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

Efficient Frontier Results (Jan 1978 - Oct 2022)

Note: The time period was constrained by the available data for Long Term Treasury [Jan 1978 - Oct 2022].

Portfolio Allocations

Max Sharpe Ratio Portfolio
Asset Class	Allocation
US Stock Market	56.57%
Long Term Treasury	43.43%
Save portfolio »

Portfolio Returns

Portfolio Statistics
Portfolio	Expected Return	Standard Deviation	Sharpe Ratio
Max Sharpe Ratio Portfolio	10.12%	10.30%	0.57

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	12.03%	15.60%	0.499	0.00%	100.00%
2	Long Term Treasury	7.62%	11.32%	0.298	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	0.05
Long Term Treasury	0.05	1.00
Based on monthly returns from Jan 1978 to Oct 2022

Efficient Frontier Points
#	US Stock Market	Long Term Treasury	Expected Return *	Standard Deviation *	Sharpe Ratio *
1	0.00%	100.00%	7.62%	11.32%	0.298
2	1.01%	98.99%	7.67%	11.22%	0.305
3	2.02%	97.98%	7.71%	11.11%	0.312
4	3.03%	96.97%	7.76%	11.01%	0.319
5	4.04%	95.96%	7.80%	10.91%	0.326
6	5.05%	94.95%	7.85%	10.82%	0.333
7	6.06%	93.94%	7.89%	10.72%	0.340
8	7.07%	92.93%	7.93%	10.63%	0.347
9	8.08%	91.92%	7.98%	10.54%	0.354
10	9.09%	90.91%	8.02%	10.46%	0.361
11	10.10%	89.90%	8.07%	10.37%	0.368
12	11.11%	88.89%	8.11%	10.29%	0.376
13	12.12%	87.88%	8.16%	10.22%	0.383
14	13.13%	86.87%	8.20%	10.14%	0.390
15	14.14%	85.86%	8.25%	10.07%	0.397
16	15.15%	84.85%	8.29%	10.00%	0.404
17	16.16%	83.84%	8.34%	9.94%	0.411
18	17.17%	82.83%	8.38%	9.87%	0.419
19	18.18%	81.82%	8.42%	9.82%	0.426
20	19.19%	80.81%	8.47%	9.76%	0.433
21	20.20%	79.80%	8.51%	9.71%	0.439
22	21.21%	78.79%	8.56%	9.66%	0.446
23	22.22%	77.78%	8.60%	9.62%	0.453
24	23.23%	76.77%	8.65%	9.57%	0.460
25	24.24%	75.76%	8.69%	9.54%	0.466
26	25.25%	74.75%	8.74%	9.50%	0.472
27	26.26%	73.74%	8.78%	9.47%	0.479
28	27.27%	72.73%	8.82%	9.45%	0.485
29	28.28%	71.72%	8.87%	9.42%	0.491
30	29.29%	70.71%	8.91%	9.40%	0.496
31	30.30%	69.70%	8.96%	9.39%	0.502
32	31.31%	68.69%	9.00%	9.38%	0.507
33	32.32%	67.68%	9.05%	9.37%	0.512
34	33.33%	66.67%	9.09%	9.37%	0.517
35	34.34%	65.66%	9.14%	9.37%	0.522
36	35.35%	64.65%	9.18%	9.37%	0.527
37	36.36%	63.64%	9.23%	9.38%	0.531
38	37.37%	62.63%	9.27%	9.39%	0.535
39	38.38%	61.62%	9.31%	9.41%	0.539
40	39.39%	60.61%	9.36%	9.43%	0.542
41	40.40%	59.60%	9.40%	9.45%	0.546
42	41.41%	58.59%	9.45%	9.48%	0.549
43	42.42%	57.58%	9.49%	9.51%	0.552
44	43.43%	56.57%	9.54%	9.54%	0.554
45	44.44%	55.56%	9.58%	9.58%	0.557
46	45.45%	54.55%	9.63%	9.62%	0.559
47	46.46%	53.54%	9.67%	9.67%	0.561
48	47.47%	52.53%	9.72%	9.71%	0.563
49	48.48%	51.52%	9.76%	9.77%	0.564
50	49.49%	50.51%	9.80%	9.82%	0.566
51	50.51%	49.49%	9.85%	9.88%	0.567
52	51.52%	48.48%	9.89%	9.94%	0.568
53	52.53%	47.47%	9.94%	10.01%	0.569
54	53.54%	46.46%	9.98%	10.08%	0.569
55	54.55%	45.45%	10.03%	10.15%	0.569
56	55.56%	44.44%	10.07%	10.22%	0.570
57	56.57%	43.43%	10.12%	10.30%	0.570
58	57.58%	42.42%	10.16%	10.38%	0.570
59	58.59%	41.41%	10.21%	10.47%	0.569
60	59.60%	40.40%	10.25%	10.55%	0.569
61	60.61%	39.39%	10.29%	10.64%	0.568
62	61.62%	38.38%	10.34%	10.73%	0.568
63	62.63%	37.37%	10.38%	10.83%	0.567
64	63.64%	36.36%	10.43%	10.92%	0.566
65	64.65%	35.35%	10.47%	11.02%	0.565
66	65.66%	34.34%	10.52%	11.13%	0.564
67	66.67%	33.33%	10.56%	11.23%	0.562
68	67.68%	32.32%	10.61%	11.34%	0.561
69	68.69%	31.31%	10.65%	11.44%	0.560
70	69.70%	30.30%	10.70%	11.55%	0.558
71	70.71%	29.29%	10.74%	11.67%	0.557
72	71.72%	28.28%	10.78%	11.78%	0.555
73	72.73%	27.27%	10.83%	11.90%	0.553
74	73.74%	26.26%	10.87%	12.02%	0.551
75	74.75%	25.25%	10.92%	12.14%	0.550
76	75.76%	24.24%	10.96%	12.26%	0.548
77	76.77%	23.23%	11.01%	12.38%	0.546
78	77.78%	22.22%	11.05%	12.51%	0.544
79	78.79%	21.21%	11.10%	12.63%	0.542
80	79.80%	20.20%	11.14%	12.76%	0.540
81	80.81%	19.19%	11.18%	12.89%	0.538
82	81.82%	18.18%	11.23%	13.02%	0.536
83	82.83%	17.17%	11.27%	13.16%	0.534
84	83.84%	16.16%	11.32%	13.29%	0.532
85	84.85%	15.15%	11.36%	13.43%	0.530
86	85.86%	14.14%	11.41%	13.56%	0.528
87	86.87%	13.13%	11.45%	13.70%	0.526
88	87.88%	12.12%	11.50%	13.84%	0.524
89	88.89%	11.11%	11.54%	13.98%	0.522
90	89.90%	10.10%	11.59%	14.12%	0.520
91	90.91%	9.09%	11.63%	14.27%	0.518
92	91.92%	8.08%	11.67%	14.41%	0.515
93	92.93%	7.07%	11.72%	14.56%	0.513
94	93.94%	6.06%	11.76%	14.70%	0.511
95	94.95%	5.05%	11.81%	14.85%	0.509
96	95.96%	4.04%	11.85%	15.00%	0.507
97	96.97%	3.03%	11.90%	15.15%	0.505
98	97.98%	2.02%	11.94%	15.30%	0.503
99	98.99%	1.01%	11.99%	15.45%	0.501
100	100.00%	0.00%	12.03%	15.60%	0.499
^*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, commissions, 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 is a process of choosing the proportions of various assets to be held in a portfolio in such a way as to make the portfolio better than any other combination according to the selected objective function such as maximizing risk-adjusted return. 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 Oct 2022
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