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 - Nov 2019)

Portfolio optimization results for risk parity. The possible range of expected annual portfolio returns for the given period is 3.93% to 15.08%. Refer to the efficient frontier section for additional details.

Portfolio Allocations

Risk Parity
Ticker Name Allocation
VTI Vanguard Total Stock Market ETF 13.93%
VXUS Vanguard Total International Stock ETF 11.83%
VNQ Vanguard Real Estate ETF 9.93%
BND Vanguard Total Bond Market ETF 64.31%
Save portfolio »

Portfolio Performance Summary

Portfolio performance statistics
MetricRisk Parity
Start Balance$10,000
End Balance$15,550
CAGR5.74%
Expected Return 5.84%
Stdev4.49%
Best Year14.26%
Worst Year-2.93%
Max. Drawdown -3.96%
Sharpe Ratio (ex-ante)1.16
Sharpe Ratio (ex-post)1.13
Sortino Ratio1.92
US Stock Market Correlation0.71
   
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 2019 are based on full calendar months from January to November
  • 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 (1-month treasury bill)
  • Drawdowns are calculated based on monthly returns.
  • The backtested results include 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)14.36%15.08%11.36%1.2730.00%100.00%
2Vanguard Total International Stock ETF (VXUS)6.56%7.40%12.57%0.5390.00%100.00%
3Vanguard Real Estate ETF (VNQ)10.48%11.49%13.69%0.7940.00%100.00%
4Vanguard Total Bond Market ETF (BND)2.77%2.82%3.11%0.7040.00%100.00%
*Expected return is annualized from historical monthly mean return. Ex ante Sharpe Ratio calculated using historical 1-month treasury bill returns as the risk-free rate (0.62% annualized).

