Efficient Frontier

This tool uses mean-variance optimization to calculate and plot the efficient frontier for the specified asset classes, mutual funds, ETFs or stocks for the specified time period. The efficient frontier shows the set of optimal portfolios that provide the best possible expected return for the level of risk in the portfolio. Monte Carlo method can be used for more robust optimization that resamples the optimization inputs in order to mitigate the impact of input estimation errors and improve diversification. You can also use the efficient frontier forecast tool to specify expected future returns for the assets. The required inputs for the efficient frontier include the portfolio assets. You can optionally specify the asset allocation and allocation constraints for the portfolio assets. If an asset allocation is specified, the provided portfolio will be rendered on the efficient frontier chart.

Chart

Portfolio Type

Start Year

End Year

Robust Optimization

Group Constraints

Excess Return Frontier

Benchmark

Benchmark Ticker

Geometric Mean

Min Variance Frontier

Chart from Origin

Efficient Frontier Results (Jan 1978 - Dec 2021)

Portfolio Allocations

Max Sharpe Ratio Portfolio
Asset Class	Allocation
US Stock Market	50.51%
Long Term Treasury	49.49%
Save portfolio »

Portfolio Returns

Portfolio Statistics
Portfolio	Expected Return	Standard Deviation	Sharpe Ratio
Max Sharpe Ratio Portfolio	11.22%	9.60%	0.66

Note: You can hover over any of the data points on the chart for more information.

Efficient Frontier Assets

Efficient Frontier Assets
#	Asset	Expected Return	Standard Deviation	Sharpe Ratio	Min. Weight	Max. Weight
1	US Stock Market	13.44%	15.37%	0.545	0.00%	100.00%
2	Long Term Treasury	8.99%	11.12%	0.390	0.00%	100.00%
Results based on historical returns. Expected return is the annualized monthly arithmetic mean return. Ex-ante Sharpe Ratio calculated using 3-month treasury bill returns as the risk-free rate.

Asset Correlations

Asset Correlations
Asset	US Stock Market	Long Term Treasury
US Stock Market	1.00	0.02
Long Term Treasury	0.02	1.00
Based on monthly returns from Jan 1978 to Dec 2021

