Portfolio Optimization

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 Type

Time Period

Start Year

First Month

End Year

Last Month

Optimization Goal

Targeted Annual Return

Targeted Annual Volatility

Targeted Tracking Error

Targeted Monthly CVaR

Robust Optimization

Use Historical Returns

Use Historical Volatility

Use Historical Correlations

Correlation Matrix

Browse…

Asset Constraints

Group Constraints

Compared Allocation

Benchmark

Benchmark Ticker

Portfolio Assets

Allocation

Expected Return

Volatility

Min. Weight

Max. Weight

Group

Select asset 1

Enter percentage allocation for asset 1 %

Expected return for asset 1 %

Expected volatility for asset 1 %

Minimum allocation for asset 1 %

Maximum allocation for asset 1 %

Group assignment for asset 1

Select asset 2

Enter percentage allocation for asset 2 %

Expected return for asset 2 %

Expected volatility for asset 2 %

Minimum allocation for asset 2 %

Maximum allocation for asset 2 %

Group assignment for asset 2

Select asset 3

Enter percentage allocation for asset 3 %

Expected return for asset 3 %

Expected volatility for asset 3 %

Minimum allocation for asset 3 %

Maximum allocation for asset 3 %

Group assignment for asset 3

Select asset 4

Enter percentage allocation for asset 4 %

Expected return for asset 4 %

Expected volatility for asset 4 %

Minimum allocation for asset 4 %

Maximum allocation for asset 4 %

Group assignment for asset 4

Select asset 5

Enter percentage allocation for asset 5 %

Expected return for asset 5 %

Expected volatility for asset 5 %

Minimum allocation for asset 5 %

Maximum allocation for asset 5 %

Group assignment for asset 5

Select asset 6

Enter percentage allocation for asset 6 %

Expected return for asset 6 %

Expected volatility for asset 6 %

Minimum allocation for asset 6 %

Maximum allocation for asset 6 %

Group assignment for asset 6

Select asset 7

Enter percentage allocation for asset 7 %

Expected return for asset 7 %

Expected volatility for asset 7 %

Minimum allocation for asset 7 %

Maximum allocation for asset 7 %

Group assignment for asset 7

Select asset 8

Enter percentage allocation for asset 8 %

Expected return for asset 8 %

Expected volatility for asset 8 %

Minimum allocation for asset 8 %

Maximum allocation for asset 8 %

Group assignment for asset 8

Select asset 9

Enter percentage allocation for asset 9 %

Expected return for asset 9 %

Expected volatility for asset 9 %

Minimum allocation for asset 9 %

Maximum allocation for asset 9 %

Group assignment for asset 9

Select asset 10

Enter percentage allocation for asset 10 %

Expected return for asset 10 %

Expected volatility for asset 10 %

Minimum allocation for asset 10 %

Maximum allocation for asset 10 %

Group assignment for asset 10

Total

Total allocation for portfolio %

Asset Groups

Min. Weight

Max. Weight

Full name for group A at index 1

Minimum allocation for group A at index 1 %

Maximum allocation for group A at index 1 %

Full name for group B at index 2

Minimum allocation for group B at index 2 %

Maximum allocation for group B at index 2 %

Full name for group C at index 3

Minimum allocation for group C at index 3 %

Maximum allocation for group C at index 3 %

Full name for group D at index 4

Minimum allocation for group D at index 4 %

Maximum allocation for group D at index 4 %

Full name for group E at index 5

Minimum allocation for group E at index 5 %

Maximum allocation for group E at index 5 %

Full name for group F at index 6

Minimum allocation for group F at index 6 %

Maximum allocation for group F at index 6 %

Portfolio Optimization Results Save

Portfolio optimization results with 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 Sep 2022 were used for non-user supplied parameters based on the selected time period and available data for the portfolio assets.

Summary
Efficient Frontier

Portfolio Allocations

Provided Portfolio
Ticker	Name	Allocation
VTI	Vanguard Total Stock Market ETF	40.00%
VXUS	Vanguard Total International Stock ETF	20.00%
BND	Vanguard Total Bond Market ETF	30.00%
VNQ	Vanguard Real Estate ETF	10.00%
Save portfolio »

Maximum Sharpe Ratio
Ticker	Name	Allocation
VTI	Vanguard Total Stock Market ETF	19.70%
VXUS	Vanguard Total International Stock ETF	80.30%
Save portfolio »

Portfolio Summary

Portfolio statistics
Portfolio	Expected Return	Standard Deviation	Sharpe Ratio
Provided Portfolio	4.38%	10.19%	0.15
Maximum Sharpe Ratio	5.66%	14.25%	0.19
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.
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.
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.

