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 results with goal to maximize Sharpe ratio. The possible range of expected annual portfolio returns based on provided parameters is 1.85% to 4.97%. Refer to the efficient frontier section for additional details. Historical values from Jan 2012 to Oct 2022 were used for non-user supplied parameters based on the selected time period and available data for the portfolio assets.
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.
Notes on results:
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.
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.
Risk-free returns are calculated based on the Federal Reserve 3-Month Treasury Bill (secondary market) rates.
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.
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. If the 5% VaR is -3% the portfolio return is expected to be greater than -3% 95% of the time and less than -3% 5% of the time. 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.
The results are based on combining user provided forecast model parameters with historical monthly return statistics of the portfolio assets.
Monte Carlo method was used to resample the efficient frontier inputs to mitigate the impact of input estimation errors.
Efficient Frontier Assets
#
Asset
Expected Return
Standard Deviation
Sharpe Ratio
Min. Weight
Max. Weight
1
Vanguard Total Stock Market ETF (VTI)
5.50%
14.70%
0.154
0.00%
100.00%
2
Vanguard Total International Stock ETF (VXUS)
5.70%
14.54%
0.169
0.00%
100.00%
3
Vanguard Total Bond Market ETF (BND)
1.80%
4.04%
-0.355
0.00%
100.00%
4
Vanguard Real Estate ETF (VNQ)
5.00%
16.55%
0.106
0.00%
100.00%
Results based on the provided capital market expectations. Expected return is the annualized monthly arithmetic mean return. Ex-ante Sharpe Ratio calculated using the current 3-month treasury bill return as the risk-free rate.
Asset Correlations
Efficient Frontier Asset Correlations
Name
Ticker
VTI
VXUS
BND
VNQ
Vanguard Total Stock Market ETF
VTI
1.00
0.86
0.26
0.70
Vanguard Total International Stock ETF
VXUS
0.86
1.00
0.28
0.63
Vanguard Total Bond Market ETF
BND
0.26
0.28
1.00
0.50
Vanguard Real Estate ETF
VNQ
0.70
0.63
0.50
1.00
Based on monthly returns from Jan 2012 to Oct 2022
Note: You can hover over any of the data points on the chart for more information.
Efficient Frontier Assets
#
VTI
VXUS
BND
VNQ
Expected Return *
Standard Deviation *
Sharpe Ratio *
1
0.88%
0.50%
98.62%
0.00%
1.85%
4.05%
-0.342
2
1.36%
0.84%
97.74%
0.06%
1.89%
4.05%
-0.334
3
1.78%
1.22%
96.86%
0.15%
1.92%
4.07%
-0.324
4
2.18%
1.57%
95.98%
0.27%
1.95%
4.09%
-0.315
5
2.60%
1.93%
95.08%
0.39%
1.98%
4.11%
-0.305
6
2.99%
2.30%
94.18%
0.53%
2.02%
4.13%
-0.295
7
3.36%
2.67%
93.28%
0.69%
2.05%
4.16%
-0.285
8
3.70%
3.04%
92.38%
0.87%
2.08%
4.19%
-0.275
9
4.01%
3.42%
91.49%
1.07%
2.12%
4.23%
-0.265
10
4.31%
3.80%
90.61%
1.28%
2.15%
4.27%
-0.255
11
4.59%
4.19%
89.72%
1.50%
2.18%
4.31%
-0.245
12
4.87%
4.56%
88.83%
1.73%
2.21%
4.36%
-0.235
13
5.16%
4.94%
87.94%
1.96%
2.25%
4.40%
-0.225
14
5.44%
5.32%
87.04%
2.20%
2.28%
4.45%
-0.215
15
5.71%
5.70%
86.14%
2.45%
2.31%
4.51%
-0.205
16
5.97%
6.08%
85.25%
2.70%
2.34%
4.56%
-0.196
17
6.23%
6.47%
84.35%
2.96%
2.38%
4.62%
-0.186
18
6.48%
6.85%
83.45%
3.22%
2.41%
4.68%
-0.177
19
6.73%
7.24%
82.56%
3.48%
2.44%
4.74%
-0.168
20
6.97%
7.62%
81.66%
3.75%
2.48%
4.81%
-0.159
21
7.22%
8.00%
80.77%
4.02%
2.51%
4.87%
-0.150
22
7.47%
8.37%
79.87%
4.29%
2.54%
4.94%
-0.141
23
7.72%
8.75%
78.97%
4.56%
2.57%
5.01%
-0.133
24
7.96%
9.12%
78.08%
4.84%
2.61%
5.08%
-0.124
25
8.21%
9.49%
77.18%
5.12%
2.64%
5.16%
-0.116
26
8.45%
9.86%
76.28%
5.40%
2.67%
5.23%
-0.108
27
8.70%
10.24%
75.39%
5.68%
