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 the goal to maximize Sharpe ratio. The possible range of expected annual portfolio returns based on provided parameters is 1.80% to 5.69%. Refer to the efficient frontier section for additional details. Historical values from Jan 2012 to May 2023 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 and Disclosures
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. 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.
The results are based on combining user provided forecast model parameters with historical monthly return statistics of the portfolio assets.
Efficient Frontier Assets
Efficient Frontier Assets
#
Asset
Expected Return
Standard Deviation
Sharpe Ratio
Min. Weight
Max. Weight
1
Vanguard Total Stock Market ETF (VTI)
5.50%
14.66%
0.035
0.00%
100.00%
2
Vanguard Total International Stock ETF (VXUS)
5.70%
15.00%
0.047
0.00%
100.00%
3
Vanguard Total Bond Market ETF (BND)
1.80%
4.38%
-0.729
0.00%
100.00%
4
Vanguard Real Estate ETF (VNQ)
5.00%
16.74%
0.001
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
0.85
0.30
0.71
Vanguard Total International Stock ETF
VXUS
0.85
1.00
0.37
0.64
Vanguard Total Bond Market ETF
BND
0.30
0.37
1.00
0.52
Vanguard Real Estate ETF
VNQ
0.71
0.64
0.52
1.00
Based on monthly returns from Jan 2012 to May 2023
Note: You can hover over any of the data points on the chart for more information.
Efficient Frontiers
Efficient Frontier Portfolios
Efficient Frontier Assets
#
VTI
VXUS
BND
VNQ
Expected Return *
Standard Deviation *
Sharpe Ratio *
1
0.00%
0.00%
100.00%
0.00%
1.80%
4.38%
-0.729
2
1.07%
0.00%
98.93%
0.00%
1.84%
4.38%
-0.720
3
2.13%
0.00%
97.87%
0.00%
1.88%
4.39%
-0.709
4
3.19%
0.00%
96.81%
0.00%
1.92%
4.40%
-0.698
5
4.26%
0.00%
95.74%
0.00%
1.96%
4.42%
-0.686
6
5.32%
0.00%
94.68%
0.00%
2.00%
4.44%
-0.674
7
6.39%
0.00%
93.61%
0.00%
2.04%
4.47%
-0.661
8
7.45%
0.00%
92.55%
0.00%
2.08%
4.50%
-0.647
9
8.52%
0.00%
91.48%
0.00%
2.12%
4.54%
-0.633
10
9.58%
0.00%
90.42%
0.00%
2.15%
4.58%
-0.619
11
10.65%
0.00%
89.35%
0.00%
2.19%
4.63%
-0.604
12
11.17%
0.51%
88.32%
0.00%
2.23%
4.68%
-0.589
13
11.54%
1.17%
87.29%
0.00%
2.27%
4.73%
-0.574
14
11.91%
1.83%
86.26%
0.00%
2.31%
4.79%
-0.559
15
12.28%
2.49%
85.23%
0.00%
2.35%
4.85%
-0.544
16
12.65%
3.15%
84.20%
0.00%
2.39%
4.92%
-0.529
17
13.02%
3.81%
83.17%
0.00%
2.43%
4.98%
-0.514
18
13.39%
4.46%
82.14%
0.00%
2.47%
5.05%
-0.499
19
13.76%
5.12%
81.11%
0.00%
2.51%
5.13%
-0.484
20
14.14%
5.78%
80.08%
0.00%
2.55%
5.20%
-0.470
21
14.51%
6.44%
79.05%
0.00%
2.59%
5.28%
-0.455
22
14.88%
7.10%
78.02%
0.00%
2.63%
5.36%
-0.441
23
15.25%
7.76%
77.00%
0.00%
2.67%
5.44%
-0.427
24
15.62%
8.42%
75.97%
0.00%
2.71%
5.53%
-0.414
25
15.99%
9.07%
74.94%
0.00%
2.75%
5.61%
-0.400
26
16.36%
9.73%
73.91%
0.00%
2.78%
5.70%
-0.387
27
16.73%
10.39%
72.88%
0.00%
2.82%
5.79%
-0.374
28
17.10%
11.05%
71.85%
0.00%
2.86%
5.88%
-0.362
29
17.47%
11.71%
70.82%
0.00%
2.90%
5.98%
-0.349
30
17.84%
12.37%
69.79%
0.00%
2.94%
6.07%
-0.337
31
18.21%
13.02%
68.76%
0.00%
2.98%
6.17%
-0.326
32
18.58%
13.68%
67.73%
0.00%
3.02%
6.27%
-0.314
33
18.95%
14.34%
66.70%
0.00%
3.06%
6.37%
-0.303
34
19.33%
15.00%
65.68%
0.00%
3.10%
6.47%
-0.292
35
19.70%
15.66%
64.65%
0.00%
3.14%
6.58%
-0.282
36
20.07%