Efficient Frontier Assets
#	Asset	Expected Return	Standard Deviation	Sharpe Ratio	Min. Weight	Max. Weight
1	Vanguard Total Stock Market ETF (VTI)	5.50%	14.60%	0.179	0.00%	100.00%
2	Vanguard Total International Stock ETF (VXUS)	5.70%	14.56%	0.193	0.00%	100.00%
3	Vanguard Total Bond Market ETF (BND)	1.80%	4.04%	-0.268	0.00%	100.00%
4	Vanguard Real Estate ETF (VNQ)	5.00%	16.60%	0.128	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	0.28	0.71
Vanguard Total International Stock ETF	VXUS	0.86	1.00	0.28	0.62
Vanguard Total Bond Market ETF	BND	0.28	0.28	1.00	0.51
Vanguard Real Estate ETF	VNQ	0.71	0.62	0.51	1.00
Based on monthly returns from Jan 2012 to Sep 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	0.00%	0.00%	100.00%	0.00%	1.80%	4.04%	-0.268
2	0.98%	0.08%	98.94%	0.00%	1.84%	4.04%	-0.258
3	1.31%	0.78%	97.91%	0.00%	1.88%	4.05%	-0.248
4	1.63%	1.48%	96.89%	0.00%	1.92%	4.06%	-0.238
5	1.96%	2.18%	95.86%	0.00%	1.96%	4.08%	-0.227
6	2.29%	2.88%	94.83%	0.00%	2.00%	4.10%	-0.216
7	2.62%	3.57%	93.80%	0.00%	2.04%	4.13%	-0.205
8	2.95%	4.27%	92.78%	0.00%	2.08%	4.16%	-0.194
9	3.28%	4.97%	91.75%	0.00%	2.12%	4.20%	-0.183
10	3.61%	5.67%	90.72%	0.00%	2.15%	4.24%	-0.172
11	3.94%	6.37%	89.70%	0.00%	2.19%	4.28%	-0.161
12	4.27%	7.06%	88.67%	0.00%	2.23%	4.33%	-0.150
13	4.60%	7.76%	87.64%	0.00%	2.27%	4.38%	-0.140
14	4.93%	8.46%	86.62%	0.00%	2.31%	4.44%	-0.129
15	5.25%	9.16%	85.59%	0.00%	2.35%	4.49%	-0.118
16	5.58%	9.85%	84.56%	0.00%	2.39%	4.56%	-0.108
17	5.91%	10.55%	83.53%	0.00%	2.43%	4.62%	-0.098
18	6.24%	11.25%	82.51%	0.00%	2.47%	4.69%	-0.088
19	6.57%	11.95%	81.48%	0.00%	2.51%	4.76%	-0.079
20	6.90%	12.65%	80.45%	0.00%	2.55%	4.84%	-0.069
21	7.23%	13.34%	79.43%	0.00%	2.59%	4.92%	-0.060
22	7.56%	14.04%	78.40%	0.00%	2.63%	5.00%	-0.051
23	7.89%	14.74%	77.37%	0.00%	2.67%	5.08%	-0.043
24	8.22%	15.44%	76.35%	0.00%	2.71%	5.17%	-0.034
25	8.54%	16.14%	75.32%	0.00%	2.75%	5.25%	-0.026
26	8.87%	16.83%	74.29%	0.00%	2.78%	5.34%	-0.019
27	9.20%	17.53%	73.27%	0.00%	2.82%	5.43%	-0.011
28	9.53%	18.23%	72.24%	0.00%	2.86%	5.53%	-0.004
29	9.86%	18.93%	71.21%	0.00%	2.90%	5.62%	0.003
30	10.19%	19.63%	70.18%	0.00%	2.94%	5.72%	0.010
31	10.52%	20.32%	69.16%	0.00%	2.98%	5.82%	0.017
32	10.85%	21.02%	68.13%	0.00%	3.02%	5.92%	0.023
33	11.18%	21.72%	67.10%	0.00%	3.06%	6.02%	0.029
34	11.51%	22.42%	66.08%	0.00%	3.10%	6.13%	0.035
35	11.84%	23.12%	65.05%	0.00%	3.14%	6.23%	0.041
36	12.16%	23.81%	64.02%	0.00%	3.18%	6.34%	0.047
37	12.49%	24.51%	63.00%	0.00%	3.22%	6.45%	0.052
38	12.82%	25.21%	61.97%	0.00%	3.26%	6.56%	0.057
39	13.15%	25.91%	60.94%	0.00%	3.30%	6.66%	0.062
40	13.48%	26.60%	59.91%	0.00%	3.34%	6.78%	0.067
41	13.81%	27.30%	58.89%	0.00%	3.38%	6.89%	0.071
42	14.14%	28.00%	57.86%	0.00%	3.42%	7.00%	0.076
43	14.47%	28.70%	56.83%	0.00%	3.45%	7.11%	0.080
44	14.80%	29.40%	55.81%	0.00%	3.49%	7.23%	0.084
