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 2012 - Sep 2021) Save

Portfolio optimization results for risk parity. The possible range of expected annual portfolio returns for the given period is 3.45% to 16.74%. Refer to the efficient frontier section for additional details.

Portfolio Allocations

Risk Parity
Ticker Name Allocation
VTI Vanguard Total Stock Market ETF 12.32%
VXUS Vanguard Total International Stock ETF 11.68%
VNQ Vanguard Real Estate ETF 9.94%
BND Vanguard Total Bond Market ETF 66.07%
Save portfolio »

Portfolio Performance Summary

Portfolio performance statistics
MetricRisk Parity
Start Balance$10,000
End Balance$17,444
CAGR5.87%
Expected Return6.02%
Stdev5.28%
Best Year14.96%
Worst Year-2.84%
Max. Drawdown -7.75%
Sharpe Ratio (ex-ante)1.00
Sharpe Ratio (ex-post)0.99
Sortino Ratio1.59
US Stock Market Correlation0.79
Results based on historical returns. Expected return is the annualized monthly arithmetic mean return.
   

Trailing Returns

Trailing Returns
NameAnnualized ReturnAnnualized Volatility
3 MonthYTD1 year3 year5 yearFull3 year5 year
Risk Parity-0.32%3.46%8.78%8.06%5.99%5.87%7.22%5.98%
Trailing annualized return and volatility are for full months ending in September 2021 excluding portfolio cashflows.
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 2021 are based on full calendar months from January to September
  • 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
#AssetExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1Vanguard Total Stock Market ETF (VTI)16.74%13.51%1.1090.00%100.00%
2Vanguard Total International Stock ETF (VXUS)8.68%14.14%0.5480.00%100.00%
3Vanguard Real Estate ETF (VNQ)11.51%15.29%0.6770.00%100.00%
4Vanguard Total Bond Market ETF (BND)2.88%3.30%0.6780.00%100.00%
Results based on historical returns. Expected return is the annualized monthly arithmetic mean return. Ex-ante Sharpe Ratio calculated using 3-month treasury bill returns as the risk-free rate.

