Minimize Menu Maximize Menu

Portfolio Optimization

Portfolio Optimization Overview

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
  • 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
  • Tracking Error – Find the portfolio that minimizes the tracking error against the selected benchmark
  • Information Ratio – Find the portfolio that maximizes the information ratio against the selected benchmark
  • Kelly Criterion – Finds the portfolio with the maximum expected geometric growth rate
  • Sortino Ratio – Find the portfolio that maximizes the Sortino ratio for the given minimum acceptable return
  • Omega Ratio – Find the portfolio that maximizes the Omega ratio for the given minimum acceptable return
  • 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.

Portfolio Optimization Configuration
Open
%
%
%
%
Portfolio Assets
Allocation
Expected Return
Volatility
Min. Weight
Max. Weight
Group
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 2017 - Sep 2026) Save

Note:
  • The time period was constrained by the available data for Vanguard Total International Stock ETF (VXUS) [Feb 2011 - Sep 2026] and Vanguard Real Estate ETF (VNQ) [Oct 2004 - Sep 2026]. You can extend the available time period by using Vanguard Total Intl Stock Index Inv (VGTSX), which is the oldest share class of the fund.
  • The time period of the results is limited to 10 years for free tier accounts.
Portfolio optimization results for risk parity. The possible range of expected annual portfolio returns for the given period is 1.60% to 21.44%. Refer to the efficient frontier section for additional details.

Risk Parity

Ticker Name Allocation
QQQ Invesco QQQ Trust 14.11%
VXUS Vanguard Total International Stock ETF 16.74%
VNQ Vanguard Real Estate ETF 14.44%
BND Vanguard Total Bond Market ETF 54.72%

Performance Summary

MetricRisk Parity
Start Balance$10,000
End Balance$18,196
Annualized Return (CAGR)6.33%
Expected Return6.55%
Standard Deviation8.96%
Best Year17.99%
Worst Year-18.18%
Maximum Drawdown -21.27%
Sharpe Ratio (ex-ante)0.46
Sharpe Ratio (ex-post)0.46
Sortino Ratio0.66
Results based on historical returns. Expected return is the annualized monthly arithmetic mean return.

Portfolio Growth

   

Annual Returns

Trailing Returns

NameTotal ReturnAnnualized ReturnAnnualized Standard Deviation
3 MonthYear To Date1 year3 year5 yearFull3 year5 year
Risk Parity-2.72%4.33%5.67%10.95%3.91%6.33%8.19%10.31%
Trailing return and volatility are as of last calendar month ending September 2026

Efficient Frontier Assets

#AssetExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1Invesco QQQ Trust21.44%19.21%0.9880.00%100.00%
2Vanguard Total International Stock ETF10.40%15.13%0.5240.00%100.00%
3Vanguard Real Estate ETF6.30%17.75%0.2160.00%100.00%
4Vanguard Total Bond Market ETF1.60%5.23%-0.1660.00%100.00%
Results based on historical returns. Expected return is the annualized monthly arithmetic mean return. Ex-ante Sharpe Ratio calculated using U.S. 3-Month Treasury Bill Rate returns as the risk-free rate.

Asset Correlations

NameTickerQQQVXUSVNQBND
Invesco QQQ TrustQQQ1.000.720.610.45
Vanguard Total International Stock ETFVXUS0.721.000.740.54
Vanguard Real Estate ETFVNQ0.610.741.000.61
Vanguard Total Bond Market ETFBND0.450.540.611.00
Based on monthly returns from Jan 2017 to Sep 2026

