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
Minimize Conditional Value-at-Risk – Optimize the portfolio to minimize the expected tail loss
Maximize Information Ratio – Find the portfolio that maximizes the information ratio against the selected benchmark
Risk Parity – Find the portfolio that equalizes the risk contribution of portfolio assets
Maximize Kelly Criterion – Finds the portfolio with the maximum expected geometric growth rate
Maximize Sortino Ratio – Find the portfolio that maximizes the Sortino ratio for the given minimum acceptable return
Maximize Omega Ratio – Find the portfolio that maximizes the Omega ratio for the given minimum acceptable return
Minimize 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

Robust Optimization

Use Historical Returns

Use Historical Volatility

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

Portfolio optimization results with goal to maximize sharpe ratio. The possible range of expected annual portfolio returns based on provided parameters is 2.17% to 5.12%. Refer to the efficient frontier section for additional details. Historical values from Jan 2012 to Feb 2020 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	23.65%
VXUS	Vanguard Total International Stock ETF	20.62%
BND	Vanguard Total Bond Market ETF	39.84%
VNQ	Vanguard Real Estate ETF	15.90%
Save portfolio »

Portfolio Summary

Portfolio statistics
Portfolio	Expected Return	Standard Deviation	Sharpe Ratio
Provided Portfolio	4.37%	7.71%	0.37
Maximum Sharpe Ratio	3.97%	6.70%	0.36
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 (1.53% annualized).

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 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%	11.65%	0.340	0.00%	100.00%
2	Vanguard Total International Stock ETF (VXUS)	5.70%	12.77%	0.326	0.00%	100.00%
3	Vanguard Total Bond Market ETF (BND)	1.80%	3.17%	0.084	0.00%	100.00%
4	Vanguard Real Estate ETF (VNQ)	5.00%	13.76%	0.252	0.00%	100.00%
^*Expected return 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 (1.53% annualized).

Monthly Correlations

Efficient Frontier Asset Correlations
Name	Ticker	VTI	VXUS	BND	VNQ
Vanguard Total Stock Market ETF	VTI	1.00	0.81	-0.17	0.50
Vanguard Total International Stock ETF	VXUS	0.81	1.00	-0.03	0.43
Vanguard Total Bond Market ETF	BND	-0.17	-0.03	1.00	0.43
Vanguard Real Estate ETF	VNQ	0.50	0.43	0.43	1.00
Based on monthly returns from Jan 2012 to Feb 2020