Asset Correlations

Efficient Frontier Asset Correlations
NameTickerVTIVXUSVNQBND
Vanguard Total Stock Market ETFVTI1.000.860.640.06
Vanguard Total International Stock ETFVXUS0.861.000.580.12
Vanguard Real Estate ETFVNQ0.640.581.000.47
Vanguard Total Bond Market ETFBND0.060.120.471.00
Based on monthly returns from Jan 2012 to Sep 2021
Efficient Frontier Assets
#VTIVXUSVNQBNDExpected Return*Standard Deviation*Sharpe Ratio*
14.40%0.00%0.00%95.60%3.45%3.25%0.863
25.37%0.00%0.00%94.63%3.58%3.25%0.900
36.33%0.00%0.00%93.67%3.71%3.26%0.936
47.30%0.00%0.00%92.70%3.84%3.27%0.969
58.26%0.00%0.00%91.74%3.96%3.29%1.001
69.23%0.00%0.00%90.77%4.09%3.31%1.031
710.20%0.00%0.00%89.80%4.22%3.34%1.059
811.16%0.00%0.00%88.84%4.35%3.37%1.085
912.13%0.00%0.00%87.87%4.47%3.41%1.109
1013.09%0.00%0.00%86.91%4.60%3.46%1.130
1114.06%0.00%0.00%85.94%4.73%3.51%1.150
1215.02%0.00%0.00%84.98%4.86%3.56%1.168
1315.99%0.00%0.00%84.01%4.99%3.61%1.183
1416.96%0.00%0.00%83.04%5.12%3.67%1.198
1517.92%0.00%0.00%82.08%5.25%3.74%1.210
1618.89%0.00%0.00%81.11%5.37%3.80%1.221
1719.85%0.00%0.00%80.15%5.50%3.88%1.230
1820.82%0.00%0.00%79.18%5.63%3.95%1.238
1921.78%0.00%0.00%78.22%5.76%4.03%1.245
2022.75%0.00%0.00%77.25%5.89%4.11%1.251
2123.71%0.00%0.00%76.29%6.02%4.19%1.256
2224.68%0.00%0.00%75.32%6.15%4.27%1.260
2325.65%0.00%0.00%74.35%6.28%4.36%1.263
2426.61%0.00%0.00%73.39%6.41%4.45%1.265
2527.58%0.00%0.00%72.42%6.54%4.54%1.266
2628.54%0.00%0.00%71.46%6.67%4.64%1.267
2729.51%0.00%0.00%70.49%6.80%4.73%1.268
2830.47%0.00%0.00%69.53%6.93%4.83%1.268
2931.44%0.00%0.00%68.56%7.06%4.93%1.267
3032.41%0.00%0.00%67.59%7.20%5.03%1.266
3133.37%0.00%0.00%66.63%7.33%5.13%1.265
3234.34%0.00%0.00%65.66%7.46%5.23%1.264
3335.30%0.00%0.00%64.70%7.59%5.34%1.262
3436.27%0.00%0.00%63.73%7.72%5.44%1.260
3537.23%0.00%0.00%62.77%7.85%5.55%1.258
3638.20%0.00%0.00%61.80%7.98%5.66%1.256
3739.16%0.00%0.00%60.84%8.12%5.77%1.253
3840.13%0.00%0.00%59.87%8.25%5.88%1.251
3941.10%0.00%0.00%58.90%8.38%5.99%1.248
4042.06%0.00%0.00%57.94%8.51%6.10%1.246
4143.03%0.00%0.00%56.97%8.65%6.21%1.243
4243.99%0.00%0.00%56.01%8.78%6.33%1.240
4344.96%0.00%0.00%55.04%8.91%6.44%1.237
4445.92%0.00%0.00%54.08%9.05%6.55%1.234
4546.89%0.00%0.00%53.11%9.18%6.67%1.231
4647.86%0.00%0.00%52.14%9.31%6.79%1.228
4748.82%0.00%0.00%51.18%9.45%6.90%1.225
4849.79%0.00%0.00%50.21%9.58%7.02%1.223
4950.75%0.00%0.00%49.25%9.71%7.14%1.220
5051.72%0.00%0.00%48.28%9.85%7.26%1.217
5152.68%0.00%0.00%47.32%9.98%7.37%1.214
5253.65%0.00%0.00%46.35%10.12%7.49%1.211
5354.61%0.00%0.00%45.39%10.25%7.61%1.208
5455.58%0.00%0.00%44.42%10.39%7.73%1.205
5556.55%0.00%0.00%43.45%10.52%7.85%1.202
5657.51%0.00%0.00%42.49%10.65%7.97%1.200
5758.48%0.00%0.00%41.52%10.79%8.10%1.197
5859.44%0.00%0.00%40.56%10.92%8.22%1.194
5960.41%0.00%0.00%39.59%11.06%8.34%1.191
6061.37%0.00%0.00%38.63%11.20%8.46%1.189
6162.34%0.00%0.00%37.66%11.33%8.58%1.186
6263.31%0.00%0.00%36.69%11.47%8.71%1.184
6364.27%0.00%0.00%35.73%11.60%8.83%1.181
6465.24%0.00%0.00%34.76%11.74%8.95%1.178
6566.20%0.00%0.00%33.80%11.88%9.08%1.176
6667.17%0.00%0.00%32.83%12.01%9.20%1.174
6768.13%0.00%0.00%31.87%12.15%9.32%1.171
6869.10%0.00%0.00%30.90%12.29%9.45%1.169
6970.07%0.00%0.00%29.93%12.42%9.57%1.166
7071.03%0.00%0.00%28.97%12.56%9.70%1.164
7172.00%0.00%0.00%28.00%12.70%9.82%1.162
7272.96%0.00%0.00%27.04%12.83%9.95%1.160
7373.93%0.00%0.00%26.07%12.97%10.07%1.157
7474.89%0.00%0.00%25.11%13.11%10.20%1.155
7575.86%0.00%0.00%24.14%13.25%10.32%1.153
7676.82%0.00%0.00%23.18%13.38%10.45%1.151
7777.79%0.00%0.00%22.21%13.52%10.58%1.149
7878.76%0.00%0.00%21.24%13.66%10.70%1.147
