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 2.15% to 5.24%. Refer to the efficient frontier section for additional details. Historical values from Jan 2012 to Nov 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	30.82%
VXUS	Vanguard Total International Stock ETF	31.74%
BND	Vanguard Total Bond Market ETF	5.31%
VNQ	Vanguard Real Estate ETF	32.13%
Save portfolio »

Portfolio Summary

Portfolio statistics
Portfolio	Expected Return	Standard Deviation	Sharpe Ratio
Provided Portfolio	4.37%	7.57%	0.29
Maximum Sharpe Ratio	5.20%	10.00%	0.30
Expected return is based on the provided capital market expectations. Ex ante Sharpe Ratio calculated using the current 1-month treasury bill return as the risk-free rate (2.18% 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%	11.36%	0.292	0.00%	100.00%
2	Vanguard Total International Stock ETF (VXUS)	5.70%	12.57%	0.280	0.00%	100.00%
3	Vanguard Total Bond Market ETF (BND)	1.80%	3.11%	-0.123	0.00%	100.00%
4	Vanguard Real Estate ETF (VNQ)	5.00%	13.69%	0.206	0.00%	100.00%
^*Expected return based on the provided capital market expectations. Ex ante Sharpe Ratio calculated using the current 1-month treasury bill return as the risk-free rate (2.18% 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	0.42
Vanguard Total Bond Market ETF	BND	-0.12	0.03	1.00	0.49
Vanguard Real Estate ETF	VNQ	0.48	0.42	0.49	1.00
Based on monthly returns from Jan 2012 to Nov 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	9.48%	0.06%	90.45%	0.00%	2.15%	2.89%	-0.012
2	10.29%	0.21%	89.45%	0.04%	2.18%	2.90%	0.001
3	10.86%	0.45%	88.58%	0.12%	2.22%	2.91%	0.012
4	11.31%	0.72%	87.76%	0.22%	2.25%	2.93%	0.022
5	11.69%	0.99%	86.97%	0.35%	2.28%	2.95%	0.032
6	12.01%	1.31%	86.19%	0.49%	2.30%	2.98%	0.041
7	12.28%	1.64%	85.42%	0.65%	2.33%	3.00%	0.050
8	12.54%	1.98%	84.65%	0.83%	2.36%	3.04%	0.059
9	12.78%	2.32%	83.88%	1.02%	2.39%	3.07%	0.067
10	12.98%	2.67%	83.11%	1.23%	2.42%	3.11%	0.075
11	13.20%	3.02%	82.33%	1.45%	2.44%	3.14%	0.083
12	13.41%	3.38%	81.55%	1.67%	2.47%	3.18%	0.091
13	13.63%	3.72%	80.76%	1.90%	2.50%	3.23%	0.099
14	13.86%	4.05%	79.95%	2.14%	2.53%	3.27%	0.106
15	14.09%	4.39%	79.12%	2.39%	2.56%	3.32%	0.114
16	14.33%	4.73%	78.29%	2.65%	2.59%	3.37%	0.121
17	14.58%	5.06%	77.45%	2.92%	2.62%	3.42%	0.128
18	14.83%	5.39%	76.60%	3.18%	2.65%	3.48%	0.135
19	15.07%	5.73%	75.76%	3.45%	2.68%	3.53%	0.141
20	15.32%	6.06%	74.90%	3.72%	2.71%	3.59%	0.147
21	15.57%	6.40%	74.04%	3.99%	2.74%	3.65%	0.154
22	15.82%	6.74%	73.17%	4.27%	2.77%	3.71%	0.159
23	16.08%	7.06%	72.29%	4.56%	2.80%	3.77%	0.165
24	16.34%	7.39%	71.41%	4.85%	2.84%	3.84%	0.171
25	16.60%	7.71%	70.53%	5.16%	2.87%	3.90%	0.176
26	16.86%	8.02%	69.65%	5.46%	2.90%	3.97%	0.181
27	17.12%	8.34%	68.76%	5.77%	2.93%	4.04%	0.186
28	17.38%	8.66%	67.87%	6.08%	2.96%	4.11%	0.190
29	17.65%	8.98%	66.97%	6.40%	2.99%	4.18%	0.195
30	17.91%	9.30%	66.08%	6.71%	3.03%	4.25%	0.199
31	18.18%	9.61%	65.18%	7.03%	3.06%	4.32%	0.203
32	18.44%	9.93%	64.28%	7.35%	3.09%	4.40%	0.207
33	18.71%	10.25%	63.37%	7.67%	3.12%	4.47%	0.211
34	18.98%	10.57%	62.47%	7.98%	3.16%	4.55%	0.214
35	19.25%	10.89%	61.56%	8.30%	3.19%	4.62%	0.218
36	19.52%	11.21%	60.65%	8.63%	3.22%	4.70%	0.221
37	19.78%	11.53%	59.74%	8.95%	3.25%	4.78%	0.224
38	20.05%	11.85%	58.82%	9.27%	3.29%	4.86%	0.227
