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.

%
%
Browse…
1
%
%
%
%
%
2
%
%
%
%
%
3
%
%
%
%
%
4
%
%
%
%
%
5
%
%
%
%
%
6
%
%
%
%
%
7
%
%
%
%
%
8
%
%
%
%
%
9
%
%
%
%
%
10
%
%
%
%
%
Total
%

Asset Groups
Min. Weight
Max. Weight
A
%
%
B
%
%
C
%
%
D
%
%
E
%
%
F
%
%

Portfolio Optimization Results (Jan 2012 - Jun 2020)

Portfolio optimization results for risk parity. The possible range of expected annual portfolio returns for the given period is 3.92% to 14.20%. Refer to the efficient frontier section for additional details.

Portfolio Allocations

Risk Parity
Ticker Name Allocation
VTI Vanguard Total Stock Market ETF 12.58%
VXUS Vanguard Total International Stock ETF 11.58%
VNQ Vanguard Real Estate ETF 9.71%
BND Vanguard Total Bond Market ETF 66.13%
Save portfolio »

Portfolio Performance Summary

Portfolio performance statistics
MetricRisk Parity
Start Balance$10,000
End Balance$15,685
CAGR5.44%
Expected Return 5.58%
Stdev5.19%
Best Year14.96%
Worst Year-2.82%
Max. Drawdown -7.72%
Sharpe Ratio (ex-ante)0.94
Sharpe Ratio (ex-post)0.92
Sortino Ratio1.40
US Stock Market Correlation0.77
   