7979.72%0.00%0.00%20.28%13.80%10.83%1.145
8080.69%0.00%0.00%19.31%13.94%10.96%1.143
8181.65%0.00%0.00%18.35%14.08%11.08%1.141
8282.62%0.00%0.00%17.38%14.22%11.21%1.139
8383.58%0.00%0.00%16.42%14.36%11.34%1.137
8484.55%0.00%0.00%15.45%14.49%11.46%1.135
8585.52%0.00%0.00%14.48%14.63%11.59%1.133
8686.48%0.00%0.00%13.52%14.77%11.72%1.132
8787.45%0.00%0.00%12.55%14.91%11.84%1.130
8888.41%0.00%0.00%11.59%15.05%11.97%1.128
8989.38%0.00%0.00%10.62%15.19%12.10%1.126
9090.34%0.00%0.00%9.66%15.33%12.23%1.125
9191.31%0.00%0.00%8.69%15.47%12.35%1.123
9292.27%0.00%0.00%7.73%15.61%12.48%1.121
9393.24%0.00%0.00%6.76%15.75%12.61%1.120
9494.21%0.00%0.00%5.79%15.89%12.74%1.118
9595.17%0.00%0.00%4.83%16.04%12.87%1.116
9696.14%0.00%0.00%3.86%16.18%12.99%1.115
9797.10%0.00%0.00%2.90%16.32%13.12%1.113
9898.07%0.00%0.00%1.93%16.46%13.25%1.112
9999.03%0.00%0.00%0.97%16.60%13.38%1.110
100100.00%0.00%0.00%0.00%16.74%13.51%1.109
*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.
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%8.09%$10,80916.45%18.61%17.63%3.16%
20131.50%4.23%$11,26633.45%14.61%2.31%-2.10%
20140.76%7.69%$12,13312.54%-4.74%30.36%5.82%
20150.73%0.41%$12,1830.36%-4.19%2.42%0.56%
20162.07%4.83%$12,77112.83%4.81%8.60%2.52%
20172.11%8.38%$13,84221.21%27.45%4.91%3.57%
20181.91%-2.84%$13,449-5.21%-14.43%-6.02%-0.12%
20192.29%14.96%$15,46130.67%21.75%28.87%8.83%
20201.36%9.05%$16,86121.03%10.69%-4.68%7.71%
20215.31%3.46%$17,44415.18%6.83%22.15%-1.83%
Annual return for 2021 is from 01/01/2021 to 09/30/2021
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)
201212.53%$10,2535.07%7.33%6.38%0.63%
201220.96%$10,3524.22%4.56%-1.15%0.04%
201230.49%$10,4033.06%-0.54%5.19%-0.51%
201240.69%$10,475-0.64%-2.08%2.86%1.10%
20125-1.86%$10,280-6.23%-10.83%-4.51%0.93%
201261.79%$10,4644.05%5.97%5.52%0.07%
201271.16%$10,5850.88%0.31%2.00%1.23%
201280.74%$10,6642.70%2.60%-0.01%0.16%
201290.64%$10,7322.49%3.41%-1.86%0.18%
201210-0.28%$10,701-1.81%0.81%-0.91%-0.10%
2012110.49%$10,7540.77%2.06%-0.26%0.27%
2012120.52%$10,8091.29%4.88%3.72%-0.88%
201310.86%$10,9035.42%2.40%3.74%-0.69%
201320.50%$10,9571.28%-1.14%1.22%0.54%
201330.93%$11,0593.95%0.93%2.87%0.08%
201341.95%$11,2751.61%3.50%6.73%1.01%
20135-1.95%$11,0552.44%-3.30%-5.98%-1.93%
20136-1.88%$10,847-1.43%-3.57%-1.98%-1.65%
201371.59%$11,0195.75%4.62%0.90%0.38%
20138-1.86%$10,814-3.03%-1.95%-6.98%-0.86%
201392.44%$11,0783.90%7.51%3.49%1.11%
2013101.97%$11,2964.27%3.67%4.52%0.86%
201311-0.37%$11,2552.70%0.13%-5.25%-0.29%
2013120.10%$11,2662.73%1.52%0.10%-0.64%
201410.43%$11,315-3.17%-5.40%4.28%1.55%
201422.07%$11,5484.87%5.59%5.07%0.47%
201430.06%$11,5550.51%0.49%0.49%-0.17%
201441.01%$11,6720.06%1.26%3.29%0.80%
201451.42%$11,8372.10%1.93%2.40%1.05%
201460.71%$11,9212.62%1.89%1.13%0.08%
20147-0.62%$11,847-1.99%-1.73%0.08%-0.28%
201481.70%$12,0494.15%1.16%3.04%1.14%
20149-1.82%$11,830-2.10%-5.01%-6.04%-0.57%
2014101.79%$12,0422.75%-0.08%9.94%0.72%
2014110.99%$12,1612.48%-0.51%2.00%0.83%
201412-0.23%$12,133-0.04%-3.87%1.88%0.06%
201511.96%$12,372-2.74%0.27%6.85%2.40%
201520.15%$12,3915.74%5.78%-3.67%-1.31%
201530.22%$12,417-1.16%-1.49%1.74%0.55%
20154-0.16%$12,3980.62%4.81%-5.85%-0.32%
20155-0.30%$12,3601.30%-0.91%-0.30%-0.50%
20156-1.72%$12,147-1.67%-2.73%-4.68%-1.11%
201571.30%$12,3051.70%-0.56%5.77%0.88%
20158-2.41%$12,009-6.09%-7.43%-6.29%-0.25%
201590.03%$12,012-2.92%-3.85%3.05%0.81%
2015102.30%$12,2887.91%6.25%5.76%0.03%
201511-0.40%$12,2390.60%-1.32%-0.63%-0.39%
201512-0.45%$12,183-2.13%-2.17%1.82%-0.18%
20161-0.89%$12,075-5.72%-5.45%-3.44%1.20%
201620.24%$12,103-0.01%-2.46%-0.36%0.85%
201633.47%$12,5247.11%8.33%10.48%0.88%
