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 2006 - Sep 2022)

Note: The time period was constrained by the available data for SPDR S&P 600 Small Cap ETF (SLY) [Dec 2005 - Sep 2022].

Portfolio Allocations

Provided Portfolio
Ticker	Name	Allocation
SPY	SPDR S&P 500 ETF Trust	12.50%
SLY	SPDR S&P 600 Small Cap ETF	12.50%
EFA	iShares MSCI EAFE ETF	12.50%
EEM	iShares MSCI Emerging Markets ETF	12.50%
VNQ	Vanguard Real Estate ETF	12.50%
TLT	iShares 20+ Year Treasury Bond ETF	12.50%
LQD	iShares iBoxx $ Invmt Grade Corp Bd ETF	12.50%
GLD	SPDR Gold Shares	12.50%
Save portfolio »

Max Sharpe Ratio Portfolio
Ticker	Name	Allocation
SPY	SPDR S&P 500 ETF Trust	24.37%
SLY	SPDR S&P 600 Small Cap ETF	12.93%
EFA	iShares MSCI EAFE ETF	0.04%
EEM	iShares MSCI Emerging Markets ETF	0.35%
VNQ	Vanguard Real Estate ETF	4.45%
TLT	iShares 20+ Year Treasury Bond ETF	30.31%
LQD	iShares iBoxx $ Invmt Grade Corp Bd ETF	10.15%
GLD	SPDR Gold Shares	17.39%
Save portfolio »

Portfolio Returns

Portfolio Statistics
Portfolio	Expected Return	Standard Deviation	Sharpe Ratio
Provided Portfolio	6.81%	12.03%	0.48
Max Sharpe Ratio Portfolio	7.24%	9.10%	0.68

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	SPDR S&P 500 ETF Trust (SPY)	9.47%	15.40%	0.546	0.00%	100.00%
2	SPDR S&P 600 Small Cap ETF (SLY)	10.35%	20.16%	0.461	0.00%	100.00%
3	iShares MSCI EAFE ETF (EFA)	4.11%	17.53%	0.174	0.00%	100.00%
4	iShares MSCI Emerging Markets ETF (EEM)	5.30%	21.67%	0.196	0.00%	100.00%
5	Vanguard Real Estate ETF (VNQ)	8.65%	22.78%	0.333	0.00%	100.00%
6	iShares 20+ Year Treasury Bond ETF (TLT)	4.59%	13.64%	0.259	0.00%	100.00%
7	iShares iBoxx $ Invmt Grade Corp Bd ETF (LQD)	3.94%	7.86%	0.367	0.00%	100.00%
8	SPDR Gold Shares (GLD)	8.05%	17.26%	0.405	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
Name	Ticker	SPY	SLY	EFA	EEM	VNQ	TLT	LQD	GLD
SPDR S&P 500 ETF Trust	SPY	1.00	0.90	0.89	0.76	0.74	-0.20	0.41	0.08
SPDR S&P 600 Small Cap ETF	SLY	0.90	1.00	0.82	0.74	0.74	-0.29	0.34	0.03
iShares MSCI EAFE ETF	EFA	0.89	0.82	1.00	0.87	0.71	-0.18	0.45	0.16
iShares MSCI Emerging Markets ETF	EEM	0.76	0.74	0.87	1.00	0.61	-0.19	0.40	0.29
Vanguard Real Estate ETF	VNQ	0.74	0.74	0.71	0.61	1.00	0.04	0.48	0.12
iShares 20+ Year Treasury Bond ETF	TLT	-0.20	-0.29	-0.18	-0.19	0.04	1.00	0.54	0.22
iShares iBoxx $ Invmt Grade Corp Bd ETF	LQD	0.41	0.34	0.45	0.40	0.48	0.54	1.00	0.26
SPDR Gold Shares	GLD	0.08	0.03	0.16	0.29	0.12	0.22	0.26	1.00
Based on monthly returns from Jan 2006 to Sep 2022