Monthly Correlations

Efficient Frontier Asset Correlations
NameTickerVTIVXUSVNQBND
Vanguard Total Stock Market ETFVTI1.000.810.48-0.12
Vanguard Total International Stock ETFVXUS0.811.000.420.03
Vanguard Real Estate ETFVNQ0.480.421.000.49
Vanguard Total Bond Market ETFBND-0.120.030.491.00
Based on monthly returns from Jan 2012 to Nov 2019
Efficient Frontier Assets
#VTIVXUSVNQBNDExpected Return*Standard Deviation*Sharpe Ratio*
19.52%0.00%0.00%90.48%3.93%2.89%1.144
210.43%0.00%0.00%89.57%4.04%2.89%1.180
311.35%0.00%0.00%88.65%4.15%2.90%1.214
412.26%0.00%0.00%87.74%4.25%2.91%1.247
513.17%0.00%0.00%86.83%4.36%2.93%1.278
614.09%0.00%0.00%85.91%4.47%2.94%1.306
715.00%0.00%0.00%85.00%4.58%2.97%1.332
815.92%0.00%0.00%84.08%4.69%2.99%1.356
916.83%0.00%0.00%83.17%4.79%3.02%1.379
1017.74%0.00%0.00%82.26%4.90%3.06%1.398
1118.66%0.00%0.00%81.34%5.01%3.10%1.416
1219.57%0.00%0.00%80.43%5.12%3.14%1.432
1320.49%0.00%0.00%79.51%5.23%3.18%1.446
1421.40%0.00%0.00%78.60%5.34%3.23%1.458
1522.31%0.00%0.00%77.69%5.45%3.28%1.469
1623.23%0.00%0.00%76.77%5.55%3.34%1.478
1724.14%0.00%0.00%75.86%5.66%3.39%1.485
1825.06%0.00%0.00%74.94%5.77%3.45%1.491
1925.97%0.00%0.00%74.03%5.88%3.51%1.496
2026.88%0.00%0.00%73.12%5.99%3.58%1.500
2127.80%0.00%0.00%72.20%6.10%3.64%1.503
2228.71%0.00%0.00%71.29%6.21%3.71%1.504
2329.63%0.00%0.00%70.37%6.32%3.78%1.505
2430.54%0.00%0.00%69.46%6.43%3.86%1.505
2531.45%0.00%0.00%68.55%6.54%3.93%1.505
2632.37%0.00%0.00%67.63%6.65%4.01%1.504
2733.28%0.00%0.00%66.72%6.76%4.08%1.502
2834.20%0.00%0.00%65.80%6.87%4.16%1.500
2935.11%0.00%0.00%64.89%6.98%4.24%1.498
3036.02%0.00%0.00%63.98%7.09%4.33%1.495
3136.94%0.00%0.00%63.06%7.20%4.41%1.492
3237.85%0.00%0.00%62.15%7.31%4.49%1.488
3338.77%0.00%0.00%61.23%7.42%4.58%1.485
3439.68%0.00%0.00%60.32%7.53%4.66%1.481
3540.59%0.00%0.00%59.41%7.64%4.75%1.477
3641.51%0.00%0.00%58.49%7.75%4.84%1.473
3742.42%0.00%0.00%57.58%7.87%4.93%1.469
3843.33%0.00%0.00%56.67%7.98%5.02%1.465
3944.25%0.00%0.00%55.75%8.09%5.11%1.460
4045.16%0.00%0.00%54.84%8.20%5.20%1.456
4146.08%0.00%0.00%53.92%8.31%5.30%1.452
4246.99%0.00%0.00%53.01%8.42%5.39%1.447
4347.90%0.00%0.00%52.10%8.54%5.48%1.443
4448.82%0.00%0.00%51.18%8.65%5.58%1.438
4549.73%0.00%0.00%50.27%8.76%5.67%1.434
4650.65%0.00%0.00%49.35%8.87%5.77%1.430
4751.56%0.00%0.00%48.44%8.98%5.86%1.425
4852.47%0.00%0.00%47.53%9.10%5.96%1.421
4953.39%0.00%0.00%46.61%9.21%6.06%1.417
5054.30%0.00%0.00%45.70%9.32%6.16%1.412
5155.22%0.00%0.00%44.78%9.43%6.25%1.408
5256.00%0.00%0.18%43.82%9.55%6.35%1.404
5356.73%0.00%0.44%42.83%9.66%6.45%1.400
5457.45%0.00%0.70%41.84%9.77%6.55%1.396
5558.18%0.00%0.96%40.86%9.88%6.65%1.392
5658.91%0.00%1.22%39.87%10.00%6.75%1.389
5759.64%0.00%1.48%38.88%10.11%6.85%1.385
5860.37%0.00%1.74%37.89%10.22%6.95%1.381
5961.09%0.00%2.00%36.91%10.34%7.05%1.378