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 June
  • 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)13.21%14.20%13.29%1.0170.00%100.00%
2Vanguard Total International Stock ETF (VXUS)5.18%6.25%14.14%0.3940.00%100.00%
3Vanguard Real Estate ETF (VNQ)7.90%9.21%15.45%0.5520.00%100.00%
4Vanguard Total Bond Market ETF (BND)3.32%3.38%3.28%0.8220.00%100.00%
Results based on historical returns. Ex ante Sharpe Ratio calculated using 3-month treasury bill returns as the risk-free rate (0.68% 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*
15.27%0.00%0.00%94.73%3.92%3.20%1.013
26.23%0.00%0.00%93.77%4.02%3.20%1.044
37.18%0.00%0.00%92.82%4.12%3.21%1.072
48.14%0.00%0.00%91.86%4.22%3.22%1.098
59.10%0.00%0.00%90.90%4.32%3.24%1.123
610.05%0.00%0.00%89.95%4.42%3.26%1.146
711.01%0.00%0.00%88.99%4.52%3.29%1.166
811.97%0.00%0.00%88.03%4.62%3.33%1.184
912.92%0.00%0.00%87.08%4.72%3.36%1.201
1013.88%0.00%0.00%86.12%4.82%3.41%1.215
1114.84%0.00%0.00%85.16%4.92%3.45%1.227
1215.80%0.00%0.00%84.20%5.02%3.51%1.238
1316.75%0.00%0.00%83.25%5.12%3.56%1.247
1417.71%0.00%0.00%82.29%5.22%3.62%1.255
1518.67%0.00%0.00%81.33%5.32%3.68%1.260
1619.62%0.00%0.00%80.38%5.42%3.75%1.265
1720.58%0.00%0.00%79.42%5.52%3.82%1.268
1821.54%0.00%0.00%78.46%5.63%3.89%1.271
1922.49%0.00%0.00%77.51%5.73%3.97%1.272
2023.45%0.00%0.00%76.55%5.83%4.05%1.272
2124.41%0.00%0.00%75.59%5.93%4.13%1.272
2225.36%0.00%0.00%74.64%6.03%4.21%1.270
2326.32%0.00%0.00%73.68%6.13%4.30%1.269
2427.28%0.00%0.00%72.72%6.23%4.38%1.266
2528.23%0.00%0.00%71.77%6.33%4.47%1.263
2629.19%0.00%0.00%70.81%6.44%4.57%1.260
2730.15%0.00%0.00%69.85%6.54%4.66%1.257
2831.11%0.00%0.00%68.89%6.64%4.76%1.253
2932.06%0.00%0.00%67.94%6.74%4.85%1.249
3033.02%0.00%0.00%66.98%6.84%4.95%1.244
3133.98%0.00%0.00%66.02%6.94%5.05%1.240
3234.93%0.00%0.00%65.07%7.05%5.15%1.235
3335.89%0.00%0.00%64.11%7.15%5.26%1.230
3436.85%0.00%0.00%63.15%7.25%5.36%1.226
3537.80%0.00%0.00%62.20%7.35%5.47%1.221
3638.76%0.00%0.00%61.24%7.46%5.57%1.216
3739.72%0.00%0.00%60.28%7.56%5.68%1.211
3840.67%0.00%0.00%59.33%7.66%5.79%1.206
3941.63%0.00%0.00%58.37%7.76%5.90%1.201
4042.59%0.00%0.00%57.41%7.87%6.01%1.196
4143.54%0.00%0.00%56.46%7.97%6.12%1.192
4244.50%0.00%0.00%55.50%8.07%6.23%1.187
4345.46%0.00%0.00%54.54%8.18%6.34%1.182
4446.42%0.00%0.00%53.58%8.28%6.45%1.177
4547.37%0.00%0.00%52.63%8.38%6.57%1.173
4648.33%0.00%0.00%51.67%8.49%6.68%1.168
4749.29%0.00%0.00%50.71%8.59%6.80%1.164
4850.24%0.00%0.00%49.76%8.69%6.91%1.159
4951.20%0.00%0.00%48.80%8.80%7.03%1.155
5052.16%0.00%0.00%47.84%8.90%7.14%1.151
5153.11%0.00%0.00%46.89%9.00%7.26%1.146
5254.07%0.00%0.00%45.93%9.11%7.38%1.142
5355.03%0.00%0.00%44.97%9.21%7.49%1.138
5455.98%0.00%0.00%44.02%9.32%7.61%1.134
5556.94%0.00%0.00%43.06%9.42%7.73%1.130
