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 - Feb 2020)

Portfolio optimization results for risk parity. The possible range of expected annual portfolio returns for the given period is 4.23% to 13.86%. Refer to the efficient frontier section for additional details.

Portfolio Allocations

Risk Parity
Ticker Name Allocation
VTI Vanguard Total Stock Market ETF 13.44%
VXUS Vanguard Total International Stock ETF 11.59%
VNQ Vanguard Real Estate ETF 9.65%
BND Vanguard Total Bond Market ETF 65.32%
Save portfolio »

Portfolio Performance Summary

Portfolio performance statistics
MetricRisk Parity
Start Balance$10,000
End Balance$15,518
CAGR5.53%
Expected Return 5.63%
Stdev4.40%
Best Year15.13%
Worst Year-2.86%
Max. Drawdown -3.97%
Sharpe Ratio (ex-ante)1.12
Sharpe Ratio (ex-post)1.09
Sortino Ratio1.83
US Stock Market Correlation0.70
   
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 February
  • 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)13.10%13.86%11.65%1.1300.00%100.00%
2Vanguard Total International Stock ETF (VXUS)5.58%6.44%12.77%0.4500.00%100.00%
3Vanguard Real Estate ETF (VNQ)9.43%10.44%13.76%0.7090.00%100.00%
4Vanguard Total Bond Market ETF (BND)3.13%3.18%3.17%0.7850.00%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 (0.69% annualized).

