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 - Feb 2020)

Note: The time period was constrained by the available data for SPDR S&P 600 Small Cap ETF (SLY) [Dec 2005 - Feb 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	22.43%
SLY	SPDR S&P 600 Small Cap ETF	9.08%
EFA	iShares MSCI EAFE ETF	0.01%
EEM	iShares MSCI Emerging Markets ETF	0.83%
VNQ	Vanguard Real Estate ETF	1.80%
TLT	iShares 20+ Year Treasury Bond ETF	30.95%
LQD	iShares iBoxx $ Invmt Grade Corp Bd ETF	23.13%
GLD	SPDR Gold Shares	11.77%
Save portfolio »

Portfolio Returns

Portfolio Statistics
Portfolio	Expected Return	Expected Volatility	Sharpe Ratio
Provided Portfolio	8.18%	11.44%	0.61
Tangency Portfolio	8.37%	7.48%	0.96

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)	8.46%	9.56%	14.22%	0.589	0.00%	100.00%
2	SPDR S&P 600 Small Cap ETF (SLY)	8.55%	10.51%	18.91%	0.493	0.00%	100.00%
3	iShares MSCI EAFE ETF (EFA)	3.25%	4.81%	17.22%	0.211	0.00%	100.00%
4	iShares MSCI Emerging Markets ETF (EEM)	4.30%	6.90%	22.17%	0.258	0.00%	100.00%
5	Vanguard Real Estate ETF (VNQ)	7.25%	10.11%	22.67%	0.394	0.00%	100.00%
6	iShares 20+ Year Treasury Bond ETF (TLT)	7.24%	8.19%	13.51%	0.518	0.00%	100.00%
7	iShares iBoxx $ Invmt Grade Corp Bd ETF (LQD)	5.78%	6.05%	7.18%	0.678	0.00%	100.00%
8	SPDR Gold Shares (GLD)	7.74%	9.41%	17.66%	0.466	0.00%	100.00%
^*Expected return is annualized from historical monthly mean return. Ex ante Sharpe Ratio calculated using historical 3-month treasury bill returns as the risk-free rate (1.19% 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	0.78	0.71	-0.33	0.27	0.03
SPDR S&P 600 Small Cap ETF	SLY	0.91	1.00	0.80	0.73	0.73	-0.38	0.20	0.00
iShares MSCI EAFE ETF	EFA	0.89	0.80	1.00	0.88	0.68	-0.26	0.36	0.15
iShares MSCI Emerging Markets ETF	EEM	0.78	0.73	0.88	1.00	0.60	-0.25	0.34	0.29
Vanguard Real Estate ETF	VNQ	0.71	0.73	0.68	0.60	1.00	0.00	0.43	0.09
iShares 20+ Year Treasury Bond ETF	TLT	-0.33	-0.38	-0.26	-0.25	0.00	1.00	0.52	0.21
iShares iBoxx $ Invmt Grade Corp Bd ETF	LQD	0.27	0.20	0.36	0.34	0.43	0.52	1.00	0.26
SPDR Gold Shares	GLD	0.03	0.00	0.15	0.29	0.09	0.21	0.26	1.00
Based on monthly returns from Jan 2006 to Feb 2020

Efficient Frontier Points
#	SPY	SLY	EFA	EEM	VNQ	TLT	LQD	GLD	Expected Return^*	Standard Deviation^*	Sharpe Ratio^*
1	15.81%	1.44%	0.00%	0.00%	0.00%	11.72%	65.10%	5.93%	7.11%	6.80%	0.871
2	16.18%	1.53%	0.00%	0.00%	0.00%	12.22%	64.00%	6.07%	7.14%	6.80%	0.876