5657.90%0.00%0.00%42.10%9.52%7.85%1.127
5758.85%0.00%0.00%41.15%9.63%7.97%1.123
5859.81%0.00%0.00%40.19%9.73%8.09%1.119
5960.77%0.00%0.00%39.23%9.84%8.21%1.115
6061.72%0.00%0.00%38.28%9.94%8.33%1.112
6162.68%0.00%0.00%37.32%10.05%8.45%1.108
6263.64%0.00%0.00%36.36%10.15%8.57%1.105
6364.60%0.00%0.00%35.40%10.26%8.69%1.102
6465.55%0.00%0.00%34.45%10.36%8.81%1.099
6566.51%0.00%0.00%33.49%10.47%8.93%1.095
6667.47%0.00%0.00%32.53%10.57%9.06%1.092
6768.42%0.00%0.00%31.58%10.68%9.18%1.089
6869.38%0.00%0.00%30.62%10.78%9.30%1.086
6970.34%0.00%0.00%29.66%10.89%9.42%1.083
7071.29%0.00%0.00%28.71%10.99%9.55%1.080
7172.25%0.00%0.00%27.75%11.10%9.67%1.078
7273.21%0.00%0.00%26.79%11.21%9.79%1.075
7374.16%0.00%0.00%25.84%11.31%9.92%1.072
7475.12%0.00%0.00%24.88%11.42%10.04%1.070
7576.08%0.00%0.00%23.92%11.52%10.16%1.067
7677.03%0.00%0.00%22.97%11.63%10.29%1.064
7777.99%0.00%0.00%22.01%11.74%10.41%1.062
7878.95%0.00%0.00%21.05%11.84%10.53%1.060
7979.91%0.00%0.00%20.09%11.95%10.66%1.057
8080.86%0.00%0.00%19.14%12.05%10.78%1.055
8181.82%0.00%0.00%18.18%12.16%10.91%1.053
8282.78%0.00%0.00%17.22%12.27%11.03%1.050
8383.73%0.00%0.00%16.27%12.37%11.16%1.048
8484.69%0.00%0.00%15.31%12.48%11.28%1.046
8585.65%0.00%0.00%14.35%12.59%11.41%1.044
8686.60%0.00%0.00%13.40%12.70%11.53%1.042
8787.56%0.00%0.00%12.44%12.80%11.66%1.040
8888.52%0.00%0.00%11.48%12.91%11.78%1.038
8989.47%0.00%0.00%10.53%13.02%11.91%1.036
9090.43%0.00%0.00%9.57%13.12%12.03%1.034
9191.39%0.00%0.00%8.61%13.23%12.16%1.032
9292.34%0.00%0.00%7.66%13.34%12.29%1.030
9393.30%0.00%0.00%6.70%13.45%12.41%1.029
9494.26%0.00%0.00%5.74%13.56%12.54%1.027
9595.22%0.00%0.00%4.78%13.66%12.66%1.025
9696.17%0.00%0.00%3.83%13.77%12.79%1.024
9797.13%0.00%0.00%2.87%13.88%12.92%1.022
9898.09%0.00%0.00%1.91%13.99%13.04%1.020
9999.04%0.00%0.00%0.96%14.10%13.17%1.019
100100.00%0.00%0.00%0.00%14.20%13.29%1.017
*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%8.08%$10,80816.45%18.61%17.63%3.16%
20131.50%4.29%$11,27133.45%14.61%2.31%-2.10%
20140.76%7.67%$12,13612.54%-4.74%30.36%5.82%
20150.73%0.41%$12,1860.36%-4.19%2.42%0.56%
20162.07%4.84%$12,77512.83%4.81%8.60%2.52%
20172.11%8.40%$13,84821.21%27.45%4.91%3.57%
20181.91%-2.82%$13,457-5.21%-14.43%-6.02%-0.12%
20192.29%14.96%$15,47130.67%21.75%28.87%8.83%
2020-0.23%1.39%$15,685-3.45%-11.00%-13.90%6.43%
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%$10,3524.22%4.56%-1.15%0.04%
201230.49%$10,4033.06%-0.54%5.19%-0.51%
201240.69%$10,475-0.64%-2.08%2.86%1.10%
20125-1.86%$10,280-6.23%-10.83%-4.51%0.93%
201261.78%$10,4634.05%5.97%5.52%0.07%
201271.15%$10,5840.88%0.31%2.00%1.23%
201280.75%$10,6632.70%2.60%-0.01%0.16%
201290.65%$10,7322.49%3.41%-1.86%0.18%
201210-0.29%$10,701-1.81%0.81%-0.91%-0.10%
2012110.49%$10,7530.77%2.06%-0.26%0.27%