201640.37%$12,5700.66%2.16%-2.35%0.40%
201650.32%$12,6101.73%-0.98%2.25%-0.01%
201661.95%$12,8560.27%-0.90%6.92%2.02%
201671.84%$13,0923.98%4.52%4.26%0.60%
20168-0.50%$13,0260.21%0.45%-3.76%-0.31%
201690.12%$13,0410.21%1.70%-1.82%0.11%
201610-1.68%$12,822-2.19%-1.91%-5.74%-0.94%
201611-1.55%$12,6234.49%-2.01%-1.68%-2.57%
2016121.17%$12,7711.98%1.96%4.82%0.33%
201710.81%$12,8741.86%4.08%-0.19%0.19%
201721.37%$13,0513.69%1.34%3.51%0.62%
201730.09%$13,0620.06%3.00%-2.42%-0.04%
201740.92%$13,1831.06%2.05%0.24%0.80%
201750.87%$13,2971.01%2.96%-0.72%0.71%
201760.45%$13,3560.95%0.63%2.23%0.05%
201771.01%$13,4921.88%3.37%1.24%0.40%
201780.62%$13,5760.15%0.54%-0.26%0.86%
201790.20%$13,6032.44%1.88%-0.11%-0.47%
2017100.38%$13,6542.17%2.03%-1.07%-0.03%
2017110.64%$13,7423.03%0.63%2.66%-0.11%
2017120.73%$13,8421.16%2.07%-0.14%0.54%
201810.07%$13,8525.23%5.72%-4.25%-1.24%
20182-2.52%$13,502-3.76%-5.24%-7.68%-1.04%
201830.55%$13,577-1.95%-0.38%3.88%0.69%
20184-0.37%$13,5260.45%0.46%0.82%-0.85%
201850.96%$13,6562.72%-1.64%3.68%0.68%
201860.23%$13,6870.70%-2.14%4.20%-0.04%
201870.74%$13,7893.32%2.55%0.60%-0.04%
201880.84%$13,9053.43%-2.40%2.58%0.67%
20189-0.57%$13,8250.20%0.21%-2.64%-0.55%
201810-2.77%$13,442-7.41%-8.56%-2.93%-0.86%
2018111.33%$13,6202.01%1.68%4.67%0.64%
201812-1.26%$13,449-9.16%-4.93%-7.96%1.87%
201913.86%$13,9688.54%7.67%11.85%1.11%
201920.64%$14,0573.56%1.63%0.70%-0.09%
201931.96%$14,3341.42%0.77%4.21%1.94%
201940.78%$14,4453.93%2.77%-0.16%-0.02%
20195-0.21%$14,415-6.45%-5.42%0.14%1.83%
201962.52%$14,7787.08%5.77%1.54%1.25%
201970.21%$14,8091.41%-1.99%1.70%0.15%
201981.69%$15,060-2.08%-2.17%3.75%2.77%
201990.35%$15,1131.78%2.73%1.93%-0.57%
2019100.98%$15,2612.11%3.43%1.13%0.31%
2019110.43%$15,3263.79%0.99%-1.30%-0.04%
2019120.88%$15,4612.80%4.38%0.76%-0.07%
202011.03%$15,620-0.06%-3.39%1.23%1.98%
20202-1.35%$15,409-8.00%-6.60%-7.03%1.67%
20203-6.49%$14,409-13.91%-16.26%-19.42%-1.43%
202045.22%$15,16113.13%7.60%8.96%2.76%
202051.86%$15,4445.40%5.01%1.73%0.67%
202061.46%$15,6692.29%4.24%2.41%0.67%
202072.51%$16,0635.74%4.15%3.64%1.45%
202080.81%$16,1947.10%4.43%0.44%-0.94%
20209-0.98%$16,035-3.54%-1.82%-2.68%-0.10%
202010-1.17%$15,847-1.95%-2.30%-3.00%-0.56%
2020114.69%$16,59011.80%12.62%9.67%1.21%
2020121.63%$16,8614.68%5.86%2.72%0.15%
20211-0.58%$16,763-0.33%0.25%0.04%-0.86%
20212-0.03%$16,7593.14%2.30%3.43%-1.55%
202130.34%$16,8163.65%1.87%5.15%-1.27%
202142.30%$17,2025.04%2.78%7.86%0.87%
202150.60%$17,3050.46%3.07%0.81%0.15%
202161.12%$17,4992.48%-0.34%2.64%0.90%
202171.29%$17,7251.74%-1.13%4.42%1.17%
202180.61%$17,8342.86%1.46%2.15%-0.19%
20219-2.19%$17,444-4.46%-3.45%-5.68%-1.01%
Portfolio return and risk metrics
MetricRisk Parity
Arithmetic Mean (monthly)0.49%
Arithmetic Mean (annualized)6.02%
Geometric Mean (monthly)0.48%
Geometric Mean (annualized)5.87%
Volatility (monthly)1.52%
Volatility (annualized)5.28%
Downside Deviation (monthly)0.93%
Max. Drawdown-7.75%
US Market Correlation0.79
Beta(*)0.31
Alpha (annualized)1.07%
R262.75%
Sharpe Ratio0.99
Sortino Ratio1.59
Treynor Ratio (%)17.00
Calmar Ratio1.04
Active Return-9.70%
Tracking Error9.87%
Information Ratio-0.98
Skewness-0.60
Excess Kurtosis3.85
Historical Value-at-Risk (5%)-1.89%
Analytical Value-at-Risk (5%)-2.01%
Conditional Value-at-Risk (5%)-3.05%
Upside Capture Ratio (%)30.65
Downside Capture Ratio (%)27.07
Safe Withdrawal Rate13.42%
Perpetual Withdrawal Rate3.93%
Positive Periods85 out of 117 (72.65%)
Gain/Loss Ratio0.90
* US stock market is used as the benchmark for calculations. Value-at-risk metrics are based on monthly values.