39	20.32%	12.17%	57.91%	9.60%	3.32%	4.94%	0.230
40	20.59%	12.49%	57.00%	9.92%	3.35%	5.02%	0.233
41	20.86%	12.81%	56.08%	10.25%	3.38%	5.10%	0.236
42	21.13%	13.14%	55.17%	10.57%	3.42%	5.18%	0.239
43	21.40%	13.45%	54.25%	10.90%	3.45%	5.26%	0.241
44	21.67%	13.77%	53.33%	11.23%	3.48%	5.34%	0.244
45	21.94%	14.09%	52.42%	11.55%	3.52%	5.43%	0.246
46	22.21%	14.41%	51.50%	11.88%	3.55%	5.51%	0.248
47	22.48%	14.73%	50.58%	12.21%	3.58%	5.59%	0.250
48	22.75%	15.05%	49.66%	12.54%	3.62%	5.68%	0.253
49	23.02%	15.36%	48.74%	12.87%	3.65%	5.76%	0.255
50	23.29%	15.68%	47.82%	13.20%	3.68%	5.84%	0.257
51	23.57%	16.00%	46.90%	13.54%	3.71%	5.93%	0.258
52	23.84%	16.31%	45.98%	13.87%	3.75%	6.02%	0.260
53	24.11%	16.63%	45.06%	14.20%	3.78%	6.10%	0.262
54	24.38%	16.94%	44.14%	14.54%	3.81%	6.19%	0.264
55	24.65%	17.26%	43.22%	14.87%	3.85%	6.27%	0.265
56	24.92%	17.57%	42.29%	15.21%	3.88%	6.36%	0.267
57	25.19%	17.89%	41.37%	15.55%	3.91%	6.45%	0.269
58	25.47%	18.20%	40.45%	15.89%	3.95%	6.53%	0.270
59	25.74%	18.51%	39.52%	16.23%	3.98%	6.62%	0.271
60	26.01%	18.82%	38.58%	16.58%	4.01%	6.71%	0.273
61	26.28%	19.14%	37.65%	16.93%	4.05%	6.80%	0.274
62	26.56%	19.45%	36.71%	17.29%	4.08%	6.89%	0.276
63	26.83%	19.76%	35.77%	17.64%	4.11%	6.98%	0.277
64	27.10%	20.07%	34.83%	18.00%	4.15%	7.07%	0.278
65	27.38%	20.38%	33.89%	18.35%	4.18%	7.16%	0.279
66	27.65%	20.69%	32.95%	18.71%	4.22%	7.25%	0.281
67	27.93%	21.00%	32.01%	19.06%	4.25%	7.34%	0.282
68	28.20%	21.31%	31.07%	19.42%	4.28%	7.43%	0.283
69	28.48%	21.62%	30.12%	19.78%	4.32%	7.52%	0.284
70	28.75%	21.93%	29.18%	20.13%	4.35%	7.62%	0.285
71	29.03%	22.24%	28.24%	20.49%	4.39%	7.71%	0.286
72	29.30%	22.55%	27.30%	20.84%	4.42%	7.80%	0.287
73	29.57%	22.86%	26.36%	21.20%	4.45%	7.89%	0.288
74	29.85%	23.18%	25.40%	21.58%	4.49%	7.98%	0.289
75	30.12%	23.49%	24.44%	21.95%	4.52%	8.08%	0.290
76	30.40%	23.80%	23.47%	22.33%	4.56%	8.17%	0.291
77	30.67%	24.11%	22.51%	22.71%	4.59%	8.27%	0.291
78	30.95%	24.42%	21.55%	23.08%	4.63%	8.36%	0.292
79	31.23%	24.73%	20.59%	23.46%	4.66%	8.46%	0.293
80	31.50%	25.04%	19.63%	23.83%	4.70%	8.55%	0.294
81	31.78%	25.35%	18.66%	24.21%	4.73%	8.65%	0.295
82	32.05%	25.66%	17.71%	24.59%	4.76%	8.74%	0.296
83	32.30%	25.97%	16.75%	24.98%	4.80%	8.83%	0.296
84	32.55%	26.28%	15.80%	25.37%	4.83%	8.93%	0.297
85	32.77%	26.59%	14.86%	25.78%	4.87%	9.02%	0.298
86	32.99%	26.89%	13.93%	26.20%	4.90%	9.11%	0.298
87	33.19%	27.17%	13.01%	26.63%	4.93%	9.21%	0.299
88	33.35%	27.44%	12.10%	27.10%	4.97%	9.30%	0.299
89	33.45%	27.68%	11.23%	27.64%	5.00%	9.38%	0.300
90	33.45%	27.98%	10.38%	28.19%	5.03%	9.47%	0.300
91	33.38%	28.31%	9.55%	28.76%	5.05%	9.55%	0.301
92	33.26%	28.62%	8.76%	29.36%	5.08%	9.63%	0.301
93	33.12%	28.92%	7.99%	29.97%	5.11%	9.71%	0.301
94	32.91%	29.29%	7.24%	30.56%	5.13%	9.79%	0.302
95	32.49%	29.83%	6.54%	31.14%	5.16%	9.86%	0.302
96	31.89%	30.61%	5.89%	31.61%	5.18%	9.93%	0.302
97	30.82%	31.74%	5.31%	32.13%	5.20%	10.00%	0.302
98	29.38%	33.17%	4.82%	32.63%	5.22%	10.06%	0.302
99	27.90%	34.57%	4.40%	33.14%	5.24%	10.12%	0.302
100	26.00%	35.50%	4.00%	34.50%	5.25%	10.18%	0.301
^*Ex-ante values shown for portfolio return and volatility. Ex ante Sharpe Ratio calculated using the current 1-month treasury bill return as the risk-free rate (2.18% annualized).