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

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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 1.96% to 5.08%. Refer to the efficient frontier section for additional details. Historical values from Jan 2012 to Dec 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	7.41%
VXUS	Vanguard Total International Stock ETF	3.59%
BND	Vanguard Total Bond Market ETF	87.07%
VNQ	Vanguard Real Estate ETF	1.93%
Save portfolio »

Portfolio Summary

Portfolio statistics
Portfolio	Expected Return	Standard Deviation	Sharpe Ratio
Provided Portfolio	4.37%	9.43%	0.45
Maximum Sharpe Ratio	2.27%	3.54%	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 (0.09% 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%	13.81%	0.392	0.00%	100.00%
2	Vanguard Total International Stock ETF (VXUS)	5.70%	14.59%	0.385	0.00%	100.00%
3	Vanguard Total Bond Market ETF (BND)	1.80%	3.27%	0.524	0.00%	100.00%
4	Vanguard Real Estate ETF (VNQ)	5.00%	15.44%	0.318	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 (0.09% annualized).

Asset Correlations

Efficient Frontier Asset Correlations
Name	Ticker	VTI	VXUS	BND	VNQ
Vanguard Total Stock Market ETF	VTI	1.00	0.86	0.05	0.63
Vanguard Total International Stock ETF	VXUS	0.86	1.00	0.13	0.58
Vanguard Total Bond Market ETF	BND	0.05	0.13	1.00	0.50
Vanguard Real Estate ETF	VNQ	0.63	0.58	0.50	1.00
Based on monthly returns from Jan 2012 to Dec 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	4.09%	0.19%	95.72%	0.00%	1.96%	3.21%	0.581
2	4.67%	0.34%	94.93%	0.06%	1.99%	3.22%	0.589
3	5.08%	0.59%	94.19%	0.14%	2.01%	3.23%	0.595
4	5.39%	0.91%	93.45%	0.25%	2.04%	3.25%	0.600
5	5.67%	1.25%	92.67%	0.41%	2.07%	3.27%	0.605
6	5.91%	1.61%	91.89%	0.58%	2.10%	3.30%	0.608
7	6.16%	1.95%	91.13%	0.77%	2.12%	3.33%	0.611
8	6.38%	2.27%	90.36%	0.99%	2.15%	3.36%	0.613
9	6.63%	2.59%	89.56%	1.22%	2.18%	3.40%	0.614
10	6.89%	2.92%	88.75%	1.45%	2.21%	3.44%	0.616
11	7.14%	3.25%	87.92%	1.69%	2.24%	3.49%	0.616
12	7.41%	3.59%	87.07%	1.93%	2.27%	3.54%	0.616
13	7.67%	3.93%	86.22%	2.18%	2.30%	3.59%	0.616
14	7.94%	4.27%	85.36%	2.44%	2.33%	3.64%	0.615
15	8.19%	4.62%	84.50%	2.69%	2.36%	3.70%	0.614
16	8.45%	4.97%	83.63%	2.96%	2.39%	3.76%	0.612
17	8.70%	5.32%	82.75%	3.23%	2.42%	3.82%	0.611
18	8.96%	5.67%	81.88%	3.50%	2.46%	3.89%	0.608
19	9.21%	6.02%	81.00%	3.78%	2.49%	3.96%	0.606
20	9.46%	6.36%	80.12%	4.05%	2.52%	4.03%	0.603
21	9.72%	6.70%	79.24%	4.33%	2.55%	4.10%	0.601
22	9.98%	7.04%	78.36%	4.62%	2.58%	4.17%	0.598
23	10.24%	7.37%	77.49%	4.90%	2.61%	4.24%	0.594
24	10.50%	7.70%	76.61%	5.19%	2.64%	4.32%	0.591
25	10.76%	8.04%	75.72%	5.48%	2.68%	4.40%	0.588
26	11.02%	8.37%	74.83%	5.78%	2.71%	4.48%	0.584
27	11.28%	8.70%	73.93%	6.08%	2.74%	4.56%	0.581
28	11.54%	9.03%	73.04%	6.38%	2.77%	4.65%	0.577
29	11.80%	9.36%	72.15%	6.69%	2.80%	4.73%	0.574
30	12.06%	9.69%	71.26%	6.99%	2.84%	4.82%	0.570
31	12.31%	10.02%	70.36%	7.30%	2.87%	4.90%	0.567
32	12.57%	10.35%	69.46%	7.62%	2.90%	4.99%	0.563
33	12.83%	10.68%	68.56%	7.93%	2.93%	5.08%	0.559
34	13.09%	11.01%	67.65%	8.24%	2.96%	5.17%	0.556
35	13.35%	11.35%	66.75%	8.56%	3.00%	5.26%	0.552
36	13.61%	11.68%	65.84%	8.88%	3.03%	5.36%	0.549
37	13.86%	12.00%	64.94%	9.20%	3.06%	5.45%	0.545
