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 - Dec 2020)

Portfolio optimization results for risk parity. The possible range of expected annual portfolio returns for the given period is 3.85% to 16.37%. Refer to the efficient frontier section for additional details.

Portfolio Allocations

Risk Parity
Ticker Name Allocation
VTI Vanguard Total Stock Market ETF 12.20%
VXUS Vanguard Total International Stock ETF 11.31%
VNQ Vanguard Real Estate ETF 9.83%
BND Vanguard Total Bond Market ETF 66.65%
Save portfolio »

Portfolio Performance Summary

Portfolio performance statistics
MetricRisk Parity
Start Balance$10,000
End Balance$16,807
CAGR5.94%
Expected Return 6.09%
Stdev5.30%
Best Year14.87%
Worst Year-2.77%
Max. Drawdown -7.62%
Sharpe Ratio (ex-ante)1.03
Sharpe Ratio (ex-post)0.99
Sortino Ratio1.60
US Stock Market Correlation0.79
   

Trailing Returns

Trailing Returns
NameAnnualized ReturnAnnualized Volatility
3 Month1 year3 year5 yearFull3 year5 year
Risk Parity5.07%9.03%6.79%6.68%5.94%7.12%5.96%
Trailing annualized return and volatility are for full months ending in December 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.
  • 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)15.29%16.38%13.81%1.1390.00%100.00%
2Vanguard Total International Stock ETF (VXUS)7.46%8.61%14.59%0.5460.00%100.00%
3Vanguard Real Estate ETF (VNQ)8.67%9.98%15.44%0.6040.00%100.00%
4Vanguard Total Bond Market ETF (BND)3.27%3.33%3.27%0.8200.00%100.00%
Results based on historical returns. Ex ante Sharpe Ratio calculated using 3-month treasury bill returns as the risk-free rate (0.65% annualized).