6061.82%0.00%2.26%35.92%10.45%7.15%1.374
6162.55%0.00%2.52%34.93%10.56%7.25%1.371
6263.28%0.00%2.78%33.95%10.68%7.35%1.368
6364.00%0.00%3.04%32.96%10.79%7.45%1.364
6464.73%0.00%3.30%31.97%10.91%7.55%1.361
6565.46%0.00%3.56%30.98%11.02%7.65%1.358
6666.19%0.00%3.82%30.00%11.13%7.76%1.355
6766.92%0.00%4.08%29.01%11.25%7.86%1.352
6867.64%0.00%4.34%28.02%11.36%7.96%1.349
6968.37%0.00%4.59%27.03%11.48%8.06%1.347
7069.10%0.00%4.85%26.05%11.59%8.16%1.344
7169.83%0.00%5.11%25.06%11.71%8.26%1.341
7270.55%0.00%5.37%24.07%11.82%8.37%1.338
7371.28%0.00%5.63%23.09%11.94%8.47%1.336
7472.01%0.00%5.89%22.10%12.05%8.57%1.333
7572.74%0.00%6.15%21.11%12.17%8.67%1.331
7673.46%0.00%6.41%20.12%12.28%8.78%1.328
7774.19%0.00%6.67%19.14%12.40%8.88%1.326
7874.92%0.00%6.93%18.15%12.51%8.98%1.324
7975.65%0.00%7.19%17.16%12.63%9.08%1.322
8076.38%0.00%7.45%16.17%12.75%9.19%1.319
8177.10%0.00%7.71%15.19%12.86%9.29%1.317
8277.83%0.00%7.97%14.20%12.98%9.39%1.315
8378.56%0.00%8.23%13.21%13.09%9.50%1.313
8479.29%0.00%8.49%12.23%13.21%9.60%1.311
8580.01%0.00%8.75%11.24%13.33%9.70%1.309
8680.74%0.00%9.01%10.25%13.44%9.81%1.307
8781.47%0.00%9.27%9.26%13.56%9.91%1.305
8882.20%0.00%9.53%8.28%13.67%10.01%1.303
8982.93%0.00%9.79%7.29%13.79%10.12%1.301
9083.65%0.00%10.04%6.30%13.91%10.22%1.300
9184.38%0.00%10.30%5.31%14.03%10.32%1.298
9285.11%0.00%10.56%4.33%14.14%10.43%1.296
9385.84%0.00%10.82%3.34%14.26%10.53%1.295
9486.56%0.00%11.08%2.35%14.38%10.64%1.293
9587.29%0.00%11.34%1.37%14.49%10.74%1.291
9688.02%0.00%11.60%0.38%14.61%10.84%1.290
9790.29%0.00%9.71%0.00%14.73%10.95%1.288
9893.53%0.00%6.47%0.00%14.85%11.07%1.285
9996.76%0.00%3.24%0.00%14.96%11.21%1.280
100100.00%0.00%0.00%0.00%15.08%11.36%1.273
*Ex-ante values shown for portfolio return and volatility. Ex ante Sharpe Ratio calculated using historical 1-month treasury bill returns as the risk-free rate (0.62% 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%8.33%$10,83316.45%18.61%17.63%3.16%
20131.50%4.78%$11,35133.45%14.61%2.31%-2.10%
20140.76%7.78%$12,23512.54%-4.74%30.36%5.82%
20150.73%0.41%$12,2850.36%-4.19%2.42%0.56%
20162.07%5.00%$12,89912.83%4.81%8.60%2.52%
20172.11%8.70%$14,02121.21%27.45%4.91%3.57%
20181.91%-2.93%$13,610-5.21%-14.43%-6.02%-0.12%
20192.43%14.26%$15,55027.11%16.65%27.91%8.91%
Annual returns for 2019 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)
201212.62%$10,2625.07%7.33%6.38%0.63%
201221.04%$10,3684.22%4.56%-1.15%0.04%
201230.55%$10,4253.06%-0.54%5.19%-0.51%
201240.66%$10,494-0.64%-2.08%2.86%1.10%
20125-2.00%$10,284-6.23%-10.83%-4.51%0.93%
201261.86%$10,4764.05%5.97%5.52%0.07%
201271.15%$10,5960.88%0.31%2.00%1.23%
201280.79%$10,6802.70%2.60%-0.01%0.16%
201290.68%$10,7532.49%3.41%-1.86%0.18%
201210-0.31%$10,719-1.81%0.81%-0.91%-0.10%
2012110.50%$10,7730.77%2.06%-0.26%0.27%
