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
Risk Parity – Find the portfolio that equalizes the risk contribution of portfolio assets
Minimize Tracking Error – Find the portfolio that minimizes the tracking error against the selected benchmark
Maximize Information Ratio – Find the portfolio that maximizes the information ratio against the selected benchmark
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

Use Historical Correlations

Correlation Matrix

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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 1.99% to 4.91%. Refer to the efficient frontier section for additional details. Historical values from Jan 2012 to Jun 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	8.76%
VXUS	Vanguard Total International Stock ETF	3.41%
BND	Vanguard Total Bond Market ETF	86.10%
VNQ	Vanguard Real Estate ETF	1.72%
Save portfolio »

Portfolio Summary

Portfolio statistics
Portfolio	Expected Return	Standard Deviation	Sharpe Ratio
Provided Portfolio	4.37%	9.07%	0.47
Maximum Sharpe Ratio	2.31%	3.50%	0.62
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 (0.14% 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%	13.29%	0.403	0.00%	100.00%
2	Vanguard Total International Stock ETF (VXUS)	5.70%	14.14%	0.393	0.00%	100.00%
3	Vanguard Total Bond Market ETF (BND)	1.80%	3.28%	0.506	0.00%	100.00%
4	Vanguard Real Estate ETF (VNQ)	5.00%	15.45%	0.315	0.00%	100.00%
Results 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 (0.14% annualized).

