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 - Jun 2022)

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

Portfolio Allocations

Max Sharpe Ratio Portfolio
Asset Class	Allocation
US Stock Market	52.53%
Long Term Treasury	47.47%
Save portfolio »

Portfolio Returns

Portfolio Statistics
Portfolio	Expected Return	Standard Deviation	Sharpe Ratio
Max Sharpe Ratio Portfolio	10.61%	9.88%	0.59

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	12.70%	15.48%	0.501	0.00%	100.00%
2	Long Term Treasury	8.33%	11.22%	0.335	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	0.04
Long Term Treasury	0.04	1.00
Based on monthly returns from Jan 1978 to Jun 2022

Efficient Frontier Points
#	US Stock Market	Long Term Treasury	Expected Return^*	Standard Deviation^*	Sharpe Ratio^*
1	0.00%	100.00%	8.33%	11.22%	0.335
2	1.01%	98.99%	8.37%	11.12%	0.342
3	2.02%	97.98%	8.41%	11.01%	0.349
4	3.03%	96.97%	8.46%	10.91%	0.356
5	4.04%	95.96%	8.50%	10.81%	0.363
6	5.05%	94.95%	8.54%	10.71%	0.370
7	6.06%	93.94%	8.59%	10.62%	0.377
8	7.07%	92.93%	8.63%	10.53%	0.384
9	8.08%	91.92%	8.67%	10.44%	0.391
10	9.09%	90.91%	8.72%	10.35%	0.399
11	10.10%	89.90%	8.76%	10.27%	0.406
12	11.11%	88.89%	8.80%	10.19%	0.413
13	12.12%	87.88%	8.85%	10.11%	0.420
14	13.13%	86.87%	8.89%	10.03%	0.427
15	14.14%	85.86%	8.93%	9.96%	0.435
16	15.15%	84.85%	8.98%	9.89%	0.442
17	16.16%	83.84%	9.02%	9.83%	0.449
18	17.17%	82.83%	9.07%	9.76%	0.456
19	18.18%	81.82%	9.11%	9.70%	0.463
20	19.19%	80.81%	9.15%	9.65%	0.470
21	20.20%	79.80%	9.20%	9.60%	0.476
22	21.21%	78.79%	9.24%	9.55%	0.483
23	22.22%	77.78%	9.28%	9.50%	0.490
24	23.23%	76.77%	9.33%	9.46%	0.496
25	24.24%	75.76%	9.37%	9.42%	0.502
26	25.25%	74.75%	9.42%	9.39%	0.508
27	26.26%	73.74%	9.46%	9.36%	0.514
28	27.27%	72.73%	9.50%	9.33%	0.520
29	28.28%	71.72%	9.55%	9.30%	0.526
30	29.29%	70.71%	9.59%	9.29%	0.531
31	30.30%	69.70%	9.64%	9.27%	0.537
32	31.31%	68.69%	9.68%	9.26%	0.542
33	32.32%	67.68%	9.72%	9.25%	0.547
34	33.33%	66.67%	9.77%	9.25%	0.551
35	34.34%	65.66%	9.81%	9.25%	0.556
36	35.35%	64.65%	9.86%	9.25%	0.560
37	36.36%	63.64%	9.90%	9.26%	0.564
38	37.37%	62.63%	9.94%	9.27%	0.567
39	38.38%	61.62%	9.99%	9.28%	0.571
40	39.39%	60.61%	10.03%	9.30%	0.574
41	40.40%	59.60%	10.08%	9.33%	0.577
42	41.41%	58.59%	10.12%	9.35%	0.579
43	42.42%	57.58%	10.16%	9.38%	0.582
44	43.43%	56.57%	10.21%	9.42%	0.584
45	44.44%	55.56%	10.25%	9.45%	0.586
46	45.45%	54.55%	10.30%	9.50%	0.588
47	46.46%	53.54%	10.34%	9.54%	0.589
48	47.47%	52.53%	10.38%	9.59%	0.590
49	48.48%	51.52%	10.43%	9.64%	0.591
50	49.49%	50.51%	10.47%	9.70%	0.592
51	50.51%	49.49%	10.52%	9.76%	0.593
52	51.52%	48.48%	10.56%	9.82%	0.593
53	52.53%	47.47%	10.61%	9.88%	0.593
54	53.54%	46.46%	10.65%	9.95%	0.593
55	54.55%	45.45%	10.69%	10.03%	0.593
56	55.56%	44.44%	10.74%	10.10%	0.592
57	56.57%	43.43%	10.78%	10.18%	0.592
58	57.58%	42.42%	10.83%	10.26%	0.591
59	58.59%	41.41%	10.87%	10.34%	0.590
60	59.60%	40.40%	10.92%	10.43%	0.589
61	60.61%	39.39%	10.96%	10.52%	0.588
62	61.62%	38.38%	11.00%	10.61%	0.587
63	62.63%	37.37%	11.05%	10.70%	0.585
64	63.64%	36.36%	11.09%	10.80%	0.584
65	64.65%	35.35%	11.14%	10.90%	0.582
66	65.66%	34.34%	11.18%	11.00%	0.581
67	66.67%	33.33%	11.23%	11.11%	0.579
68	67.68%	32.32%	11.27%	11.21%	0.577
69	68.69%	31.31%	11.32%	11.32%	0.575
70	69.70%	30.30%	11.36%	11.43%	0.573
71	70.71%	29.29%	11.40%	11.54%	0.571
72	71.72%	28.28%	11.45%	11.66%	0.569
73	72.73%	27.27%	11.49%	11.77%	0.566
74	73.74%	26.26%	11.54%	11.89%	0.564
75	74.75%	25.25%	11.58%	12.01%	0.562
76	75.76%	24.24%	11.63%	12.13%	0.560
77	76.77%	23.23%	11.67%	12.26%	0.557
78	77.78%	22.22%	11.72%	12.38%	0.555
79	78.79%	21.21%	11.76%	12.51%	0.552
80	79.80%	20.20%	11.81%	12.64%	0.550
81	80.81%	19.19%	11.85%	12.77%	0.548
82	81.82%	18.18%	11.90%	12.90%	0.545
83	82.83%	17.17%	11.94%	13.03%	0.543
84	83.84%	16.16%	11.99%	13.17%	0.540
85	84.85%	15.15%	12.03%	13.30%	0.538
86	85.86%	14.14%	12.08%	13.44%	0.535
87	86.87%	13.13%	12.12%	13.58%	0.533
88	87.88%	12.12%	12.16%	13.72%	0.530
89	88.89%	11.11%	12.21%	13.86%	0.528
90	89.90%	10.10%	12.25%	14.00%	0.525
91	90.91%	9.09%	12.30%	14.14%	0.523
92	91.92%	8.08%	12.34%	14.29%	0.520
93	92.93%	7.07%	12.39%	14.43%	0.518
94	93.94%	6.06%	12.43%	14.58%	0.516
95	94.95%	5.05%	12.48%	14.73%	0.513
96	95.96%	4.04%	12.52%	14.87%	0.511
97	96.97%	3.03%	12.57%	15.02%	0.508
98	97.98%	2.02%	12.61%	15.17%	0.506
99	98.99%	1.01%	12.66%	15.32%	0.504
100	100.00%	0.00%	12.70%	15.48%	0.501
^*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 Jun 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