2012120.56%$10,8331.29%4.88%3.72%-0.88%
201310.97%$10,9385.42%2.40%3.74%-0.69%
201320.51%$10,9941.28%-1.14%1.22%0.54%
201331.00%$11,1033.95%0.93%2.87%0.08%
201341.96%$11,3211.61%3.50%6.73%1.01%
20135-1.88%$11,1072.44%-3.30%-5.98%-1.93%
20136-1.88%$10,899-1.43%-3.57%-1.98%-1.65%
201371.68%$11,0825.75%4.62%0.90%0.38%
20138-1.90%$10,872-3.03%-1.95%-6.98%-0.86%
201392.49%$11,1433.90%7.51%3.49%1.11%
2013102.03%$11,3694.27%3.67%4.52%0.86%
201311-0.32%$11,3332.70%0.13%-5.25%-0.29%
2013120.16%$11,3512.73%1.52%0.10%-0.64%
201410.34%$11,390-3.17%-5.40%4.28%1.55%
201422.14%$11,6344.87%5.59%5.07%0.47%
201430.07%$11,6420.51%0.49%0.49%-0.17%
201441.00%$11,7590.06%1.26%3.29%0.80%
201451.44%$11,9272.10%1.93%2.40%1.05%
201460.76%$12,0182.62%1.89%1.13%0.08%
20147-0.65%$11,939-1.99%-1.73%0.08%-0.28%
201481.75%$12,1484.15%1.16%3.04%1.14%
20149-1.85%$11,923-2.10%-5.01%-6.04%-0.57%
2014101.82%$12,1412.75%-0.08%9.94%0.72%
2014111.02%$12,2642.48%-0.51%2.00%0.83%
201412-0.24%$12,235-0.04%-3.87%1.88%0.06%
201511.88%$12,465-2.74%0.27%6.85%2.40%
201520.28%$12,4995.74%5.78%-3.67%-1.31%
201530.19%$12,523-1.16%-1.49%1.74%0.55%
20154-0.13%$12,5060.62%4.81%-5.85%-0.32%
20155-0.28%$12,4711.30%-0.91%-0.30%-0.50%
20156-1.74%$12,255-1.67%-2.73%-4.68%-1.11%
201571.31%$12,4151.70%-0.56%5.77%0.88%
20158-2.51%$12,104-6.09%-7.43%-6.29%-0.25%
20159-0.04%$12,099-2.92%-3.85%3.05%0.81%
2015102.43%$12,3937.91%6.25%5.76%0.03%
201511-0.39%$12,3450.60%-1.32%-0.63%-0.39%
201512-0.49%$12,285-2.13%-2.17%1.82%-0.18%
20161-1.01%$12,161-5.72%-5.45%-3.44%1.20%
201620.22%$12,187-0.01%-2.46%-0.36%0.85%
201633.59%$12,6247.11%8.33%10.48%0.88%
201640.37%$12,6710.66%2.16%-2.35%0.40%
201650.34%$12,7151.73%-0.98%2.25%-0.01%
201661.92%$12,9590.27%-0.90%6.92%2.02%
201671.90%$13,2053.98%4.52%4.26%0.60%
20168-0.49%$13,1400.21%0.45%-3.76%-0.31%
201690.12%$13,1560.21%1.70%-1.82%0.11%
201610-1.70%$12,931-2.19%-1.91%-5.74%-0.94%
201611-1.43%$12,7464.49%-2.01%-1.68%-2.57%
2016121.20%$12,8991.98%1.96%4.82%0.33%
201710.84%$13,0081.86%4.08%-0.19%0.19%
201721.42%$13,1923.69%1.34%3.51%0.62%
201730.10%$13,2050.06%3.00%-2.42%-0.04%
201740.93%$13,3271.06%2.05%0.24%0.80%
201750.88%$13,4441.01%2.96%-0.72%0.71%
201760.46%$13,5060.95%0.63%2.23%0.05%
201771.04%$13,6471.88%3.37%1.24%0.40%
201780.61%$13,7300.15%0.54%-0.26%0.86%
201790.25%$13,7642.44%1.88%-0.11%-0.47%
2017100.42%$13,8222.17%2.03%-1.07%-0.03%
2017110.69%$13,9183.03%0.63%2.66%-0.11%
2017120.74%$14,0211.16%2.07%-0.14%0.54%
201810.19%$14,0475.23%5.72%-4.25%-1.24%
20182-2.57%$13,686-3.76%-5.24%-7.68%-1.04%
201830.51%$13,755-1.95%-0.38%3.88%0.69%
20184-0.35%$13,7070.45%0.46%0.82%-0.85%
201850.99%$13,8432.72%-1.64%3.68%0.68%
201860.23%$13,8750.70%-2.14%4.20%-0.04%
201870.80%$13,9863.32%2.55%0.60%-0.04%
201880.88%$14,1093.43%-2.40%2.58%0.67%
