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 - Dec 2020)

Note: The time period was constrained by the available data for SPDR S&P 600 Small Cap ETF (SLY) [Dec 2005 - Dec 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	24.63%
SLY	SPDR S&P 600 Small Cap ETF	10.12%
EFA	iShares MSCI EAFE ETF	0.01%
EEM	iShares MSCI Emerging Markets ETF	0.67%
VNQ	Vanguard Real Estate ETF	1.12%
TLT	iShares 20+ Year Treasury Bond ETF	32.08%
LQD	iShares iBoxx $ Invmt Grade Corp Bd ETF	19.72%
GLD	SPDR Gold Shares	11.65%
Save portfolio »

Portfolio Returns

Portfolio Statistics
Portfolio	Expected Return	Expected Volatility	Sharpe Ratio
Provided Portfolio	9.00%	11.93%	0.66
Tangency Portfolio	9.09%	7.87%	1.01

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)	9.80%	11.05%	15.07%	0.658	0.00%	100.00%
2	SPDR S&P 600 Small Cap ETF (SLY)	9.86%	12.17%	20.34%	0.543	0.00%	100.00%
3	iShares MSCI EAFE ETF (EFA)	4.33%	6.01%	17.76%	0.275	0.00%	100.00%
4	iShares MSCI Emerging Markets ETF (EEM)	5.87%	8.56%	22.36%	0.332	0.00%	100.00%
5	Vanguard Real Estate ETF (VNQ)	6.92%	9.85%	22.92%	0.380	0.00%	100.00%
6	iShares 20+ Year Treasury Bond ETF (TLT)	7.02%	7.96%	13.40%	0.510	0.00%	100.00%
7	iShares iBoxx $ Invmt Grade Corp Bd ETF (LQD)	5.94%	6.23%	7.42%	0.686	0.00%	100.00%
8	SPDR Gold Shares (GLD)	8.62%	10.30%	17.65%	0.519	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 (1.13% annualized).

Asset Correlations

Asset Correlations
Name	Ticker	SPY	SLY	EFA	EEM	VNQ	TLT	LQD	GLD
SPDR S&P 500 ETF Trust	SPY	1.00	0.91	0.89	0.79	0.72	-0.32	0.34	0.06
SPDR S&P 600 Small Cap ETF	SLY	0.91	1.00	0.81	0.74	0.74	-0.37	0.30	0.02
iShares MSCI EAFE ETF	EFA	0.89	0.81	1.00	0.88	0.70	-0.27	0.41	0.14
iShares MSCI Emerging Markets ETF	EEM	0.79	0.74	0.88	1.00	0.62	-0.25	0.38	0.29
Vanguard Real Estate ETF	VNQ	0.72	0.74	0.70	0.62	1.00	-0.01	0.47	0.10
iShares 20+ Year Treasury Bond ETF	TLT	-0.32	-0.37	-0.27	-0.25	-0.01	1.00	0.47	0.21
iShares iBoxx $ Invmt Grade Corp Bd ETF	LQD	0.34	0.30	0.41	0.38	0.47	0.47	1.00	0.27
SPDR Gold Shares	GLD	0.06	0.02	0.14	0.29	0.10	0.21	0.27	1.00
Based on monthly returns from Jan 2006 to Dec 2020