3	16.49%	1.67%	0.00%	0.00%	0.00%	12.74%	62.89%	6.21%	7.18%	6.81%	0.880
4	16.78%	1.83%	0.00%	0.00%	0.00%	13.27%	61.78%	6.35%	7.21%	6.81%	0.885
5	17.04%	2.00%	0.00%	0.00%	0.00%	13.80%	60.68%	6.48%	7.24%	6.81%	0.889
6	17.27%	2.20%	0.00%	0.00%	0.01%	14.31%	59.61%	6.60%	7.27%	6.82%	0.893
7	17.49%	2.40%	0.00%	0.00%	0.02%	14.83%	58.53%	6.73%	7.31%	6.82%	0.897
8	17.72%	2.59%	0.00%	0.00%	0.04%	15.34%	57.45%	6.87%	7.34%	6.83%	0.901
9	17.93%	2.79%	0.00%	0.01%	0.05%	15.85%	56.36%	7.00%	7.37%	6.84%	0.905
10	18.10%	3.03%	0.00%	0.02%	0.07%	16.37%	55.28%	7.14%	7.40%	6.84%	0.908
11	18.25%	3.27%	0.00%	0.03%	0.08%	16.89%	54.20%	7.28%	7.44%	6.85%	0.912
12	18.41%	3.53%	0.00%	0.04%	0.10%	17.42%	53.09%	7.42%	7.47%	6.86%	0.916
13	18.57%	3.77%	0.00%	0.05%	0.12%	17.94%	51.98%	7.56%	7.50%	6.87%	0.919
14	18.73%	4.02%	0.00%	0.06%	0.14%	18.47%	50.86%	7.71%	7.54%	6.89%	0.922
15	18.90%	4.26%	0.00%	0.07%	0.17%	18.99%	49.74%	7.87%	7.57%	6.90%	0.926
16	19.09%	4.49%	0.00%	0.08%	0.19%	19.51%	48.60%	8.02%	7.61%	6.91%	0.929
17	19.28%	4.72%	0.00%	0.10%	0.23%	20.02%	47.45%	8.18%	7.64%	6.93%	0.932
18	19.45%	4.96%	0.01%	0.13%	0.26%	20.55%	46.30%	8.35%	7.68%	6.94%	0.935
19	19.62%	5.18%	0.01%	0.15%	0.30%	21.09%	45.13%	8.52%	7.71%	6.96%	0.937
20	19.76%	5.41%	0.01%	0.18%	0.36%	21.62%	43.98%	8.68%	7.75%	6.98%	0.940
21	19.91%	5.62%	0.01%	0.21%	0.41%	22.15%	42.83%	8.85%	7.78%	7.00%	0.942
22	20.05%	5.84%	0.01%	0.25%	0.47%	22.68%	41.68%	9.01%	7.81%	7.02%	0.944
23	20.21%	6.05%	0.01%	0.28%	0.54%	23.22%	40.51%	9.18%	7.85%	7.04%	0.946
24	20.37%	6.26%	0.01%	0.31%	0.60%	23.76%	39.34%	9.34%	7.88%	7.07%	0.948
25	20.53%	6.46%	0.01%	0.35%	0.67%	24.29%	38.17%	9.51%	7.92%	7.09%	0.949
26	20.70%	6.66%	0.01%	0.38%	0.74%	24.82%	37.00%	9.68%	7.95%	7.12%	0.951
27	20.87%	6.85%	0.02%	0.42%	0.82%	25.35%	35.83%	9.85%	7.99%	7.14%	0.952
28	21.03%	7.05%	0.02%	0.45%	0.89%	25.88%	34.65%	10.02%	8.02%	7.17%	0.954
29	21.19%	7.25%	0.02%	0.48%	0.97%	26.40%	33.49%	10.20%	8.06%	7.20%	0.955
30	21.34%	7.45%	0.02%	0.52%	1.06%	26.92%	32.33%	10.37%	8.09%	7.22%	0.956
31	21.48%	7.66%	0.02%	0.55%	1.14%	27.43%	31.17%	10.55%	8.13%	7.25%	0.957
32	21.61%	7.87%	0.02%	0.59%	1.23%	27.95%	30.01%	10.72%	8.16%	7.28%	0.958
33	21.75%	8.08%	0.02%	0.63%	1.31%	28.46%	28.85%	10.89%	8.20%	7.31%	0.959
34	21.89%	8.29%	0.02%	0.67%	1.40%	28.97%	27.69%	11.07%	8.23%	7.35%	0.959
35	22.03%	8.50%	0.02%	0.71%	1.49%	29.48%	26.54%	11.24%	8.27%	7.38%	0.960
36	22.17%	8.70%	0.01%	0.75%	1.58%	29.98%	25.39%	11.42%	8.30%	7.41%	0.960