Efficient Frontier Points
#	SPY	SLY	EFA	EEM	VNQ	TLT	LQD	GLD	Expected Return^*	Standard Deviation^*	Sharpe Ratio^*
1	8.79%	1.49%	0.03%	0.00%	0.00%	9.77%	71.32%	8.60%	4.94%	7.63%	0.508
2	9.44%	1.55%	0.03%	0.00%	0.00%	10.21%	70.02%	8.76%	4.99%	7.63%	0.515
3	10.06%	1.62%	0.02%	0.00%	0.00%	10.67%	68.73%	8.90%	5.04%	7.64%	0.521
4	10.65%	1.71%	0.02%	0.00%	0.00%	11.13%	67.44%	9.05%	5.09%	7.64%	0.527
5	11.20%	1.82%	0.01%	0.00%	0.01%	11.59%	66.18%	9.19%	5.13%	7.64%	0.533
6	11.74%	1.93%	0.01%	0.00%	0.02%	12.06%	64.90%	9.34%	5.18%	7.65%	0.538
7	12.25%	2.07%	0.01%	0.00%	0.02%	12.53%	63.62%	9.49%	5.23%	7.66%	0.544
8	12.73%	2.24%	0.00%	0.00%	0.03%	13.01%	62.34%	9.64%	5.27%	7.67%	0.549
9	13.20%	2.43%	0.00%	0.00%	0.04%	13.49%	61.05%	9.79%	5.32%	7.68%	0.555
10	13.65%	2.62%	0.00%	0.00%	0.06%	13.98%	59.75%	9.94%	5.37%	7.69%	0.560
11	14.05%	2.82%	0.00%	0.01%	0.08%	14.48%	58.47%	10.09%	5.41%	7.70%	0.565
12	14.43%	3.04%	0.00%	0.01%	0.11%	14.97%	57.19%	10.24%	5.46%	7.71%	0.570
13	14.80%	3.27%	0.00%	0.01%	0.14%	15.47%	55.92%	10.39%	5.50%	7.73%	0.575
14	15.15%	3.51%	0.00%	0.01%	0.17%	15.96%	54.65%	10.54%	5.55%	7.74%	0.580
15	15.51%	3.74%	0.00%	0.02%	0.20%	16.46%	53.37%	10.70%	5.60%	7.76%	0.585
16	15.87%	3.98%	0.00%	0.03%	0.23%	16.97%	52.08%	10.85%	5.64%	7.78%	0.589
17	16.22%	4.22%	0.00%	0.03%	0.26%	17.47%	50.79%	11.00%	5.69%	7.79%	0.594
18	16.58%	4.45%	0.00%	0.04%	0.29%	17.98%	49.49%	11.16%	5.73%	7.81%	0.598
19	16.95%	4.69%	0.01%	0.05%	0.32%	18.49%	48.18%	11.31%	5.78%	7.83%	0.602
20	17.31%	4.93%	0.01%	0.06%	0.36%	19.00%	46.87%	11.47%	5.83%	7.86%	0.607
21	17.66%	5.17%	0.01%	0.07%	0.40%	19.51%	45.55%	11.64%	5.87%	7.88%	0.611
22	18.02%	5.40%	0.01%	0.08%	0.44%	20.01%	44.24%	11.80%	5.92%	7.90%	0.615
23	18.36%	5.63%	0.01%	0.09%	0.49%	20.51%	42.94%	11.97%	5.97%	7.93%	0.619
24	18.70%	5.87%	0.01%	0.10%	0.54%	21.02%	41.63%	12.13%	6.01%	7.95%	0.623
25	19.03%	6.11%	0.01%	0.11%	0.60%	21.52%	40.33%	12.30%	6.06%	7.98%	0.627
26	19.36%	6.35%	0.01%	0.12%	0.65%	22.02%	39.02%	12.46%	6.11%	8.01%	0.630
27	19.69%	6.59%	0.01%	0.12%	0.71%	22.53%	37.71%	12.63%	6.15%	8.04%	0.634
28	20.01%	6.83%	0.02%	0.13%	0.77%	23.03%	36.41%	12.81%	6.20%	8.07%	0.637
29	20.34%	7.07%	0.02%	0.14%	0.83%	23.53%	35.10%	12.98%	6.25%	8.10%	0.641
30	20.66%	7.31%	0.02%	0.15%	0.89%	24.02%	33.79%	13.15%	6.29%	8.13%	0.644
31	20.97%	7.55%	0.02%	0.16%	0.96%	24.53%	32.49%	13.31%	6.34%	8.16%	0.647
32	21.29%	7.78%	0.02%	0.17%	1.04%	25.01%	31.20%	13.49%	6.39%	8.19%	0.650
33	21.60%	8.02%	0.02%	0.18%	1.11%	25.50%	29.90%	13.66%	6.43%	8.23%	0.653
34	21.90%	8.25%	0.02%	0.19%	1.19%	25.96%	28.64%	13.84%	6.48%	8.26%	0.655
