# Portfolio Optimization

This portfolio optimizer tool supports the following portfolio optimization strategies:

• Mean Variance Optimization – Find the optimal risk adjusted portfolio that lies on the efficient frontier
• Minimize Conditional Value-at-Risk – Optimize the portfolio to minimize the expected tail loss
• Risk Parity – Find the portfolio that equalizes the risk contribution of portfolio assets
• Minimize Tracking Error – Find the portfolio that minimizes the tracking error against the selected benchmark
• Maximize Information Ratio – Find the portfolio that maximizes the information ratio against the selected benchmark
• Maximize Kelly Criterion – Finds the portfolio with the maximum expected geometric growth rate
• Maximize Sortino Ratio – Find the portfolio that maximizes the Sortino ratio for the given minimum acceptable return
• Maximize Omega Ratio – Find the portfolio that maximizes the Omega ratio for the given minimum acceptable return
• Minimize Maximum Drawdown – Find the portfolio with the minimum worst case drawdown with optional minimum acceptable return

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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## Portfolio Optimization Results

Portfolio optimization results with goal to minimize volatility subject to 6.00% targeted annual return. The possible range of expected annual portfolio returns based on provided parameters taking into account the specified constraints is 4.59% to 6.08%. Refer to the efficient frontier section for additional details. Historical values from Jan 2016 to Dec 2019 were used for non-user supplied parameters based on the selected time period and available data for the portfolio assets.

### Portfolio Allocations

Provided Portfolio
Ticker Name Allocation
SPHQ Invesco S&P 500 Quality ETF 40.00%
SPYD SPDR Portfolio S&P 500 High Div ETF 40.00%
VFIUX Vanguard Interm-Term Treasury Adm 20.00%
Save portfolio »
Minimum Volatility at 6.00% Return
Ticker Name Allocation
SPHQ Invesco S&P 500 Quality ETF 15.00%
SPYD SPDR Portfolio S&P 500 High Div ETF 68.49%
VFIUX Vanguard Interm-Term Treasury Adm 16.51%
Save portfolio »
Equal Weighted
Ticker Name Allocation
SPHQ Invesco S&P 500 Quality ETF 33.33%
SPYD SPDR Portfolio S&P 500 High Div ETF 33.33%
VFIUX Vanguard Interm-Term Treasury Adm 33.33%
Save portfolio »

### Portfolio Summary

Portfolio statistics
PortfolioExpected ReturnStandard DeviationSharpe Ratio
Provided Portfolio5.58%8.52%0.64
Minimum Volatility at 6.00% Return6.01%9.30%0.64
Equal Weighted4.98%6.98%0.70
Expected return is based on the provided capital market expectations. Ex ante Sharpe Ratio calculated using the current 3-month treasury bill return as the risk-free rate (0.09% annualized).
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 results are based on combining user provided forecast model parameters with historical monthly return statistics of the portfolio assets
• Allocation constraints are only applied to the optimized portfolio, not to compared allocations and benchmarks
Efficient Frontier Assets
#AssetExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1Invesco S&P 500 Quality ETF (SPHQ)6.00%11.08%0.53315.00%90.00%
2SPDR Portfolio S&P 500 High Div ETF (SPYD)7.00%11.74%0.58815.00%90.00%
Results based on the provided capital market expectations. Ex ante Sharpe Ratio calculated using the current 3-month treasury bill return as the risk-free rate (0.09% annualized).