Monthly Correlations

Efficient Frontier Asset Correlations
NameTickerVTIVXUSVNQBND
Vanguard Total Stock Market ETFVTI1.000.810.50-0.17
Vanguard Total International Stock ETFVXUS0.811.000.43-0.03
Vanguard Real Estate ETFVNQ0.500.431.000.43
Vanguard Total Bond Market ETFBND-0.17-0.030.431.00
Based on monthly returns from Jan 2012 to Feb 2020
Efficient Frontier Assets
#VTIVXUSVNQBNDExpected Return*Standard Deviation*Sharpe Ratio*
110.22%0.00%0.00%89.78%4.23%2.89%1.221
211.12%0.00%0.00%88.88%4.32%2.90%1.252
312.03%0.00%0.00%87.97%4.41%2.90%1.282
412.94%0.00%0.00%87.06%4.51%2.91%1.309
513.84%0.00%0.00%86.16%4.60%2.93%1.334
614.75%0.00%0.00%85.25%4.70%2.95%1.357
715.66%0.00%0.00%84.34%4.79%2.97%1.377
816.56%0.00%0.00%83.44%4.88%3.00%1.396
917.47%0.00%0.00%82.53%4.98%3.04%1.412
1018.38%0.00%0.00%81.62%5.07%3.07%1.426
1119.29%0.00%0.00%80.71%5.17%3.11%1.438
1220.19%0.00%0.00%79.81%5.26%3.15%1.448
1321.10%0.00%0.00%78.90%5.35%3.20%1.456
1422.01%0.00%0.00%77.99%5.45%3.25%1.462
1522.91%0.00%0.00%77.09%5.54%3.31%1.467
1623.82%0.00%0.00%76.18%5.64%3.36%1.471
1724.73%0.00%0.00%75.27%5.73%3.42%1.473
1825.63%0.00%0.00%74.37%5.83%3.48%1.474
1926.54%0.00%0.00%73.46%5.92%3.55%1.474
2027.45%0.00%0.00%72.55%6.02%3.62%1.473
2128.35%0.00%0.00%71.65%6.11%3.69%1.471
2229.26%0.00%0.00%70.74%6.21%3.76%1.468
2330.17%0.00%0.00%69.83%6.30%3.83%1.464
2431.08%0.00%0.00%68.92%6.40%3.91%1.460
2531.98%0.00%0.00%68.02%6.49%3.98%1.456
2632.89%0.00%0.00%67.11%6.59%4.06%1.451
2733.80%0.00%0.00%66.20%6.68%4.14%1.446
2834.70%0.00%0.00%65.30%6.78%4.23%1.440
2935.61%0.00%0.00%64.39%6.87%4.31%1.434
3036.52%0.00%0.00%63.48%6.97%4.39%1.428
3137.42%0.00%0.00%62.58%7.07%4.48%1.422
3238.33%0.00%0.00%61.67%7.16%4.57%1.416
3339.24%0.00%0.00%60.76%7.26%4.66%1.410
3440.14%0.00%0.00%59.86%7.35%4.75%1.403
3541.05%0.00%0.00%58.95%7.45%4.84%1.397
3641.96%0.00%0.00%58.04%7.55%4.93%1.390
3742.86%0.00%0.00%57.14%7.64%5.02%1.384
3843.77%0.00%0.00%56.23%7.74%5.12%1.377
3944.68%0.00%0.00%55.32%7.83%5.21%1.371
4045.59%0.00%0.00%54.41%7.93%5.31%1.364
4146.49%0.00%0.00%53.51%8.03%5.40%1.358
4247.40%0.00%0.00%52.60%8.12%5.50%1.352
4348.31%0.00%0.00%51.69%8.22%5.60%1.345
4449.21%0.00%0.00%50.79%8.32%5.69%1.339
4550.12%0.00%0.00%49.88%8.41%5.79%1.333
4651.03%0.00%0.00%48.97%8.51%5.89%1.327
4751.93%0.00%0.00%48.07%8.61%5.99%1.321
4852.84%0.00%0.00%47.16%8.71%6.09%1.316
4953.75%0.00%0.00%46.25%8.80%6.19%1.310
5054.65%0.00%0.00%45.35%8.90%6.29%1.304
5155.56%0.00%0.00%44.44%9.00%6.39%1.299
5256.47%0.00%0.00%43.53%9.09%6.50%1.293
5357.38%0.00%0.00%42.62%9.19%6.60%1.288
5458.28%0.00%0.00%41.72%9.29%6.70%1.283
5559.19%0.00%0.00%40.81%9.39%6.80%1.278
5660.10%0.00%0.00%39.90%9.48%6.91%1.273
5761.00%0.00%0.00%39.00%9.58%7.01%1.268
5861.91%0.00%0.00%38.09%9.68%7.11%1.263
5962.82%0.00%0.00%37.18%9.78%7.22%1.259