Asset Correlations

Efficient Frontier Asset Correlations
NameTickerVTIVXUSVNQBND
Vanguard Total Stock Market ETFVTI1.000.860.630.05
Vanguard Total International Stock ETFVXUS0.861.000.580.13
Vanguard Real Estate ETFVNQ0.630.581.000.50
Vanguard Total Bond Market ETFBND0.050.130.501.00
Based on monthly returns from Jan 2012 to Dec 2020
Efficient Frontier Assets
#VTIVXUSVNQBNDExpected Return*Standard Deviation*Sharpe Ratio*
14.26%0.00%0.00%95.74%3.85%3.21%0.998
25.23%0.00%0.00%94.77%3.97%3.21%1.035
36.20%0.00%0.00%93.80%4.09%3.22%1.069
47.16%0.00%0.00%92.84%4.21%3.24%1.102
58.13%0.00%0.00%91.87%4.33%3.26%1.132
69.10%0.00%0.00%90.90%4.46%3.28%1.160
710.07%0.00%0.00%89.93%4.58%3.31%1.186
811.03%0.00%0.00%88.97%4.70%3.35%1.209
912.00%0.00%0.00%88.00%4.82%3.39%1.230
1012.97%0.00%0.00%87.03%4.94%3.43%1.249
1113.93%0.00%0.00%86.07%5.06%3.48%1.266
1214.90%0.00%0.00%85.10%5.18%3.54%1.280
1315.87%0.00%0.00%84.13%5.30%3.60%1.293
1416.83%0.00%0.00%83.17%5.42%3.66%1.304
1517.80%0.00%0.00%82.20%5.55%3.73%1.313
1618.77%0.00%0.00%81.23%5.67%3.80%1.321
1719.74%0.00%0.00%80.26%5.79%3.87%1.327
1820.70%0.00%0.00%79.30%5.91%3.95%1.332
1921.67%0.00%0.00%78.33%6.03%4.03%1.335
2022.64%0.00%0.00%77.36%6.16%4.12%1.338
2123.60%0.00%0.00%76.40%6.28%4.20%1.340
2224.57%0.00%0.00%75.43%6.40%4.29%1.340
2325.54%0.00%0.00%74.46%6.52%4.38%1.341
2426.50%0.00%0.00%73.50%6.65%4.48%1.340
2527.47%0.00%0.00%72.53%6.77%4.57%1.339
2628.44%0.00%0.00%71.56%6.89%4.67%1.337
2729.41%0.00%0.00%70.59%7.02%4.77%1.335
2830.37%0.00%0.00%69.63%7.14%4.87%1.333
2931.34%0.00%0.00%68.66%7.26%4.97%1.330
3032.31%0.00%0.00%67.69%7.39%5.08%1.327
3133.27%0.00%0.00%66.73%7.51%5.18%1.324
3234.24%0.00%0.00%65.76%7.64%5.29%1.320
3335.21%0.00%0.00%64.79%7.76%5.40%1.317
3436.18%0.00%0.00%63.82%7.88%5.51%1.313
3537.14%0.00%0.00%62.86%8.01%5.62%1.309
3638.11%0.00%0.00%61.89%8.13%5.73%1.306
3739.08%0.00%0.00%60.92%8.26%5.84%1.302
3840.04%0.00%0.00%59.96%8.38%5.96%1.298
3941.01%0.00%0.00%58.99%8.51%6.07%1.294
4041.98%0.00%0.00%58.02%8.63%6.19%1.290
4142.94%0.00%0.00%57.06%8.76%6.30%1.286
4243.91%0.00%0.00%56.09%8.88%6.42%1.282
4344.88%0.00%0.00%55.12%9.01%6.54%1.278
4445.85%0.00%0.00%54.15%9.13%6.66%1.274
4546.81%0.00%0.00%53.19%9.26%6.78%1.270
4647.78%0.00%0.00%52.22%9.38%6.90%1.266
4748.75%0.00%0.00%51.25%9.51%7.02%1.263
4849.71%0.00%0.00%50.29%9.64%7.14%1.259
4950.68%0.00%0.00%49.32%9.76%7.26%1.255
5051.65%0.00%0.00%48.35%9.89%7.38%1.252
5152.61%0.00%0.00%47.39%10.01%7.50%1.248
5253.58%0.00%0.00%46.42%10.14%7.63%1.245
5354.55%0.00%0.00%45.45%10.27%7.75%1.241
5455.52%0.00%0.00%44.48%10.39%7.87%1.238
5556.48%0.00%0.00%43.52%10.52%8.00%1.234
5657.45%0.00%0.00%42.55%10.65%8.12%1.231
5758.42%0.00%0.00%41.58%10.78%8.25%1.228
5859.38%0.00%0.00%40.62%10.90%8.37%1.225
5960.35%0.00%0.00%39.65%11.03%8.50%1.222
6061.32%0.00%0.00%38.68%11.16%8.62%1.219
6162.29%0.00%0.00%37.71%11.29%8.75%1.216