Drawdowns for Historical Market Stress Periods

Drawdowns for Historical Market Stress Periods
Stress PeriodStartEndRisk Parity
COVID-19 StartJan 2020Mar 2020-7.75%

Drawdowns for Risk Parity

Drawdowns for Risk Parity (worst 10)
RankStartEndLengthRecovery ByRecovery TimeUnderwater PeriodDrawdown
1Feb 2020Mar 20202 monthsJun 20203 months5 months-7.75%
2May 2013Aug 20134 monthsOct 20132 months6 months-4.08%
3Aug 2016Nov 20164 monthsApr 20175 months9 months-3.58%
4Sep 2018Oct 20182 monthsJan 20193 months5 months-3.33%
5Apr 2015Aug 20155 monthsMar 20167 months1 year-3.29%
6Feb 2018Feb 20181 monthAug 20186 months7 months-2.52%
7Sep 2021Sep 20211 month-2.19%
8Sep 2020Oct 20202 monthsNov 20201 month3 months-2.14%
9May 2012May 20121 monthJul 20122 months3 months-1.86%
10Sep 2014Sep 20141 monthNov 20142 months3 months-1.82%
Worst 10 drawdowns included above

Portfolio Assets

Performance statistics for portfolio components
TickerNameCAGRStdevBest YearWorst YearMax. DrawdownSharpe RatioSortino RatioUS Mkt Correlation
VTIVanguard Total Stock Market ETF15.70%13.51%33.45%-5.21%-20.84%1.111.791.00
VXUSVanguard Total International Stock ETF7.60%14.14%27.45%-14.43%-25.54%0.550.810.85
VNQVanguard Real Estate ETF10.22%15.29%30.36%-6.02%-25.08%0.681.010.64
BNDVanguard Total Bond Market ETF2.82%3.30%8.83%-2.10%-4.01%0.681.140.06

Monthly Correlations

Correlations for the portfolio assets
TickerNameVTIVXUSVNQBNDRisk Parity
VTIVanguard Total Stock Market ETF1.000.860.640.060.79
VXUSVanguard Total International Stock ETF0.861.000.580.120.80
VNQVanguard Real Estate ETF0.640.581.000.470.87
BNDVanguard Total Bond Market ETF0.060.120.471.000.61

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 year5.74%16.70%-2.84%
3 years5.12%8.73%2.91%
5 years4.99%6.78%3.02%
7 years5.19%5.94%3.85%