6063.72%0.00%0.00%36.28%9.88%7.32%1.254
6164.63%0.00%0.00%35.37%9.97%7.43%1.250
6265.41%0.00%0.18%34.41%10.07%7.53%1.245
6366.17%0.00%0.40%33.43%10.17%7.64%1.241
6466.93%0.00%0.61%32.46%10.27%7.74%1.237
6567.69%0.00%0.83%31.48%10.37%7.85%1.233
6668.44%0.00%1.05%30.51%10.47%7.96%1.229
6769.20%0.00%1.26%29.54%10.56%8.06%1.225
6869.96%0.00%1.48%28.56%10.66%8.17%1.221
6970.72%0.00%1.70%27.59%10.76%8.27%1.217
7071.47%0.00%1.91%26.61%10.86%8.38%1.213
7172.23%0.00%2.13%25.64%10.96%8.49%1.210
7272.99%0.00%2.35%24.66%11.06%8.59%1.206
7373.75%0.00%2.56%23.69%11.16%8.70%1.203
7474.50%0.00%2.78%22.72%11.26%8.81%1.200
7575.26%0.00%3.00%21.74%11.36%8.91%1.196
7676.02%0.00%3.21%20.77%11.46%9.02%1.193
7776.78%0.00%3.43%19.79%11.56%9.13%1.190
7877.53%0.00%3.65%18.82%11.65%9.24%1.187
7978.29%0.00%3.86%17.84%11.75%9.34%1.184
8079.05%0.00%4.08%16.87%11.85%9.45%1.181
8179.81%0.00%4.30%15.90%11.95%9.56%1.178
8280.56%0.00%4.51%14.92%12.05%9.66%1.175
8381.32%0.00%4.73%13.95%12.15%9.77%1.173
8482.08%0.00%4.95%12.97%12.25%9.88%1.170
8582.84%0.00%5.16%12.00%12.35%9.99%1.167
8683.59%0.00%5.38%11.03%12.45%10.10%1.165
8784.35%0.00%5.60%10.05%12.55%10.20%1.162
8885.11%0.00%5.81%9.08%12.65%10.31%1.160
8985.87%0.00%6.03%8.10%12.75%10.42%1.158
9086.62%0.00%6.25%7.13%12.86%10.53%1.155
9187.38%0.00%6.46%6.15%12.96%10.64%1.153
9288.14%0.00%6.68%5.18%13.06%10.75%1.151
9388.90%0.00%6.90%4.21%13.16%10.85%1.148
9489.65%0.00%7.11%3.23%13.26%10.96%1.146
9590.41%0.00%7.33%2.26%13.36%11.07%1.144
9691.17%0.00%7.55%1.28%13.46%11.18%1.142
9791.93%0.00%7.76%0.31%13.56%11.29%1.140
9894.16%0.00%5.84%0.00%13.66%11.40%1.138
9997.08%0.00%2.92%0.00%13.76%11.52%1.135
100100.00%0.00%0.00%0.00%13.86%11.65%1.130
*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 (0.69% 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%8.19%$10,81916.45%18.61%17.63%3.16%
20131.50%4.57%$11,31333.45%14.61%2.31%-2.10%
20140.76%7.71%$12,18512.54%-4.74%30.36%5.82%
20150.73%0.41%$12,2350.36%-4.19%2.42%0.56%
20162.07%4.92%$12,83712.83%4.81%8.60%2.52%
20172.11%8.55%$13,93521.21%27.45%4.91%3.57%
20181.91%-2.86%$13,537-5.21%-14.43%-6.02%-0.12%
20192.29%15.13%$15,58530.67%21.75%28.87%8.83%
20200.66%-0.43%$15,518-8.06%-9.77%-5.88%3.68%
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)
201212.56%$10,2565.07%7.33%6.38%0.63%
201221.01%$10,3604.22%4.56%-1.15%0.04%
201230.52%$10,4133.06%-0.54%5.19%-0.51%
201240.67%$10,483-0.64%-2.08%2.86%1.10%
20125-1.92%$10,282-6.23%-10.83%-4.51%0.93%
201261.81%$10,4694.05%5.97%5.52%0.07%
201271.15%$10,5890.88%0.31%2.00%1.23%
201280.77%$10,6702.70%2.60%-0.01%0.16%
201290.67%$10,7422.49%3.41%-1.86%0.18%
201210-0.30%$10,709-1.81%0.81%-0.91%-0.10%
2012110.49%$10,7620.77%2.06%-0.26%0.27%
2012120.53%$10,8191.29%4.88%3.72%-0.88%
201310.92%$10,9185.42%2.40%3.74%-0.69%