2.70%
5.31%
-0.101
28
8.95%
10.61%
74.49%
5.96%
2.74%
5.38%
-0.093
29
9.19%
10.98%
73.59%
6.24%
2.77%
5.46%
-0.086
30
9.43%
11.35%
72.69%
6.52%
2.80%
5.54%
-0.079
31
9.67%
11.72%
71.80%
6.81%
2.83%
5.62%
-0.072
32
9.91%
12.09%
70.90%
7.10%
2.87%
5.71%
-0.065
33
10.14%
12.45%
70.00%
7.40%
2.90%
5.79%
-0.059
34
10.38%
12.82%
69.10%
7.70%
2.93%
5.87%
-0.052
35
10.61%
13.19%
68.21%
8.00%
2.96%
5.96%
-0.046
36
10.85%
13.55%
67.31%
8.29%
3.00%
6.05%
-0.040
37
11.08%
13.92%
66.41%
8.59%
3.03%
6.13%
-0.034
38
11.31%
14.28%
65.51%
8.89%
3.06%
6.22%
-0.028
39
11.55%
14.65%
64.61%
9.19%
3.09%
6.31%
-0.023
40
11.78%
15.02%
63.71%
9.49%
3.13%
6.40%
-0.018
41
12.02%
15.38%
62.81%
9.78%
3.16%
6.49%
-0.012
42
12.25%
15.75%
61.91%
10.09%
3.19%
6.59%
-0.007
43
12.49%
16.11%
61.01%
10.39%
3.22%
6.68%
-0.002
44
12.72%
16.48%
60.11%
10.69%
3.26%
6.77%
0.003
45
12.95%
16.84%
59.21%
11.00%
3.29%
6.87%
0.007
46
13.18%
17.20%
58.31%
11.30%
3.32%
6.96%
0.012
47
13.41%
17.57%
57.41%
11.61%
3.35%
7.06%
0.016
48
13.64%
17.93%
56.51%
11.91%
3.39%
7.15%
0.021
49
13.87%
18.30%
55.61%
12.22%
3.42%
7.25%
0.025
50
14.10%
18.66%
54.71%
12.53%
3.45%
7.34%
0.029
51
14.33%
19.02%
53.81%
12.84%
3.48%
7.44%
0.033
52
14.56%
19.39%
52.91%
13.14%
3.52%
7.54%
0.037
53
14.78%
19.75%
52.01%
13.45%
3.55%
7.64%
0.041
54
15.01%
20.11%
51.11%
13.76%
3.58%
7.74%
0.044
55
15.24%
20.48%
50.21%
14.07%
3.61%
7.84%
0.048
56
15.46%
20.84%
49.31%
14.38%
3.65%
7.94%
0.051
57
15.69%
21.21%
48.41%
14.70%
3.68%
8.04%
0.055
58
15.91%
21.57%
47.51%
15.01%
3.71%
8.14%
0.058
59
16.14%
21.93%
46.61%
15.32%
3.74%
8.24%
0.061
60
16.37%
22.30%
45.71%
15.63%
3.78%
8.34%
0.065
61
16.59%
22.66%
44.81%
15.94%
3.81%
8.44%
0.068
62
16.82%
23.02%
43.91%
16.25%
3.84%
8.54%
0.071
63
17.05%
23.39%
43.01%
16.56%
3.87%
8.64%
0.074
64
17.27%
23.75%
42.11%
16.87%
3.91%
8.75%
0.076
65
17.50%
24.11%
41.20%
17.18%
3.94%
8.85%
0.079
66
17.73%
24.47%
40.30%
17.50%
3.97%
8.95%
0.082
67
17.95%
24.84%
39.40%
17.81%
4.00%
9.06%
0.085
68
18.18%
25.20%
38.50%
18.12%
4.04%
9.16%
0.087
69
18.40%
25.56%
37.60%
18.44%
4.07%
9.26%
0.090
70
18.63%
25.92%
36.70%
18.75%
4.10%
9.37%
0.092
71
18.85%
26.29%
35.80%
19.06%
4.13%
9.47%
0.095
72
19.08%
26.65%
34.90%
19.38%
4.17%
9.58%
0.097
73
19.31%
27.01%
33.99%
19.69%
4.20%
9.68%
0.099
74
19.53%
27.37%
33.09%
20.01%
4.23%
9.79%
0.101
75
19.76%
27.73%
32.19%
20.32%
4.26%
9.89%
0.104
76
19.98%
28.09%
31.29%
20.64%
4.30%
10.00%
0.106
77
20.21%
28.45%
30.39%
20.95%
4.33%
10.10%
0.108
78
20.44%
28.81%
29.49%
21.26%
4.36%
10.21%
0.110
79
20.66%
29.18%
28.58%
21.58%
4.39%
10.32%
0.112
80
20.89%
29.54%
27.68%
21.89%
4.43%
10.42%
0.114
81
21.11%
29.90%
26.78%
22.21%
4.46%
10.53%
0.116
82
21.34%
30.26%
25.88%
22.52%
4.49%
10.64%
0.118
83
21.57%
30.62%
24.98%
22.83%
4.52%
10.74%
0.120
84
21.79%
30.98%
24.08%
23.15%
4.56%
10.85%
0.121
85
22.02%
31.33%
23.18%
23.47%
4.59%
10.96%
0.123
86
22.24%
31.67%
22.29%
23.80%
4.62%
11.06%
0.125
87
22.46%
32.01%
21.40%
24.13%
4.65%
11.17%
0.127
88
22.66%
32.36%
20.51%
24.48%
4.68%
11.28%
0.128
89
22.84%
32.71%
19.62%
24.83%
4.72%
11.38%
0.130
90
23.02%
33.02%
18.75%
25.22%
4.75%
11.49%
0.131
91
23.17%
33.26%
17.89%
25.67%
4.78%
11.59%
0.133
92
23.32%
33.51%
17.04%
26.13%
4.81%
11.69%
0.134
93
23.40%
33.70%
16.22%
26.69%
4.83%
11.80%
0.135
94
23.31%
33.88%
15.42%
27.39%
4.86%
11.89%
0.136
95
23.20%
34.04%
14.65%
28.12%
4.89%
11.99%
0.137
96
23.08%
34.05%
13.90%
28.96%
4.91%
12.09%
0.138
97
22.84%
33.90%
13.21%
30.05%
4.93%
12.18%
0.139
98
22.29%
33.80%
12.58%
31.34%
4.95%
12.27%
0.139
99
21.99%
33.52%
12.00%
32.49%
4.96%
12.35%
0.140
100
22.00%
33.50%
11.50%
33.00%
4.98%
12.41%
0.140
*Annualized 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.