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 - Jun 2021) Save

Portfolio optimization results for risk parity. The possible range of expected annual portfolio returns for the given period is 3.59% to 17.20%. Refer to the efficient frontier section for additional details.

Portfolio Allocations

Risk Parity
Ticker Name Allocation
VTI Vanguard Total Stock Market ETF 12.30%
VXUS Vanguard Total International Stock ETF 11.52%
VNQ Vanguard Real Estate ETF 9.91%
BND Vanguard Total Bond Market ETF 66.27%
Save portfolio »

Portfolio Performance Summary

Portfolio performance statistics
MetricRisk Parity
Start Balance$10,000
End Balance$17,478
CAGR6.05%
Expected Return6.20%
Stdev5.25%
Best Year14.93%
Worst Year-2.81%
Max. Drawdown -7.70%
Sharpe Ratio (ex-ante)1.03
Sharpe Ratio (ex-post)1.03
Sortino Ratio1.67
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 Parity4.05%3.76%11.60%8.52%6.34%6.05%7.02%5.87%
Trailing annualized return and volatility are for full months ending in June 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 June
  • 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)17.20%13.55%1.1340.00%100.00%
2Vanguard Total International Stock ETF (VXUS)9.27%14.25%0.5810.00%100.00%
3Vanguard Real Estate ETF (VNQ)11.73%15.30%0.6880.00%100.00%
4Vanguard Total Bond Market ETF (BND)2.96%3.30%0.6970.00%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 ETFVTI1.000.860.640.04
Vanguard Total International Stock ETFVXUS0.861.000.580.11
Vanguard Real Estate ETFVNQ0.640.581.000.46
Vanguard Total Bond Market ETFBND0.040.110.461.00
Based on monthly returns from Jan 2012 to Jun 2021
Efficient Frontier Assets
#VTIVXUSVNQBNDExpected Return*Standard Deviation*Sharpe Ratio*
14.70%0.00%0.00%95.30%3.59%3.24%0.901
25.67%0.00%0.00%94.33%3.72%3.24%0.939
36.63%0.00%0.00%93.37%3.85%3.25%0.975
47.59%0.00%0.00%92.41%3.98%3.26%1.010
58.56%0.00%0.00%91.44%4.11%3.28%1.042
69.52%0.00%0.00%90.48%4.24%3.31%1.073
710.48%0.00%0.00%89.52%4.37%3.33%1.101
811.44%0.00%0.00%88.56%4.50%3.37%1.127
912.41%0.00%0.00%87.59%4.63%3.41%1.151
1013.37%0.00%0.00%86.63%4.76%3.45%1.173
1114.33%0.00%0.00%85.67%4.90%3.50%1.193
1215.29%0.00%0.00%84.71%5.03%3.55%1.210
1316.26%0.00%0.00%83.74%5.16%3.61%1.226
1417.22%0.00%0.00%82.78%5.29%3.67%1.240
1518.18%0.00%0.00%81.82%5.42%3.73%1.253
1619.14%0.00%0.00%80.86%5.55%3.80%1.263
1720.11%0.00%0.00%79.89%5.69%3.87%1.272
1821.07%0.00%0.00%78.93%5.82%3.95%1.280
1922.03%0.00%0.00%77.97%5.95%4.03%1.287
2022.99%0.00%0.00%77.01%6.08%4.11%1.292
2123.96%0.00%0.00%76.04%6.22%4.19%1.297
2224.92%0.00%0.00%75.08%6.35%4.27%1.300
2325.88%0.00%0.00%74.12%6.48%4.36%1.303
2426.84%0.00%0.00%73.16%6.62%4.45%1.305
