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

Geometric Mean

Min Variance Frontier

Chart from Origin

Efficient Frontier Results (Jan 2006 - Jul 2020)

Note: The time period was constrained by the available data for SPDR S&P 600 Small Cap ETF (SLY) [Dec 2005 - Jul 2020].

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 »

Tangency Portfolio
Ticker	Name	Allocation
SPY	SPDR S&P 500 ETF Trust	27.28%
SLY	SPDR S&P 600 Small Cap ETF	5.23%
EEM	iShares MSCI Emerging Markets ETF	0.77%
VNQ	Vanguard Real Estate ETF	1.22%
TLT	iShares 20+ Year Treasury Bond ETF	33.25%
LQD	iShares iBoxx $ Invmt Grade Corp Bd ETF	18.95%
GLD	SPDR Gold Shares	13.31%
Save portfolio »

Portfolio Returns

Portfolio Statistics
Portfolio	Expected Return	Expected Volatility	Sharpe Ratio
Provided Portfolio	8.53%	11.89%	0.62
Tangency Portfolio	9.04%	7.75%	1.02

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

Efficient Frontier Assets

Efficient Frontier Assets
#	Asset	CAGR	Expected Return	Standard Deviation	Sharpe Ratio	Min. Weight	Max. Weight
1	SPDR S&P 500 ETF Trust (SPY)	9.01%	10.22%	14.87%	0.609	0.00%	100.00%
2	SPDR S&P 600 Small Cap ETF (SLY)	8.19%	10.39%	19.95%	0.463	0.00%	100.00%
3	iShares MSCI EAFE ETF (EFA)	3.23%	4.86%	17.52%	0.211	0.00%	100.00%
4	iShares MSCI Emerging Markets ETF (EEM)	4.69%	7.38%	22.49%	0.276	0.00%	100.00%
5	Vanguard Real Estate ETF (VNQ)	6.64%	9.61%	23.09%	0.366	0.00%	100.00%
6	iShares 20+ Year Treasury Bond ETF (TLT)	7.78%	8.73%	13.45%	0.563	0.00%	100.00%
7	iShares iBoxx $ Invmt Grade Corp Bd ETF (LQD)	6.04%	6.32%	7.45%	0.693	0.00%	100.00%
8	SPDR Gold Shares (GLD)	9.17%	10.86%	17.70%	0.548	0.00%	100.00%
Results based on historical returns. Ex ante Sharpe Ratio calculated using 3-month treasury bill returns as the risk-free rate (1.16% annualized).

Asset Correlations

Asset Correlations
Name	Ticker	SPY	SLY	EFA	EEM	VNQ	TLT	LQD	GLD
SPDR S&P 500 ETF Trust	SPY	1.00	0.92	0.89	0.79	0.72	-0.33	0.34	0.07
SPDR S&P 600 Small Cap ETF	SLY	0.92	1.00	0.81	0.74	0.75	-0.38	0.29	0.03
iShares MSCI EAFE ETF	EFA	0.89	0.81	1.00	0.88	0.69	-0.27	0.41	0.16
iShares MSCI Emerging Markets ETF	EEM	0.79	0.74	0.88	1.00	0.62	-0.25	0.38	0.30
Vanguard Real Estate ETF	VNQ	0.72	0.75	0.69	0.62	1.00	-0.02	0.47	0.11
iShares 20+ Year Treasury Bond ETF	TLT	-0.33	-0.38	-0.27	-0.25	-0.02	1.00	0.47	0.22
iShares iBoxx $ Invmt Grade Corp Bd ETF	LQD	0.34	0.29	0.41	0.38	0.47	0.47	1.00	0.28
SPDR Gold Shares	GLD	0.07	0.03	0.16	0.30	0.11	0.22	0.28	1.00
Based on provided custom correlation matrix