Efficient Frontier

Efficient Frontier Portfolios

#Invesco QQQ TrustVanguard Total International Stock ETFVanguard Real Estate ETFVanguard Total Bond Market ETFExpected Return *Standard Deviation *Sharpe Ratio *
10.00%0.00%0.00%100.00%1.60%5.23%-0.166
21.01%0.00%0.00%98.99%1.80%5.27%-0.127
32.02%0.00%0.00%97.98%2.00%5.31%-0.088
43.03%0.00%0.00%96.97%2.20%5.36%-0.050
54.04%0.00%0.00%95.96%2.40%5.41%-0.012
65.05%0.00%0.00%94.95%2.60%5.47%0.025
76.06%0.00%0.00%93.94%2.81%5.54%0.061
87.07%0.00%0.00%92.93%3.01%5.61%0.095
98.08%0.00%0.00%91.92%3.21%5.68%0.130
109.09%0.00%0.00%90.91%3.41%5.76%0.163
1110.10%0.00%0.00%89.90%3.61%5.84%0.195
1211.11%0.00%0.00%88.89%3.81%5.93%0.225
1312.12%0.00%0.00%87.88%4.01%6.02%0.255
1413.13%0.00%0.00%86.87%4.21%6.12%0.284
1514.14%0.00%0.00%85.86%4.41%6.21%0.312
1615.15%0.00%0.00%84.85%4.61%6.32%0.339
1716.16%0.00%0.00%83.84%4.81%6.42%0.364
1817.17%0.00%0.00%82.83%5.01%6.53%0.389
1918.18%0.00%0.00%81.82%5.21%6.64%0.413
2019.19%0.00%0.00%80.81%5.41%6.75%0.435
2120.20%0.00%0.00%79.80%5.61%6.87%0.457
2221.21%0.00%0.00%78.79%5.81%6.99%0.478
2322.22%0.00%0.00%77.78%6.01%7.11%0.498
2423.23%0.00%0.00%76.77%6.21%7.23%0.517
2524.24%0.00%0.00%75.76%6.41%7.36%0.536
2625.25%0.00%0.00%74.75%6.61%7.48%0.553
2726.26%0.00%0.00%73.74%6.81%7.61%0.570
2827.27%0.00%0.00%72.73%7.01%7.75%0.587
2928.28%0.00%0.00%71.72%7.21%7.88%0.602
3029.29%0.00%0.00%70.71%7.41%8.01%0.617
3130.30%0.00%0.00%69.70%7.61%8.15%0.631
3231.31%0.00%0.00%68.69%7.81%8.29%0.645
3332.32%0.00%0.00%67.68%8.02%8.43%0.658
3433.33%0.00%0.00%66.67%8.22%8.57%0.671
3534.34%0.00%0.00%65.66%8.42%8.71%0.683
3635.35%0.00%0.00%64.65%8.62%8.85%0.694
3736.36%0.00%0.00%63.64%8.82%9.00%0.705
3837.37%0.00%0.00%62.63%9.02%9.14%0.716
3938.38%0.00%0.00%61.62%9.22%9.29%0.726
4039.39%0.00%0.00%60.61%9.42%9.44%0.736
4140.40%0.00%0.00%59.60%9.62%9.59%0.746
4241.41%0.00%0.00%58.59%9.82%9.74%0.755
4342.42%0.00%0.00%57.58%10.02%9.89%0.764
4443.43%0.00%0.00%56.57%10.22%10.04%0.772
4544.44%0.00%0.00%55.56%10.42%10.19%0.780
4645.45%0.00%0.00%54.55%10.62%10.34%0.788
4746.46%0.00%0.00%53.54%10.82%10.50%0.796
4847.47%0.00%0.00%52.53%11.02%10.65%0.803
4948.48%0.00%0.00%51.52%11.22%10.81%0.810
5049.49%0.00%0.00%50.51%11.42%10.96%0.817
5150.51%0.00%0.00%49.49%11.62%11.12%0.823
5251.52%0.00%0.00%48.48%11.82%11.27%0.830
5352.53%0.00%0.00%47.47%12.02%11.43%0.836
5453.54%0.00%0.00%46.46%12.22%11.59%0.842
5554.55%0.00%0.00%45.45%12.42%11.75%0.847
5655.56%0.00%0.00%44.44%12.62%11.91%0.853
5756.57%0.00%0.00%43.43%12.82%12.07%0.858
5857.58%0.00%0.00%42.42%13.02%12.23%0.863
5958.59%0.00%0.00%41.41%13.23%12.39%0.868
6059.60%0.00%0.00%40.40%13.43%12.55%0.873
6160.61%0.00%0.00%39.39%13.63%12.71%0.878
6261.62%0.00%0.00%38.38%13.83%12.87%0.882
6362.63%0.00%0.00%37.37%14.03%13.03%0.887
6463.64%0.00%0.00%36.36%14.23%13.19%0.891
6564.65%0.00%0.00%35.35%14.43%13.36%0.895
6665.66%0.00%0.00%34.34%14.63%13.52%0.899
6766.67%0.00%0.00%33.33%14.83%13.68%0.903
6867.68%0.00%0.00%32.32%15.03%13.85%0.907
6968.69%0.00%0.00%31.31%15.23%14.01%0.911
7069.70%0.00%0.00%30.30%15.43%14.18%0.914
7170.71%0.00%0.00%29.29%15.63%14.34%0.918
7271.72%0.00%0.00%28.28%15.83%14.51%0.921
7372.73%0.00%0.00%27.27%16.03%14.67%0.924
7473.74%0.00%0.00%26.26%16.23%14.84%0.928
7574.75%0.00%0.00%25.25%16.43%15.00%0.931
7675.76%0.00%0.00%24.24%16.63%15.17%0.934
7776.77%0.00%0.00%23.23%16.83%15.33%0.937
7877.78%0.00%0.00%22.22%17.03%15.50%0.939
7978.79%0.00%0.00%21.21%17.23%15.67%0.942
8079.80%0.00%0.00%20.20%17.43%15.83%0.945
8180.81%0.00%0.00%19.19%17.63%16.00%0.948
8281.82%0.00%0.00%18.18%17.83%16.17%0.950
8382.83%0.00%0.00%17.17%18.03%16.34%0.953
8483.84%0.00%0.00%16.16%18.23%16.50%0.955
8584.85%0.00%0.00%15.15%18.44%16.67%0.958
8685.86%0.00%0.00%14.14%18.64%16.84%0.960
8786.87%0.00%0.00%13.13%18.84%17.01%0.962
8887.88%0.00%0.00%12.12%19.04%17.17%0.965
8988.89%0.00%0.00%11.11%19.24%17.34%0.967
9089.90%0.00%0.00%10.10%19.44%17.51%0.969
9190.91%0.00%0.00%9.09%19.64%17.68%0.971
9291.92%0.00%0.00%8.08%19.84%17.85%0.973
9392.93%0.00%0.00%7.07%20.04%18.02%0.975
9493.94%0.00%0.00%6.06%20.24%18.19%0.977
9594.95%0.00%0.00%5.05%20.44%18.36%0.979
9695.96%0.00%0.00%4.04%20.64%18.53%0.981
9796.97%0.00%0.00%3.03%20.84%18.70%0.983
9897.98%0.00%0.00%2.02%21.04%18.87%0.984
9998.99%0.00%0.00%1.01%21.24%19.04%0.986
100100.00%0.00%0.00%0.00%21.44%19.21%0.988
*Annualized ex-ante values shown for portfolio return and volatility. Ex-ante Sharpe Ratio calculated using historical U.S. 3-Month Treasury Bill Rate returns as the risk-free rate.