35	22.19%	8.48%	0.02%	0.20%	1.28%	26.41%	27.38%	14.02%	6.52%	8.30%	0.658
36	22.47%	8.72%	0.02%	0.21%	1.38%	26.83%	26.16%	14.20%	6.57%	8.34%	0.661
37	22.74%	8.95%	0.03%	0.22%	1.48%	27.23%	24.97%	14.38%	6.61%	8.38%	0.663
38	22.99%	9.20%	0.03%	0.23%	1.59%	27.62%	23.79%	14.56%	6.66%	8.41%	0.665
39	23.21%	9.43%	0.03%	0.24%	1.71%	27.98%	22.66%	14.74%	6.70%	8.45%	0.667
40	23.40%	9.68%	0.03%	0.25%	1.84%	28.29%	21.60%	14.92%	6.74%	8.49%	0.669
41	23.56%	9.93%	0.03%	0.26%	1.99%	28.58%	20.55%	15.10%	6.78%	8.53%	0.671
42	23.70%	10.18%	0.03%	0.26%	2.16%	28.86%	19.52%	15.29%	6.83%	8.58%	0.672
43	23.84%	10.42%	0.03%	0.27%	2.33%	29.13%	18.50%	15.48%	6.87%	8.62%	0.673
44	23.96%	10.66%	0.03%	0.28%	2.50%	29.38%	17.51%	15.67%	6.91%	8.66%	0.675
45	24.07%	10.91%	0.03%	0.29%	2.68%	29.62%	16.53%	15.86%	6.95%	8.71%	0.676
46	24.13%	11.19%	0.04%	0.30%	2.87%	29.85%	15.58%	16.04%	6.99%	8.75%	0.677
47	24.18%	11.47%	0.04%	0.31%	3.06%	30.03%	14.69%	16.23%	7.02%	8.80%	0.678
48	24.21%	11.74%	0.04%	0.31%	3.27%	30.16%	13.85%	16.42%	7.06%	8.85%	0.678
49	24.24%	12.00%	0.04%	0.32%	3.48%	30.24%	13.06%	16.61%	7.10%	8.89%	0.679
50	24.27%	12.26%	0.04%	0.33%	3.71%	30.29%	12.30%	16.80%	7.13%	8.94%	0.679
51	24.29%	12.50%	0.04%	0.34%	3.95%	30.33%	11.56%	16.99%	7.17%	8.99%	0.679
52	24.32%	12.72%	0.04%	0.35%	4.20%	30.33%	10.85%	17.19%	7.21%	9.04%	0.680
53	24.37%	12.93%	0.04%	0.35%	4.45%	30.31%	10.15%	17.39%	7.24%	9.10%	0.680
54	24.39%	13.14%	0.04%	0.36%	4.71%	30.26%	9.50%	17.60%	7.28%	9.15%	0.680
55	24.41%	13.35%	0.05%	0.37%	4.98%	30.19%	8.85%	17.81%	7.31%	9.20%	0.679
56	24.42%	13.56%	0.05%	0.38%	5.24%	30.09%	8.24%	18.02%	7.35%	9.26%	0.679
57	24.45%	13.76%	0.05%	0.39%	5.50%	29.95%	7.67%	18.24%	7.38%	9.31%	0.679
58	24.49%	13.95%	0.05%	0.40%	5.77%	29.77%	7.12%	18.46%	7.42%	9.37%	0.679
59	24.52%	14.14%	0.05%	0.40%	6.04%	29.57%	6.59%	18.69%	7.45%	9.43%	0.678
60	24.56%	14.34%	0.05%	0.41%	6.30%	29.32%	6.09%	18.93%	7.49%	9.48%	0.678
61	24.58%	14.55%	0.05%	0.41%	6.57%	29.05%	5.63%	19.17%	7.52%	9.54%	0.677
62	24.60%	14.74%	0.05%	0.41%	6.85%	28.72%	5.20%	19.42%	7.56%	9.61%	0.676
63	24.62%	14.93%	0.05%	0.42%	7.13%	28.35%	4.81%	19.69%	7.59%	9.67%	0.675
64	24.64%	15.12%	0.06%	0.42%	7.41%	27.97%	4.42%	19.96%	7.63%	9.74%	0.675
65	24.67%	15.31%	0.06%	0.43%	7.69%	27.57%	4.06%	20.22%	7.66%	9.80%	0.673
66	24.68%	15.49%	0.06%	0.43%	7.97%	27.15%	3.73%	20.48%	7.70%	9.87%	0.672
67	24.70%	15.67%	0.06%	0.44%	8.26%	26.71%	3.42%	20.74%	7.73%	9.94%	0.671
68	24.72%	15.87%	0.06%	0.44%	8.56%	26.23%	3.14%	20.99%	7.77%	10.01%	0.670
69	24.70%	16.08%	0.06%	0.45%	8.87%	25.74%	2.88%	21.22%	7.80%	10.09%	0.668
70	24.67%	16.31%	0.06%	0.47%	9.17%	25.23%	2.64%	21.46%	7.83%	10.16%	0.666