2012120.51%$10,8081.29%4.88%3.72%-0.88%
201310.87%$10,9025.42%2.40%3.74%-0.69%
201320.50%$10,9561.28%-1.14%1.22%0.54%
201330.94%$11,0593.95%0.93%2.87%0.08%
201341.93%$11,2721.61%3.50%6.73%1.01%
20135-1.93%$11,0552.44%-3.30%-5.98%-1.93%
20136-1.87%$10,848-1.43%-3.57%-1.98%-1.65%
201371.60%$11,0215.75%4.62%0.90%0.38%
20138-1.85%$10,817-3.03%-1.95%-6.98%-0.86%
201392.44%$11,0803.90%7.51%3.49%1.11%
2013101.97%$11,2984.27%3.67%4.52%0.86%
201311-0.35%$11,2592.70%0.13%-5.25%-0.29%
2013120.11%$11,2712.73%1.52%0.10%-0.64%
201410.41%$11,318-3.17%-5.40%4.28%1.55%
201422.06%$11,5514.87%5.59%5.07%0.47%
201430.06%$11,5580.51%0.49%0.49%-0.17%
201441.00%$11,6740.06%1.26%3.29%0.80%
201451.42%$11,8392.10%1.93%2.40%1.05%
201460.71%$11,9242.62%1.89%1.13%0.08%
20147-0.63%$11,849-1.99%-1.73%0.08%-0.28%
201481.71%$12,0514.15%1.16%3.04%1.14%
20149-1.81%$11,834-2.10%-5.01%-6.04%-0.57%
2014101.78%$12,0442.75%-0.08%9.94%0.72%
2014111.00%$12,1642.48%-0.51%2.00%0.83%
201412-0.23%$12,136-0.04%-3.87%1.88%0.06%
201511.94%$12,371-2.74%0.27%6.85%2.40%
201520.17%$12,3935.74%5.78%-3.67%-1.31%
201530.21%$12,419-1.16%-1.49%1.74%0.55%
20154-0.15%$12,4000.62%4.81%-5.85%-0.32%
20155-0.30%$12,3631.30%-0.91%-0.30%-0.50%
20156-1.72%$12,151-1.67%-2.73%-4.68%-1.11%
201571.29%$12,3081.70%-0.56%5.77%0.88%
20158-2.40%$12,013-6.09%-7.43%-6.29%-0.25%
201590.02%$12,015-2.92%-3.85%3.05%0.81%
2015102.30%$12,2917.91%6.25%5.76%0.03%
201511-0.40%$12,2420.60%-1.32%-0.63%-0.39%
201512-0.46%$12,186-2.13%-2.17%1.82%-0.18%
20161-0.89%$12,077-5.72%-5.45%-3.44%1.20%
201620.24%$12,106-0.01%-2.46%-0.36%0.85%
201633.46%$12,5257.11%8.33%10.48%0.88%
201640.37%$12,5720.66%2.16%-2.35%0.40%
201650.32%$12,6121.73%-0.98%2.25%-0.01%
201661.94%$12,8560.27%-0.90%6.92%2.02%
201671.83%$13,0923.98%4.52%4.26%0.60%
20168-0.49%$13,0270.21%0.45%-3.76%-0.31%
201690.12%$13,0430.21%1.70%-1.82%0.11%
201610-1.67%$12,824-2.19%-1.91%-5.74%-0.94%
201611-1.53%$12,6284.49%-2.01%-1.68%-2.57%
2016121.16%$12,7751.98%1.96%4.82%0.33%
201710.81%$12,8781.86%4.08%-0.19%0.19%
201721.37%$13,0553.69%1.34%3.51%0.62%
201730.09%$13,0670.06%3.00%-2.42%-0.04%
201740.92%$13,1871.06%2.05%0.24%0.80%
201750.87%$13,3021.01%2.96%-0.72%0.71%
201760.44%$13,3610.95%0.63%2.23%0.05%
201771.01%$13,4961.88%3.37%1.24%0.40%
201780.62%$13,5800.15%0.54%-0.26%0.86%
201790.20%$13,6082.44%1.88%-0.11%-0.47%
2017100.39%$13,6602.17%2.03%-1.07%-0.03%
2017110.64%$13,7483.03%0.63%2.66%-0.11%
2017120.73%$13,8481.16%2.07%-0.14%0.54%
201810.09%$13,8615.23%5.72%-4.25%-1.24%
20182-2.51%$13,513-3.76%-5.24%-7.68%-1.04%
201830.54%$13,586-1.95%-0.38%3.88%0.69%
20184-0.37%$13,5350.45%0.46%0.82%-0.85%
201850.96%$13,6652.72%-1.64%3.68%0.68%
201860.22%$13,6950.70%-2.14%4.20%-0.04%
201870.75%$13,7973.32%2.55%0.60%-0.04%
201880.85%$13,9143.43%-2.40%2.58%0.67%