2527.81%0.00%0.00%72.19%6.75%4.54%1.306
2628.77%0.00%0.00%71.23%6.88%4.64%1.306
2729.73%0.00%0.00%70.27%7.02%4.73%1.306
2830.69%0.00%0.00%69.31%7.15%4.83%1.306
2931.66%0.00%0.00%68.34%7.28%4.93%1.305
3032.62%0.00%0.00%67.38%7.42%5.03%1.304
3133.58%0.00%0.00%66.42%7.55%5.14%1.302
3234.54%0.00%0.00%65.46%7.69%5.24%1.301
3335.51%0.00%0.00%64.49%7.82%5.34%1.299
3436.47%0.00%0.00%63.53%7.96%5.45%1.296
3537.43%0.00%0.00%62.57%8.09%5.56%1.294
3638.40%0.00%0.00%61.60%8.23%5.67%1.291
3739.36%0.00%0.00%60.64%8.36%5.78%1.289
3840.32%0.00%0.00%59.68%8.50%5.89%1.286
3941.28%0.00%0.00%58.72%8.63%6.00%1.283
4042.25%0.00%0.00%57.75%8.77%6.11%1.280
4143.21%0.00%0.00%56.79%8.90%6.22%1.277
4244.17%0.00%0.00%55.83%9.04%6.34%1.274
4345.13%0.00%0.00%54.87%9.18%6.45%1.271
4446.10%0.00%0.00%53.90%9.31%6.57%1.267
4547.06%0.00%0.00%52.94%9.45%6.68%1.264
4648.02%0.00%0.00%51.98%9.59%6.80%1.261
4748.98%0.00%0.00%51.02%9.72%6.92%1.258
4849.95%0.00%0.00%50.05%9.86%7.03%1.255
4950.91%0.00%0.00%49.09%10.00%7.15%1.251
5051.87%0.00%0.00%48.13%10.13%7.27%1.248
5152.83%0.00%0.00%47.17%10.27%7.39%1.245
5253.80%0.00%0.00%46.20%10.41%7.51%1.242
5354.76%0.00%0.00%45.24%10.55%7.63%1.239
5455.72%0.00%0.00%44.28%10.68%7.75%1.236
5556.68%0.00%0.00%43.32%10.82%7.87%1.233
5657.65%0.00%0.00%42.35%10.96%7.99%1.230
5758.61%0.00%0.00%41.39%11.10%8.11%1.227
5859.57%0.00%0.00%40.43%11.24%8.24%1.224
5960.53%0.00%0.00%39.47%11.38%8.36%1.221
6061.50%0.00%0.00%38.50%11.52%8.48%1.218
6162.46%0.00%0.00%37.54%11.65%8.60%1.216
6263.42%0.00%0.00%36.58%11.79%8.73%1.213
6364.38%0.00%0.00%35.62%11.93%8.85%1.210
6465.35%0.00%0.00%34.65%12.07%8.97%1.207
6566.31%0.00%0.00%33.69%12.21%9.10%1.205
6667.27%0.00%0.00%32.73%12.35%9.22%1.202
6768.23%0.00%0.00%31.77%12.49%9.35%1.200
6869.20%0.00%0.00%30.80%12.63%9.47%1.197
6970.16%0.00%0.00%29.84%12.77%9.60%1.195
7071.12%0.00%0.00%28.88%12.91%9.72%1.192
7172.09%0.00%0.00%27.91%13.05%9.85%1.190
7273.05%0.00%0.00%26.95%13.19%9.97%1.187
7374.01%0.00%0.00%25.99%13.33%10.10%1.185
7474.97%0.00%0.00%25.03%13.48%10.23%1.183
7575.94%0.00%0.00%24.06%13.62%10.35%1.180
7676.90%0.00%0.00%23.10%13.76%10.48%1.178
7777.86%0.00%0.00%22.14%13.90%10.60%1.176
7878.82%0.00%0.00%21.18%14.04%10.73%1.174
7979.79%0.00%0.00%20.21%14.18%10.86%1.172
8080.75%0.00%0.00%19.25%14.33%10.98%1.170
8181.71%0.00%0.00%18.29%14.47%11.11%1.168
8282.67%0.00%0.00%17.33%14.61%11.24%1.166
8383.64%0.00%0.00%16.36%14.75%11.37%1.164
8484.60%0.00%0.00%15.40%14.90%11.49%1.162
8585.56%0.00%0.00%14.44%15.04%11.62%1.160
8686.52%0.00%0.00%13.48%15.18%11.75%1.158
8787.49%0.00%0.00%12.51%15.32%11.88%1.156
8888.45%0.00%0.00%11.55%15.47%12.00%1.154