Efficient Frontier Points
#	US Stock Market	Long Term Treasury	Expected Return^*	Standard Deviation^*	Sharpe Ratio^*
1	0.00%	100.00%	8.99%	11.12%	0.390
2	1.01%	98.99%	9.03%	11.01%	0.397
3	2.02%	97.98%	9.07%	10.91%	0.405
4	3.03%	96.97%	9.12%	10.80%	0.413
5	4.04%	95.96%	9.16%	10.70%	0.420
6	5.05%	94.95%	9.21%	10.60%	0.428
7	6.06%	93.94%	9.25%	10.50%	0.436
8	7.07%	92.93%	9.30%	10.41%	0.444
9	8.08%	91.92%	9.34%	10.32%	0.452
10	9.09%	90.91%	9.38%	10.23%	0.459
11	10.10%	89.90%	9.43%	10.15%	0.467
12	11.11%	88.89%	9.47%	10.06%	0.475
13	12.12%	87.88%	9.52%	9.98%	0.483
14	13.13%	86.87%	9.56%	9.91%	0.491
15	14.14%	85.86%	9.61%	9.83%	0.499
16	15.15%	84.85%	9.65%	9.76%	0.507
17	16.16%	83.84%	9.70%	9.69%	0.514
18	17.17%	82.83%	9.74%	9.63%	0.522
19	18.18%	81.82%	9.78%	9.57%	0.530
20	19.19%	80.81%	9.83%	9.51%	0.537
21	20.20%	79.80%	9.87%	9.46%	0.545
22	21.21%	78.79%	9.92%	9.41%	0.552
23	22.22%	77.78%	9.96%	9.36%	0.559
24	23.23%	76.77%	10.01%	9.32%	0.566
25	24.24%	75.76%	10.05%	9.28%	0.573
26	25.25%	74.75%	10.10%	9.24%	0.580
27	26.26%	73.74%	10.14%	9.21%	0.586
28	27.27%	72.73%	10.19%	9.18%	0.592
29	28.28%	71.72%	10.23%	9.15%	0.598
30	29.29%	70.71%	10.27%	9.13%	0.604
31	30.30%	69.70%	10.32%	9.12%	0.610
32	31.31%	68.69%	10.36%	9.10%	0.615
33	32.32%	67.68%	10.41%	9.10%	0.620
34	33.33%	66.67%	10.45%	9.09%	0.625
35	34.34%	65.66%	10.50%	9.09%	0.629
36	35.35%	64.65%	10.54%	9.09%	0.634
37	36.36%	63.64%	10.59%	9.10%	0.638
38	37.37%	62.63%	10.63%	9.11%	0.641
39	38.38%	61.62%	10.68%	9.13%	0.645
40	39.39%	60.61%	10.72%	9.15%	0.648
41	40.40%	59.60%	10.77%	9.17%	0.651
42	41.41%	58.59%	10.81%	9.19%	0.653
43	42.42%	57.58%	10.86%	9.23%	0.656
44	43.43%	56.57%	10.90%	9.26%	0.658
45	44.44%	55.56%	10.95%	9.30%	0.659
46	45.45%	54.55%	10.99%	9.34%	0.661
47	46.46%	53.54%	11.04%	9.38%	0.662
48	47.47%	52.53%	11.08%	9.43%	0.663
49	48.48%	51.52%	11.13%	9.49%	0.663
50	49.49%	50.51%	11.17%	9.54%	0.664
51	50.51%	49.49%	11.22%	9.60%	0.664
52	51.52%	48.48%	11.26%	9.66%	0.664
53	52.53%	47.47%	11.31%	9.73%	0.664
54	53.54%	46.46%	11.35%	9.80%	0.663
55	54.55%	45.45%	11.40%	9.87%	0.662
56	55.56%	44.44%	11.44%	9.95%	0.661
57	56.57%	43.43%	11.49%	10.03%	0.660
58	57.58%	42.42%	11.53%	10.11%	0.659
59	58.59%	41.41%	11.58%	10.19%	0.658
60	59.60%	40.40%	11.62%	10.28%	0.656
61	60.61%	39.39%	11.67%	10.37%	0.654
62	61.62%	38.38%	11.71%	10.46%	0.652
63	62.63%	37.37%	11.76%	10.56%	0.650
64	63.64%	36.36%	11.80%	10.66%	0.648
65	64.65%	35.35%	11.85%	10.76%	0.646
66	65.66%	34.34%	11.89%	10.86%	0.644
67	66.67%	33.33%	11.94%	10.96%	0.641
68	67.68%	32.32%	11.98%	11.07%	0.639
69	68.69%	31.31%	12.03%	11.18%	0.636
70	69.70%	30.30%	12.07%	11.29%	0.633
71	70.71%	29.29%	12.12%	11.41%	0.631
72	71.72%	28.28%	12.17%	11.52%	0.628
73	72.73%	27.27%	12.21%	11.64%	0.625
74	73.74%	26.26%	12.26%	11.76%	0.622
75	74.75%	25.25%	12.30%	11.88%	0.619
76	75.76%	24.24%	12.35%	12.00%	0.616
77	76.77%	23.23%	12.39%	12.13%	0.613
78	77.78%	22.22%	12.44%	12.26%	0.610
79	78.79%	21.21%	12.48%	12.38%	0.607
80	79.80%	20.20%	12.53%	12.51%	0.604
81	80.81%	19.19%	12.57%	12.64%	0.601
82	81.82%	18.18%	12.62%	12.78%	0.598
83	82.83%	17.17%	12.67%	12.91%	0.595
84	83.84%	16.16%	12.71%	13.05%	0.592
85	84.85%	15.15%	12.76%	13.18%	0.589
86	85.86%	14.14%	12.80%	13.32%	0.586
87	86.87%	13.13%	12.85%	13.46%	0.583
88	87.88%	12.12%	12.89%	13.60%	0.580
89	88.89%	11.11%	12.94%	13.74%	0.577
90	89.90%	10.10%	12.99%	13.89%	0.574
91	90.91%	9.09%	13.03%	14.03%	0.571
92	91.92%	8.08%	13.08%	14.18%	0.568
93	92.93%	7.07%	13.12%	14.32%	0.565
94	93.94%	6.06%	13.17%	14.47%	0.562
95	94.95%	5.05%	13.21%	14.62%	0.559
96	95.96%	4.04%	13.26%	14.77%	0.556
97	96.97%	3.03%	13.31%	14.92%	0.553
98	97.98%	2.02%	13.35%	15.07%	0.550
99	98.99%	1.01%	13.40%	15.22%	0.548
100	100.00%	0.00%	13.44%	15.37%	0.545
^*Annualized ex-ante values shown for portfolio return and volatility. Ex-ante Sharpe Ratio calculated using historical 3-month treasury bill returns as the risk-free rate.

Notes on results:

IMPORTANT: The projections or other information generated by Portfolio Visualizer regarding the likelihood of various investment outcomes are hypothetical in nature, do not reflect actual investment results and are not guarantees of future results. Results may vary with each use and over time.
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. All use is subject to terms of service.
Investing involves risk, including possible loss of principal. Past performance is not a guarantee of future results.
Asset allocation and diversification strategies do not guarantee a profit or protect against a loss.
Hypothetical returns do not reflect trading costs, transaction fees, or actual taxes due on investment returns.
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.
Refer to the related documentation sections for more details on terms and definitions, methodology, and data sources.
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 the total return of assets and assume that all received dividends and distributions are reinvested.
Historical asset statistics are based on monthly returns from Jan 1978 to Dec 2021
The efficient frontier is based on the monthly returns, volatilities, and correlations of the specified assets
The displayed standard deviation and expected return in the efficient frontier are annualized from the monthly returns
Ex-ante Sharpe Ratio for the efficient frontier data points is calculated using historical 3-month treasury bill returns as the risk free rate