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 2019 - Dec 2019)

Portfolio optimization results with goal to minimize volatility subject to 8.00% targeted annual return. The possible range of expected annual portfolio returns for the given period is 0.08% to 32.20%. Refer to the efficient frontier section for additional details.

Portfolio Allocations

Minimum Volatility at 8.00% Return
Ticker Name Allocation
SPY SPDR S&P 500 ETF Trust 71.10%
TLT iShares 20+ Year Treasury Bond ETF 14.42%
VXX iPath B S&P 500 VIX S/T Futs ETN 14.47%
Save portfolio »

Portfolio Performance Summary

Portfolio performance statistics
MetricMinimum Volatility at 8.00% Return
Start Balance$10,000
End Balance$10,790
CAGR7.90%
Expected Return 8.00%
Stdev4.63%
Best Year7.90%
Worst Year7.90%
Max. Drawdown -1.76%
Sharpe Ratio (ex-ante)1.27
Sharpe Ratio (ex-post)1.22
Sortino Ratio2.99
US Stock Market Correlation0.47
   
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
1SPDR S&P 500 ETF Trust (SPY)31.22%32.20%12.90%2.3320.00%100.00%
2iShares 20+ Year Treasury Bond ETF (TLT)14.12%15.26%15.08%0.8700.00%100.00%
3iPath B S&P 500 VIX S/T Futs ETN (VXX)-67.82%-64.66%43.27%-1.5440.00%100.00%
Results based on historical returns. Ex ante Sharpe Ratio calculated using 3-month treasury bill returns as the risk-free rate (2.13% annualized).