Risk and Return Metrics

MetricRisk Parity
Arithmetic Mean (monthly)0.55%
Arithmetic Mean (annualized)6.75%
Geometric Mean (monthly)0.51%
Geometric Mean (annualized)6.33%
Standard Deviation (monthly)2.59%
Standard Deviation (annualized)8.96%
Downside Deviation (monthly)1.68%
Maximum Drawdown-21.27%
Benchmark Correlation0.88
Beta(*)0.50
Alpha (annualized)-0.84%
R278.18%
Sharpe Ratio0.46
Sortino Ratio0.66
Treynor Ratio (%)8.23
Calmar Ratio2.83
Modigliani–Modigliani Measure9.75%
Active Return-8.18%
Tracking Error9.06%
Information Ratio-0.90
Skewness-0.39
Excess Kurtosis1.06
Historical Value-at-Risk (5%)3.87%
Analytical Value-at-Risk (5%)3.69%
Conditional Value-at-Risk (5%)5.48%
Upside Capture Ratio (%)43.84
Downside Capture Ratio (%)58.46
Safe Withdrawal Rate13.06%
Perpetual Withdrawal Rate2.97%
Positive Periods82 out of 117 (70.09%)
Gain/Loss Ratio0.74
* U.S. Stock Market is used as the benchmark for calculations. Value-at-risk metrics are monthly values.