Efficient Frontier Points
#	SPY	SLY	EFA	EEM	VNQ	TLT	LQD	GLD	Expected Return^*	Standard Deviation^*	Sharpe Ratio^*
1	15.48%	0.69%	0.05%	0.00%	0.00%	16.68%	61.74%	5.35%	7.59%	7.10%	0.906
2	16.01%	0.73%	0.04%	0.00%	0.00%	17.17%	60.50%	5.56%	7.63%	7.10%	0.912
3	16.53%	0.76%	0.03%	0.00%	0.00%	17.66%	59.26%	5.77%	7.67%	7.10%	0.917
4	17.02%	0.81%	0.02%	0.00%	0.00%	18.15%	58.03%	5.98%	7.72%	7.10%	0.923
5	17.47%	0.87%	0.02%	0.00%	0.01%	18.63%	56.82%	6.19%	7.76%	7.11%	0.928
6	17.90%	0.96%	0.01%	0.00%	0.01%	19.11%	55.60%	6.41%	7.80%	7.11%	0.934
7	18.31%	1.04%	0.01%	0.00%	0.02%	19.60%	54.40%	6.62%	7.84%	7.12%	0.939
8	18.70%	1.14%	0.01%	0.01%	0.03%	20.08%	53.21%	6.83%	7.88%	7.12%	0.943
9	19.07%	1.25%	0.00%	0.03%	0.04%	20.56%	52.03%	7.03%	7.92%	7.13%	0.948
10	19.43%	1.36%	0.00%	0.04%	0.05%	21.03%	50.85%	7.23%	7.96%	7.14%	0.952
11	19.79%	1.47%	0.00%	0.06%	0.06%	21.50%	49.67%	7.44%	8.00%	7.15%	0.956
12	20.14%	1.60%	0.00%	0.07%	0.07%	21.98%	48.49%	7.65%	8.04%	7.16%	0.961
13	20.47%	1.73%	0.00%	0.09%	0.08%	22.46%	47.30%	7.86%	8.08%	7.17%	0.965
14	20.81%	1.87%	0.00%	0.10%	0.10%	22.94%	46.11%	8.07%	8.12%	7.19%	0.969
15	21.13%	2.00%	0.00%	0.12%	0.12%	23.42%	44.93%	8.28%	8.16%	7.20%	0.972
16	21.44%	2.14%	0.00%	0.14%	0.14%	23.89%	43.76%	8.48%	8.20%	7.21%	0.976
17	21.74%	2.29%	0.00%	0.16%	0.16%	24.36%	42.60%	8.69%	8.24%	7.23%	0.979
18	22.03%	2.44%	0.00%	0.18%	0.18%	24.83%	41.43%	8.90%	8.28%	7.25%	0.982
19	22.32%	2.59%	0.00%	0.20%	0.20%	25.31%	40.26%	9.12%	8.32%	7.26%	0.985
20	22.62%	2.74%	0.00%	0.22%	0.22%	25.78%	39.09%	9.33%	8.36%	7.28%	0.989
21	22.91%	2.90%	0.00%	0.24%	0.24%	26.26%	37.90%	9.54%	8.40%	7.30%	0.991
22	23.21%	3.05%	0.00%	0.27%	0.27%	26.74%	36.72%	9.76%	8.44%	7.32%	0.994
23	23.50%	3.19%	0.00%	0.29%	0.30%	27.21%	35.53%	9.98%	8.48%	7.34%	0.997
24	23.78%	3.35%	0.00%	0.32%	0.33%	27.68%	34.35%	10.20%	8.52%	7.36%	0.999
25	24.06%	3.49%	0.00%	0.34%	0.38%	28.14%	33.18%	10.42%	8.56%	7.38%	1.002
26	24.33%	3.62%	0.00%	0.37%	0.42%	28.59%	32.03%	10.64%	8.60%	7.41%	1.004
27	24.60%	3.76%	0.00%	0.40%	0.47%	29.04%	30.87%	10.86%	8.64%	7.43%	1.006
28	24.86%	3.91%	0.00%	0.43%	0.51%	29.49%	29.72%	11.08%	8.67%	7.46%	1.008
29	25.12%	4.04%	0.00%	0.46%	0.57%	29.92%	28.58%	11.31%	8.71%	7.48%	1.009
30	25.38%	4.18%	0.00%	0.49%	0.63%	30.34%	27.46%	11.53%	8.75%	7.51%	1.011
31	25.65%	4.31%	0.00%	0.52%	0.69%	30.75%	26.34%	11.75%	8.79%	7.54%	1.012
32	25.93%	4.43%	0.00%	0.55%	0.75%	31.15%	25.22%	11.96%	8.83%	7.57%	1.013
33	26.20%	4.56%	0.00%	0.58%	0.82%	31.56%	24.10%	12.19%	8.87%	7.59%	1.014
34	26.45%	4.69%	0.00%	0.61%	0.89%	31.95%	23.00%	12.41%	8.90%	7.63%	1.015