8989.41%0.00%0.00%10.59%15.61%12.13%1.152
9090.37%0.00%0.00%9.63%15.75%12.26%1.150
9191.34%0.00%0.00%8.66%15.90%12.39%1.149
9292.30%0.00%0.00%7.70%16.04%12.52%1.147
9393.26%0.00%0.00%6.74%16.19%12.64%1.145
9494.22%0.00%0.00%5.78%16.33%12.77%1.144
9595.19%0.00%0.00%4.81%16.48%12.90%1.142
9696.15%0.00%0.00%3.85%16.62%13.03%1.140
9797.11%0.00%0.00%2.89%16.76%13.16%1.139
9898.07%0.00%0.00%1.93%16.91%13.29%1.137
9999.04%0.00%0.00%0.96%17.05%13.42%1.136
100100.00%0.00%0.00%0.00%17.20%13.55%1.134
*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%8.06%$10,80616.45%18.61%17.63%3.16%
20131.50%4.20%$11,26033.45%14.61%2.31%-2.10%
20140.76%7.70%$12,12712.54%-4.74%30.36%5.82%
20150.73%0.42%$12,1780.36%-4.19%2.42%0.56%
20162.07%4.82%$12,76512.83%4.81%8.60%2.52%
20172.11%8.34%$13,83021.21%27.45%4.91%3.57%
20181.91%-2.81%$13,441-5.21%-14.43%-6.02%-0.12%
20192.29%14.93%$15,44730.67%21.75%28.87%8.83%
20201.36%9.05%$16,84521.03%10.69%-4.68%7.71%
20214.31%3.76%$17,47815.21%10.30%21.41%-1.78%
Annual return for 2021 is from 01/01/2021 to 06/30/2021
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)
201212.52%$10,2525.07%7.33%6.38%0.63%
201220.96%$10,3504.22%4.56%-1.15%0.04%
201230.49%$10,4013.06%-0.54%5.19%-0.51%
201240.70%$10,474-0.64%-2.08%2.86%1.10%
20125-1.84%$10,281-6.23%-10.83%-4.51%0.93%
201261.78%$10,4634.05%5.97%5.52%0.07%
201271.16%$10,5850.88%0.31%2.00%1.23%
201280.74%$10,6632.70%2.60%-0.01%0.16%
201290.64%$10,7302.49%3.41%-1.86%0.18%
201210-0.29%$10,700-1.81%0.81%-0.91%-0.10%
2012110.49%$10,7520.77%2.06%-0.26%0.27%
2012120.51%$10,8061.29%4.88%3.72%-0.88%
201310.86%$10,8995.42%2.40%3.74%-0.69%
201320.50%$10,9531.28%-1.14%1.22%0.54%
201330.93%$11,0553.95%0.93%2.87%0.08%
201341.94%$11,2701.61%3.50%6.73%1.01%
20135-1.95%$11,0502.44%-3.30%-5.98%-1.93%
20136-1.87%$10,843-1.43%-3.57%-1.98%-1.65%
201371.58%$11,0145.75%4.62%0.90%0.38%
20138-1.86%$10,810-3.03%-1.95%-6.98%-0.86%
201392.43%$11,0723.90%7.51%3.49%1.11%
2013101.96%$11,2904.27%3.67%4.52%0.86%
201311-0.37%$11,2482.70%0.13%-5.25%-0.29%
2013120.10%$11,2602.73%1.52%0.10%-0.64%
201410.44%$11,309-3.17%-5.40%4.28%1.55%
201422.06%$11,5414.87%5.59%5.07%0.47%
201430.05%$11,5480.51%0.49%0.49%-0.17%
201441.01%$11,6640.06%1.26%3.29%0.80%
201451.42%$11,8302.10%1.93%2.40%1.05%
201460.71%$11,9132.62%1.89%1.13%0.08%
20147-0.62%$11,839-1.99%-1.73%0.08%-0.28%
201481.70%$12,0414.15%1.16%3.04%1.14%
20149-1.81%$11,823-2.10%-5.01%-6.04%-0.57%
2014101.79%$12,0352.75%-0.08%9.94%0.72%
2014111.00%$12,1552.48%-0.51%2.00%0.83%
201412-0.23%$12,127-0.04%-3.87%1.88%0.06%
201511.97%$12,366-2.74%0.27%6.85%2.40%
201520.14%$12,3835.74%5.78%-3.67%-1.31%
201530.22%$12,410-1.16%-1.49%1.74%0.55%
