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 2.14% to 5.28%. Refer to the efficient frontier section for additional details. Historical values from Jan 2012 to Dec 2019 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	26.40%
VXUS	Vanguard Total International Stock ETF	26.50%
BND	Vanguard Total Bond Market ETF	31.73%
VNQ	Vanguard Real Estate ETF	15.37%
Save portfolio »

Portfolio Summary

Portfolio statistics
Portfolio	Expected Return	Standard Deviation	Sharpe Ratio
Provided Portfolio	4.37%	7.54%	0.38
Maximum Sharpe Ratio	4.29%	7.39%	0.37
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%	11.31%	0.351	0.00%	100.00%
2	Vanguard Total International Stock ETF (VXUS)	5.70%	12.57%	0.331	0.00%	100.00%
3	Vanguard Total Bond Market ETF (BND)	1.80%	3.10%	0.086	0.00%	100.00%
4	Vanguard Real Estate ETF (VNQ)	5.00%	13.62%	0.255	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	-0.12	0.48
Vanguard Total International Stock ETF	VXUS	0.81	1.00	0.03	0.41
Vanguard Total Bond Market ETF	BND	-0.12	0.03	1.00	0.49
Vanguard Real Estate ETF	VNQ	0.48	0.41	0.49	1.00
Based on monthly returns from Jan 2012 to Dec 2019

