%)30.50
Downside Capture Ratio (%)24.95
Safe Withdrawal Rate14.79%
Perpetual Withdrawal Rate4.22%
Positive Periods77 out of 104 (74.04%)
Gain/Loss Ratio0.83
* 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-7.75%
2May 2013Aug 20134 monthsOct 20132 months6 months-4.05%
3Aug 2016Nov 20164 monthsApr 20175 months9 months-3.55%
4Sep 2018Oct 20182 monthsJan 20193 months5 months-3.33%
5Apr 2015Aug 20155 monthsMar 20167 months1 year-3.28%
6Feb 2018Feb 20181 monthAug 20186 months7 months-2.52%
7May 2012May 20121 monthJul 20122 months3 months-1.86%
8Sep 2014Sep 20141 monthNov 20142 months3 months-1.81%
9Jul 2014Jul 20141 monthAug 20141 month2 months-0.63%
10Nov 2013Nov 20131 monthJan 20142 months3 months-0.35%
Worst 10 drawdowns included above

Portfolio Assets

Performance statistics for portfolio components
TickerNameCAGRStdevBest YearWorst YearMax. DrawdownSharpe RatioSortino RatioUS Mkt Correlation
VTIVanguard Total Stock Market ETF14.57%13.41%33.45%-5.21%-20.84%1.031.611.00
VXUSVanguard Total International Stock ETF6.11%14.12%27.45%-14.43%-25.54%0.440.630.85
VNQVanguard Real Estate ETF8.25%15.33%30.36%-10.37%-25.08%0.550.800.61
BNDVanguard Total Bond Market ETF3.32%3.30%8.83%-2.10%-4.01%0.811.400.01

Monthly Correlations

Correlations for the portfolio assets
TickerNameVTIVXUSVNQBNDRisk Parity
VTIVanguard Total Stock Market ETF1.000.850.610.020.77
VXUSVanguard Total International Stock ETF0.851.000.560.100.79
VNQVanguard Real Estate ETF0.610.561.000.490.87
BNDVanguard Total Bond Market ETF0.020.100.491.000.60

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 year5.73%14.97%-2.83%
3 years4.91%6.67%3.36%
5 years4.67%5.09%3.61%
7 years4.80%5.26%4.34%
Result statistics are based on annualized rolling returns over full calendar year periods