35	26.66%	4.84%	0.00%	0.65%	0.96%	32.31%	21.95%	12.64%	8.94%	7.66%	1.016
36	26.88%	4.96%	0.00%	0.69%	1.04%	32.63%	20.93%	12.86%	8.97%	7.69%	1.016
37	27.08%	5.10%	0.00%	0.73%	1.13%	32.95%	19.93%	13.08%	9.01%	7.72%	1.017
38	27.28%	5.23%	0.00%	0.77%	1.22%	33.25%	18.95%	13.31%	9.04%	7.75%	1.017
39	27.44%	5.37%	0.00%	0.81%	1.31%	33.54%	17.99%	13.53%	9.08%	7.78%	1.017
40	27.60%	5.52%	0.00%	0.86%	1.40%	33.81%	17.05%	13.76%	9.11%	7.82%	1.017
41	27.74%	5.67%	0.00%	0.90%	1.50%	34.08%	16.11%	13.99%	9.14%	7.85%	1.016
42	27.87%	5.83%	0.00%	0.95%	1.60%	34.33%	15.19%	14.23%	9.17%	7.89%	1.016
43	27.96%	6.00%	0.00%	1.00%	1.70%	34.55%	14.31%	14.48%	9.20%	7.92%	1.015
44	28.03%	6.17%	0.00%	1.05%	1.81%	34.74%	13.47%	14.73%	9.23%	7.96%	1.014
45	28.08%	6.34%	0.00%	1.10%	1.93%	34.88%	12.69%	14.98%	9.26%	7.99%	1.013
46	28.11%	6.51%	0.00%	1.15%	2.05%	34.96%	11.96%	15.25%	9.29%	8.03%	1.012
47	28.10%	6.68%	0.00%	1.21%	2.19%	35.00%	11.28%	15.53%	9.32%	8.07%	1.011
48	28.08%	6.84%	0.00%	1.26%	2.34%	35.00%	10.65%	15.83%	9.34%	8.11%	1.009
49	28.03%	7.00%	0.00%	1.32%	2.50%	34.98%	10.06%	16.12%	9.36%	8.15%	1.007
50	27.99%	7.15%	0.00%	1.37%	2.65%	34.94%	9.48%	16.42%	9.39%	8.19%	1.005
51	27.95%	7.30%	0.00%	1.42%	2.81%	34.85%	8.94%	16.73%	9.41%	8.23%	1.003
52	27.89%	7.46%	0.00%	1.48%	2.97%	34.74%	8.42%	17.05%	9.43%	8.27%	1.000
53	27.80%	7.63%	0.00%	1.53%	3.13%	34.60%	7.94%	17.38%	9.45%	8.31%	0.998
54	27.68%	7.79%	0.00%	1.58%	3.30%	34.45%	7.48%	17.72%	9.47%	8.35%	0.995
55	27.56%	7.95%	0.00%	1.64%	3.47%	34.30%	7.05%	18.04%	9.49%	8.39%	0.992
56	27.42%	8.11%	0.00%	1.70%	3.64%	34.13%	6.64%	18.36%	9.51%	8.44%	0.989
57	27.27%	8.26%	0.00%	1.77%	3.83%	33.96%	6.24%	18.68%	9.53%	8.48%	0.986
58	27.11%	8.41%	0.00%	1.85%	4.01%	33.78%	5.87%	18.99%	9.54%	8.52%	0.983
59	26.95%	8.56%	0.00%	1.92%	4.20%	33.57%	5.50%	19.30%	9.56%	8.57%	0.980
60	26.78%	8.70%	0.00%	2.00%	4.39%	33.34%	5.16%	19.64%	9.58%	8.62%	0.976
61	26.61%	8.84%	0.00%	2.08%	4.59%	33.09%	4.83%	19.97%	9.59%	8.67%	0.973
62	26.42%	8.99%	0.00%	2.15%	4.79%	32.83%	4.52%	20.31%	9.61%	8.71%	0.969
63	26.23%	9.14%	0.00%	2.23%	4.99%	32.55%	4.21%	20.64%	9.62%	8.76%	0.965
64	26.04%	9.29%	0.00%	2.30%	5.21%	32.27%	3.92%	20.98%	9.64%	8.82%	0.961
65	25.84%	9.43%	0.00%	2.38%	5.43%	31.97%	3.65%	21.31%	9.65%	8.87%	0.957
66	25.63%	9.57%	0.00%	2.47%	5.65%	31.67%	3.38%	21.64%	9.66%	8.92%	0.953
67	25.42%	9.71%	0.00%	2.56%	5.87%	31.35%	3.13%	21.97%	9.68%	8.97%	0.949
68	25.23%	9.82%	0.00%	2.65%	6.11%	31.00%	2.90%	22.29%	9.69%	9.03%	0.944
69	25.05%	9.92%	0.00%	2.74%	6.36%	30.64%	2.67%	22.62%	9.70%	9.09%	0.940