Asset Correlations

Efficient Frontier Asset Correlations
Name	Ticker	VTI	VXUS	BND	VNQ
Vanguard Total Stock Market ETF	VTI	1.00	0.85	0.02	0.61
Vanguard Total International Stock ETF	VXUS	0.85	1.00	0.10	0.56
Vanguard Total Bond Market ETF	BND	0.02	0.10	1.00	0.49
Vanguard Real Estate ETF	VNQ	0.61	0.56	0.49	1.00
Based on monthly returns from Jan 2012 to Jun 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	4.93%	0.16%	94.91%	0.00%	1.99%	3.20%	0.577
2	5.68%	0.32%	93.97%	0.03%	2.02%	3.21%	0.587
3	6.14%	0.60%	93.16%	0.10%	2.05%	3.22%	0.594
4	6.51%	0.91%	92.38%	0.20%	2.08%	3.23%	0.599
5	6.84%	1.22%	91.62%	0.32%	2.11%	3.25%	0.604
6	7.16%	1.52%	90.86%	0.46%	2.13%	3.28%	0.608
7	7.45%	1.84%	90.08%	0.63%	2.16%	3.31%	0.612
8	7.71%	2.17%	89.30%	0.82%	2.19%	3.34%	0.614
9	7.96%	2.48%	88.52%	1.04%	2.22%	3.38%	0.616
10	8.22%	2.80%	87.72%	1.26%	2.25%	3.42%	0.617
11	8.49%	3.11%	86.92%	1.49%	2.28%	3.46%	0.618
12	8.76%	3.41%	86.10%	1.72%	2.31%	3.50%	0.618
13	9.03%	3.72%	85.29%	1.97%	2.33%	3.55%	0.618
14	9.29%	4.03%	84.47%	2.21%	2.36%	3.60%	0.617
15	9.54%	4.34%	83.65%	2.47%	2.39%	3.65%	0.617
16	9.80%	4.64%	82.83%	2.73%	2.42%	3.71%	0.615
17	10.06%	4.95%	81.99%	3.00%	2.45%	3.77%	0.614
18	10.31%	5.25%	81.15%	3.29%	2.48%	3.83%	0.612
19	10.56%	5.55%	80.31%	3.58%	2.51%	3.89%	0.610
20	10.81%	5.84%	79.48%	3.87%	2.54%	3.96%	0.607
21	11.05%	6.13%	78.64%	4.18%	2.57%	4.02%	0.605
22	11.30%	6.43%	77.80%	4.48%	2.60%	4.09%	0.602
23	11.54%	6.72%	76.95%	4.79%	2.63%	4.16%	0.599
24	11.78%	7.01%	76.11%	5.10%	2.66%	4.23%	0.596
25	12.02%	7.30%	75.27%	5.42%	2.69%	4.30%	0.593
26	12.26%	7.59%	74.42%	5.73%	2.72%	4.38%	0.590
27	12.49%	7.89%	73.58%	6.05%	2.75%	4.45%	0.586
28	12.73%	8.18%	72.73%	6.36%	2.78%	4.53%	0.583
29	12.97%	8.46%	71.88%	6.69%	2.81%	4.61%	0.580
30	13.21%	8.74%	71.03%	7.02%	2.84%	4.69%	0.577
31	13.46%	9.03%	70.18%	7.34%	2.87%	4.77%	0.573
32	13.70%	9.31%	69.32%	7.67%	2.90%	4.85%	0.570
33	13.95%	9.60%	68.46%	8.00%	2.93%	4.93%	0.567
34	14.19%	9.88%	67.60%	8.33%	2.96%	5.01%	0.563
35	14.44%	10.16%	66.74%	8.66%	2.99%	5.10%	0.560
36	14.68%	10.45%	65.88%	8.99%	3.03%	5.18%	0.557
37	14.93%	10.73%	65.02%	9.33%	3.06%	5.27%	0.553
38	15.17%	11.01%	64.16%	9.66%	3.09%	5.36%	0.550
39	15.42%	11.29%	63.30%	9.99%	3.12%	5.44%	0.547
40	15.66%	11.58%	62.44%	10.33%	3.15%	5.53%	0.544
41	15.91%	11.85%	61.58%	10.66%	3.18%	5.62%	0.541
42	16.16%	12.13%	60.72%	11.00%	3.21%	5.71%	0.538
43	16.40%	12.40%	59.86%	11.33%	3.24%	5.80%	0.535
44	16.65%	12.68%	59.00%	11.67%	3.27%	5.89%	0.532
45	16.89%	12.95%	58.14%	12.01%	3.30%	5.98%	0.529
46	17.14%	13.22%	57.29%	12.35%	3.33%	6.07%	0.526
47	17.39%	13.49%	56.43%	12.69%	3.36%	6.16%	0.523
48	17.63%	13.77%	55.57%	13.04%	3.39%	6.25%	0.520
49	17.87%	14.04%	54.70%	13.38%	3.42%	6.34%	0.518
50	18.12%	14.31%	53.84%	13.73%	3.45%	6.43%	0.515
51	18.36%	14.59%	52.97%	14.08%	3.48%	6.53%	0.512
52	18.61%	14.87%	52.10%	14.43%	3.52%	6.62%	0.510
53	18.85%	15.14%	51.22%	14.79%	3.55%	6.72%	0.507
54	19.09%	15.42%	50.35%	15.14%	3.58%	6.81%	0.504
55	19.34%	15.70%	49.47%	15.50%	3.61%	6.91%	0.502
56	19.58%	15.97%	48.60%	15.85%	3.64%	7.01%	0.500
57	19.82%	16.25%	47.72%	16.21%	3.67%	7.10%	0.497
58	20.06%	16.53%	46.85%	16.57%	3.70%	7.20%	0.495
59	20.30%	16.80%	45.97%	16.93%	3.73%	7.30%	0.492
60	20.54%	17.08%	45.10%	17.28%	3.76%	7.39%	0.490
61	20.78%	17.36%	44.22%	17.64%	3.80%	7.49%	0.488
62	21.02%	17.63%	43.35%	18.00%	3.83%	7.59%	0.486
63	21.26%	17.91%	42.47%	18.36%	3.86%	7.69%	0.484
64	21.50%	18.19%	41.59%	18.72%	3.89%	7.79%	0.482
65	21.74%	18.46%	40.72%	19.08%	3.92%	7.89%	0.479
66	21.98%	18.74%	39.84%	19.43%	3.95%	7.98%	0.477
67	22.22%	19.02%	38.97%	19.79%	3.98%	8.08%	0.475
68	22.47%	19.29%	38.09%	20.15%	4.01%	8.18%	0.474
69	22.71%	19.57%	37.22%	20.51%	4.05%	8.28%	0.472
70	22.95%	19.84%	36.34%	20.87%	4.08%	8.38%	0.470
71	23.19%	20.12%	35.47%	21.23%	4.11%	8.48%	0.468
72	23.43%	20.39%	34.59%	21.59%	4.14%	8.58%	0.466
73	23.67%	20.67%	33.72%	21.94%	4.17%	8.68%	0.464
74	23.91%	20.94%	32.84%	22.30%	4.20%	8.78%	0.463
75	24.16%	21.22%	31.96%	22.66%	4.23%	8.88%	0.461
76	24.40%	21.49%	31.09%	23.02%	4.27%	8.98%	0.459
77	24.64%	21.77%	30.21%	23.38%	4.30%	9.08%	0.458
78	24.88%	22.04%	29.34%	23.74%	4.33%	9.18%	0.456
79	25.12%	22.32%	28.46%	24.10%	4.36%	9.28%	0.454
80	25.37%	22.60%	27.58%	24.46%	4.39%	9.38%	0.453
81	25.61%	22.87%	26.70%	24.81%	4.42%	9.49%	0.451
82	25.85%	23.15%	25.83%	25.17%	4.45%	9.59%	0.450
83	26.09%	23.42%	24.95%	25.53%	4.48%	9.69%	0.448
84	26.34%	23.70%	24.08%	25.89%	4.52%	9.79%	0.447
85	26.56%	23.96%	23.21%	26.27%	4.55%	9.89%	0.446
86	26.77%	24.22%	22.34%	26.66%	4.58%	9.99%	0.444
87	26.98%	24.46%	21.49%	27.07%	4.61%	10.09%	0.443
88	27.17%	24.70%	20.64%	27.49%	4.64%	10.19%	0.441
89	27.31%	24.94%	19.80%	27.95%	4.67%	10.29%	0.440
90	27.39%	25.18%	18.98%	28.45%	4.70%	10.39%	0.439
91	27.40%	25.42%	18.18%	29.00%	4.72%	10.48%	0.437
92	27.32%	25.63%	17.41%	29.64%	4.75%	10.58%	0.436
93	27.21%	25.80%	16.66%	30.34%	4.78%	10.67%	0.434
94	27.05%	25.93%	15.93%	31.09%	4.80%	10.76%	0.433
95	26.83%	26.14%	15.26%	31.78%	4.82%	10.84%	0.432
96	26.55%	26.35%	14.61%	32.48%	4.84%	10.93%	0.430
97	26.07%	26.79%	14.02%	33.12%	4.86%	11.00%	0.429
98	25.26%	27.37%	13.48%	33.89%	4.88%	11.08%	0.428
99	24.07%	28.36%	12.98%	34.60%	4.90%	11.15%	0.427
100	21.50%	30.50%	12.50%	35.50%	4.91%	11.23%	0.425
^*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 (0.14% annualized).