Annual Returns

YearInflationRisk Parity ReturnRisk Parity BalanceInvesco QQQ Trust (QQQ)Vanguard Total International Stock ETF (VXUS)Vanguard Real Estate ETF (VNQ)Vanguard Total Bond Market ETF (BND)
20263.37%4.33%$18,19620.83%13.45%4.19%-2.72%
20252.68%12.49%$17,44120.77%32.35%3.26%7.08%
20242.89%5.85%$15,50425.58%5.08%4.81%1.38%
20233.35%14.54%$14,64854.85%15.88%11.79%5.65%
20226.45%-18.18%$12,789-32.58%-16.09%-26.24%-13.11%
20217.04%9.44%$15,62927.42%9.00%40.52%-1.86%
20201.36%12.18%$14,28148.62%10.69%-4.68%7.71%
20192.29%17.99%$12,73038.96%21.75%28.87%8.84%
20181.91%-3.12%$10,789-0.12%-14.43%-6.02%-0.11%
20172.11%11.36%$11,13632.66%27.45%4.91%3.57%
Annual return for 2026 is from 01/01/2026 to 09/30/2026

Monthly Returns

YearMonthRisk Parity ReturnRisk Parity BalanceInvesco QQQ Trust (QQQ)Vanguard Total International Stock ETF (VXUS)Vanguard Real Estate ETF (VNQ)Vanguard Total Bond Market ETF (BND)
20269-2.25%$18,1963.31%-2.53%-6.24%-2.55%
202680.96%$18,6154.18%3.23%-2.54%0.36%
20267-1.43%$18,438-6.57%-1.05%2.61%-1.28%
202660.33%$18,704-0.15%-0.22%1.65%0.27%
202652.15%$18,64310.57%3.61%-0.65%0.27%
202644.83%$18,25015.69%7.72%8.60%0.15%
20263-3.87%$17,410-4.84%-7.90%-6.31%-1.74%
202622.20%$18,110-2.34%5.21%5.39%1.60%
202611.60%$17,7211.23%5.59%2.61%0.22%
202512-0.16%$17,441-0.67%2.50%-2.24%-0.30%
2025110.53%$17,469-1.56%0.42%2.42%0.60%
2025100.92%$17,3784.78%1.59%-2.45%0.60%
202591.95%$17,2205.38%3.43%0.07%1.11%
202581.98%$16,8910.95%4.24%3.48%1.15%
202570.06%$16,5642.42%-0.90%0.09%-0.26%
202562.49%$16,5546.38%3.96%0.69%1.52%
202551.90%$16,1519.18%4.82%1.12%-0.67%
202540.54%$15,8501.40%2.83%-2.44%0.40%
20253-1.37%$15,766-7.59%0.38%-2.58%0.01%
202521.64%$15,985-2.70%1.85%3.70%2.16%
202511.44%$15,7272.16%3.38%1.65%0.60%
202412-2.55%$15,5040.45%-2.88%-8.38%-1.68%
2024111.92%$15,9105.35%-0.23%4.26%1.07%
202410-2.70%$15,610-0.86%-4.46%-3.36%-2.46%
202492.00%$16,0432.62%2.60%3.27%1.31%
202482.11%$15,7291.10%2.41%5.22%1.45%
202472.64%$15,405-1.68%2.62%7.94%2.36%
202461.53%$15,0096.47%-0.79%1.87%0.88%
202453.12%$14,7836.15%4.02%4.56%1.68%
20244-3.47%$14,336-4.37%-2.32%-7.94%-2.41%
202431.47%$14,8511.27%3.23%1.96%0.85%
202420.77%$14,6365.28%2.91%1.98%-1.36%
20241-0.85%$14,5241.82%-1.71%-5.06%-0.16%
2023124.95%$14,6485.59%5.09%9.43%3.55%
2023117.13%$13,95810.82%8.24%12.08%4.54%
202310-2.21%$13,028-2.07%-3.36%-3.62%-1.52%
20239-3.69%$13,322-5.08%-3.40%-7.27%-2.48%
20238-1.79%$13,833-1.48%-4.39%-3.38%-0.66%
202371.42%$14,0863.86%3.89%2.03%-0.12%
202362.32%$13,8886.30%4.45%5.62%-0.22%
20235-0.68%$13,5737.88%-3.50%-3.96%-1.16%
202340.75%$13,6660.51%1.88%0.31%0.59%
202332.96%$13,5639.49%2.84%-2.18%2.68%
20232-3.07%$13,173-0.36%-4.27%-5.86%-2.67%
202316.27%$13,59010.64%8.68%10.40%3.31%
202212-2.80%$12,789-9.01%-2.14%-5.03%-0.81%
2022115.86%$13,1575.54%13.04%6.15%3.67%