6263.25%0.00%0.00%36.75%11.41%8.88%1.213
6364.22%0.00%0.00%35.78%11.54%9.00%1.210
6465.19%0.00%0.00%34.81%11.67%9.13%1.207
6566.15%0.00%0.00%33.85%11.80%9.26%1.205
6667.12%0.00%0.00%32.88%11.93%9.38%1.202
6768.09%0.00%0.00%31.91%12.06%9.51%1.199
6869.05%0.00%0.00%30.95%12.18%9.64%1.197
6970.02%0.00%0.00%29.98%12.31%9.77%1.194
7070.99%0.00%0.00%29.01%12.44%9.90%1.192
7171.96%0.00%0.00%28.04%12.57%10.02%1.189
7272.92%0.00%0.00%27.08%12.70%10.15%1.187
7373.89%0.00%0.00%26.11%12.83%10.28%1.185
7474.86%0.00%0.00%25.14%12.96%10.41%1.183
7575.82%0.00%0.00%24.18%13.09%10.54%1.180
7676.79%0.00%0.00%23.21%13.22%10.67%1.178
7777.76%0.00%0.00%22.24%13.35%10.80%1.176
7878.72%0.00%0.00%21.28%13.48%10.93%1.174
7979.69%0.00%0.00%20.31%13.61%11.06%1.172
8080.66%0.00%0.00%19.34%13.74%11.19%1.170
8181.63%0.00%0.00%18.37%13.87%11.32%1.168
8282.59%0.00%0.00%17.41%14.00%11.45%1.166
8383.56%0.00%0.00%16.44%14.13%11.58%1.164
8484.53%0.00%0.00%15.47%14.26%11.71%1.163
8585.49%0.00%0.00%14.51%14.39%11.84%1.161
8686.46%0.00%0.00%13.54%14.52%11.97%1.159
8787.43%0.00%0.00%12.57%14.66%12.10%1.158
8888.40%0.00%0.00%11.60%14.79%12.23%1.156
8989.36%0.00%0.00%10.64%14.92%12.36%1.154
9090.33%0.00%0.00%9.67%15.05%12.49%1.153
9191.30%0.00%0.00%8.70%15.18%12.62%1.151
9292.26%0.00%0.00%7.74%15.31%12.76%1.150
9393.23%0.00%0.00%6.77%15.45%12.89%1.148
9494.20%0.00%0.00%5.80%15.58%13.02%1.147
9595.16%0.00%0.00%4.84%15.71%13.15%1.145
9696.13%0.00%0.00%3.87%15.84%13.28%1.144
9797.10%0.00%0.00%2.90%15.98%13.41%1.143
9898.07%0.00%0.00%1.93%16.11%13.55%1.141
9999.03%0.00%0.00%0.97%16.24%13.68%1.140
100100.00%0.00%0.00%0.00%16.38%13.81%1.139
*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 (0.65% 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%8.00%$10,80016.45%18.61%17.63%3.16%
20131.50%4.12%$11,24633.45%14.61%2.31%-2.10%
20140.76%7.70%$12,11212.54%-4.74%30.36%5.82%
20150.73%0.42%$12,1630.36%-4.19%2.42%0.56%
20162.07%4.80%$12,74712.83%4.81%8.60%2.52%
20172.11%8.28%$13,80221.21%27.45%4.91%3.57%
20181.91%-2.77%$13,419-5.21%-14.43%-6.02%-0.12%
20192.29%14.87%$15,41430.67%21.75%28.87%8.83%
20201.36%9.03%$16,80721.03%10.69%-4.68%7.71%
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)
201212.50%$10,2505.07%7.33%6.38%0.63%
201220.94%$10,3474.22%4.56%-1.15%0.04%
201230.48%$10,3973.06%-0.54%5.19%-0.51%
201240.70%$10,470-0.64%-2.08%2.86%1.10%
20125-1.81%$10,281-6.23%-10.83%-4.51%0.93%
201261.76%$10,4614.05%5.97%5.52%0.07%
201271.16%$10,5830.88%0.31%2.00%1.23%
201280.73%$10,6602.70%2.60%-0.01%0.16%
201290.63%$10,7272.49%3.41%-1.86%0.18%
201210-0.29%$10,696-1.81%0.81%-0.91%-0.10%
2012110.48%$10,7480.77%2.06%-0.26%0.27%
2012120.49%$10,8001.29%4.88%3.72%-0.88%
201310.84%$10,8915.42%2.40%3.74%-0.69%
201320.50%$10,9461.28%-1.14%1.22%0.54%
201330.92%$11,0473.95%0.93%2.87%0.08%
201341.93%$11,2601.61%3.50%6.73%1.01%
20135-1.95%$11,0412.44%-3.30%-5.98%-1.93%
20136-1.87%$10,834-1.43%-3.57%-1.98%-1.65%