### Asset Correlations

Efficient Frontier Asset Correlations
NameTickerSPHQSPYDVFIUX
Invesco S&P 500 Quality ETFSPHQ1.000.82-0.31
SPDR Portfolio S&P 500 High Div ETFSPYD0.821.00-0.30
Based on monthly returns from Jan 2016 to Dec 2019
Efficient Frontier Assets
#SPHQSPYDVFIUXExpected Return*Standard Deviation*Sharpe Ratio*
139.42%20.58%40.00%4.59%6.20%0.725
237.89%22.11%40.00%4.60%6.20%0.727
336.36%23.64%40.00%4.62%6.20%0.729
434.83%25.17%40.00%4.63%6.21%0.731
533.30%26.70%40.00%4.65%6.21%0.733
631.77%28.23%40.00%4.66%6.22%0.735
730.23%29.77%40.00%4.68%6.23%0.736
828.70%31.30%40.00%4.69%6.24%0.737
927.17%32.83%40.00%4.71%6.26%0.738
1025.64%34.36%40.00%4.72%6.27%0.738
1124.11%35.89%40.00%4.74%6.29%0.739
1222.58%37.42%40.00%4.75%6.31%0.739
1321.04%38.96%40.00%4.77%6.33%0.739
1419.51%40.49%40.00%4.78%6.35%0.739
1517.98%42.02%40.00%4.80%6.37%0.739
1616.45%43.55%40.00%4.81%6.40%0.738
1715.00%45.02%39.98%4.83%6.42%0.737
1815.00%45.32%39.68%4.84%6.46%0.736
1915.00%45.62%39.38%4.86%6.49%0.734
2015.00%45.92%39.08%4.87%6.53%0.732
2115.00%46.22%38.78%4.89%6.57%0.731
2215.00%46.52%38.48%4.90%6.60%0.729
2315.00%46.82%38.18%4.92%6.64%0.727
2415.00%47.12%37.88%4.93%6.67%0.726
2515.00%47.42%37.58%4.95%6.71%0.724
2615.00%47.73%37.27%4.96%6.74%0.722
2715.00%48.03%36.97%4.98%6.78%0.721
2815.00%48.33%36.67%4.99%6.82%0.719
2915.00%48.63%36.37%5.01%6.85%0.718
3015.00%48.93%36.07%5.02%6.89%0.716
3115.00%49.23%35.77%5.04%6.92%0.715
3215.00%49.53%35.47%5.05%6.96%0.713
3315.00%49.83%35.17%5.07%7.00%0.711
3415.00%50.13%34.87%5.08%7.03%0.710
3515.00%50.43%34.57%5.10%7.07%0.708
3615.00%50.74%34.26%5.11%7.11%0.707
3715.00%51.04%33.96%5.13%7.14%0.705
3815.00%51.34%33.66%5.14%7.18%0.704
3915.00%51.64%33.36%5.16%7.22%0.703
4015.00%51.94%33.06%5.17%7.25%0.701
4115.00%52.24%32.76%5.19%7.29%0.700
4215.00%52.54%32.46%5.20%7.32%0.698
4315.00%52.84%32.16%5.22%7.36%0.697
4415.00%53.14%31.86%5.23%7.40%0.695
4515.00%53.44%31.56%5.25%7.43%0.694
4615.00%53.75%31.25%5.27%7.47%0.693
4715.00%54.05%30.95%5.28%7.51%0.691
4815.00%54.35%30.65%5.30%7.54%0.690
4915.00%54.65%30.35%5.31%7.58%0.689
5015.00%54.95%30.05%5.33%7.62%0.687
5115.00%55.25%29.75%5.34%7.65%0.686
5215.00%55.55%29.45%5.36%7.69%0.685
5315.00%55.85%29.15%5.37%7.73%0.683
5415.00%56.15%28.85%5.39%7.77%0.682
5515.00%56.45%28.55%5.40%7.80%0.681
5615.00%56.76%28.24%5.42%7.84%0.680
5715.00%57.06%27.94%5.43%7.88%0.678
5815.00%57.36%27.64%5.45%7.91%0.677
5915.00%57.66%27.34%5.46%7.95%0.676
6015.00%57.96%27.04%5.48%7.99%0.675
6115.00%58.26%26.74%5.49%8.02%0.673
6215.00%58.56%26.44%5.51%8.06%0.672
6315.00%58.86%26.14%5.52%8.10%0.671
6415.00%59.16%25.84%5.54%8.14%0.670
6515.00%59.46%25.54%5.55%8.17%0.668
6615.00%59.77%25.23%5.57%8.21%0.667
6715.00%60.07%24.93%5.58%8.25%0.666
6815.00%60.37%24.63%5.60%8.28%0.665
6915.00%60.67%24.33%5.61%8.32%0.664
7015.00%60.97%24.03%5.63%8.36%0.663
7115.00%61.27%23.73%5.64%8.40%0.662
7215.00%61.57%23.43%5.66%8.43%0.660
7315.00%61.87%23.13%5.68%8.47%0.659
7415.00%62.17%22.83%5.69%8.51%0.658
7515.00%62.47%22.53%5.71%8.55%0.657
7615.00%62.78%22.22%5.72%8.58%0.656
7715.00%63.08%21.92%5.74%8.62%0.655
7815.00%63.38%21.62%5.75%8.66%0.654
7915.00%63.68%21.32%5.77%8.70%0.653
8015.00%63.98%21.02%5.78%8.73%0.652
8115.00%64.28%20.72%5.80%8.77%0.651
8215.00%64.58%20.42%5.81%8.81%0.650
8315.00%64.88%20.12%5.83%8.85%0.649
8415.00%65.18%19.82%5.84%8.88%0.648
8515.00%65.48%19.52%5.86%8.92%0.647
8615.00%65.79%19.21%5.87%8.96%0.646
8715.00%66.09%18.91%5.89%9.00%0.645
8815.00%66.39%18.61%5.90%9.03%0.644
8915.00%66.69%18.31%5.92%9.07%0.643
9015.00%66.99%18.01%5.93%9.11%0.642
9115.00%67.29%17.71%5.95%9.15%0.641
9215.00%67.59%17.41%5.96%9.18%0.640
9315.00%67.89%17.11%5.98%9.22%0.639
9415.00%68.19%16.81%5.99%9.26%0.638
9515.00%68.49%16.51%6.01%9.30%0.637
9615.00%68.80%16.20%6.03%9.34%0.636
9715.00%69.10%15.90%6.04%9.37%0.635
9815.00%69.40%15.60%6.06%9.41%0.634
9915.00%69.70%15.30%6.07%9.45%0.633
10015.00%70.00%15.00%6.09%9.49%0.632
*Ex-ante values shown for portfolio return and volatility. Ex ante Sharpe Ratio calculated using the current 3-month treasury bill return as the risk-free rate (0.09% annualized).