71	24.63%	16.56%	0.06%	0.48%	9.48%	24.70%	2.40%	21.69%	7.87%	10.24%	0.665
72	24.59%	16.81%	0.07%	0.49%	9.78%	24.16%	2.18%	21.91%	7.90%	10.32%	0.663
73	24.55%	17.08%	0.07%	0.51%	10.09%	23.59%	1.98%	22.14%	7.94%	10.41%	0.661
74	24.50%	17.36%	0.07%	0.53%	10.40%	22.98%	1.79%	22.37%	7.97%	10.50%	0.658
75	24.46%	17.61%	0.08%	0.56%	10.72%	22.36%	1.62%	22.59%	8.01%	10.59%	0.656
76	24.41%	17.88%	0.08%	0.58%	11.05%	21.74%	1.46%	22.80%	8.04%	10.68%	0.654
77	24.35%	18.16%	0.08%	0.61%	11.38%	21.09%	1.32%	23.01%	8.08%	10.78%	0.651
78	24.26%	18.47%	0.08%	0.64%	11.71%	20.44%	1.18%	23.20%	8.11%	10.88%	0.648
79	24.16%	18.80%	0.08%	0.67%	12.06%	19.80%	1.06%	23.36%	8.15%	10.98%	0.645
80	24.04%	19.13%	0.09%	0.70%	12.42%	19.16%	0.94%	23.51%	8.18%	11.08%	0.642
81	23.95%	19.44%	0.10%	0.75%	12.78%	18.50%	0.83%	23.65%	8.21%	11.19%	0.639
82	23.83%	19.75%	0.12%	0.80%	13.16%	17.88%	0.72%	23.74%	8.25%	11.30%	0.636
83	23.65%	20.10%	0.13%	0.85%	13.55%	17.27%	0.63%	23.83%	8.28%	11.40%	0.633
84	23.46%	20.48%	0.13%	0.89%	13.95%	16.66%	0.54%	23.89%	8.31%	11.52%	0.629
85	23.23%	20.88%	0.14%	0.93%	14.35%	16.06%	0.47%	23.93%	8.34%	11.63%	0.626
86	23.01%	21.31%	0.13%	0.98%	14.76%	15.46%	0.41%	23.94%	8.37%	11.75%	0.622
87	22.80%	21.72%	0.12%	1.03%	15.22%	14.82%	0.35%	23.94%	8.40%	11.87%	0.619
88	22.50%	22.23%	0.12%	1.09%	15.67%	14.19%	0.30%	23.90%	8.44%	12.00%	0.615
89	22.16%	22.76%	0.11%	1.16%	16.15%	13.57%	0.24%	23.84%	8.47%	12.14%	0.610
90	21.77%	23.34%	0.10%	1.22%	16.65%	12.96%	0.20%	23.76%	8.50%	12.27%	0.606
91	21.25%	24.03%	0.09%	1.27%	17.15%	12.37%	0.15%	23.68%	8.53%	12.42%	0.602
92	20.74%	24.70%	0.08%	1.33%	17.65%	11.83%	0.12%	23.56%	8.56%	12.55%	0.598
93	20.19%	25.37%	0.07%	1.38%	18.18%	11.33%	0.09%	23.38%	8.59%	12.69%	0.593
94	19.41%	26.15%	0.06%	1.45%	18.80%	10.87%	0.06%	23.20%	8.62%	12.84%	0.589
95	18.57%	26.94%	0.05%	1.52%	19.47%	10.48%	0.05%	22.93%	8.64%	12.99%	0.584
96	17.62%	27.71%	0.04%	1.59%	20.19%	10.12%	0.04%	22.71%	8.66%	13.13%	0.579
97	16.78%	28.51%	0.03%	1.65%	20.87%	9.78%	0.02%	22.35%	8.68%	13.28%	0.574
98	15.79%	29.41%	0.02%	1.76%	21.67%	9.49%	0.02%	21.84%	8.70%	13.45%	0.568
99	14.64%	30.14%	0.01%	1.90%	22.63%	9.32%	0.01%	21.36%	8.71%	13.61%	0.562
100	13.50%	30.50%	0.00%	2.00%	23.50%	9.50%	0.00%	21.00%	8.70%	13.69%	0.558
^*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 2006 to Sep 2022
The efficient frontier is based on the monthly returns, volatilities, and correlations of the specified assets
Monte Carlo method was used to resample the efficient frontier inputs to mitigate the impact of input estimation errors
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