201320.51%$10,9731.28%-1.14%1.22%0.54%
201330.97%$11,0793.95%0.93%2.87%0.08%
201341.93%$11,2941.61%3.50%6.73%1.01%
20135-1.89%$11,0802.44%-3.30%-5.98%-1.93%
20136-1.87%$10,873-1.43%-3.57%-1.98%-1.65%
201371.64%$11,0515.75%4.62%0.90%0.38%
20138-1.87%$10,845-3.03%-1.95%-6.98%-0.86%
201392.46%$11,1123.90%7.51%3.49%1.11%
2013102.00%$11,3334.27%3.67%4.52%0.86%
201311-0.32%$11,2972.70%0.13%-5.25%-0.29%
2013120.14%$11,3132.73%1.52%0.10%-0.64%
201410.37%$11,355-3.17%-5.40%4.28%1.55%
201422.10%$11,5934.87%5.59%5.07%0.47%
201430.06%$11,6000.51%0.49%0.49%-0.17%
201441.00%$11,7160.06%1.26%3.29%0.80%
201451.43%$11,8832.10%1.93%2.40%1.05%
201460.74%$11,9702.62%1.89%1.13%0.08%
20147-0.64%$11,893-1.99%-1.73%0.08%-0.28%
201481.73%$12,0994.15%1.16%3.04%1.14%
20149-1.82%$11,879-2.10%-5.01%-6.04%-0.57%
2014101.79%$12,0922.75%-0.08%9.94%0.72%
2014111.01%$12,2142.48%-0.51%2.00%0.83%
201412-0.23%$12,185-0.04%-3.87%1.88%0.06%
201511.89%$12,416-2.74%0.27%6.85%2.40%
201520.23%$12,4455.74%5.78%-3.67%-1.31%
201530.20%$12,470-1.16%-1.49%1.74%0.55%
20154-0.14%$12,4530.62%4.81%-5.85%-0.32%
20155-0.28%$12,4171.30%-0.91%-0.30%-0.50%
20156-1.72%$12,204-1.67%-2.73%-4.68%-1.11%
201571.30%$12,3621.70%-0.56%5.77%0.88%
20158-2.45%$12,059-6.09%-7.43%-6.29%-0.25%
20159-0.02%$12,057-2.92%-3.85%3.05%0.81%
2015102.36%$12,3427.91%6.25%5.76%0.03%
201511-0.39%$12,2940.60%-1.32%-0.63%-0.39%
201512-0.48%$12,235-2.13%-2.17%1.82%-0.18%
20161-0.95%$12,119-5.72%-5.45%-3.44%1.20%
201620.23%$12,148-0.01%-2.46%-0.36%0.85%
201633.51%$12,5747.11%8.33%10.48%0.88%
201640.38%$12,6210.66%2.16%-2.35%0.40%
201650.33%$12,6631.73%-0.98%2.25%-0.01%
201661.92%$12,9060.27%-0.90%6.92%2.02%
201671.86%$13,1463.98%4.52%4.26%0.60%
20168-0.49%$13,0820.21%0.45%-3.76%-0.31%
201690.12%$13,0980.21%1.70%-1.82%0.11%
201610-1.68%$12,878-2.19%-1.91%-5.74%-0.94%
201611-1.47%$12,6884.49%-2.01%-1.68%-2.57%
2016121.18%$12,8371.98%1.96%4.82%0.33%
201710.82%$12,9431.86%4.08%-0.19%0.19%
201721.39%$13,1243.69%1.34%3.51%0.62%
201730.10%$13,1360.06%3.00%-2.42%-0.04%
201740.92%$13,2581.06%2.05%0.24%0.80%
201750.87%$13,3731.01%2.96%-0.72%0.71%
201760.45%$13,4330.95%0.63%2.23%0.05%
201771.03%$13,5711.88%3.37%1.24%0.40%
201780.62%$13,6550.15%0.54%-0.26%0.86%
201790.23%$13,6862.44%1.88%-0.11%-0.47%
2017100.41%$13,7422.17%2.03%-1.07%-0.03%
2017110.67%$13,8343.03%0.63%2.66%-0.11%
2017120.74%$13,9351.16%2.07%-0.14%0.54%
201810.15%$13,9565.23%5.72%-4.25%-1.24%
20182-2.53%$13,603-3.76%-5.24%-7.68%-1.04%
201830.52%$13,673-1.95%-0.38%3.88%0.69%
20184-0.36%$13,6230.45%0.46%0.82%-0.85%
201850.98%$13,7562.72%-1.64%3.68%0.68%
201860.22%$13,7870.70%-2.14%4.20%-0.04%
201870.78%$13,8943.32%2.55%0.60%-0.04%
201880.87%$14,0143.43%-2.40%2.58%0.67%
20189-0.56%$13,9360.20%0.21%-2.64%-0.55%
201810-2.83%$13,541-7.41%-8.56%-2.93%-0.86%
2018111.33%$13,7222.01%1.68%4.67%0.64%