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	9.26%	0.06%	90.68%	0.00%	2.14%	2.88%	0.210
2	9.94%	0.21%	89.81%	0.04%	2.17%	2.88%	0.221
3	10.47%	0.43%	89.01%	0.10%	2.20%	2.89%	0.230
4	10.89%	0.69%	88.24%	0.17%	2.23%	2.91%	0.239
5	11.22%	1.03%	87.50%	0.26%	2.26%	2.92%	0.247
6	11.48%	1.39%	86.77%	0.35%	2.28%	2.94%	0.254
7	11.69%	1.78%	86.05%	0.47%	2.31%	2.97%	0.261
8	11.88%	2.18%	85.33%	0.60%	2.34%	3.00%	0.268
9	12.06%	2.59%	84.61%	0.74%	2.36%	3.02%	0.274
10	12.25%	3.00%	83.88%	0.88%	2.39%	3.06%	0.280
11	12.42%	3.43%	83.12%	1.04%	2.42%	3.09%	0.286
12	12.60%	3.84%	82.35%	1.20%	2.45%	3.13%	0.291
13	12.80%	4.25%	81.57%	1.38%	2.47%	3.17%	0.297
14	13.01%	4.66%	80.77%	1.56%	2.50%	3.21%	0.302
15	13.22%	5.07%	79.96%	1.75%	2.53%	3.25%	0.307
16	13.44%	5.48%	79.14%	1.94%	2.56%	3.30%	0.312
17	13.66%	5.89%	78.31%	2.14%	2.59%	3.35%	0.316
18	13.90%	6.30%	77.47%	2.34%	2.62%	3.40%	0.320
19	14.13%	6.71%	76.61%	2.55%	2.66%	3.46%	0.324
20	14.38%	7.12%	75.75%	2.75%	2.69%	3.51%	0.328
21	14.62%	7.52%	74.89%	2.96%	2.72%	3.57%	0.332
22	14.87%	7.94%	74.02%	3.17%	2.75%	3.63%	0.335
23	15.12%	8.35%	73.15%	3.39%	2.78%	3.69%	0.338
24	15.37%	8.76%	72.27%	3.60%	2.81%	3.75%	0.341
25	15.62%	9.16%	71.39%	3.82%	2.85%	3.82%	0.343
26	15.88%	9.57%	70.51%	4.04%	2.88%	3.88%	0.346
27	16.14%	9.98%	69.62%	4.26%	2.91%	3.95%	0.348
28	16.39%	10.39%	68.74%	4.48%	2.94%	4.02%	0.350
29	16.64%	10.80%	67.85%	4.71%	2.97%	4.09%	0.352
30	16.89%	11.21%	66.96%	4.94%	3.01%	4.16%	0.354
31	17.13%	11.62%	66.07%	5.18%	3.04%	4.23%	0.356
32	17.37%	12.03%	65.17%	5.42%	3.07%	4.30%	0.357
33	17.62%	12.44%	64.27%	5.67%	3.10%	4.38%	0.359
34	17.86%	12.85%	63.37%	5.92%	3.14%	4.45%	0.360
35	18.10%	13.26%	62.46%	6.18%	3.17%	4.53%	0.361
36	18.35%	13.67%	61.55%	6.44%	3.20%	4.61%	0.362
37	18.59%	14.07%	60.63%	6.70%	3.24%	4.69%	0.363
38	18.83%	14.48%	59.72%	6.97%	3.27%	4.77%	0.364
39	19.07%	14.88%	58.81%	7.23%	3.30%	4.85%	0.365
40	19.32%	15.29%	57.89%	7.50%	3.34%	4.93%	0.366
41	19.56%	15.69%	56.98%	7.77%	3.37%	5.01%	0.366
42	19.81%	16.09%	56.06%	8.04%	3.40%	5.09%	0.367
43	20.05%	16.50%	55.14%	8.31%	3.44%	5.17%	0.368
44	20.30%	16.90%	54.21%	8.59%	3.47%	5.26%	0.368
45	20.56%	17.30%	53.28%	8.86%	3.50%	5.34%	0.369
46	20.81%	17.71%	52.35%	9.14%	3.54%	5.43%	0.369
47	21.06%	18.11%	51.42%	9.41%	3.57%	5.51%	0.370
48	21.32%	18.51%	50.48%	9.69%	3.61%	5.60%	0.370
49	21.57%	18.92%	49.55%	9.97%	3.64%	5.68%	0.370
50	21.81%	19.32%	48.61%	10.26%	3.67%	5.77%	0.371
51	22.06%	19.72%	47.68%	10.54%	3.71%	5.86%	0.371
52	22.31%	20.12%	46.74%	10.82%	3.74%	5.95%	0.371
53	22.56%	20.53%	45.80%	11.11%	3.78%	6.03%	0.371
54	22.81%	20.93%	44.87%	11.39%	3.81%	6.12%	0.372
55	23.06%	21.33%	43.93%	11.67%	3.84%	6.21%	0.372
56	23.32%	21.73%	43.00%	11.96%	3.88%	6.30%	0.372
57	23.57%	22.13%	42.06%	12.24%	3.91%	6.39%	0.372
58	23.82%	22.53%	41.12%	12.52%	3.95%	6.48%	0.372
59	24.08%	22.93%	40.19%	12.80%	3.98%	6.57%	0.372
60	24.34%	23.33%	39.25%	13.09%	4.01%	6.66%	0.372
61	24.60%	23.72%	38.31%	13.37%	4.05%	6.75%	0.373
62	24.85%	24.12%	37.37%	13.65%	4.08%	6.84%	0.373
63	25.11%	24.52%	36.43%	13.94%	4.12%	6.93%	0.373
64	25.37%	24.92%	35.49%	14.22%	4.15%	7.02%	0.373
65	25.63%	25.31%	34.55%	14.51%	4.19%	7.11%	0.373
66	25.89%	25.71%	33.61%	14.79%	4.22%	7.21%	0.373
67	26.14%	26.10%	32.67%	15.08%	4.25%	7.30%	0.373
68	26.40%	26.50%	31.73%	15.37%	4.29%	7.39%	0.373
69	26.66%	26.90%	30.79%	15.65%	4.32%	7.48%	0.373
70	26.92%	27.29%	29.85%	15.94%	4.36%	7.57%	0.373
71	27.18%	27.69%	28.91%	16.22%	4.39%	7.67%	0.373
72	27.43%	28.09%	27.97%	16.51%	4.43%	7.76%	0.373
73	27.69%	28.48%	27.03%	16.80%	4.46%	7.85%	0.373
74	27.95%	28.88%	26.09%	17.08%	4.50%	7.95%	0.373
75	28.21%	29.27%	25.14%	17.37%	4.53%	8.04%	0.373
76	28.47%	29.67%	24.20%	17.66%	4.56%	8.13%	0.373
77	28.73%	30.07%	23.26%	17.94%	4.60%	8.23%	0.373
78	28.99%	30.46%	22.32%	18.23%	4.63%	8.32%	0.373
79	29.25%	30.86%	21.38%	18.52%	4.67%	8.41%	0.372
80	29.51%	31.25%	20.44%	18.80%	4.70%	8.51%	0.372
81	29.77%	31.64%	19.50%	19.09%	4.74%	8.60%	0.372
82	30.03%	32.04%	18.55%	19.38%	4.77%	8.69%	0.372
83	30.27%	32.43%	17.62%	19.68%	4.81%	8.79%	0.372
84	30.51%	32.83%	16.68%	19.98%	4.84%	8.88%	0.372
85	30.72%	33.22%	15.76%	20.30%	4.87%	8.97%	0.372
86	30.92%	33.62%	14.84%	20.63%	4.91%	9.07%	0.372
87	31.11%	33.99%	13.93%	20.98%	4.94%	9.16%	0.372
88	31.26%	34.36%	13.05%	21.33%	4.97%	9.25%	0.372
89	31.40%	34.75%	12.18%	21.67%	5.00%	9.33%	0.372
90	31.54%	35.15%	11.33%	21.99%	5.04%	9.42%	0.372
91	31.60%	35.60%	10.50%	22.30%	5.07%	9.50%	0.372
92	31.57%	36.12%	9.71%	22.60%	5.09%	9.58%	0.371
93	31.41%	36.71%	8.96%	22.92%	5.12%	9.66%	0.371
94	31.09%	37.45%	8.26%	23.20%	5.15%	9.74%	0.371
95	30.71%	38.25%	7.61%	23.44%	5.17%	9.81%	0.371
96	30.30%	39.16%	7.00%	23.54%	5.20%	9.88%	0.371
97	29.99%	40.05%	6.42%	23.54%	5.22%	9.95%	0.371
98	29.31%	41.24%	5.91%	23.55%	5.24%	10.01%	0.370
99	28.39%	42.48%	5.43%	23.71%	5.26%	10.08%	0.370
100	27.00%	44.50%	5.00%	23.50%	5.28%	10.15%	0.369
^*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).