Asset Correlations

Efficient Frontier Asset Correlations
NameTickerSPYTLTVXX
SPDR S&P 500 ETF TrustSPY1.00-0.60-0.91
iShares 20+ Year Treasury Bond ETFTLT-0.601.000.78
iPath B S&P 500 VIX S/T Futs ETNVXX-0.910.781.00
Based on provided custom correlation matrix
Efficient Frontier Assets
#SPYTLTVXXExpected Return*Standard Deviation*Sharpe Ratio*
177.97%0.00%22.03%0.08%4.29%-0.477
278.20%0.00%21.80%0.36%4.30%-0.411
378.07%0.39%21.54%0.65%4.30%-0.344
477.79%0.96%21.25%0.93%4.31%-0.277
577.51%1.52%20.97%1.22%4.31%-0.210
677.23%2.08%20.69%1.51%4.32%-0.143
776.95%2.65%20.40%1.80%4.33%-0.076
876.67%3.21%20.12%2.09%4.34%-0.009
976.39%3.78%19.83%2.38%4.34%0.058
1076.11%4.34%19.55%2.67%4.35%0.125
1175.83%4.90%19.27%2.96%4.36%0.191
1275.55%5.47%18.98%3.25%4.37%0.258
1375.27%6.03%18.70%3.55%4.39%0.324
1474.99%6.60%18.41%3.84%4.40%0.390
1574.71%7.16%18.13%4.14%4.41%0.456
1674.43%7.73%17.85%4.43%4.42%0.521
1774.15%8.29%17.56%4.73%4.44%0.586
1873.87%8.85%17.28%5.02%4.45%0.651
1973.59%9.42%16.99%5.32%4.47%0.716
2073.31%9.98%16.71%5.62%4.48%0.780
2173.03%10.55%16.43%5.92%4.50%0.843
2272.75%11.11%16.14%6.22%4.52%0.907
2372.47%11.67%15.86%6.52%4.54%0.969
2472.19%12.24%15.57%6.82%4.55%1.032
2571.91%12.80%15.29%7.13%4.57%1.094
2671.63%13.37%15.00%7.43%4.59%1.155
2771.35%13.93%14.72%7.73%4.61%1.216
2871.07%14.50%14.44%8.04%4.63%1.277
2970.79%15.06%14.15%8.35%4.65%1.336
3070.51%15.62%13.87%8.65%4.68%1.396
3170.23%16.19%13.58%8.96%4.70%1.455
3269.95%16.75%13.30%9.27%4.72%1.513
3369.67%17.32%13.02%9.58%4.74%1.571
3469.39%17.88%12.73%9.89%4.77%1.628
3569.11%18.44%12.45%10.20%4.79%1.684
3668.83%19.01%12.16%10.51%4.82%1.740
3768.55%19.57%11.88%10.82%4.84%1.796
3868.27%20.14%11.60%11.13%4.87%1.850
3967.99%20.70%11.31%11.45%4.89%1.904
4067.71%21.27%11.03%11.76%4.92%1.958
4167.43%21.83%10.74%12.08%4.95%2.011
4267.15%22.39%10.46%12.39%4.98%2.063
4366.87%22.96%10.18%12.71%5.00%2.115
4466.59%23.52%9.89%13.03%5.03%2.166
4566.31%24.09%9.61%13.35%5.06%2.217
4666.03%24.65%9.32%13.67%5.09%2.267
4765.75%25.21%9.04%13.99%5.12%2.316
4865.47%25.78%8.76%14.31%5.15%2.365
4965.19%26.34%8.47%14.63%5.18%2.413
5064.91%26.91%8.19%14.95%5.21%2.461
5164.63%27.47%7.90%15.28%5.24%2.508
5264.35%28.04%7.62%15.60%5.28%2.554
5364.07%28.60%7.33%15.93%5.31%2.600
5463.79%29.16%7.05%16.25%5.34%2.645
5563.51%29.73%6.77%16.58%5.37%2.690
5663.23%30.29%6.48%16.91%5.41%2.734
5762.95%30.86%6.20%17.24%5.44%2.777
5862.67%31.42%5.91%17.57%5.48%2.820
5962.39%31.98%5.63%17.90%5.51%2.863
6062.11%32.55%5.35%18.23%5.54%2.905
6161.83%33.11%5.06%18.56%5.58%2.946
6261.54%33.68%4.78%18.89%5.61%2.987
6361.26%34.24%4.49%19.23%5.65%3.027
6460.98%34.81%4.21%19.56%5.69%3.067
6560.70%35.37%3.93%19.90%5.72%3.106
6660.42%35.93%3.64%20.23%5.76%3.145
6760.14%36.50%3.36%20.57%5.80%3.183
6859.86%37.06%3.07%20.91%5.83%3.221
6959.58%37.63%2.79%21.25%5.87%3.258
7059.30%38.19%2.51%21.59%5.91%3.295
7159.02%38.75%2.22%21.93%5.95%3.331
7258.74%39.32%1.94%22.27%5.98%3.367
7358.46%39.88%1.65%22.61%6.02%3.402
7458.18%40.45%1.37%22.96%6.06%3.437
7557.90%41.01%1.08%23.30%6.10%3.472
7657.62%41.58%0.80%23.65%6.14%3.506
7757.34%42.14%0.52%23.99%6.18%3.540
7857.06%42.70%0.23%24.34%6.22%3.573
7957.20%42.80%0.00%24.69%6.26%3.605
8059.24%40.76%0.00%25.04%6.33%3.622
8161.28%38.72%0.00%25.39%6.43%3.616
8263.32%36.68%0.00%25.74%6.58%3.589
8365.35%34.65%0.00%26.09%6.76%3.545
8467.39%32.61%0.00%26.44%6.97%3.487
8569.43%30.57%0.00%26.79%7.22%3.418
8671.47%28.53%0.00%27.15%7.49%3.342
8773.51%26.49%0.00%27.50%7.78%3.261
8875.54%24.46%0.00%27.86%8.10%3.178
8977.58%22.42%0.00%28.22%8.43%3.094
9079.62%20.38%0.00%28.57%8.78%3.011
9181.66%18.34%0.00%28.93%9.15%2.929
9283.70%16.30%0.00%29.29%9.53%2.850
9385.73%14.27%0.00%29.65%9.92%2.774
9487.77%12.23%0.00%30.01%10.32%2.701
9589.81%10.19%0.00%30.38%10.74%2.631
9691.85%8.15%0.00%30.74%11.16%2.565
9793.89%6.11%0.00%31.10%11.58%2.502
9895.92%4.08%0.00%31.47%12.02%2.442
9997.96%2.04%0.00%31.83%12.45%2.385
100100.00%0.00%0.00%32.20%12.90%2.332
*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 (2.13% annualized).
Annual returns for the configured portfolios
YearInflationMinimum Volatility at 8.00% Return ReturnMinimum Volatility at 8.00% Return BalanceSPDR S&P 500 ETF Trust (SPY)iShares 20+ Year Treasury Bond ETF (TLT)iPath B S&P 500 VIX S/T Futs ETN (VXX)
20192.29%7.90%$10,79031.22%14.12%-67.82%
Monthly returns for the configured portfolios
YearMonthMinimum Volatility at 8.00% Return ReturnMinimum Volatility at 8.00% Return BalanceSPDR S&P 500 ETF Trust (SPY)iShares 20+ Year Treasury Bond ETF (TLT)iPath B S&P 500 VIX S/T Futs ETN (VXX)
201912.19%$10,2198.01%0.38%-24.60%
201920.46%$10,2663.24%-1.38%-11.35%
201931.10%$10,3791.81%5.57%-6.84%
201940.85%$10,4674.09%-1.99%-12.24%
20195-0.88%$10,375-6.38%6.84%18.46%
201962.98%$10,6856.96%0.95%-14.53%
20197-0.23%$10,6601.51%0.26%-9.27%
201982.49%$10,926-1.67%11.04%14.46%
20199-0.75%$10,8441.95%-2.68%-12.07%
201910-1.02%$10,7332.21%-1.11%-16.81%
2019110.16%$10,7513.62%-0.41%-16.25%
2019120.36%$10,7902.90%-3.20%-8.59%
Portfolio return and risk metrics
MetricMinimum Volatility at 8.00% Return
Arithmetic Mean (monthly)0.64%
Arithmetic Mean (annualized)8.00%
Geometric Mean (monthly)0.64%
Geometric Mean (annualized)7.90%
Volatility (monthly)1.34%
Volatility (annualized)4.63%
Downside Deviation (monthly)0.45%
Max. Drawdown-1.76%
US Market Correlation0.47
Beta(*)0.16
Alpha (annualized)3.22%
R221.97%
Sharpe Ratio1.22
Sortino Ratio2.99
Treynor Ratio (%)34.73
Active Return-22.75%
Tracking Error11.97%
Information Ratio-1.90
Skewness0.52
Excess Kurtosis-0.83
Historical Value-at-Risk (5%)-1.02%
Analytical Value-at-Risk (5%)-1.46%
Conditional Value-at-Risk (5%)N/A
Upside Capture Ratio (%)14.58
Downside Capture Ratio (%)-19.13
Safe Withdrawal Rate100.00%
Perpetual Withdrawal Rate5.20%
Positive Periods8 out of 12 (66.67%)
Gain/Loss Ratio1.84
* US stock market is used as the benchmark for calculations. Value-at-risk metrics are based on monthly values.