70	24.84%	10.04%	0.00%	2.84%	6.62%	30.26%	2.45%	22.96%	9.71%	9.15%	0.935
71	24.61%	10.17%	0.00%	2.94%	6.89%	29.88%	2.24%	23.28%	9.73%	9.21%	0.930
72	24.36%	10.30%	0.00%	3.04%	7.17%	29.51%	2.04%	23.59%	9.74%	9.27%	0.925
73	24.06%	10.47%	0.00%	3.15%	7.44%	29.13%	1.86%	23.89%	9.75%	9.34%	0.919
74	23.74%	10.66%	0.00%	3.25%	7.72%	28.75%	1.70%	24.18%	9.76%	9.40%	0.914
75	23.41%	10.84%	0.00%	3.35%	8.03%	28.35%	1.56%	24.47%	9.77%	9.47%	0.909
76	23.09%	11.00%	0.00%	3.44%	8.35%	27.94%	1.42%	24.77%	9.77%	9.53%	0.903
77	22.77%	11.16%	0.00%	3.54%	8.67%	27.50%	1.28%	25.09%	9.78%	9.60%	0.898
78	22.42%	11.34%	0.00%	3.63%	8.99%	27.08%	1.15%	25.38%	9.79%	9.67%	0.892
79	22.03%	11.54%	0.00%	3.73%	9.32%	26.65%	1.04%	25.68%	9.80%	9.75%	0.886
80	21.65%	11.73%	0.00%	3.84%	9.66%	26.21%	0.92%	26.00%	9.81%	9.82%	0.881
81	21.22%	11.95%	0.00%	3.94%	10.01%	25.75%	0.81%	26.32%	9.82%	9.90%	0.875
82	20.75%	12.16%	0.00%	4.05%	10.39%	25.30%	0.71%	26.63%	9.83%	9.98%	0.868
83	20.29%	12.39%	0.00%	4.16%	10.79%	24.82%	0.62%	26.92%	9.83%	10.06%	0.862
84	19.80%	12.63%	0.00%	4.28%	11.20%	24.32%	0.55%	27.22%	9.84%	10.15%	0.855
85	19.31%	12.88%	0.00%	4.40%	11.61%	23.82%	0.48%	27.50%	9.85%	10.23%	0.848
86	18.80%	13.13%	0.00%	4.56%	12.01%	23.32%	0.42%	27.76%	9.85%	10.32%	0.842
87	18.26%	13.37%	0.00%	4.73%	12.44%	22.82%	0.36%	28.02%	9.86%	10.42%	0.835
88	17.72%	13.59%	0.00%	4.90%	12.91%	22.30%	0.31%	28.27%	9.86%	10.51%	0.827
89	17.14%	13.79%	0.00%	5.10%	13.41%	21.76%	0.27%	28.53%	9.86%	10.62%	0.820
90	16.53%	13.95%	0.00%	5.34%	13.92%	21.21%	0.24%	28.81%	9.86%	10.72%	0.812
91	15.83%	14.17%	0.00%	5.60%	14.45%	20.70%	0.20%	29.05%	9.86%	10.83%	0.804
92	14.94%	14.44%	0.00%	5.90%	15.08%	20.19%	0.18%	29.27%	9.86%	10.95%	0.795
93	14.10%	14.67%	0.00%	6.20%	15.79%	19.65%	0.15%	29.44%	9.86%	11.08%	0.785
94	13.22%	15.00%	0.00%	6.48%	16.54%	19.06%	0.13%	29.58%	9.86%	11.22%	0.775
95	12.31%	15.43%	0.00%	6.75%	17.32%	18.42%	0.10%	29.67%	9.86%	11.37%	0.765
96	11.30%	15.95%	0.00%	6.98%	18.15%	17.77%	0.08%	29.78%	9.86%	11.52%	0.755
97	10.18%	16.46%	0.00%	7.16%	19.04%	17.10%	0.06%	30.01%	9.86%	11.69%	0.744
98	8.96%	16.87%	0.00%	7.45%	20.03%	16.45%	0.04%	30.20%	9.86%	11.86%	0.733
99	7.72%	16.82%	0.00%	8.04%	21.24%	15.81%	0.02%	30.36%	9.85%	12.05%	0.721
100	6.50%	16.99%	0.00%	8.50%	23.50%	14.50%	0.00%	30.01%	9.84%	12.41%	0.699
^*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 (1.16% 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.
Historical asset statistics are based on monthly returns from Jan 2006 to Jul 2020
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