Efficient Frontier Points
#	SPY	SLY	EFA	EEM	VNQ	TLT	LQD	GLD	Expected Return^*	Standard Deviation^*	Sharpe Ratio^*
1	14.17%	0.63%	0.00%	0.00%	0.00%	14.71%	64.72%	5.76%	7.42%	7.09%	0.887
2	14.77%	0.69%	0.00%	0.00%	0.00%	15.19%	63.43%	5.91%	7.47%	7.09%	0.894
3	15.31%	0.78%	0.00%	0.00%	0.00%	15.68%	62.18%	6.05%	7.52%	7.09%	0.900
4	15.81%	0.91%	0.00%	0.00%	0.00%	16.16%	60.94%	6.18%	7.56%	7.10%	0.906
5	16.27%	1.05%	0.00%	0.00%	0.00%	16.64%	59.73%	6.32%	7.60%	7.10%	0.911
6	16.69%	1.22%	0.00%	0.00%	0.00%	17.11%	58.53%	6.45%	7.65%	7.11%	0.917
7	17.08%	1.41%	0.00%	0.01%	0.00%	17.59%	57.33%	6.58%	7.69%	7.11%	0.922
8	17.45%	1.62%	0.00%	0.01%	0.01%	18.08%	56.12%	6.72%	7.74%	7.12%	0.927
9	17.80%	1.84%	0.00%	0.02%	0.01%	18.56%	54.91%	6.85%	7.78%	7.13%	0.932
10	18.15%	2.05%	0.00%	0.03%	0.02%	19.05%	53.71%	7.00%	7.82%	7.14%	0.937
11	18.48%	2.28%	0.00%	0.04%	0.03%	19.53%	52.49%	7.14%	7.87%	7.15%	0.942
12	18.77%	2.55%	0.00%	0.04%	0.05%	20.03%	51.27%	7.29%	7.91%	7.16%	0.947
13	19.04%	2.82%	0.00%	0.05%	0.06%	20.52%	50.06%	7.44%	7.96%	7.18%	0.951
14	19.31%	3.09%	0.00%	0.06%	0.08%	21.01%	48.85%	7.60%	8.00%	7.19%	0.955
15	19.57%	3.37%	0.00%	0.07%	0.10%	21.49%	47.64%	7.75%	8.05%	7.21%	0.959
16	19.83%	3.65%	0.00%	0.08%	0.13%	21.98%	46.43%	7.91%	8.09%	7.22%	0.963
17	20.09%	3.92%	0.00%	0.10%	0.15%	22.47%	45.20%	8.07%	8.14%	7.24%	0.967
18	20.35%	4.20%	0.00%	0.11%	0.17%	22.97%	43.97%	8.22%	8.18%	7.26%	0.971
19	20.61%	4.49%	0.00%	0.13%	0.20%	23.46%	42.73%	8.38%	8.23%	7.28%	0.974
20	20.86%	4.78%	0.00%	0.14%	0.22%	23.96%	41.49%	8.55%	8.27%	7.30%	0.978
21	21.11%	5.08%	0.00%	0.16%	0.25%	24.45%	40.24%	8.71%	8.32%	7.33%	0.981
22	21.36%	5.37%	0.01%	0.18%	0.28%	24.95%	38.98%	8.88%	8.37%	7.35%	0.984
23	21.61%	5.67%	0.01%	0.20%	0.30%	25.45%	37.72%	9.05%	8.41%	7.37%	0.987
24	21.85%	5.97%	0.01%	0.22%	0.33%	25.95%	36.45%	9.22%	8.46%	7.40%	0.990
25	22.08%	6.27%	0.01%	0.25%	0.36%	26.45%	35.18%	9.39%	8.51%	7.43%	0.993
26	22.31%	6.57%	0.01%	0.28%	0.40%	26.94%	33.92%	9.57%	8.55%	7.46%	0.995
27	22.54%	6.87%	0.02%	0.31%	0.44%	27.43%	32.66%	9.74%	8.60%	7.48%	0.998
28	22.77%	7.16%	0.02%	0.33%	0.48%	27.93%	31.39%	9.92%	8.65%	7.52%	1.000
29	23.00%	7.46%	0.02%	0.36%	0.52%	28.41%	30.13%	10.09%	8.69%	7.55%	1.002
30	23.23%	7.75%	0.02%	0.39%	0.56%	28.88%	28.89%	10.27%	8.74%	7.58%	1.004
31	23.43%	8.05%	0.02%	0.42%	0.62%	29.33%	27.69%	10.45%	8.78%	7.61%	1.005
32	23.62%	8.35%	0.01%	0.46%	0.67%	29.77%	26.49%	10.63%	8.83%	7.65%	1.006
33	23.81%	8.66%	0.01%	0.49%	0.73%	30.20%	25.30%	10.81%	8.87%	7.68%	1.008
34	23.99%	8.96%	0.01%	0.52%	0.79%	30.60%	24.14%	10.99%	8.92%	7.72%	1.009