20154-0.17%$12,3900.62%4.81%-5.85%-0.32%
20155-0.30%$12,3521.30%-0.91%-0.30%-0.50%
20156-1.72%$12,140-1.67%-2.73%-4.68%-1.11%
201571.30%$12,2981.70%-0.56%5.77%0.88%
20158-2.39%$12,003-6.09%-7.43%-6.29%-0.25%
201590.04%$12,008-2.92%-3.85%3.05%0.81%
2015102.28%$12,2827.91%6.25%5.76%0.03%
201511-0.40%$12,2330.60%-1.32%-0.63%-0.39%
201512-0.45%$12,178-2.13%-2.17%1.82%-0.18%
20161-0.88%$12,071-5.72%-5.45%-3.44%1.20%
201620.24%$12,100-0.01%-2.46%-0.36%0.85%
201633.46%$12,5197.11%8.33%10.48%0.88%
201640.36%$12,5640.66%2.16%-2.35%0.40%
201650.32%$12,6041.73%-0.98%2.25%-0.01%
201661.96%$12,8510.27%-0.90%6.92%2.02%
201671.83%$13,0863.98%4.52%4.26%0.60%
20168-0.50%$13,0200.21%0.45%-3.76%-0.31%
201690.12%$13,0350.21%1.70%-1.82%0.11%
201610-1.68%$12,816-2.19%-1.91%-5.74%-0.94%
201611-1.55%$12,6174.49%-2.01%-1.68%-2.57%
2016121.17%$12,7651.98%1.96%4.82%0.33%
201710.80%$12,8671.86%4.08%-0.19%0.19%
201721.37%$13,0433.69%1.34%3.51%0.62%
201730.09%$13,0540.06%3.00%-2.42%-0.04%
201740.92%$13,1741.06%2.05%0.24%0.80%
201750.86%$13,2881.01%2.96%-0.72%0.71%
201760.44%$13,3470.95%0.63%2.23%0.05%
201771.01%$13,4811.88%3.37%1.24%0.40%
201780.62%$13,5650.15%0.54%-0.26%0.86%
201790.20%$13,5922.44%1.88%-0.11%-0.47%
2017100.38%$13,6432.17%2.03%-1.07%-0.03%
2017110.64%$13,7303.03%0.63%2.66%-0.11%
2017120.73%$13,8301.16%2.07%-0.14%0.54%
201810.06%$13,8385.23%5.72%-4.25%-1.24%
20182-2.51%$13,490-3.76%-5.24%-7.68%-1.04%
201830.56%$13,565-1.95%-0.38%3.88%0.69%
20184-0.38%$13,5140.45%0.46%0.82%-0.85%
201850.96%$13,6442.72%-1.64%3.68%0.68%
201860.23%$13,6750.70%-2.14%4.20%-0.04%
201870.74%$13,7763.32%2.55%0.60%-0.04%
201880.84%$13,8923.43%-2.40%2.58%0.67%
20189-0.57%$13,8130.20%0.21%-2.64%-0.55%
201810-2.76%$13,432-7.41%-8.56%-2.93%-0.86%
2018111.33%$13,6102.01%1.68%4.67%0.64%
201812-1.24%$13,441-9.16%-4.93%-7.96%1.87%
201913.85%$13,9578.54%7.67%11.85%1.11%
201920.64%$14,0463.56%1.63%0.70%-0.09%
201931.97%$14,3221.42%0.77%4.21%1.94%
201940.77%$14,4333.93%2.77%-0.16%-0.02%
20195-0.19%$14,405-6.45%-5.42%0.14%1.83%
201962.51%$14,7677.08%5.77%1.54%1.25%
201970.21%$14,7981.41%-1.99%1.70%0.15%
201981.70%$15,050-2.08%-2.17%3.75%2.77%
201990.35%$15,1021.78%2.73%1.93%-0.57%
2019100.97%$15,2492.11%3.43%1.13%0.31%
2019110.42%$15,3133.79%0.99%-1.30%-0.04%
2019120.88%$15,4472.80%4.38%0.76%-0.07%
202011.04%$15,607-0.06%-3.39%1.23%1.98%
20202-1.34%$15,399-8.00%-6.60%-7.03%1.67%
20203-6.46%$14,405-13.91%-16.26%-19.42%-1.43%
202045.21%$15,15513.13%7.60%8.96%2.76%
202051.86%$15,4365.40%5.01%1.73%0.67%
202061.45%$15,6612.29%4.24%2.41%0.67%
202072.51%$16,0535.74%4.15%3.64%1.45%
202080.80%$16,1837.10%4.43%0.44%-0.94%
20209-0.98%$16,025-3.54%-1.82%-2.68%-0.10%