45	15.13%	30.09%	54.78%	0.00%	3.53%	7.34%	0.088
46	15.46%	30.79%	53.75%	0.00%	3.57%	7.46%	0.092
47	15.78%	31.49%	52.73%	0.00%	3.61%	7.58%	0.096
48	16.11%	32.19%	51.70%	0.00%	3.65%	7.70%	0.100
49	16.44%	32.89%	50.67%	0.00%	3.69%	7.81%	0.103
50	16.77%	33.58%	49.64%	0.00%	3.73%	7.93%	0.107
51	17.10%	34.28%	48.62%	0.00%	3.77%	8.05%	0.110
52	17.43%	34.98%	47.59%	0.00%	3.81%	8.17%	0.113
53	17.76%	35.68%	46.56%	0.00%	3.85%	8.30%	0.116
54	18.09%	36.38%	45.54%	0.00%	3.89%	8.42%	0.119
55	18.42%	37.07%	44.51%	0.00%	3.93%	8.54%	0.122
56	18.75%	37.77%	43.48%	0.00%	3.97%	8.66%	0.125
57	19.07%	38.47%	42.46%	0.00%	4.01%	8.78%	0.128
58	19.40%	39.17%	41.43%	0.00%	4.05%	8.91%	0.130
59	19.73%	39.86%	40.40%	0.00%	4.08%	9.03%	0.133
60	19.90%	40.54%	39.34%	0.22%	4.12%	9.16%	0.135
61	20.06%	41.21%	38.28%	0.45%	4.16%	9.28%	0.138
62	20.22%	41.88%	37.23%	0.68%	4.20%	9.41%	0.140
63	20.38%	42.55%	36.17%	0.91%	4.24%	9.53%	0.143
64	20.54%	43.22%	35.11%	1.14%	4.28%	9.66%	0.145
65	20.69%	43.89%	34.05%	1.37%	4.32%	9.78%	0.147
66	20.85%	44.56%	32.99%	1.60%	4.36%	9.91%	0.149
67	21.01%	45.23%	31.93%	1.83%	4.40%	10.04%	0.151
68	21.17%	45.90%	30.87%	2.05%	4.44%	10.16%	0.153
69	21.33%	46.58%	29.81%	2.28%	4.48%	10.29%	0.155
70	21.49%	47.25%	28.75%	2.51%	4.52%	10.42%	0.157
71	21.65%	47.92%	27.69%	2.74%	4.56%	10.54%	0.159
72	21.81%	48.59%	26.63%	2.97%	4.60%	10.67%	0.161
73	21.97%	49.26%	25.57%	3.20%	4.64%	10.80%	0.162
74	22.13%	49.93%	24.51%	3.43%	4.68%	10.93%	0.164
75	22.29%	50.60%	23.45%	3.66%	4.72%	11.06%	0.166
76	22.45%	51.27%	22.39%	3.89%	4.75%	11.18%	0.167
77	22.61%	51.94%	21.33%	4.12%	4.79%	11.31%	0.169
78	22.77%	52.61%	20.28%	4.34%	4.83%	11.44%	0.170
79	22.93%	53.29%	19.22%	4.57%	4.87%	11.57%	0.172
80	23.08%	53.96%	18.16%	4.80%	4.91%	11.70%	0.173
81	23.24%	54.63%	17.10%	5.03%	4.95%	11.83%	0.175
82	23.40%	55.30%	16.04%	5.26%	4.99%	11.96%	0.176
83	23.56%	55.97%	14.98%	5.49%	5.03%	12.09%	0.178
84	23.72%	56.64%	13.92%	5.72%	5.07%	12.22%	0.179
85	23.88%	57.31%	12.86%	5.95%	5.11%	12.35%	0.180
86	24.04%	57.98%	11.80%	6.18%	5.15%	12.48%	0.181
87	24.20%	58.65%	10.74%	6.41%	5.19%	12.61%	0.183
88	24.36%	59.32%	9.68%	6.64%	5.23%	12.74%	0.184
89	24.52%	60.00%	8.62%	6.86%	5.27%	12.87%	0.185
90	24.68%	60.67%	7.56%	7.09%	5.31%	13.00%	0.186
91	24.84%	61.34%	6.50%	7.32%	5.35%	13.13%	0.187
92	25.00%	62.01%	5.44%	7.55%	5.38%	13.26%	0.189
93	25.16%	62.68%	4.38%	7.78%	5.42%	13.39%	0.190
94	25.32%	63.35%	3.33%	8.01%	5.46%	13.52%	0.191
95	25.47%	64.02%	2.27%	8.24%	5.50%	13.65%	0.192
96	25.63%	64.69%	1.21%	8.47%	5.54%	13.79%	0.193
97	25.79%	65.36%	0.15%	8.70%	5.58%	13.92%	0.194
98	25.33%	70.65%	0.00%	4.02%	5.62%	14.06%	0.195
99	19.70%	80.30%	0.00%	0.00%	5.66%	14.25%	0.195
100	0.01%	99.99%	0.00%	0.00%	5.70%	14.56%	0.193
^*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.