37	22.30%	8.89%	0.01%	0.79%	1.69%	30.48%	24.25%	11.60%	8.34%	7.44%	0.961
38	22.43%	9.08%	0.01%	0.83%	1.80%	30.95%	23.13%	11.77%	8.37%	7.48%	0.961
39	22.54%	9.28%	0.00%	0.87%	1.91%	31.41%	22.04%	11.95%	8.41%	7.51%	0.961
40	22.62%	9.48%	0.00%	0.91%	2.03%	31.84%	20.99%	12.12%	8.44%	7.55%	0.960
41	22.69%	9.68%	0.00%	0.96%	2.16%	32.24%	19.96%	12.30%	8.47%	7.59%	0.960
42	22.75%	9.88%	0.00%	1.00%	2.29%	32.63%	18.95%	12.49%	8.50%	7.62%	0.960
43	22.81%	10.08%	0.00%	1.05%	2.42%	33.00%	17.97%	12.67%	8.53%	7.66%	0.959
44	22.86%	10.29%	0.00%	1.09%	2.56%	33.34%	17.01%	12.85%	8.56%	7.70%	0.958
45	22.88%	10.51%	0.00%	1.14%	2.70%	33.64%	16.10%	13.03%	8.59%	7.74%	0.957
46	22.86%	10.74%	0.00%	1.20%	2.85%	33.89%	15.25%	13.22%	8.62%	7.78%	0.956
47	22.83%	10.97%	0.00%	1.25%	3.02%	34.11%	14.41%	13.41%	8.65%	7.82%	0.955
48	22.79%	11.19%	0.00%	1.30%	3.19%	34.33%	13.59%	13.61%	8.67%	7.86%	0.953
49	22.73%	11.43%	0.00%	1.36%	3.36%	34.54%	12.78%	13.81%	8.70%	7.90%	0.951
50	22.64%	11.67%	0.00%	1.42%	3.54%	34.72%	12.00%	14.01%	8.73%	7.94%	0.950
51	22.55%	11.90%	0.00%	1.48%	3.72%	34.87%	11.26%	14.22%	8.75%	7.98%	0.948
52	22.43%	12.12%	0.00%	1.54%	3.91%	34.96%	10.59%	14.44%	8.78%	8.03%	0.946
53	22.32%	12.34%	0.00%	1.61%	4.10%	35.03%	9.93%	14.67%	8.80%	8.07%	0.943
54	22.20%	12.55%	0.00%	1.67%	4.31%	35.07%	9.30%	14.90%	8.82%	8.11%	0.941
55	22.06%	12.75%	0.00%	1.73%	4.53%	35.09%	8.72%	15.12%	8.84%	8.16%	0.939
56	21.90%	12.96%	0.00%	1.79%	4.75%	35.08%	8.17%	15.35%	8.87%	8.20%	0.936
57	21.73%	13.16%	0.00%	1.85%	4.99%	35.05%	7.66%	15.57%	8.89%	8.25%	0.933
58	21.56%	13.33%	0.00%	1.91%	5.24%	34.99%	7.18%	15.79%	8.90%	8.30%	0.930
59	21.40%	13.49%	0.00%	1.97%	5.50%	34.90%	6.74%	16.00%	8.92%	8.34%	0.927
60	21.21%	13.66%	0.00%	2.03%	5.77%	34.77%	6.34%	16.23%	8.94%	8.39%	0.924
61	21.02%	13.81%	0.00%	2.08%	6.05%	34.64%	5.94%	16.46%	8.96%	8.44%	0.921
62	20.82%	13.96%	0.00%	2.14%	6.34%	34.49%	5.56%	16.68%	8.97%	8.49%	0.917
63	20.62%	14.10%	0.00%	2.21%	6.63%	34.32%	5.21%	16.92%	8.99%	8.54%	0.914
64	20.40%	14.24%	0.00%	2.27%	6.92%	34.12%	4.88%	17.16%	9.00%	8.59%	0.910
65	20.21%	14.39%	0.00%	2.33%	7.22%	33.88%	4.56%	17.42%	9.02%	8.64%	0.907
66	20.01%	14.52%	0.00%	2.40%	7.52%	33.63%	4.25%	17.67%	9.03%	8.69%	0.903
67	19.80%	14.67%	0.00%	2.46%	7.83%	33.37%	3.95%	17.92%	9.05%	8.75%	0.899
68	19.55%	14.84%	0.00%	2.52%	8.16%	33.08%	3.68%	18.17%	9.06%	8.81%	0.895
69	19.30%	15.01%	0.00%	2.59%	8.48%	32.78%	3.41%	18.43%	9.08%	8.87%	0.890
70	19.08%	15.16%	0.00%	2.66%	8.79%	32.47%	3.15%	18.69%	9.09%	8.92%	0.886