20189-0.57%$13,8350.20%0.21%-2.64%-0.55%
201810-2.78%$13,451-7.41%-8.56%-2.93%-0.86%
2018111.32%$13,6292.01%1.68%4.67%0.64%
201812-1.26%$13,457-9.16%-4.93%-7.96%1.87%
201913.85%$13,9758.54%7.67%11.85%1.11%
201920.65%$14,0653.56%1.63%0.70%-0.09%
201931.96%$14,3411.42%0.77%4.21%1.94%
201940.78%$14,4533.93%2.77%-0.16%-0.02%
20195-0.22%$14,422-6.45%-5.42%0.14%1.83%
201962.53%$14,7877.08%5.77%1.54%1.25%
201970.21%$14,8181.41%-1.99%1.70%0.15%
201981.68%$15,068-2.08%-2.17%3.75%2.77%
201990.35%$15,1201.78%2.73%1.93%-0.57%
2019100.98%$15,2682.11%3.43%1.13%0.31%
2019110.44%$15,3353.79%0.99%-1.30%-0.04%
2019120.88%$15,4712.80%4.38%0.76%-0.07%
202011.03%$15,630-0.06%-3.39%1.23%1.98%
20202-1.35%$15,419-8.00%-6.60%-7.03%1.67%
20203-6.46%$14,422-13.91%-16.26%-19.42%-1.43%
202045.23%$15,17613.13%7.60%8.96%2.76%
202051.87%$15,4605.40%5.01%1.73%0.67%
202061.46%$15,6852.29%4.24%2.41%0.67%
Portfolio return and risk metrics
MetricRisk Parity
Arithmetic Mean (monthly)0.45%
Arithmetic Mean (annualized)5.58%
Geometric Mean (monthly)0.44%
Geometric Mean (annualized)5.44%
Volatility (monthly)1.50%
Volatility (annualized)5.19%
Downside Deviation (monthly)0.96%
Max. Drawdown-7.72%
US Market Correlation0.77
Beta(*)0.30
Alpha (annualized)1.43%
R259.92%
Sharpe Ratio0.92
Sortino Ratio1.40
Treynor Ratio (%)15.71
Calmar Ratio0.71
Active Return-7.66%
Tracking Error9.81%
Information Ratio-0.78
Skewness-0.82
Excess Kurtosis4.46
Historical Value-at-Risk (5%)-1.92%
Analytical Value-at-Risk (5%)-2.00%
Conditional Value-at-Risk (5%)-3.22%
Upside Capture Ratio (%)30.96
Downside Capture Ratio (%)24.91
Safe Withdrawal Rate14.79%
Perpetual Withdrawal Rate3.95%
Positive Periods75 out of 102 (73.53%)
Gain/Loss Ratio0.82
* 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-7.72%
2May 2013Aug 20134 monthsOct 20132 months6 months-4.04%
3Aug 2016Nov 20164 monthsApr 20175 months9 months-3.54%
4Sep 2018Oct 20182 monthsJan 20193 months5 months-3.33%
5Apr 2015Aug 20155 monthsMar 20167 months1 year-3.27%
6Feb 2018Feb 20181 monthAug 20186 months7 months-2.51%
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 ETF13.21%13.29%33.45%-5.21%-20.84%0.951.451.00
VXUSVanguard Total International Stock ETF5.18%14.14%27.45%-14.43%-25.54%0.380.530.84
VNQVanguard Real Estate ETF7.90%15.45%30.36%-13.90%-25.08%0.530.770.61
BNDVanguard Total Bond Market ETF3.32%3.28%8.83%-2.10%-4.01%0.811.400.02

Monthly Correlations

Correlations for the portfolio assets
TickerNameVTIVXUSVNQBNDRisk Parity
VTIVanguard Total Stock Market ETF1.000.850.610.020.78
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%14.96%-2.82%
3 years4.91%6.67%3.36%
5 years4.67%5.08%3.61%
7 years4.80%5.26%4.33%
Result statistics are based on annualized rolling returns over full calendar year periods