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 Save

Portfolio optimization results with goal to maximize Sharpe ratio. The possible range of expected annual portfolio returns based on provided parameters is 1.97% to 5.00%. Refer to the efficient frontier section for additional details. Historical values from Jan 2012 to Sep 2021 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	7.91%
VXUS	Vanguard Total International Stock ETF	4.03%
BND	Vanguard Total Bond Market ETF	86.77%
VNQ	Vanguard Real Estate ETF	1.29%
Save portfolio »

Portfolio Summary

Portfolio statistics
Portfolio	Expected Return	Standard Deviation	Sharpe Ratio
Provided Portfolio	4.37%	9.22%	0.47
Maximum Sharpe Ratio	2.28%	3.53%	0.64
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.

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%	13.51%	0.394	0.00%	100.00%
2	Vanguard Total International Stock ETF (VXUS)	5.70%	14.14%	0.390	0.00%	100.00%
3	Vanguard Total Bond Market ETF (BND)	1.80%	3.30%	0.529	0.00%	100.00%
4	Vanguard Real Estate ETF (VNQ)	5.00%	15.29%	0.317	0.00%	100.00%
Results based on the provided capital market expectations. Expected return is the annualized monthly arithmetic mean return. Ex-ante Sharpe Ratio calculated using the current 3-month treasury bill return as the risk-free rate.

Asset Correlations

Efficient Frontier Asset Correlations
Name	Ticker	VTI	VXUS	BND	VNQ
Vanguard Total Stock Market ETF	VTI	1.00	0.86	0.06	0.64
Vanguard Total International Stock ETF	VXUS	0.86	1.00	0.12	0.58
Vanguard Total Bond Market ETF	BND	0.06	0.12	1.00	0.47
Vanguard Real Estate ETF	VNQ	0.64	0.58	0.47	1.00
Based on monthly returns from Jan 2012 to Sep 2021