201371.57%$11,0045.75%4.62%0.90%0.38%
20138-1.85%$10,801-3.03%-1.95%-6.98%-0.86%
201392.41%$11,0613.90%7.51%3.49%1.11%
2013101.95%$11,2774.27%3.67%4.52%0.86%
201311-0.37%$11,2362.70%0.13%-5.25%-0.29%
2013120.09%$11,2462.73%1.52%0.10%-0.64%
201410.46%$11,297-3.17%-5.40%4.28%1.55%
201422.04%$11,5274.87%5.59%5.07%0.47%
201430.05%$11,5330.51%0.49%0.49%-0.17%
201441.01%$11,6490.06%1.26%3.29%0.80%
201451.41%$11,8142.10%1.93%2.40%1.05%
201460.70%$11,8972.62%1.89%1.13%0.08%
20147-0.62%$11,823-1.99%-1.73%0.08%-0.28%
201481.70%$12,0244.15%1.16%3.04%1.14%
20149-1.80%$11,808-2.10%-5.01%-6.04%-0.57%
2014101.78%$12,0192.75%-0.08%9.94%0.72%
2014111.00%$12,1382.48%-0.51%2.00%0.83%
201412-0.22%$12,112-0.04%-3.87%1.88%0.06%
201511.97%$12,351-2.74%0.27%6.85%2.40%
201520.12%$12,3665.74%5.78%-3.67%-1.31%
201530.23%$12,394-1.16%-1.49%1.74%0.55%
20154-0.17%$12,3720.62%4.81%-5.85%-0.32%
20155-0.31%$12,3351.30%-0.91%-0.30%-0.50%
20156-1.71%$12,123-1.67%-2.73%-4.68%-1.11%
201571.30%$12,2811.70%-0.56%5.77%0.88%
20158-2.37%$11,990-6.09%-7.43%-6.29%-0.25%
201590.05%$11,996-2.92%-3.85%3.05%0.81%
2015102.26%$12,2677.91%6.25%5.76%0.03%
201511-0.40%$12,2180.60%-1.32%-0.63%-0.39%
201512-0.44%$12,163-2.13%-2.17%1.82%-0.18%
20161-0.85%$12,060-5.72%-5.45%-3.44%1.20%
201620.25%$12,090-0.01%-2.46%-0.36%0.85%
201633.43%$12,5057.11%8.33%10.48%0.88%
201640.36%$12,5500.66%2.16%-2.35%0.40%
201650.32%$12,5901.73%-0.98%2.25%-0.01%
201661.96%$12,8360.27%-0.90%6.92%2.02%
201671.81%$13,0693.98%4.52%4.26%0.60%
20168-0.50%$13,0030.21%0.45%-3.76%-0.31%
201690.11%$13,0180.21%1.70%-1.82%0.11%
201610-1.67%$12,800-2.19%-1.91%-5.74%-0.94%
201611-1.56%$12,6014.49%-2.01%-1.68%-2.57%
2016121.16%$12,7471.98%1.96%4.82%0.33%
201710.79%$12,8481.86%4.08%-0.19%0.19%
201721.36%$13,0223.69%1.34%3.51%0.62%
201730.08%$13,0330.06%3.00%-2.42%-0.04%
201740.92%$13,1521.06%2.05%0.24%0.80%
201750.86%$13,2661.01%2.96%-0.72%0.71%
201760.44%$13,3240.95%0.63%2.23%0.05%
201771.00%$13,4571.88%3.37%1.24%0.40%
201780.62%$13,5410.15%0.54%-0.26%0.86%
201790.19%$13,5672.44%1.88%-0.11%-0.47%
2017100.37%$13,6172.17%2.03%-1.07%-0.03%
2017110.63%$13,7033.03%0.63%2.66%-0.11%
2017120.72%$13,8021.16%2.07%-0.14%0.54%
201810.04%$13,8085.23%5.72%-4.25%-1.24%
20182-2.50%$13,463-3.76%-5.24%-7.68%-1.04%
201830.56%$13,538-1.95%-0.38%3.88%0.69%
20184-0.38%$13,4870.45%0.46%0.82%-0.85%
201850.96%$13,6162.72%-1.64%3.68%0.68%
201860.23%$13,6480.70%-2.14%4.20%-0.04%
201870.73%$13,7473.32%2.55%0.60%-0.04%
201880.85%$13,8633.43%-2.40%2.58%0.67%
20189-0.58%$13,7840.20%0.21%-2.64%-0.55%
201810-2.73%$13,407-7.41%-8.56%-2.93%-0.86%
2018111.32%$13,5842.01%1.68%4.67%0.64%
201812-1.21%$13,419-9.16%-4.93%-7.96%1.87%
201913.82%$13,9318.54%7.67%11.85%1.11%
201920.63%$14,0193.56%1.63%0.70%-0.09%
201931.97%$14,2941.42%0.77%4.21%1.94%
201940.76%$14,4033.93%2.77%-0.16%-0.02%
20195-0.17%$14,379-6.45%-5.42%0.14%1.83%