2022101.01%$12,4294.00%3.41%3.51%-1.16%
20229-7.29%$12,305-10.54%-9.91%-12.86%-4.18%
20228-3.87%$13,272-5.13%-4.49%-6.01%-2.80%
202274.93%$13,80712.55%3.64%8.62%2.38%
20226-4.58%$13,159-8.91%-7.96%-7.46%-1.66%
20225-0.19%$13,790-1.59%1.52%-4.69%0.83%
20224-5.77%$13,816-13.60%-6.49%-4.09%-3.97%
202230.01%$14,6624.67%-0.28%6.27%-2.75%
20222-2.23%$14,661-4.48%-2.85%-3.48%-1.14%
20221-4.05%$14,996-8.75%-2.83%-8.42%-2.06%
2021121.99%$15,6291.15%3.58%9.69%-0.31%
202111-0.62%$15,3242.00%-4.26%-2.11%0.20%
2021102.66%$15,4207.86%2.88%7.13%0.07%
20219-2.75%$15,021-5.68%-3.45%-5.68%-1.01%
202181.05%$15,4464.22%1.46%2.15%-0.19%
202171.49%$15,2862.86%-1.13%4.42%1.17%
202161.70%$15,0616.26%-0.34%2.64%0.90%
202150.55%$14,809-1.20%3.07%0.81%0.15%
202142.91%$14,7295.91%2.78%7.86%0.87%
202130.60%$14,3131.71%1.87%5.15%-1.27%
202120.01%$14,227-0.13%2.30%3.43%-1.55%
20211-0.39%$14,2250.26%0.25%0.04%-0.86%
2020122.15%$14,2814.90%5.86%2.72%0.15%
2020115.76%$13,98011.23%12.62%9.67%1.21%
202010-1.55%$13,219-3.04%-2.30%-3.00%-0.56%
20209-1.54%$13,428-5.64%-1.82%-2.68%-0.10%
202081.83%$13,63810.94%4.43%0.44%-0.94%
202073.05%$13,3927.35%4.15%3.64%1.45%
202062.31%$12,9966.28%4.24%2.41%0.67%
202052.39%$12,7026.60%5.01%1.73%0.67%
202046.19%$12,40614.97%7.60%8.96%2.76%
20203-7.33%$11,683-7.29%-16.26%-19.42%-1.43%
20202-2.06%$12,608-6.06%-6.60%-7.03%1.67%
202011.12%$12,8733.04%-3.39%1.23%1.98%
2019121.35%$12,7303.89%4.38%0.76%-0.07%
2019110.53%$12,5614.07%0.99%-1.30%-0.04%
2019101.52%$12,4954.38%3.43%1.13%0.31%
201990.55%$12,3070.92%2.73%1.93%-0.57%
201981.42%$12,239-1.90%-2.17%3.75%2.77%
201970.32%$12,0672.33%-1.99%1.70%0.15%
201962.94%$12,0287.59%5.77%1.54%1.25%
20195-1.05%$11,684-8.23%-5.42%0.14%1.83%
201941.20%$11,8085.50%2.77%-0.16%-0.02%
201932.35%$11,6683.92%0.77%4.21%1.94%
201920.75%$11,4002.99%1.63%0.70%-0.09%
201914.87%$11,3159.01%7.67%11.85%1.11%
201812-2.17%$10,789-8.65%-4.93%-7.96%1.87%
2018111.27%$11,029-0.26%1.68%4.67%0.64%
201810-3.54%$10,891-8.60%-8.56%-2.93%-0.86%
20189-0.68%$11,290-0.28%0.21%-2.64%-0.55%
201881.15%$11,3685.78%-2.40%2.58%0.67%
201870.89%$11,2392.80%2.55%0.60%-0.04%
201860.39%$11,1401.15%-2.14%4.20%-0.04%
201851.43%$11,0975.67%-1.64%3.68%0.68%
20184-0.20%$10,9400.51%0.46%0.82%-0.85%
201830.30%$10,962-4.08%-0.38%3.88%0.69%
20182-2.74%$10,930-1.29%-5.24%-7.68%-1.04%
201810.90%$11,2378.76%5.72%-4.25%-1.24%
2017120.71%$11,1360.60%2.07%-0.14%0.54%
2017110.71%$11,0581.97%0.63%2.66%-0.11%
2017100.82%$10,9804.61%2.03%-1.07%-0.03%
201790.00%$10,891-0.29%1.88%-0.11%-0.47%
201780.81%$10,8912.07%0.54%-0.26%0.86%
201771.54%$10,8034.06%3.37%1.24%0.40%
201760.13%$10,639-2.32%0.63%2.23%0.05%
201751.33%$10,6263.90%2.96%-0.72%0.71%
201741.20%$10,4862.73%2.05%0.24%0.79%
201730.42%$10,3622.03%3.00%-2.42%-0.04%
201721.69%$10,3194.38%1.34%3.51%0.62%
201711.48%$10,1485.14%4.08%-0.19%0.19%