202010-1.17%$15,837-1.95%-2.30%-3.00%-0.56%
2020114.67%$16,57611.80%12.62%9.67%1.21%
2020121.62%$16,8454.68%5.86%2.72%0.15%
20211-0.58%$16,747-0.33%0.25%0.04%-0.86%
20212-0.03%$16,7423.14%2.30%3.43%-1.55%
202130.33%$16,7973.65%1.87%5.15%-1.27%
202142.29%$17,1825.04%2.78%7.86%0.87%
202150.59%$17,2840.46%3.07%0.81%0.15%
202161.12%$17,4782.48%-0.34%2.64%0.90%
Portfolio return and risk metrics
MetricRisk Parity
Arithmetic Mean (monthly)0.50%
Arithmetic Mean (annualized)6.20%
Geometric Mean (monthly)0.49%
Geometric Mean (annualized)6.05%
Volatility (monthly)1.52%
Volatility (annualized)5.25%
Downside Deviation (monthly)0.92%
Max. Drawdown-7.70%
US Market Correlation0.79
Beta(*)0.30
Alpha (annualized)1.19%
R261.91%
Sharpe Ratio1.03
Sortino Ratio1.67
Treynor Ratio (%)17.76
Calmar Ratio1.11
Active Return-9.97%
Tracking Error9.96%
Information Ratio-1.00
Skewness-0.60
Excess Kurtosis4.01
Historical Value-at-Risk (5%)-1.86%
Analytical Value-at-Risk (5%)-1.98%
Conditional Value-at-Risk (5%)-2.99%
Upside Capture Ratio (%)30.34
Downside Capture Ratio (%)25.84
Safe Withdrawal Rate13.41%
Perpetual Withdrawal Rate4.06%
Positive Periods83 out of 114 (72.81%)
Gain/Loss Ratio0.92
* 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
1Feb 2020Mar 20202 monthsJun 20203 months5 months-7.70%
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-3.32%
5Apr 2015Aug 20155 monthsMar 20167 months1 year-3.28%
6Feb 2018Feb 20181 monthAug 20186 months7 months-2.51%
7Sep 2020Oct 20202 monthsNov 20201 month3 months-2.14%
8May 2012May 20121 monthJul 20122 months3 months-1.84%
9Sep 2014Sep 20141 monthNov 20142 months3 months-1.81%
10Jul 2014Jul 20141 monthAug 20141 month2 months-0.62%
Worst 10 drawdowns included above

Portfolio Assets

Performance statistics for portfolio components
TickerNameCAGRStdevBest YearWorst YearMax. DrawdownSharpe RatioSortino RatioUS Mkt Correlation
VTIVanguard Total Stock Market ETF16.15%13.55%33.45%-5.21%-20.84%1.131.841.00
VXUSVanguard Total International Stock ETF8.17%14.25%27.45%-14.43%-25.54%0.580.860.85
VNQVanguard Real Estate ETF10.43%15.30%30.36%-6.02%-25.08%0.691.030.64
BNDVanguard Total Bond Market ETF2.90%3.30%8.83%-2.10%-4.01%0.701.180.04

Monthly Correlations

Correlations for the portfolio assets
TickerNameVTIVXUSVNQBNDRisk Parity
VTIVanguard Total Stock Market ETF1.000.860.640.040.79
VXUSVanguard Total International Stock ETF0.861.000.580.110.80
VNQVanguard Real Estate ETF0.640.581.000.460.87
BNDVanguard Total Bond Market ETF0.040.110.461.000.60

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 year5.61%16.61%-2.81%
3 years4.99%8.52%2.90%
5 years4.91%6.77%3.03%
7 years5.13%5.93%3.85%