16.32%
63.62%
0.00%
3.18%
6.68%
-0.271
37
20.44%
16.97%
62.59%
0.00%
3.22%
6.79%
-0.261
38
20.81%
17.63%
61.56%
0.00%
3.26%
6.89%
-0.251
39
21.18%
18.29%
60.53%
0.00%
3.30%
7.00%
-0.242
40
21.55%
18.95%
59.50%
0.00%
3.34%
7.11%
-0.233
41
21.92%
19.61%
58.47%
0.00%
3.38%
7.22%
-0.224
42
22.29%
20.27%
57.44%
0.00%
3.42%
7.33%
-0.215
43
22.66%
20.92%
56.41%
0.00%
3.45%
7.45%
-0.206
44
23.03%
21.58%
55.38%
0.00%
3.49%
7.56%
-0.198
45
23.40%
22.24%
54.36%
0.00%
3.53%
7.67%
-0.190
46
23.77%
22.90%
53.33%
0.00%
3.57%
7.79%
-0.182
47
24.14%
23.56%
52.30%
0.00%
3.61%
7.90%
-0.175
48
24.51%
24.22%
51.27%
0.00%
3.65%
8.02%
-0.167
49
24.89%
24.88%
50.24%
0.00%
3.69%
8.13%
-0.160
50
25.26%
25.53%
49.21%
0.00%
3.73%
8.25%
-0.153
51
25.63%
26.19%
48.18%
0.00%
3.77%
8.37%
-0.146
52
26.00%
26.85%
47.15%
0.00%
3.81%
8.49%
-0.139
53
26.37%
27.51%
46.12%
0.00%
3.85%
8.61%
-0.133
54
26.74%
28.17%
45.09%
0.00%
3.89%
8.73%
-0.126
55
27.11%
28.83%
44.06%
0.00%
3.93%
8.85%
-0.120
56
27.48%
29.48%
43.04%
0.00%
3.97%
8.97%
-0.114
57
27.85%
30.14%
42.01%
0.00%
4.01%
9.09%
-0.108
58
28.22%
30.80%
40.98%
0.00%
4.05%
9.21%
-0.103
59
28.59%
31.46%
39.95%
0.00%
4.08%
9.33%
-0.097
60
28.96%
32.12%
38.92%
0.00%
4.12%
9.45%
-0.092
61
29.33%
32.78%
37.89%
0.00%
4.16%
9.58%
-0.086
62
29.70%
33.43%
36.86%
0.00%
4.20%
9.70%
-0.081
63
30.08%
34.09%
35.83%
0.00%
4.24%
9.82%
-0.076
64
30.45%
34.75%
34.80%
0.00%
4.28%
9.95%
-0.071
65
30.82%
35.41%
33.77%
0.00%
4.32%
10.07%
-0.067
66
31.19%
36.07%
32.74%
0.00%
4.36%
10.20%
-0.062
67
31.56%
36.73%
31.72%
0.00%
4.40%
10.32%
-0.057
68
31.85%
37.37%
30.67%
0.11%
4.44%
10.45%
-0.053
69
32.08%
37.99%
29.61%
0.32%
4.48%
10.58%
-0.048
70
32.30%
38.62%
28.55%
0.53%
4.52%
10.70%
-0.044
71
32.53%
39.24%
27.49%
0.74%
4.56%
10.83%
-0.040
72
32.75%
39.87%
26.43%
0.94%
4.60%
10.95%
-0.036
73
32.98%
40.49%
25.37%
1.15%
4.64%
11.08%
-0.032
74
33.21%
41.12%
24.32%
1.36%
4.68%
11.21%
-0.028
75
33.43%
41.74%
23.26%
1.57%
4.72%
11.34%
-0.024
76
33.66%
42.37%
22.20%
1.78%
4.75%
11.46%
-0.021
77
33.89%
42.99%
21.14%
1.98%
4.79%
11.59%
-0.017
78
34.11%
43.62%
20.08%
2.19%
4.83%
11.72%
-0.013
79
34.34%
44.24%
19.02%
2.40%
4.87%
11.85%
-0.010
80
34.56%
44.87%
17.96%
2.61%
4.91%
11.97%
-0.007
81
34.79%
45.49%
16.90%
2.82%
4.95%
12.10%
-0.003
82
35.02%
46.12%
15.84%
3.02%
4.99%
12.23%
-0.000
83
35.24%
46.74%
14.78%
3.23%
5.03%
12.36%
0.003
84
35.47%
47.37%
13.73%
3.44%
5.07%
12.49%
0.006
85
35.70%
47.99%
12.67%
3.65%
5.11%
12.62%
0.009
86
35.92%
48.62%
11.61%
3.85%
5.15%
12.75%
0.012
87
36.15%
49.24%
10.55%
4.06%
5.19%
12.88%
0.015
88
36.37%
49.86%
9.49%
4.27%
5.23%
13.01%
0.018
89
36.60%
50.49%
8.43%
4.48%
5.27%
13.14%
0.021
90
36.83%
51.11%
7.37%
4.69%
5.31%
13.26%
0.024
91
37.05%
51.74%
6.31%
4.89%
5.35%
13.39%
0.026
92
37.28%
52.36%
5.25%
5.10%
5.38%
13.52%
0.029
93
37.51%
52.99%
4.19%
5.31%
5.42%
13.65%
0.032
94
37.73%
53.61%
3.14%
5.52%
5.46%
13.78%
0.034
95
37.96%
54.24%
2.08%
5.73%
5.50%
13.92%
0.037
96
38.18%
54.86%
1.02%
5.93%
5.54%
14.05%
0.039
97
38.40%
55.69%
0.00%
5.91%
5.58%
14.18%
0.042
98
38.35%
61.35%
0.00%
0.30%
5.62%
14.33%
0.044
99
19.70%
80.30%
0.00%
0.00%
5.66%
14.58%
0.046
100
0.01%
99.99%
0.00%
0.00%
5.70%
15.00%
0.047
*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.