Drawdowns

Historical Market Stress Periods

Stress PeriodStartEndRisk Parity
COVID-19 StartJan 2020Mar 2020-9.24%

Drawdowns for Risk Parity

RankStartEndLengthRecovery ByRecovery TimeUnderwater PeriodDrawdown
1Jan 2022Sep 20229 monthsAug 20241 year 11 months2 years 8 months-21.27%
2Feb 2020Mar 20202 monthsJun 20203 months5 months-9.24%
3Sep 2018Dec 20184 monthsFeb 20192 months6 months-5.09%
4Mar 2026Mar 20261 monthApr 20261 month2 months-3.87%
5Oct 2024Dec 20243 monthsMay 20255 months8 months-3.36%
6Sep 2020Oct 20202 monthsNov 20201 month3 months-3.07%
7Sep 2021Sep 20211 monthDec 20213 months4 months-2.75%
8Feb 2018Feb 20181 monthJul 20185 months6 months-2.74%
9Jul 2026Sep 20263 months-2.72%
10May 2019May 20191 monthJun 20191 month2 months-1.05%
Worst 10 drawdowns included above

Portfolio Assets

TickerNameCAGRStdevBest YearWorst YearMax DrawdownSharpe RatioSortino Ratio
QQQInvesco QQQ Trust21.49%19.21%54.85%-32.58%-32.58%0.991.67
VXUSVanguard Total International Stock ETF9.66%15.13%32.35%-16.09%-27.76%0.520.77
VNQVanguard Real Estate ETF4.82%17.75%40.52%-26.24%-32.78%0.220.30
BNDVanguard Total Bond Market ETF1.48%5.23%8.84%-13.11%-17.28%-0.17-0.22

Portfolio Asset Performance

NameTotal ReturnAnnualized ReturnExpense Ratio
3 MonthYear To Date1 year3 year5 yearNetGross
Invesco QQQ Trust0.56%20.83%23.79%28.05%16.32%0.18%0.18%
Vanguard Total International Stock ETF-0.44%13.45%18.63%20.14%9.37%0.05%0.05%
Vanguard Real Estate ETF-6.23%4.19%1.76%10.05%1.35%0.13%0.13%
Vanguard Total Bond Market ETF-3.45%-2.72%-1.85%4.03%-0.63%0.03%0.03%
Trailing returns as of last calendar month ending September 2026