35	24.17%	9.24%	0.01%	0.56%	0.87%	30.99%	23.00%	11.16%	8.96%	7.76%	1.009
36	24.33%	9.53%	0.01%	0.59%	0.95%	31.37%	21.88%	11.33%	9.00%	7.79%	1.010
37	24.48%	9.83%	0.01%	0.63%	1.03%	31.75%	20.78%	11.49%	9.04%	7.83%	1.010
38	24.63%	10.12%	0.01%	0.67%	1.12%	32.08%	19.72%	11.65%	9.09%	7.87%	1.010
39	24.74%	10.42%	0.01%	0.72%	1.21%	32.40%	18.67%	11.83%	9.13%	7.91%	1.010
40	24.83%	10.72%	0.01%	0.77%	1.31%	32.70%	17.64%	12.01%	9.17%	7.96%	1.010
41	24.93%	11.02%	0.01%	0.82%	1.42%	32.98%	16.63%	12.20%	9.21%	8.00%	1.009
42	24.98%	11.34%	0.01%	0.87%	1.53%	33.22%	15.68%	12.38%	9.24%	8.04%	1.008
43	25.01%	11.67%	0.01%	0.92%	1.65%	33.42%	14.77%	12.56%	9.28%	8.09%	1.007
44	25.03%	11.99%	0.00%	0.97%	1.79%	33.59%	13.90%	12.74%	9.32%	8.14%	1.006
45	25.01%	12.32%	0.00%	1.02%	1.93%	33.72%	13.08%	12.92%	9.35%	8.18%	1.005
46	24.96%	12.67%	0.00%	1.07%	2.07%	33.80%	12.31%	13.11%	9.39%	8.23%	1.003
47	24.87%	13.02%	0.00%	1.13%	2.22%	33.84%	11.61%	13.31%	9.42%	8.28%	1.001
48	24.76%	13.37%	0.00%	1.19%	2.37%	33.82%	10.97%	13.51%	9.45%	8.33%	0.998
49	24.64%	13.72%	0.00%	1.25%	2.54%	33.79%	10.35%	13.71%	9.48%	8.38%	0.996
50	24.49%	14.07%	0.00%	1.32%	2.70%	33.74%	9.77%	13.92%	9.51%	8.43%	0.993
51	24.34%	14.42%	0.00%	1.38%	2.88%	33.66%	9.21%	14.12%	9.54%	8.49%	0.991
52	24.17%	14.77%	0.00%	1.44%	3.06%	33.54%	8.69%	14.32%	9.56%	8.54%	0.988
53	24.01%	15.10%	0.00%	1.51%	3.25%	33.40%	8.19%	14.54%	9.59%	8.59%	0.984
54	23.87%	15.43%	0.00%	1.57%	3.44%	33.22%	7.71%	14.77%	9.62%	8.65%	0.981
55	23.73%	15.75%	0.00%	1.64%	3.63%	33.02%	7.24%	14.99%	9.65%	8.71%	0.977
56	23.59%	16.08%	0.00%	1.70%	3.82%	32.80%	6.78%	15.22%	9.67%	8.77%	0.974
57	23.47%	16.41%	0.00%	1.77%	4.01%	32.54%	6.36%	15.45%	9.70%	8.83%	0.970
58	23.36%	16.73%	0.00%	1.83%	4.21%	32.24%	5.96%	15.67%	9.73%	8.90%	0.966
59	23.22%	17.05%	0.00%	1.90%	4.41%	31.93%	5.58%	15.91%	9.75%	8.96%	0.962
60	23.07%	17.39%	0.00%	1.96%	4.63%	31.58%	5.23%	16.15%	9.78%	9.03%	0.957
61	22.93%	17.72%	0.00%	2.03%	4.84%	31.21%	4.90%	16.38%	9.80%	9.10%	0.953
62	22.83%	18.02%	0.00%	2.09%	5.06%	30.82%	4.57%	16.61%	9.83%	9.17%	0.948
63	22.74%	18.30%	0.00%	2.15%	5.30%	30.40%	4.26%	16.85%	9.85%	9.25%	0.943
64	22.67%	18.56%	0.00%	2.22%	5.54%	29.95%	3.97%	17.09%	9.88%	9.32%	0.938
65	22.60%	18.82%	0.00%	2.28%	5.79%	29.49%	3.69%	17.33%	9.90%	9.40%	0.933
66	22.53%	19.07%	0.00%	2.35%	6.04%	29.00%	3.45%	17.57%	9.93%	9.48%	0.927
67	22.45%	19.31%	0.00%	2.41%	6.29%	28.49%	3.22%	17.82%	9.95%	9.56%	0.922
68	22.38%	19.55%	0.00%	2.47%	6.55%	27.97%	3.00%	18.08%	9.97%	9.65%	0.916
69	22.29%	19.79%	0.00%	2.54%	6.81%	27.44%	2.81%	18.32%	9.99%	9.73%	0.911