20189-0.56%$14,0300.20%0.21%-2.64%-0.55%
201810-2.89%$13,625-7.41%-8.56%-2.93%-0.86%
2018111.35%$13,8092.01%1.68%4.67%0.64%
201812-1.45%$13,610-9.16%-4.93%-7.96%1.87%
201913.99%$14,1528.54%7.67%11.85%1.11%
201920.70%$14,2523.56%1.63%0.70%-0.09%
201931.95%$14,5301.42%0.77%4.21%1.94%
201940.84%$14,6533.93%2.77%-0.16%-0.02%
20195-0.35%$14,601-6.45%-5.42%0.14%1.83%
201962.62%$14,9847.08%5.77%1.54%1.25%
201970.23%$15,0181.41%-1.99%1.70%0.15%
201981.61%$15,259-2.08%-2.17%3.75%2.77%
201990.40%$15,3201.78%2.73%1.93%-0.57%
2019101.01%$15,4752.11%3.43%1.13%0.31%
2019110.49%$15,5503.79%0.99%-1.30%-0.04%
Portfolio return and risk metrics
MetricRisk Parity
Arithmetic Mean (monthly)0.47%
Arithmetic Mean (annualized)5.84%
Geometric Mean (monthly)0.47%
Geometric Mean (annualized)5.74%
Volatility (monthly)1.30%
Volatility (annualized)4.49%
Downside Deviation (monthly)0.74%
Max. Drawdown-3.96%
US Market Correlation0.71
Beta(*)0.28
Alpha (annualized)1.75%
R250.06%
Sharpe Ratio1.13
Sortino Ratio1.92
Treynor Ratio (%)18.02
Calmar Ratio1.93
Active Return-8.49%
Tracking Error8.72%
Information Ratio-0.97
Skewness-0.29
Excess Kurtosis0.56
Historical Value-at-Risk (5%)-1.92%
Analytical Value-at-Risk (5%)-1.65%
Conditional Value-at-Risk (5%)-2.49%
Upside Capture Ratio (%)31.73
Downside Capture Ratio (%)24.78
Safe Withdrawal Rate16.73%
Perpetual Withdrawal Rate4.34%
Positive Periods69 out of 95 (72.63%)
Gain/Loss Ratio0.95
* 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-3.96%
2Sep 2018Dec 20184 monthsJan 20191 month5 months-3.54%
3Aug 2016Nov 20164 monthsMar 20174 months8 months-3.47%
4Apr 2015Sep 20156 monthsMar 20166 months1 year-3.38%
5Feb 2018Feb 20181 monthAug 20186 months7 months-2.57%
6May 2012May 20121 monthJul 20122 months3 months-2.00%
7Sep 2014Sep 20141 monthNov 20142 months3 months-1.85%
8Jul 2014Jul 20141 monthAug 20141 month2 months-0.65%
9May 2019May 20191 monthJun 20191 month2 months-0.35%
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 ETF14.36%11.36%33.45%-5.21%-14.20%1.191.941.00
VXUSVanguard Total International Stock ETF6.56%12.57%27.45%-14.43%-20.26%0.520.790.80
VNQVanguard Real Estate ETF10.48%13.69%30.36%-6.02%-14.88%0.751.250.48
BNDVanguard Total Bond Market ETF2.77%3.11%8.91%-2.10%-4.01%0.701.15-0.12

Monthly Correlations

Correlations for the portfolio assets
TickerNameVTIVXUSVNQBNDRisk Parity
VTIVanguard Total Stock Market ETF-0.810.48-0.120.71
VXUSVanguard Total International Stock ETF0.81-0.420.030.76
VNQVanguard Real Estate ETF0.480.42-0.490.83
BNDVanguard Total Bond Market ETF-0.120.030.49-0.56

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 year4.58%8.70%-2.93%
3 years4.74%6.96%3.47%
5 years4.74%5.29%3.70%
7 years4.50%4.50%4.50%
Result statistics are based on annualized rolling returns over full calendar year periods