Monthly Correlations

TickerNameQQQVXUSVNQBNDRisk Parity
QQQInvesco QQQ Trust1.000.720.610.450.83
VXUSVanguard Total International Stock ETF0.721.000.740.540.88
VNQVanguard Real Estate ETF0.610.741.000.610.87
BNDVanguard Total Bond Market ETF0.450.540.611.000.78

Portfolio Return Decomposition

TickerNameRisk Parity
QQQInvesco QQQ Trust$3,918
VXUSVanguard Total International Stock ETF$2,298
VNQVanguard Real Estate ETF$1,127
BNDVanguard Total Bond Market ETF$853
Return attribution decomposes portfolio gains into its constituent parts and identifies the contribution to returns by each of the assets.

Portfolio Risk Decomposition

TickerNameRisk Parity
QQQInvesco QQQ Trust25.00%
VXUSVanguard Total International Stock ETF25.00%
VNQVanguard Real Estate ETF25.00%
BNDVanguard Total Bond Market ETF25.00%
Risk attribution decomposes portfolio risk into its constituent parts and identifies the contribution to overall volatility by each of the assets.

Annual Asset Returns

Rolling Returns

Roll PeriodAverageHighLow
1 year6.55%22.51%-19.40%
3 years5.71%13.15%-0.90%
5 years4.72%9.34%2.47%
7 years5.76%7.10%4.57%