201962.50%$14,7387.08%5.77%1.54%1.25%
201970.21%$14,7701.41%-1.99%1.70%0.15%
201981.71%$15,023-2.08%-2.17%3.75%2.77%
201990.34%$15,0741.78%2.73%1.93%-0.57%
2019100.96%$15,2192.11%3.43%1.13%0.31%
2019110.42%$15,2823.79%0.99%-1.30%-0.04%
2019120.86%$15,4142.80%4.38%0.76%-0.07%
202011.05%$15,576-0.06%-3.39%1.23%1.98%
20202-1.30%$15,373-8.00%-6.60%-7.03%1.67%
20203-6.40%$14,390-13.91%-16.26%-19.42%-1.43%
202045.18%$15,13513.13%7.60%8.96%2.76%
202051.84%$15,4145.40%5.01%1.73%0.67%
202061.44%$15,6362.29%4.24%2.41%0.67%
202072.50%$16,0275.74%4.15%3.64%1.45%
202080.78%$16,1527.10%4.43%0.44%-0.94%
20209-0.97%$15,996-3.54%-1.82%-2.68%-0.10%
202010-1.16%$15,810-1.95%-2.30%-3.00%-0.56%
2020114.63%$16,54211.80%12.62%9.67%1.21%
2020121.60%$16,8074.68%5.86%2.72%0.15%
Portfolio return and risk metrics
MetricRisk Parity
Arithmetic Mean (monthly)0.49%
Arithmetic Mean (annualized)6.09%
Geometric Mean (monthly)0.48%
Geometric Mean (annualized)5.94%
Volatility (monthly)1.53%
Volatility (annualized)5.30%
Downside Deviation (monthly)0.93%
Max. Drawdown-7.62%
US Market Correlation0.79
Beta(*)0.30
Alpha (annualized)1.35%
R261.77%
Sharpe Ratio0.99
Sortino Ratio1.60
Treynor Ratio (%)17.48
Calmar Ratio0.89
Active Return-9.22%
Tracking Error10.19%
Information Ratio-0.91
Skewness-0.59
Excess Kurtosis3.87
Historical Value-at-Risk (5%)-1.86%
Analytical Value-at-Risk (5%)-2.01%
Conditional Value-at-Risk (5%)-2.97%
Upside Capture Ratio (%)30.30
Downside Capture Ratio (%)24.98
Safe Withdrawal Rate13.39%
Perpetual Withdrawal Rate4.09%
Positive Periods79 out of 108 (73.15%)
Gain/Loss Ratio0.88
* 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-7.62%
2May 2013Aug 20134 monthsOct 20132 months6 months-4.08%
3Aug 2016Nov 20164 monthsApr 20175 months9 months-3.58%
4Sep 2018Oct 20182 monthsJan 20193 months5 months-3.29%
5Apr 2015Aug 20155 monthsMar 20167 months1 year-3.26%
6Feb 2018Feb 20181 monthAug 20186 months7 months-2.50%
7Sep 2020Oct 20202 monthsNov 20201 month3 months-2.12%
8May 2012May 20121 monthJul 20122 months3 months-1.81%
9Sep 2014Sep 20141 monthNov 20142 months3 months-1.80%
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 ETF15.29%13.81%33.45%-5.21%-20.84%1.061.701.00
VXUSVanguard Total International Stock ETF7.46%14.59%27.45%-14.43%-25.54%0.520.770.86
VNQVanguard Real Estate ETF8.67%15.44%30.36%-6.02%-25.08%0.580.850.63
BNDVanguard Total Bond Market ETF3.27%3.27%8.83%-2.10%-4.01%0.811.400.05

Monthly Correlations

Correlations for the portfolio assets
TickerNameVTIVXUSVNQBNDRisk Parity
VTIVanguard Total Stock Market ETF1.000.860.630.050.79
VXUSVanguard Total International Stock ETF0.861.000.580.130.80
VNQVanguard Real Estate ETF0.630.581.000.500.87
BNDVanguard Total Bond Market ETF0.050.130.501.000.61

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 year5.22%14.87%-2.77%
3 years4.74%6.79%2.87%
5 years4.70%6.68%3.03%
7 years5.00%5.92%3.85%