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	4.15%	0.50%	95.35%	0.00%	1.97%	3.25%	0.589
2	4.76%	0.65%	94.56%	0.02%	2.00%	3.25%	0.597
3	5.24%	0.89%	93.80%	0.08%	2.03%	3.26%	0.603
4	5.67%	1.16%	93.02%	0.15%	2.06%	3.28%	0.609
5	6.04%	1.47%	92.25%	0.24%	2.08%	3.30%	0.614
6	6.33%	1.84%	91.50%	0.34%	2.11%	3.32%	0.618
7	6.59%	2.22%	90.75%	0.45%	2.14%	3.34%	0.622
8	6.84%	2.58%	89.99%	0.59%	2.17%	3.37%	0.624
9	7.11%	2.96%	89.20%	0.74%	2.20%	3.41%	0.627
10	7.38%	3.32%	88.39%	0.91%	2.23%	3.44%	0.628
11	7.65%	3.68%	87.58%	1.09%	2.25%	3.48%	0.629
12	7.91%	4.03%	86.77%	1.29%	2.28%	3.53%	0.630
13	8.16%	4.39%	85.95%	1.49%	2.31%	3.57%	0.630
14	8.41%	4.75%	85.13%	1.70%	2.34%	3.62%	0.629
15	8.65%	5.11%	84.32%	1.92%	2.37%	3.67%	0.628
16	8.90%	5.47%	83.50%	2.14%	2.40%	3.73%	0.627
17	9.15%	5.82%	82.67%	2.36%	2.43%	3.78%	0.626
18	9.40%	6.18%	81.83%	2.58%	2.46%	3.84%	0.624
19	9.65%	6.54%	81.00%	2.81%	2.49%	3.90%	0.622
20	9.91%	6.89%	80.16%	3.04%	2.52%	3.96%	0.619
21	10.16%	7.24%	79.33%	3.27%	2.55%	4.03%	0.617
22	10.42%	7.59%	78.47%	3.52%	2.58%	4.09%	0.614
23	10.67%	7.94%	77.62%	3.77%	2.61%	4.16%	0.611
24	10.92%	8.28%	76.77%	4.02%	2.65%	4.23%	0.608
25	11.18%	8.61%	75.92%	4.29%	2.68%	4.31%	0.604
26	11.44%	8.95%	75.06%	4.56%	2.71%	4.38%	0.601
27	11.69%	9.28%	74.20%	4.83%	2.74%	4.46%	0.598
28	11.94%	9.61%	73.33%	5.11%	2.77%	4.53%	0.594
29	12.20%	9.95%	72.47%	5.39%	2.80%	4.61%	0.591
30	12.45%	10.28%	71.60%	5.66%	2.83%	4.69%	0.587
31	12.71%	10.62%	70.74%	5.94%	2.86%	4.77%	0.583
32	12.96%	10.95%	69.88%	6.22%	2.89%	4.86%	0.580
33	13.21%	11.28%	69.01%	6.50%	2.92%	4.94%	0.576
34	13.46%	11.61%	68.15%	6.78%	2.95%	5.02%	0.573
35	13.71%	11.95%	67.27%	7.07%	2.99%	5.11%	0.569
36	13.97%	12.28%	66.40%	7.36%	3.02%	5.19%	0.565
37	14.22%	12.61%	65.52%	7.65%	3.05%	5.28%	0.562
38	14.47%	12.95%	64.65%	7.94%	3.08%	5.37%	0.558
39	14.72%	13.28%	63.77%	8.23%	3.11%	5.46%	0.555
40	14.97%	13.61%	62.90%	8.52%	3.14%	5.55%	0.551
41	15.22%	13.95%	62.02%	8.82%	3.18%	5.64%	0.548
42	15.47%	14.28%	61.14%	9.11%	3.21%	5.73%	0.545
43	15.72%	14.61%	60.27%	9.40%	3.24%	5.82%	0.541
44	15.97%	14.95%	59.38%	9.70%	3.27%	5.91%	0.538
45	16.23%	15.29%	58.49%	9.99%	3.30%	6.01%	0.535
46	16.48%	15.62%	57.61%	10.29%	3.33%	6.10%	0.532
47	16.73%	15.96%	56.72%	10.59%	3.37%	6.20%	0.529
48	16.98%	16.31%	55.82%	10.89%	3.40%	6.29%	0.525
49	17.24%	16.64%	54.93%	11.20%	3.43%	6.39%	0.522
50	17.49%	16.97%	54.03%	11.51%	3.46%	6.49%	0.519
51	17.74%	17.30%	53.13%	11.83%	3.49%	6.58%	0.516
52	17.99%	17.63%	52.24%	12.14%	3.53%	6.68%	0.514
53	18.25%	17.96%	51.34%	12.45%	3.56%	6.78%	0.511
54	18.50%	18.29%	50.44%	12.77%	3.59%	6.88%	0.508
55	18.75%	18.63%	49.54%	13.08%	3.62%	6.98%	0.505
56	19.01%	18.96%	48.64%	13.39%	3.66%	7.08%	0.502
57	19.26%	19.29%	47.75%	13.71%	3.69%	7.18%	0.500
58	19.52%	19.62%	46.85%	14.02%	3.72%	7.28%	0.497
59	19.77%	19.95%	45.95%	14.33%	3.75%	7.38%	0.495
60	20.03%	20.28%	45.05%	14.64%	3.79%	7.48%	0.492
61	20.28%	20.61%	44.15%	14.96%	3.82%	7.58%	0.490
62	20.54%	20.94%	43.25%	15.27%	3.85%	7.68%	0.487
63	20.80%	21.27%	42.35%	15.58%	3.88%	7.78%	0.485
64	21.05%	21.60%	41.45%	15.90%	3.92%	7.89%	0.483
65	21.31%	21.94%	40.55%	16.21%	3.95%	7.99%	0.481
66	21.56%	22.27%	39.65%	16.52%	3.98%	8.09%	0.478
67	21.82%	22.60%	38.74%	16.84%	4.01%	8.19%	0.476
68	22.07%	22.93%	37.84%	17.16%	4.05%	8.30%	0.474
69	22.32%	23.26%	36.94%	17.47%	4.08%	8.40%	0.472
70	22.58%	23.60%	36.04%	17.79%	4.11%	8.50%	0.470
71	22.83%	23.93%	35.14%	18.10%	4.14%	8.61%	0.468
72	23.09%	24.26%	34.24%	18.42%	4.18%	8.71%	0.466
73	23.34%	24.59%	33.33%	18.73%	4.21%	8.82%	0.464
74	23.59%	24.92%	32.43%	19.05%	4.24%	8.92%	0.462
75	23.85%	25.25%	31.53%	19.37%	4.27%	9.02%	0.460
76	24.10%	25.58%	30.63%	19.69%	4.31%	9.13%	0.458
77	24.35%	25.92%	29.73%	20.00%	4.34%	9.23%	0.457
78	24.61%	26.25%	28.83%	20.32%	4.37%	9.34%	0.455
79	24.86%	26.58%	27.92%	20.64%	4.40%	9.44%	0.453
80	25.11%	26.91%	27.02%	20.95%	4.44%	9.55%	0.451
81	25.37%	27.24%	26.12%	21.27%	4.47%	9.65%	0.450
82	25.62%	27.57%	25.22%	21.59%	4.50%	9.76%	0.448
83	25.88%	27.90%	24.32%	21.91%	4.54%	9.86%	0.446
84	26.13%	28.23%	23.42%	22.22%	4.57%	9.97%	0.445
85	26.38%	28.56%	22.52%	22.54%	4.60%	10.08%	0.443
86	26.61%	28.90%	21.62%	22.87%	4.63%	10.18%	0.442
87	26.84%	29.23%	20.73%	23.20%	4.67%	10.29%	0.440
88	27.05%	29.57%	19.84%	23.54%	4.70%	10.39%	0.439
89	27.24%	29.90%	18.95%	23.91%	4.73%	10.49%	0.437
90	27.41%	30.21%	18.09%	24.29%	4.76%	10.60%	0.436
91	27.59%	30.49%	17.23%	24.69%	4.79%	10.70%	0.435
92	27.75%	30.72%	16.39%	25.15%	4.82%	10.80%	0.433
93	27.86%	30.91%	15.58%	25.66%	4.85%	10.89%	0.432
94	27.93%	31.03%	14.79%	26.25%	4.88%	10.99%	0.431
95	27.91%	31.16%	14.04%	26.89%	4.90%	11.08%	0.429
96	27.85%	31.29%	13.33%	27.53%	4.92%	11.16%	0.428
97	27.68%	31.60%	12.66%	28.07%	4.95%	11.24%	0.427
98	27.15%	32.23%	12.03%	28.58%	4.97%	11.32%	0.426
99	26.61%	32.92%	11.47%	29.00%	4.99%	11.39%	0.425
100	26.00%	34.00%	11.00%	29.00%	5.01%	11.45%	0.424
^*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.