70	22.18%	20.06%	0.00%	2.61%	7.08%	26.89%	2.63%	18.56%	10.02%	9.82%	0.905
71	22.07%	20.31%	0.00%	2.68%	7.36%	26.32%	2.47%	18.79%	10.04%	9.91%	0.899
72	21.94%	20.58%	0.00%	2.74%	7.64%	25.75%	2.32%	19.02%	10.06%	10.00%	0.893
73	21.81%	20.83%	0.00%	2.80%	7.95%	25.18%	2.18%	19.25%	10.08%	10.09%	0.887
74	21.68%	21.08%	0.00%	2.86%	8.26%	24.60%	2.05%	19.47%	10.10%	10.19%	0.880
75	21.53%	21.36%	0.00%	2.92%	8.56%	24.02%	1.93%	19.67%	10.12%	10.28%	0.874
76	21.34%	21.68%	0.00%	2.98%	8.87%	23.44%	1.82%	19.86%	10.14%	10.38%	0.868
77	21.13%	22.01%	0.00%	3.04%	9.18%	22.87%	1.71%	20.06%	10.16%	10.48%	0.861
78	20.94%	22.31%	0.00%	3.11%	9.50%	22.29%	1.60%	20.25%	10.18%	10.58%	0.855
79	20.74%	22.60%	0.00%	3.19%	9.82%	21.70%	1.50%	20.45%	10.20%	10.68%	0.849
80	20.56%	22.87%	0.00%	3.27%	10.17%	21.11%	1.41%	20.62%	10.22%	10.79%	0.842
81	20.39%	23.13%	0.00%	3.35%	10.50%	20.52%	1.32%	20.79%	10.24%	10.89%	0.836
82	20.18%	23.42%	0.00%	3.44%	10.85%	19.99%	1.21%	20.91%	10.25%	11.00%	0.829
83	19.89%	23.78%	0.00%	3.53%	11.19%	19.48%	1.10%	21.02%	10.27%	11.11%	0.823
84	19.49%	24.21%	0.00%	3.65%	11.56%	18.98%	1.01%	21.11%	10.29%	11.22%	0.816
85	19.08%	24.62%	0.00%	3.78%	11.94%	18.50%	0.92%	21.16%	10.30%	11.33%	0.809
86	18.67%	25.05%	0.00%	3.93%	12.32%	18.02%	0.84%	21.18%	10.32%	11.45%	0.802
87	18.24%	25.49%	0.00%	4.07%	12.70%	17.55%	0.77%	21.19%	10.33%	11.56%	0.796
88	17.73%	25.96%	0.00%	4.25%	13.10%	17.09%	0.69%	21.18%	10.35%	11.69%	0.789
89	17.10%	26.45%	0.00%	4.51%	13.51%	16.66%	0.62%	21.15%	10.36%	11.81%	0.781
90	16.39%	26.98%	0.00%	4.80%	13.97%	16.23%	0.54%	21.10%	10.37%	11.94%	0.773
91	15.53%	27.55%	0.00%	5.10%	14.46%	15.84%	0.47%	21.04%	10.38%	12.08%	0.765
92	14.50%	28.23%	0.00%	5.42%	14.99%	15.47%	0.41%	20.98%	10.39%	12.22%	0.757
93	13.45%	28.91%	0.00%	5.78%	15.50%	15.10%	0.35%	20.91%	10.39%	12.36%	0.749
94	12.46%	29.60%	0.00%	6.15%	16.01%	14.76%	0.28%	20.74%	10.40%	12.51%	0.741
95	11.49%	30.22%	0.00%	6.51%	16.57%	14.45%	0.23%	20.54%	10.41%	12.66%	0.733
96	10.53%	30.73%	0.00%	6.85%	17.20%	14.17%	0.18%	20.32%	10.41%	12.80%	0.725
97	9.60%	31.09%	0.00%	7.25%	17.85%	13.93%	0.14%	20.14%	10.41%	12.93%	0.718
98	8.66%	31.32%	0.00%	7.62%	18.80%	13.62%	0.09%	19.89%	10.40%	13.09%	0.708
99	7.75%	31.42%	0.00%	7.99%	19.89%	13.53%	0.05%	19.37%	10.39%	13.24%	0.699
100	6.50%	32.00%	0.00%	8.50%	20.50%	13.50%	0.00%	19.00%	10.38%	13.37%	0.692
^*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 (1.13% 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 Dec 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