Drawdowns for Minimum Volatility at 8.00% Return

Drawdowns for Minimum Volatility at 8.00% Return
RankStartEndLengthRecovery ByRecovery TimeUnderwater PeriodDrawdown
1Sep 2019Oct 20192 months-1.76%
2May 2019May 20191 monthJun 20191 month2 months-0.88%
3Jul 2019Jul 20191 monthAug 20191 month2 months-0.23%

Portfolio Assets

Performance statistics for portfolio components
TickerNameCAGRStdevBest YearWorst YearMax. DrawdownSharpe RatioSortino RatioUS Mkt Correlation
SPYSPDR S&P 500 ETF Trust31.22%12.90%31.22%31.22%-6.38%2.033.831.00
TLTiShares 20+ Year Treasury Bond ETF14.12%15.08%14.12%14.12%-7.22%0.812.29-0.60
VXXiPath B S&P 500 VIX S/T Futs ETN-67.82%43.27%-67.82%-67.82%-67.82%-2.35-2.25-0.91

Monthly Correlations

Correlations for the portfolio assets
TickerNameSPYTLTVXXMinimum Volatility at 8.00% Return
SPYSPDR S&P 500 ETF Trust1.00-0.60-0.910.48
TLTiShares 20+ Year Treasury Bond ETF-0.601.000.780.34
VXXiPath B S&P 500 VIX S/T Futs ETN-0.910.781.00-0.07

Portfolio Risk Decomposition

Portfolio risk decomposition
TickerNameMinimum Volatility at 8.00% Return
SPYSPDR S&P 500 ETF Trust94.18%
TLTiShares 20+ Year Treasury Bond ETF15.92%
VXXiPath B S&P 500 VIX S/T Futs ETN-10.09%

Annual Asset Returns