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

Browse…

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 1.98% to 5.20%. Refer to the efficient frontier section for additional details. Historical values from Jan 2012 to Mar 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	8.69%
VXUS	Vanguard Total International Stock ETF	2.92%
BND	Vanguard Total Bond Market ETF	86.59%
VNQ	Vanguard Real Estate ETF	1.80%
Save portfolio »

Portfolio Summary

Portfolio statistics
Portfolio	Expected Return	Standard Deviation	Sharpe Ratio
Provided Portfolio	4.37%	9.32%	0.46
Maximum Sharpe Ratio	2.29%	3.56%	0.63
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 (0.04% 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%	13.67%	0.400	0.00%	100.00%
2	Vanguard Total International Stock ETF (VXUS)	5.70%	14.40%	0.393	0.00%	100.00%
3	Vanguard Total Bond Market ETF (BND)	1.80%	3.33%	0.528	0.00%	100.00%
4	Vanguard Real Estate ETF (VNQ)	5.00%	15.32%	0.324	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 (0.04% annualized).

Asset Correlations

Efficient Frontier Asset Correlations
Name	Ticker	VTI	VXUS	BND	VNQ
Vanguard Total Stock Market ETF	VTI	1.00	0.86	0.04	0.63
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	0.63	0.58	0.46	1.00
Based on monthly returns from Jan 2012 to Mar 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	4.55%	0.30%	95.15%	0.00%	1.98%	3.27%	0.593
2	5.27%	0.45%	94.24%	0.04%	2.01%	3.27%	0.602
3	5.77%	0.70%	93.40%	0.14%	2.04%	3.29%	0.609
4	6.18%	0.97%	92.58%	0.27%	2.07%	3.30%	0.615
5	6.55%	1.26%	91.76%	0.43%	2.10%	3.33%	0.619
6	6.91%	1.55%	90.93%	0.62%	2.13%	3.36%	0.623
7	7.28%	1.82%	90.08%	0.82%	2.16%	3.39%	0.626
8	7.65%	2.09%	89.22%	1.05%	2.19%	3.42%	0.628
9	7.99%	2.37%	88.34%	1.30%	2.22%	3.47%	0.630
10	8.34%	2.64%	87.47%	1.55%	2.25%	3.51%	0.631
11	8.69%	2.92%	86.59%	1.80%	2.29%	3.56%	0.631
12	9.05%	3.19%	85.70%	2.06%	2.32%	3.61%	0.631
13	9.40%	3.48%	84.81%	2.31%	2.35%	3.66%	0.631
14	9.74%	3.76%	83.93%	2.58%	2.38%	3.72%	0.630
15	10.08%	4.03%	83.03%	2.85%	2.41%	3.78%	0.628
16	10.43%	4.31%	82.14%	3.12%	2.45%	3.84%	0.626
17	10.78%	4.58%	81.23%	3.40%	2.48%	3.90%	0.624
18	11.14%	4.84%	80.33%	3.69%	2.51%	3.97%	0.622
19	11.49%	5.11%	79.43%	3.97%	2.54%	4.04%	0.619
20	11.83%	5.38%	78.52%	4.26%	2.57%	4.11%	0.616
21	12.18%	5.65%	77.62%	4.56%	2.61%	4.19%	0.613
22	12.52%	5.92%	76.72%	4.85%	2.64%	4.26%	0.610
23	12.87%	6.18%	75.80%	5.15%	2.67%	4.34%	0.606
24	13.21%	6.45%	74.89%	5.45%	2.70%	4.42%	0.603
25	13.56%	6.72%	73.97%	5.76%	2.74%	4.50%	0.599
26	13.90%	6.99%	73.05%	6.06%	2.77%	4.58%	0.596
27	14.24%	7.25%	72.13%	6.37%	2.80%	4.67%	0.592
28	14.58%	7.52%	71.21%	6.69%	2.83%	4.75%	0.588
29	14.92%	7.78%	70.29%	7.00%	2.87%	4.84%	0.584
30	15.26%	8.05%	69.38%	7.31%	2.90%	4.93%	0.581
31	15.60%	8.32%	68.45%	7.63%	2.93%	5.02%	0.577
32	15.93%	8.58%	67.53%	7.95%	2.97%	5.11%	0.573
33	16.27%	8.85%	66.61%	8.27%	3.00%	5.20%	0.569
34	16.60%	9.12%	65.69%	8.59%	3.03%	5.29%	0.566
35	16.93%	9.38%	64.77%	8.92%	3.06%	5.38%	0.562
36	17.27%	9.65%	63.84%	9.25%	3.10%	5.48%	0.558
37	17.60%	9.92%	62.91%	9.58%	3.13%	5.57%	0.555
38	17.93%	10.18%	61.98%	9.91%	3.16%	5.67%	0.551
