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 2019)

Note: The time period was constrained by the available data for SPDR S&P 600 Small Cap ETF (SLY) [Dec 2005 - Dec 2019].

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	24.71%
SLY	SPDR S&P 600 Small Cap ETF	10.43%
EFA	iShares MSCI EAFE ETF	0.03%
EEM	iShares MSCI Emerging Markets ETF	0.28%
VNQ	Vanguard Real Estate ETF	1.40%
TLT	iShares 20+ Year Treasury Bond ETF	28.99%
LQD	iShares iBoxx $ Invmt Grade Corp Bd ETF	21.46%
GLD	SPDR Gold Shares	12.70%
Save portfolio »

Portfolio Returns

Portfolio Statistics
Portfolio	Expected Return	Expected Volatility	Sharpe Ratio
Provided Portfolio	8.53%	11.45%	0.64
Tangency Portfolio	8.44%	7.55%	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)	9.21%	10.30%	14.11%	0.646	0.00%	100.00%
2	SPDR S&P 600 Small Cap ETF (SLY)	9.75%	11.70%	18.77%	0.560	0.00%	100.00%
3	iShares MSCI EAFE ETF (EFA)	4.10%	5.66%	17.16%	0.261	0.00%	100.00%
4	iShares MSCI Emerging Markets ETF (EEM)	5.11%	7.74%	22.20%	0.295	0.00%	100.00%
5	Vanguard Real Estate ETF (VNQ)	7.80%	10.69%	22.71%	0.419	0.00%	100.00%
6	iShares 20+ Year Treasury Bond ETF (TLT)	6.27%	7.20%	13.36%	0.450	0.00%	100.00%
7	iShares iBoxx $ Invmt Grade Corp Bd ETF (LQD)	5.59%	5.86%	7.20%	0.650	0.00%	100.00%
8	SPDR Gold Shares (GLD)	7.55%	9.23%	17.73%	0.454	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 (1.18% 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	0.70	-0.32	0.28	0.03
SPDR S&P 600 Small Cap ETF	SLY	0.91	1.00	0.79	0.73	0.73	-0.36	0.21	0.01
iShares MSCI EAFE ETF	EFA	0.89	0.79	1.00	0.88	0.67	-0.24	0.37	0.15
iShares MSCI Emerging Markets ETF	EEM	0.79	0.73	0.88	1.00	0.60	-0.23	0.35	0.29
Vanguard Real Estate ETF	VNQ	0.70	0.73	0.67	0.60	1.00	0.01	0.43	0.09
iShares 20+ Year Treasury Bond ETF	TLT	-0.32	-0.36	-0.24	-0.23	0.01	1.00	0.52	0.21
iShares iBoxx $ Invmt Grade Corp Bd ETF	LQD	0.28	0.21	0.37	0.35	0.43	0.52	1.00	0.26
SPDR Gold Shares	GLD	0.03	0.01	0.15	0.29	0.09	0.21	0.26	1.00
Based on monthly returns from Jan 2006 to Dec 2019