201812-1.35%$13,537-9.16%-4.93%-7.96%1.87%
201913.91%$14,0658.54%7.67%11.85%1.11%
201920.68%$14,1603.56%1.63%0.70%-0.09%
201931.95%$14,4371.42%0.77%4.21%1.94%
201940.82%$14,5553.93%2.77%-0.16%-0.02%
20195-0.29%$14,513-6.45%-5.42%0.14%1.83%
201962.58%$14,8887.08%5.77%1.54%1.25%
201970.22%$14,9211.41%-1.99%1.70%0.15%
201981.64%$15,165-2.08%-2.17%3.75%2.77%
201990.37%$15,2221.78%2.73%1.93%-0.57%
2019100.99%$15,3732.11%3.43%1.13%0.31%
2019110.47%$15,4453.79%0.99%-1.30%-0.04%
2019120.91%$15,5852.80%4.38%0.76%-0.07%
202011.01%$15,743-0.06%-3.39%1.23%1.98%
20202-1.43%$15,518-8.00%-6.60%-7.03%1.67%
Portfolio return and risk metrics
MetricRisk Parity
Arithmetic Mean (monthly)0.46%
Arithmetic Mean (annualized)5.63%
Geometric Mean (monthly)0.45%
Geometric Mean (annualized)5.53%
Volatility (monthly)1.27%
Volatility (annualized)4.40%
Downside Deviation (monthly)0.73%
Max. Drawdown-3.97%
US Market Correlation0.70
Beta(*)0.27
Alpha (annualized)2.06%
R249.12%
Sharpe Ratio1.09
Sortino Ratio1.83
Treynor Ratio (%)18.06
Calmar Ratio1.69
Active Return-7.43%
Tracking Error9.09%
Information Ratio-0.82
Skewness-0.30
Excess Kurtosis0.50
Historical Value-at-Risk (5%)-1.89%
Analytical Value-at-Risk (5%)-1.62%
Conditional Value-at-Risk (5%)-2.43%
Upside Capture Ratio (%)30.99
Downside Capture Ratio (%)21.99
Safe Withdrawal Rate14.85%
Perpetual Withdrawal Rate3.71%
Positive Periods71 out of 98 (72.45%)
Gain/Loss Ratio0.94
* 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-3.97%
2Aug 2016Nov 20164 monthsApr 20175 months9 months-3.48%
3Sep 2018Dec 20184 monthsJan 20191 month5 months-3.41%
4Apr 2015Sep 20156 monthsMar 20166 months1 year-3.31%
5Feb 2018Feb 20181 monthAug 20186 months7 months-2.53%
6May 2012May 20121 monthJul 20122 months3 months-1.92%
7Sep 2014Sep 20141 monthNov 20142 months3 months-1.82%
8Feb 2020Feb 20201 month-1.43%
9Jul 2014Jul 20141 monthAug 20141 month2 months-0.64%
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 ETF13.10%11.65%33.45%-8.06%-14.20%1.061.661.00
VXUSVanguard Total International Stock ETF5.58%12.77%27.45%-14.43%-20.26%0.430.650.81
VNQVanguard Real Estate ETF9.43%13.76%30.36%-6.02%-14.88%0.671.100.50
BNDVanguard Total Bond Market ETF3.13%3.17%8.83%-2.10%-4.01%0.781.32-0.17

Monthly Correlations

Correlations for the portfolio assets
TickerNameVTIVXUSVNQBNDRisk Parity
VTIVanguard Total Stock Market ETF1.000.810.50-0.170.70
VXUSVanguard Total International Stock ETF0.811.000.43-0.030.74
VNQVanguard Real Estate ETF0.500.431.000.430.83
BNDVanguard Total Bond Market ETF-0.17-0.030.431.000.53

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 year5.83%15.13%-2.86%
3 years5.00%6.81%3.43%
5 years4.75%5.19%3.65%
7 years4.89%5.35%4.42%
Result statistics are based on annualized rolling returns over full calendar year periods