39	18.26%	10.45%	61.05%	10.25%	3.20%	5.77%	0.547
40	18.59%	10.72%	60.11%	10.58%	3.23%	5.87%	0.544
41	18.92%	10.99%	59.18%	10.92%	3.26%	5.96%	0.540
42	19.24%	11.25%	58.25%	11.25%	3.30%	6.06%	0.537
43	19.57%	11.52%	57.32%	11.59%	3.33%	6.16%	0.534
44	19.90%	11.79%	56.39%	11.93%	3.36%	6.26%	0.530
45	20.23%	12.06%	55.45%	12.26%	3.40%	6.37%	0.527
46	20.56%	12.32%	54.52%	12.60%	3.43%	6.47%	0.524
47	20.88%	12.59%	53.59%	12.94%	3.46%	6.57%	0.521
48	21.21%	12.86%	52.66%	13.27%	3.50%	6.67%	0.518
49	21.54%	13.13%	51.72%	13.61%	3.53%	6.78%	0.515
50	21.86%	13.40%	50.79%	13.95%	3.56%	6.88%	0.512
51	22.19%	13.66%	49.86%	14.29%	3.60%	6.98%	0.509
52	22.51%	13.93%	48.92%	14.64%	3.63%	7.09%	0.506
53	22.84%	14.20%	47.99%	14.98%	3.66%	7.19%	0.504
54	23.16%	14.46%	47.05%	15.32%	3.70%	7.30%	0.501
55	23.49%	14.73%	46.12%	15.66%	3.73%	7.40%	0.498
56	23.81%	14.99%	45.19%	16.01%	3.76%	7.51%	0.496
57	24.14%	15.26%	44.25%	16.35%	3.80%	7.62%	0.493
58	24.46%	15.53%	43.32%	16.69%	3.83%	7.72%	0.491
59	24.79%	15.79%	42.38%	17.03%	3.86%	7.83%	0.488
60	25.12%	16.06%	41.44%	17.38%	3.90%	7.94%	0.486
61	25.44%	16.33%	40.51%	17.72%	3.93%	8.04%	0.484
62	25.77%	16.59%	39.57%	18.06%	3.96%	8.15%	0.481
63	26.10%	16.86%	38.64%	18.41%	4.00%	8.26%	0.479
64	26.42%	17.13%	37.70%	18.75%	4.03%	8.37%	0.477
65	26.75%	17.39%	36.76%	19.09%	4.07%	8.48%	0.475
66	27.08%	17.66%	35.83%	19.44%	4.10%	8.59%	0.473
67	27.40%	17.92%	34.89%	19.78%	4.13%	8.69%	0.471
68	27.73%	18.19%	33.95%	20.12%	4.17%	8.80%	0.469
69	28.06%	18.45%	33.02%	20.47%	4.20%	8.91%	0.467
70	28.39%	18.72%	32.08%	20.81%	4.23%	9.02%	0.465
71	28.72%	18.98%	31.14%	21.15%	4.27%	9.13%	0.463
72	29.05%	19.25%	30.20%	21.50%	4.30%	9.24%	0.461
73	29.38%	19.51%	29.26%	21.84%	4.33%	9.35%	0.459
74	29.71%	19.77%	28.32%	22.19%	4.37%	9.46%	0.457
75	30.05%	20.04%	27.39%	22.53%	4.40%	9.57%	0.456
76	30.38%	20.30%	26.45%	22.87%	4.44%	9.68%	0.454
77	30.71%	20.57%	25.51%	23.22%	4.47%	9.80%	0.452
78	31.04%	20.83%	24.57%	23.56%	4.50%	9.91%	0.451
79	31.37%	21.10%	23.63%	23.90%	4.54%	10.02%	0.449
80	31.70%	21.36%	22.69%	24.24%	4.57%	10.13%	0.447
81	32.03%	21.62%	21.76%	24.59%	4.61%	10.24%	0.446
82	32.36%	21.89%	20.82%	24.93%	4.64%	10.35%	0.444
83	32.70%	22.15%	19.88%	25.27%	4.67%	10.46%	0.443
84	33.03%	22.41%	18.94%	25.62%	4.71%	10.58%	0.441
85	33.36%	22.68%	18.00%	25.96%	4.74%	10.69%	0.440
86	33.69%	22.94%	17.06%	26.30%	4.77%	10.80%	0.438
87	34.02%	23.21%	16.13%	26.65%	4.81%	10.91%	0.437
88	34.35%	23.47%	15.19%	26.99%	4.84%	11.02%	0.436
89	34.64%	23.74%	14.26%	27.36%	4.88%	11.13%	0.434
90	34.92%	24.00%	13.33%	27.75%	4.91%	11.25%	0.433
91	35.19%	24.26%	12.41%	28.13%	4.94%	11.36%	0.432
92	35.40%	24.56%	11.50%	28.54%	4.97%	11.46%	0.430
93	35.58%	24.83%	10.61%	28.98%	5.01%	11.57%	0.429
94	35.69%	25.11%	9.74%	29.47%	5.04%	11.68%	0.428
95	35.79%	25.41%	8.89%	29.91%	5.07%	11.78%	0.427
96	35.79%	25.80%	8.05%	30.37%	5.10%	11.88%	0.426
97	35.60%	26.29%	7.21%	30.89%	5.13%	11.98%	0.425
98	35.22%	26.84%	6.42%	31.52%	5.15%	12.08%	0.423
99	34.89%	27.49%	5.67%	31.94%	5.18%	12.17%	0.422
100	34.50%	28.00%	5.00%	32.50%	5.21%	12.25%	0.422
^*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 (0.04% annualized).