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 4.92%. Refer to the efficient frontier section for additional details. Historical values from Jan 2012 to Jun 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	7.44%
VXUS	Vanguard Total International Stock ETF	3.61%
BND	Vanguard Total Bond Market ETF	87.11%
VNQ	Vanguard Real Estate ETF	1.84%
Save portfolio »

Portfolio Summary

Portfolio statistics
Portfolio	Expected Return	Standard Deviation	Sharpe Ratio
Provided Portfolio	4.37%	9.24%	0.47
Maximum Sharpe Ratio	2.27%	3.52%	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%	13.55%	0.395	0.00%	100.00%
2	Vanguard Total International Stock ETF (VXUS)	5.70%	14.25%	0.389	0.00%	100.00%
3	Vanguard Total Bond Market ETF (BND)	1.80%	3.30%	0.538	0.00%	100.00%
4	Vanguard Real Estate ETF (VNQ)	5.00%	15.30%	0.319	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	0.04	0.64
Vanguard Total International Stock ETF	VXUS	0.86	1.00	0.11	0.58
Vanguard Total Bond Market ETF	BND	0.04	0.11	1.00	0.46
Vanguard Real Estate ETF	VNQ	0.64	0.58	0.46	1.00
Based on monthly returns from Jan 2012 to Jun 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	4.42%	0.21%	95.38%	0.00%	1.97%	3.24%	0.599
2	4.98%	0.45%	94.54%	0.02%	2.00%	3.24%	0.608
3	5.40%	0.74%	93.77%	0.09%	2.03%	3.25%	0.614
4	5.70%	1.05%	93.04%	0.21%	2.05%	3.27%	0.619
5	5.95%	1.36%	92.33%	0.36%	2.08%	3.29%	0.623
6	6.19%	1.67%	91.60%	0.53%	2.11%	3.31%	0.627
7	6.40%	1.99%	90.88%	0.72%	2.13%	3.34%	0.629
8	6.60%	2.32%	90.15%	0.93%	2.16%	3.37%	0.631
9	6.81%	2.64%	89.41%	1.14%	2.19%	3.40%	0.633
10	7.02%	2.97%	88.64%	1.37%	2.21%	3.44%	0.634
11	7.23%	3.29%	87.88%	1.60%	2.24%	3.48%	0.635
12	7.44%	3.61%	87.11%	1.84%	2.27%	3.52%	0.635
13	7.66%	3.93%	86.33%	2.09%	2.30%	3.56%	0.635
14	7.87%	4.25%	85.54%	2.33%	2.32%	3.61%	0.634
15	8.10%	4.58%	84.74%	2.59%	2.35%	3.66%	0.633
16	8.32%	4.91%	83.93%	2.85%	2.38%	3.71%	0.632
17	8.55%	5.23%	83.11%	3.11%	2.41%	3.77%	0.630
18	8.78%	5.55%	82.29%	3.38%	2.44%	3.82%	0.628
19	9.01%	5.87%	81.47%	3.65%	2.47%	3.88%	0.626
20	9.24%	6.18%	80.65%	3.93%	2.50%	3.94%	0.624
21	9.48%	6.50%	79.83%	4.20%	2.53%	4.01%	0.621
22	9.70%	6.81%	79.01%	4.48%	2.56%	4.07%	0.619
23	9.93%	7.12%	78.18%	4.77%	2.59%	4.14%	0.616
24	10.15%	7.43%	77.35%	5.07%	2.62%	4.21%	0.612
25	10.38%	7.74%	76.53%	5.36%	2.65%	4.28%	0.609
26	10.61%	8.04%	75.70%	5.65%	2.68%	4.35%	0.606
27	10.84%	8.35%	74.87%	5.95%	2.71%	4.42%	0.603
28	11.06%	8.65%	74.03%	6.25%	2.74%	4.49%	0.599
29	11.29%	8.96%	73.19%	6.56%	2.77%	4.57%	0.596
30	11.52%	9.26%	72.35%	6.88%	2.80%	4.65%	0.592
31	11.74%	9.56%	71.51%	7.19%	2.83%	4.72%	0.588
32	11.97%	9.86%	70.66%	7.51%	2.86%	4.80%	0.585
33	12.19%	10.16%	69.81%	7.84%	2.89%	4.88%	0.581
34	12.42%	10.45%	68.96%	8.17%	2.92%	4.97%	0.577
35	12.64%	10.75%	68.11%	8.50%	2.95%	5.05%	0.574
36	12.86%	11.04%	67.26%	8.84%	2.98%	5.13%	0.570
37	13.09%	11.34%	66.40%	9.17%	3.01%	5.22%	0.567
38	13.32%	11.65%	65.53%	9.51%	3.04%	5.30%	0.563
39	13.54%	11.95%	64.66%	9.85%	3.07%	5.39%	0.559
40	13.77%	12.25%	63.79%	10.19%	3.10%	5.48%	0.556