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	9.96%	0.10%	89.94%	0.00%	2.17%	2.90%	0.218
2	10.59%	0.26%	89.11%	0.04%	2.20%	2.90%	0.229
3	10.96%	0.55%	88.39%	0.10%	2.22%	2.91%	0.237
4	11.20%	0.88%	87.72%	0.20%	2.25%	2.93%	0.244
5	11.40%	1.23%	87.07%	0.31%	2.27%	2.94%	0.251
6	11.58%	1.59%	86.41%	0.42%	2.30%	2.96%	0.257
7	11.71%	1.98%	85.76%	0.55%	2.32%	2.98%	0.263
8	11.85%	2.36%	85.11%	0.68%	2.34%	3.01%	0.269
9	11.98%	2.75%	84.44%	0.82%	2.37%	3.03%	0.275
10	12.12%	3.14%	83.76%	0.98%	2.39%	3.06%	0.281
11	12.25%	3.52%	83.08%	1.15%	2.42%	3.09%	0.286
12	12.38%	3.91%	82.37%	1.34%	2.44%	3.13%	0.291
13	12.53%	4.29%	81.65%	1.53%	2.47%	3.17%	0.296
14	12.69%	4.65%	80.92%	1.74%	2.50%	3.20%	0.300
15	12.87%	5.02%	80.16%	1.95%	2.52%	3.25%	0.305
16	13.06%	5.38%	79.39%	2.17%	2.55%	3.29%	0.309
17	13.25%	5.75%	78.61%	2.39%	2.58%	3.34%	0.314
18	13.43%	6.10%	77.82%	2.64%	2.61%	3.39%	0.317
19	13.63%	6.44%	77.03%	2.90%	2.64%	3.44%	0.321
20	13.84%	6.79%	76.22%	3.15%	2.67%	3.49%	0.324
21	14.05%	7.13%	75.40%	3.42%	2.70%	3.55%	0.328
22	14.26%	7.47%	74.58%	3.69%	2.73%	3.60%	0.331
23	14.46%	7.81%	73.76%	3.97%	2.75%	3.66%	0.333
24	14.66%	8.15%	72.94%	4.25%	2.78%	3.72%	0.336
25	14.87%	8.48%	72.12%	4.53%	2.81%	3.78%	0.338
26	15.07%	8.82%	71.29%	4.82%	2.84%	3.84%	0.341
27	15.28%	9.15%	70.46%	5.11%	2.87%	3.91%	0.343
28	15.51%	9.48%	69.61%	5.40%	2.90%	3.97%	0.345
29	15.73%	9.81%	68.76%	5.69%	2.93%	4.04%	0.346
30	15.96%	10.13%	67.91%	5.99%	2.96%	4.11%	0.348
31	16.20%	10.45%	67.06%	6.29%	3.00%	4.18%	0.349
32	16.43%	10.78%	66.20%	6.60%	3.03%	4.25%	0.351
33	16.66%	11.10%	65.34%	6.90%	3.06%	4.32%	0.352
34	16.88%	11.43%	64.48%	7.20%	3.09%	4.39%	0.353
35	17.11%	11.76%	63.62%	7.51%	3.12%	4.47%	0.354
36	17.34%	12.09%	62.76%	7.81%	3.15%	4.54%	0.355
37	17.57%	12.41%	61.90%	8.12%	3.18%	4.62%	0.356
38	17.80%	12.74%	61.04%	8.42%	3.21%	4.69%	0.357
39	18.04%	13.06%	60.17%	8.73%	3.24%	4.77%	0.358
40	18.27%	13.39%	59.31%	9.04%	3.27%	4.85%	0.359
41	18.51%	13.71%	58.44%	9.35%	3.30%	4.92%	0.359
42	18.74%	14.03%	57.57%	9.66%	3.34%	5.00%	0.360
43	18.98%	14.35%	56.71%	9.96%	3.37%	5.08%	0.360
44	19.21%	14.67%	55.84%	10.27%	3.40%	5.16%	0.361
45	19.45%	15.00%	54.97%	10.58%	3.43%	5.24%	0.361
46	19.70%	15.32%	54.09%	10.89%	3.46%	5.32%	0.362
47	19.94%	15.65%	53.21%	11.20%	3.49%	5.41%	0.362
48	20.18%	15.99%	52.32%	11.51%	3.52%	5.49%	0.362
49	20.42%	16.33%	51.44%	11.82%	3.56%	5.57%	0.363
50	20.66%	16.66%	50.55%	12.13%	3.59%	5.66%	0.363
51	20.91%	17.00%	49.66%	12.44%	3.62%	5.74%	0.363
52	21.15%	17.33%	48.77%	12.75%	3.65%	5.83%	0.363
53	21.40%	17.66%	47.88%	13.06%	3.68%	5.91%	0.364
54	21.64%	17.99%	46.98%	13.38%	3.72%	6.00%	0.364
55	21.89%	18.32%	46.09%	13.69%	3.75%	6.08%	0.364
56	22.14%	18.65%	45.20%	14.01%	3.78%	6.17%	0.364
57	22.39%	18.98%	44.31%	14.32%	3.81%	6.26%	0.364
58	22.64%	19.31%	43.41%	14.64%	3.84%	6.34%	0.364
59	22.89%	19.64%	42.52%	14.95%	3.88%	6.43%	0.364
60	23.14%	19.97%	41.62%	15.27%	3.91%	6.52%	0.364
61	23.40%	20.29%	40.73%	15.58%	3.94%	6.61%	0.364
62	23.65%	20.62%	39.84%	15.90%	3.97%	6.70%	0.364
63	23.90%	20.95%	38.94%	16.21%	4.01%	6.79%	0.364
64	24.15%	21.28%	38.04%	16.53%	4.04%	6.87%	0.364
65	24.40%	21.60%	37.14%	16.85%	4.07%	6.96%	0.364
66	24.66%	21.93%	36.23%	17.18%	4.10%	7.05%	0.364
67	24.91%	22.26%	35.32%	17.51%	4.14%	7.15%	0.364
68	25.16%	22.59%	34.41%	17.84%	4.17%	7.24%	0.364
69	25.41%	22.92%	33.50%	18.17%	4.20%	7.33%	0.364
70	25.66%	23.25%	32.59%	18.50%	4.24%	7.42%	0.364
71	25.91%	23.58%	31.68%	18.83%	4.27%	7.51%	0.364
72	26.17%	23.91%	30.77%	19.16%	4.30%	7.60%	0.364
73	26.42%	24.23%	29.85%	19.49%	4.33%	7.70%	0.364
74	26.67%	24.56%	28.94%	19.82%	4.37%	7.79%	0.364
75	26.92%	24.89%	28.03%	20.15%	4.40%	7.88%	0.364
76	27.17%	25.22%	27.12%	20.49%	4.43%	7.97%	0.363
77	27.43%	25.55%	26.21%	20.82%	4.47%	8.07%	0.363
78	27.68%	25.88%	25.29%	21.15%	4.50%	8.16%	0.363
79	27.93%	26.21%	24.38%	21.48%	4.53%	8.25%	0.363
80	28.17%	26.54%	23.47%	21.82%	4.56%	8.35%	0.363
81	28.40%	26.87%	22.57%	22.16%	4.60%	8.44%	0.363
82	28.64%	27.20%	21.66%	22.50%	4.63%	8.53%	0.363
83	28.88%	27.53%	20.75%	22.84%	4.66%	8.63%	0.363
84	29.12%	27.86%	19.85%	23.18%	4.70%	8.72%	0.363
85	29.34%	28.18%	18.94%	23.53%	4.73%	8.81%	0.362
86	29.56%	28.49%	18.05%	23.90%	4.76%	8.90%	0.362
87	29.75%	28.79%	17.17%	24.29%	4.79%	9.00%	0.362
88	29.90%	29.08%	16.30%	24.71%	4.82%	9.09%	0.362
89	30.01%	29.40%	15.45%	25.15%	4.85%	9.17%	0.362
90	30.09%	29.72%	14.60%	25.59%	4.88%	9.26%	0.362
91	30.16%	30.05%	13.77%	26.03%	4.91%	9.35%	0.361
92	30.12%	30.42%	12.97%	26.49%	4.94%	9.43%	0.361
93	30.03%	30.80%	12.19%	26.99%	4.97%	9.51%	0.361
94	29.91%	31.24%	11.44%	27.40%	5.00%	9.59%	0.361
95	29.71%	31.73%	10.75%	27.81%	5.02%	9.67%	0.361
96	29.46%	32.19%	10.10%	28.26%	5.04%	9.74%	0.360
97	29.07%	32.83%	9.51%	28.58%	5.07%	9.80%	0.360
98	28.37%	33.81%	8.97%	28.85%	5.09%	9.86%	0.360
99	27.73%	34.95%	8.47%	28.86%	5.11%	9.93%	0.360
100	26.50%	36.50%	8.00%	29.00%	5.13%	9.99%	0.360
^*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 (1.53% annualized).