38	14.12%	12.33%	64.03%	9.52%	3.09%	5.54%	0.542
39	14.38%	12.65%	63.13%	9.84%	3.13%	5.64%	0.539
40	14.64%	12.98%	62.22%	10.16%	3.16%	5.73%	0.535
41	14.91%	13.30%	61.31%	10.48%	3.19%	5.83%	0.532
42	15.17%	13.62%	60.40%	10.81%	3.22%	5.93%	0.529
43	15.43%	13.94%	59.49%	11.13%	3.26%	6.03%	0.525
44	15.69%	14.27%	58.57%	11.46%	3.29%	6.13%	0.522
45	15.95%	14.60%	57.66%	11.79%	3.32%	6.23%	0.519
46	16.22%	14.93%	56.74%	12.12%	3.36%	6.33%	0.516
47	16.48%	15.26%	55.82%	12.44%	3.39%	6.43%	0.513
48	16.74%	15.59%	54.90%	12.77%	3.42%	6.53%	0.510
49	17.00%	15.92%	53.98%	13.10%	3.45%	6.63%	0.507
50	17.26%	16.24%	53.06%	13.43%	3.49%	6.73%	0.505
51	17.53%	16.57%	52.15%	13.75%	3.52%	6.84%	0.502
52	17.79%	16.90%	51.23%	14.08%	3.55%	6.94%	0.499
53	18.05%	17.23%	50.31%	14.41%	3.59%	7.04%	0.496
54	18.32%	17.56%	49.39%	14.73%	3.62%	7.15%	0.494
55	18.58%	17.89%	48.47%	15.06%	3.65%	7.25%	0.491
56	18.84%	18.22%	47.55%	15.39%	3.69%	7.35%	0.489
57	19.11%	18.55%	46.63%	15.71%	3.72%	7.46%	0.486
58	19.37%	18.88%	45.71%	16.04%	3.75%	7.56%	0.484
59	19.64%	19.20%	44.79%	16.37%	3.78%	7.67%	0.482
60	19.90%	19.53%	43.87%	16.70%	3.82%	7.78%	0.479
61	20.17%	19.86%	42.95%	17.03%	3.85%	7.88%	0.477
62	20.43%	20.19%	42.03%	17.35%	3.88%	7.99%	0.475
63	20.70%	20.52%	41.11%	17.68%	3.92%	8.10%	0.473
64	20.96%	20.84%	40.19%	18.01%	3.95%	8.20%	0.471
65	21.23%	21.17%	39.27%	18.34%	3.98%	8.31%	0.469
66	21.49%	21.50%	38.34%	18.67%	4.02%	8.42%	0.467
67	21.76%	21.82%	37.42%	19.00%	4.05%	8.52%	0.465
68	22.02%	22.15%	36.50%	19.33%	4.08%	8.63%	0.463
69	22.29%	22.47%	35.58%	19.66%	4.12%	8.74%	0.461
70	22.56%	22.80%	34.66%	19.99%	4.15%	8.85%	0.459
71	22.82%	23.13%	33.74%	20.31%	4.18%	8.96%	0.457
72	23.09%	23.45%	32.82%	20.64%	4.22%	9.06%	0.455
73	23.35%	23.78%	31.89%	20.97%	4.25%	9.17%	0.453
74	23.62%	24.11%	30.97%	21.30%	4.28%	9.28%	0.452
75	23.88%	24.43%	30.05%	21.63%	4.32%	9.39%	0.450
76	24.15%	24.76%	29.13%	21.96%	4.35%	9.50%	0.448
77	24.41%	25.09%	28.20%	22.29%	4.38%	9.61%	0.447
78	24.68%	25.42%	27.28%	22.62%	4.42%	9.72%	0.445
79	24.94%	25.74%	26.36%	22.95%	4.45%	9.83%	0.444
80	25.21%	26.07%	25.44%	23.28%	4.48%	9.94%	0.442
81	25.47%	26.40%	24.51%	23.61%	4.52%	10.05%	0.441
82	25.74%	26.73%	23.59%	23.94%	4.55%	10.16%	0.439
83	26.00%	27.05%	22.67%	24.28%	4.58%	10.27%	0.438
84	26.27%	27.38%	21.75%	24.61%	4.62%	10.38%	0.436
85	26.53%	27.71%	20.82%	24.94%	4.65%	10.49%	0.435
86	26.80%	28.03%	19.90%	25.27%	4.68%	10.60%	0.433
87	27.06%	28.36%	18.98%	25.60%	4.72%	10.71%	0.432
88	27.31%	28.67%	18.07%	25.94%	4.75%	10.82%	0.431
89	27.57%	28.99%	17.16%	26.28%	4.78%	10.93%	0.429
90	27.82%	29.30%	16.25%	26.63%	4.82%	11.04%	0.428
91	28.08%	29.60%	15.34%	26.98%	4.85%	11.15%	0.427
92	28.27%	29.89%	14.45%	27.39%	4.88%	11.25%	0.426
93	28.39%	30.18%	13.58%	27.85%	4.91%	11.36%	0.424
94	28.48%	30.46%	12.74%	28.31%	4.94%	11.46%	0.423
95	28.55%	30.74%	11.93%	28.78%	4.97%	11.56%	0.422
96	28.59%	31.00%	11.16%	29.25%	5.00%	11.65%	0.421
97	28.33%	31.39%	10.44%	29.84%	5.02%	11.74%	0.420
98	27.68%	32.10%	9.75%	30.47%	5.05%	11.83%	0.419
99	26.71%	33.18%	9.10%	31.02%	5.07%	11.91%	0.418
100	26.00%	33.00%	8.50%	32.50%	5.08%	11.99%	0.417
^*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 (0.09% annualized).