41	14.00%	12.55%	62.91%	10.53%	3.13%	5.57%	0.552
42	14.23%	12.85%	62.04%	10.88%	3.16%	5.66%	0.549
43	14.46%	13.16%	61.17%	11.22%	3.19%	5.75%	0.545
44	14.69%	13.46%	60.29%	11.56%	3.22%	5.84%	0.542
45	14.92%	13.76%	59.42%	11.90%	3.26%	5.94%	0.539
46	15.15%	14.06%	58.55%	12.25%	3.29%	6.03%	0.535
47	15.38%	14.35%	57.67%	12.59%	3.32%	6.12%	0.532
48	15.61%	14.65%	56.80%	12.94%	3.35%	6.22%	0.529
49	15.84%	14.95%	55.92%	13.29%	3.38%	6.31%	0.526
50	16.08%	15.25%	55.05%	13.63%	3.41%	6.40%	0.523
51	16.31%	15.54%	54.17%	13.98%	3.44%	6.50%	0.520
52	16.54%	15.84%	53.30%	14.32%	3.47%	6.59%	0.517
53	16.77%	16.14%	52.42%	14.67%	3.50%	6.69%	0.514
54	17.01%	16.43%	51.54%	15.02%	3.54%	6.79%	0.511
55	17.24%	16.73%	50.66%	15.37%	3.57%	6.88%	0.509
56	17.47%	17.03%	49.79%	15.71%	3.60%	6.98%	0.506
57	17.70%	17.33%	48.91%	16.06%	3.63%	7.08%	0.503
58	17.93%	17.63%	48.03%	16.41%	3.66%	7.18%	0.501
59	18.17%	17.92%	47.15%	16.76%	3.69%	7.27%	0.498
60	18.40%	18.22%	46.27%	17.11%	3.72%	7.37%	0.495
61	18.63%	18.52%	45.40%	17.46%	3.76%	7.47%	0.493
62	18.86%	18.82%	44.52%	17.80%	3.79%	7.57%	0.490
63	19.09%	19.11%	43.64%	18.15%	3.82%	7.67%	0.488
64	19.33%	19.41%	42.76%	18.50%	3.85%	7.77%	0.486
65	19.56%	19.71%	41.88%	18.85%	3.88%	7.87%	0.483
66	19.79%	20.01%	41.00%	19.20%	3.91%	7.97%	0.481
67	20.02%	20.30%	40.13%	19.55%	3.94%	8.07%	0.479
68	20.26%	20.60%	39.25%	19.90%	3.98%	8.17%	0.477
69	20.49%	20.90%	38.37%	20.25%	4.01%	8.27%	0.475
70	20.72%	21.19%	37.49%	20.59%	4.04%	8.37%	0.473
71	20.96%	21.49%	36.61%	20.94%	4.07%	8.47%	0.471
72	21.19%	21.79%	35.73%	21.29%	4.10%	8.57%	0.469
73	21.42%	22.08%	34.85%	21.64%	4.13%	8.67%	0.467
74	21.66%	22.38%	33.97%	21.99%	4.16%	8.77%	0.465
75	21.89%	22.68%	33.08%	22.36%	4.20%	8.88%	0.463
76	22.12%	22.97%	32.18%	22.73%	4.23%	8.98%	0.461
77	22.35%	23.27%	31.28%	23.10%	4.26%	9.09%	0.459
78	22.59%	23.57%	30.38%	23.47%	4.29%	9.19%	0.457
79	22.82%	23.86%	29.48%	23.84%	4.33%	9.30%	0.455
80	23.05%	24.16%	28.58%	24.21%	4.36%	9.40%	0.453
81	23.29%	24.46%	27.68%	24.58%	4.39%	9.51%	0.452
82	23.52%	24.75%	26.78%	24.95%	4.42%	9.61%	0.450
83	23.75%	25.05%	25.88%	25.32%	4.45%	9.72%	0.448
84	23.99%	25.35%	24.98%	25.69%	4.49%	9.82%	0.447
85	24.22%	25.64%	24.08%	26.06%	4.52%	9.93%	0.445
86	24.45%	25.94%	23.18%	26.43%	4.55%	10.03%	0.443
87	24.68%	26.23%	22.28%	26.80%	4.58%	10.14%	0.442
88	24.89%	26.53%	21.39%	27.19%	4.62%	10.24%	0.440
89	25.08%	26.83%	20.50%	27.59%	4.65%	10.35%	0.439
90	25.26%	27.12%	19.61%	28.01%	4.68%	10.45%	0.437
91	25.38%	27.39%	18.74%	28.49%	4.71%	10.56%	0.436
92	25.46%	27.63%	17.89%	29.01%	4.74%	10.66%	0.434
93	25.54%	27.81%	17.06%	29.59%	4.77%	10.76%	0.433
94	25.53%	27.95%	16.26%	30.26%	4.79%	10.86%	0.431
95	25.33%	28.14%	15.50%	31.03%	4.82%	10.95%	0.430
96	24.83%	28.57%	14.81%	31.79%	4.84%	11.04%	0.428
97	24.25%	29.11%	14.16%	32.48%	4.86%	11.12%	0.427
98	23.42%	30.00%	13.56%	33.02%	4.89%	11.20%	0.426
99	22.32%	31.26%	13.01%	33.41%	4.91%	11.27%	0.425
100	21.50%	32.50%	12.50%	33.50%	4.93%	11.34%	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.