Annualized Rolling Return - 3 Years

Annualized Rolling Return - 5 Years

  • IMPORTANT: The projections or other information generated by Portfolio Visualizer regarding the likelihood of various investment outcomes are hypothetical in nature, do not reflect actual investment results and are not guarantees of future results. Results may vary with each use and over time.
  • 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. All use is subject to terms of service.
  • Investing involves risk, including possible loss of principal. Past performance is not a guarantee of future results.
  • Asset allocation and diversification strategies do not guarantee a profit or protect against a loss.
  • Hypothetical returns do not reflect trading costs, transaction fees, commissions, or actual taxes due on investment returns.
  • 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. Other investments not considered may have characteristics similar or superior to those being analyzed.
  • Refer to the related documentation sections for more details on terms and definitions, methodology, and data sources.
  • Portfolio optimization is a process of choosing the proportions of various assets to be held in a portfolio in such a way as to make the portfolio better than any other combination according to the selected objective function such as maximizing risk-adjusted return. 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 the total return of assets and assume that all received dividends and distributions are reinvested.
  • Compound annualized growth rate (CAGR) is the annualized geometric mean return of the portfolio. It is calculated from the portfolio start and end balance and is thus impacted by any cashflows.
  • The time-weighted rate of return (TWRR) is a measure of the compound rate of growth in a portfolio. This is calculated from the holding period returns (e.g. monthly returns), and TWRR will thus not be impacted by cashflows. If there are no external cashflows, TWRR will equal CAGR.
  • The money-weighted rate of return (MWRR) is the internal rate of return (IRR) taking into account cashflows. This is the discount rate at which the present value of cash inflows equals the present value of cash outflows.
  • Standard deviation (Stdev) is used to measure the dispersion of returns around the mean and is often used as a measure of risk. A higher standard deviation implies greater the dispersion of data points around the mean.
  • Sharpe Ratio is a measure of risk-adjusted performance of the portfolio, and it is calculated by dividing the mean monthly excess return of the portfolio over the risk-free rate by the standard deviation of excess return, and the displayed value is annualized.
  • Sortino Ratio is a measure of risk-adjusted return which is a modification of the Sharpe Ratio. While the latter is the ratio of average returns in excess of a risk-free rate divided by the standard deviation of those excess returns, the Sortino Ratio has the same denominator divided by the standard deviation of returns below the risk-free rate.
  • Treynor Ratio is a measure of risk-adjusted performance of the portfolio. It is similar to the Sharpe Ratio, but it uses portfolio beta (systematic risk) as the risk metric in the denominator.
  • Calmar Ratio is a measure of risk-adjusted performance of the portfolio. It is calculated as the annualized return over the past 36 months divided by the maximum drawdown over the past 36 months based on monthly returns.
  • Downside deviation measures the downside volatility of the portfolio returns unlike standard deviation, which includes both upside and downside deviations. Downside deviation is calculated based on negative returns that hurt the portfolio performance.
  • Risk-free returns are calculated based on U.S. 3-Month Treasury Bill Rate.
  • Inflation is calculated based on U.S. Consumer Price Index.
  • Correlation measures to what degree the returns of the two assets move in relation to each other. Correlation coefficient is a numerical value between -1 and +1. If one variable goes up by a certain amount, the correlation coefficient indicates which way the other variable moves and by how much. Asset correlations are calculated based on monthly returns.
  • Skewness is a measure of the asymmetry of the probability distribution or returns from a normal Gaussian distribution shape about its mean. Negative skewness is associated with the left (typically negative returns) tail of the distribution extending further than the right tail; and positive skewness is associated with the right (typically positive returns) tail of the distribution extending further than the left tail.
  • Excess kurtosis is a measure of whether a data distribution is peaked or flat relative to a normal distribution. Distributions with high kurtosis tend to have a distinct peak near the mean, decline rather rapidly, and have heavy or fat tails.
  • A drawdown refers to the decline in value of a single investment or an investment portfolio from a relative peak value to a relative trough. A maximum drawdown (Max Drawdown) is the maximum observed loss from a peak to a trough of a portfolio before a new peak is attained. Drawdown values are calculated based on monthly returns.
  • Value at Risk (VaR) measures the scale of loss at a given confidence level. For example, if the 95% confidence one-month VaR is 3%, there is 95% confidence that over the next month the portfolio will not lose more than 3%. Value at Risk can be calculated directly based on historical returns based on a given percentile or analytically based on the mean and standard deviation of the returns.
  • Conditional Value at Risk (CVaR) measures the scale of the expected loss once the specific Value at Risk (VaR) breakpoint has been breached, i.e., it calculates the average tail loss by taking a weighted average between the value at risk and losses exceeding the value at risk.
  • Beta is a measure of systematic risk and measures the volatility of a particular investment relative to the market or its benchmark. Alpha measures the active return of the investment compared to the market benchmark return. R-squared is the percentage of a portfolio's movements that can be explained by movements in the selected benchmark index.
  • Active return is the investment return minus the return of its benchmark. For periods longer than 12 months this is displayed as annualized value, i.e., annualized investment return minus annualized benchmark return.
  • Tracking error, also known as active risk, is the standard deviation of active return. This is displayed as annualized value based on the standard deviation of monthly active returns.
  • Information ratio is the active return divided by the tracking error. It measures whether the investment outperformed its benchmark consistently.
  • Gain/Loss ratio is a measure of downside risk, and it is calculated as the average positive return in up periods divided by the average negative return in down periods.
  • Upside Capture Ratio measures how well the fund performed relative to the benchmark when the market was up, and Downside Capture Ratio measures how well the fund performed relative to the benchmark when the market was down. An upside capture ratio greater than 100 would indicate that the fund outperformed its benchmark when the market was up, and a downside capture ratio below 100 would indicate that the fund lost less than its benchmark when the market was down. To calculate upside capture ratio a new series from the portfolio returns is constructed by dropping all time periods where the benchmark return is less than equal to zero. The up capture is then the quotient of the annualized return of the resulting manager series, divided by the annualized return of the resulting benchmark series. The downside capture ratio is calculated analogously.
  • All risk measures for the portfolio and portfolio assets are calculated based on monthly returns.
  • Invesco QQQ is a paid sponsor of the SRL Analytics Tool, Portfolio Visualizer. The model portfolios are for illustrative purposes only and do not constitute a recommendation or suitability for any investor. Inveso is not affiliated with SRL Global.
  • The annual results for 2026 are based on full calendar months from January to September.
  • The optimization results assume monthly rebalancing of portfolio assets to match the specified allocation.