71	18.88%	15.27%	0.00%	2.74%	9.11%	32.13%	2.93%	18.94%	9.11%	8.98%	0.882
72	18.69%	15.37%	0.00%	2.81%	9.44%	31.78%	2.71%	19.19%	9.12%	9.04%	0.877
73	18.50%	15.47%	0.00%	2.89%	9.77%	31.42%	2.51%	19.45%	9.13%	9.10%	0.873
74	18.30%	15.57%	0.00%	2.97%	10.12%	31.05%	2.30%	19.69%	9.14%	9.17%	0.868
75	18.09%	15.69%	0.00%	3.04%	10.48%	30.69%	2.11%	19.90%	9.16%	9.23%	0.863
76	17.86%	15.79%	0.00%	3.13%	10.85%	30.33%	1.93%	20.11%	9.17%	9.30%	0.859
77	17.62%	15.88%	0.00%	3.24%	11.23%	29.92%	1.76%	20.34%	9.18%	9.37%	0.853
78	17.38%	16.00%	0.00%	3.36%	11.63%	29.48%	1.61%	20.56%	9.19%	9.44%	0.848
79	17.13%	16.12%	0.00%	3.47%	12.03%	29.03%	1.46%	20.76%	9.20%	9.52%	0.842
80	16.89%	16.23%	0.00%	3.60%	12.42%	28.58%	1.33%	20.95%	9.21%	9.60%	0.836
81	16.61%	16.38%	0.00%	3.75%	12.82%	28.11%	1.20%	21.11%	9.22%	9.68%	0.830
82	16.34%	16.55%	0.00%	3.91%	13.21%	27.63%	1.09%	21.27%	9.23%	9.76%	0.824
83	16.04%	16.75%	0.00%	4.07%	13.61%	27.16%	0.97%	21.40%	9.24%	9.85%	0.818
84	15.72%	16.99%	0.00%	4.23%	14.02%	26.69%	0.86%	21.50%	9.25%	9.94%	0.812
85	15.35%	17.26%	0.01%	4.38%	14.44%	26.23%	0.75%	21.58%	9.26%	10.03%	0.806
86	14.97%	17.51%	0.04%	4.53%	14.87%	25.79%	0.66%	21.63%	9.27%	10.12%	0.799
87	14.58%	17.77%	0.06%	4.69%	15.32%	25.32%	0.57%	21.70%	9.28%	10.21%	0.793
88	14.03%	18.18%	0.08%	4.85%	15.76%	24.84%	0.49%	21.76%	9.29%	10.31%	0.786
89	13.39%	18.71%	0.10%	5.02%	16.21%	24.35%	0.43%	21.79%	9.30%	10.42%	0.779
90	12.65%	19.28%	0.13%	5.18%	16.70%	23.87%	0.37%	21.82%	9.31%	10.53%	0.772
91	11.94%	19.76%	0.11%	5.38%	17.20%	23.41%	0.32%	21.88%	9.32%	10.64%	0.765
92	11.23%	20.24%	0.09%	5.59%	17.68%	22.98%	0.27%	21.92%	9.34%	10.75%	0.758
93	10.53%	20.73%	0.06%	5.82%	18.20%	22.51%	0.23%	21.91%	9.35%	10.87%	0.751
94	9.86%	21.10%	0.03%	6.10%	18.82%	21.99%	0.19%	21.91%	9.36%	11.00%	0.743
95	9.14%	21.40%	0.01%	6.46%	19.47%	21.47%	0.14%	21.92%	9.36%	11.13%	0.734
96	8.15%	21.74%	0.00%	6.98%	20.09%	20.94%	0.11%	21.99%	9.36%	11.28%	0.725
97	7.13%	22.13%	0.00%	7.57%	20.68%	20.45%	0.08%	21.95%	9.36%	11.43%	0.715
98	6.15%	22.42%	0.00%	8.20%	21.32%	20.05%	0.05%	21.82%	9.36%	11.58%	0.706
99	5.29%	22.01%	0.00%	8.99%	22.43%	19.81%	0.02%	21.45%	9.34%	11.74%	0.695
100	4.50%	21.00%	0.00%	10.00%	23.50%	20.00%	0.00%	21.00%	9.31%	11.86%	0.685
^*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 (1.19% 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 Feb 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