Efficient Frontier Points
#	SPY	SLY	EFA	EEM	VNQ	TLT	LQD	GLD	Expected Return^*	Standard Deviation^*	Sharpe Ratio^*
1	16.73%	1.13%	0.00%	0.00%	0.00%	12.58%	64.01%	5.55%	7.01%	6.82%	0.855
2	17.26%	1.24%	0.00%	0.00%	0.00%	13.11%	62.63%	5.75%	7.05%	6.82%	0.861
3	17.71%	1.39%	0.00%	0.00%	0.00%	13.62%	61.33%	5.95%	7.10%	6.82%	0.867
4	18.08%	1.58%	0.00%	0.00%	0.00%	14.12%	60.06%	6.16%	7.14%	6.82%	0.873
5	18.41%	1.80%	0.00%	0.00%	0.00%	14.62%	58.81%	6.36%	7.18%	6.83%	0.878
6	18.72%	2.04%	0.00%	0.00%	0.00%	15.12%	57.56%	6.56%	7.22%	6.84%	0.883
7	19.01%	2.29%	0.00%	0.00%	0.01%	15.61%	56.32%	6.75%	7.26%	6.84%	0.888
8	19.27%	2.56%	0.00%	0.00%	0.02%	16.11%	55.08%	6.96%	7.30%	6.85%	0.893
9	19.53%	2.84%	0.00%	0.00%	0.02%	16.61%	53.83%	7.16%	7.34%	6.86%	0.898
10	19.78%	3.12%	0.00%	0.00%	0.04%	17.11%	52.58%	7.37%	7.38%	6.87%	0.902
11	20.03%	3.41%	0.00%	0.00%	0.05%	17.62%	51.32%	7.57%	7.42%	6.89%	0.907
12	20.26%	3.70%	0.00%	0.00%	0.06%	18.12%	50.07%	7.78%	7.47%	6.90%	0.911
13	20.49%	4.00%	0.00%	0.00%	0.08%	18.63%	48.81%	7.99%	7.51%	6.91%	0.915
14	20.72%	4.30%	0.00%	0.00%	0.10%	19.13%	47.54%	8.20%	7.55%	6.93%	0.919
15	20.95%	4.60%	0.00%	0.00%	0.13%	19.63%	46.28%	8.42%	7.59%	6.95%	0.923
16	21.16%	4.90%	0.00%	0.00%	0.16%	20.13%	45.01%	8.63%	7.64%	6.97%	0.927
17	21.39%	5.20%	0.00%	0.00%	0.19%	20.63%	43.74%	8.84%	7.68%	6.99%	0.930
18	21.62%	5.50%	0.00%	0.00%	0.23%	21.12%	42.47%	9.06%	7.72%	7.01%	0.933
19	21.85%	5.80%	0.00%	0.00%	0.27%	21.63%	41.18%	9.27%	7.77%	7.03%	0.936
20	22.09%	6.10%	0.00%	0.00%	0.31%	22.12%	39.89%	9.49%	7.81%	7.05%	0.940
21	22.32%	6.38%	0.00%	0.01%	0.36%	22.61%	38.61%	9.71%	7.85%	7.08%	0.942
22	22.52%	6.68%	0.00%	0.02%	0.41%	23.10%	37.34%	9.93%	7.90%	7.11%	0.945
23	22.71%	6.97%	0.00%	0.04%	0.47%	23.59%	36.07%	10.14%	7.94%	7.13%	0.947
24	22.90%	7.26%	0.01%	0.05%	0.54%	24.07%	34.81%	10.36%	7.98%	7.16%	0.949
25	23.10%	7.55%	0.01%	0.07%	0.60%	24.56%	33.54%	10.57%	8.02%	7.20%	0.951
26	23.28%	7.84%	0.01%	0.09%	0.67%	25.04%	32.28%	10.79%	8.07%	7.23%	0.952
27	23.47%	8.12%	0.02%	0.11%	0.73%	25.52%	31.02%	11.00%	8.11%	7.26%	0.954
28	23.64%	8.41%	0.02%	0.13%	0.81%	25.98%	29.79%	11.22%	8.15%	7.29%	0.955
29	23.81%	8.71%	0.02%	0.16%	0.88%	26.45%	28.55%	11.43%	8.19%	7.33%	0.957
30	23.99%	9.00%	0.03%	0.18%	0.95%	26.92%	27.31%	11.65%	8.23%	7.36%	0.958
31	24.16%	9.28%	0.03%	0.20%	1.02%	27.38%	26.08%	11.85%	8.28%	7.40%	0.959
32	24.32%	9.56%	0.03%	0.22%	1.11%	27.81%	24.89%	12.07%	8.32%	7.44%	0.959
33	24.46%	9.85%	0.03%	0.24%	1.20%	28.22%	23.72%	12.28%	8.36%	7.48%	0.960
34	24.59%	10.14%	0.03%	0.26%	1.30%	28.61%	22.58%	12.49%	8.40%	7.51%	0.960
35	24.71%	10.43%	0.03%	0.28%	1.40%	28.99%	21.46%	12.70%	8.44%	7.55%	0.960
36	24.78%	10.74%	0.03%	0.30%	1.52%	29.35%	20.38%	12.91%	8.48%	7.60%	0.960
37	24.83%	11.05%	0.02%	0.33%	1.64%	29.68%	19.33%	13.12%	8.51%	7.64%	0.960
38	24.86%	11.36%	0.03%	0.35%	1.77%	29.98%	18.31%	13.33%	8.55%	7.68%	0.960
39	24.88%	11.68%	0.03%	0.37%	1.91%	30.24%	17.33%	13.56%	8.59%	7.73%	0.959
40	24.86%	12.01%	0.04%	0.39%	2.05%	30.45%	16.41%	13.79%	8.63%	7.77%	0.958
41	24.82%	12.32%	0.05%	0.41%	2.20%	30.63%	15.54%	14.03%	8.66%	7.82%	0.957
42	24.78%	12.62%	0.05%	0.44%	2.37%	30.77%	14.71%	14.26%	8.69%	7.86%	0.956
43	24.73%	12.93%	0.06%	0.46%	2.53%	30.88%	13.93%	14.49%	8.73%	7.91%	0.954
44	24.65%	13.22%	0.06%	0.48%	2.71%	30.94%	13.20%	14.73%	8.76%	7.95%	0.953
45	24.57%	13.52%	0.07%	0.50%	2.88%	30.99%	12.49%	14.97%	8.79%	8.00%	0.951
46	24.48%	13.82%	0.08%	0.52%	3.06%	31.04%	11.78%	15.22%	8.82%	8.05%	0.949
47	24.39%	14.12%	0.08%	0.55%	3.25%	31.05%	11.11%	15.47%	8.85%	8.10%	0.947
48	24.29%	14.41%	0.09%	0.57%	3.43%	31.02%	10.48%	15.70%	8.88%	8.15%	0.945
49	24.19%	14.70%	0.09%	0.60%	3.63%	30.95%	9.89%	15.95%	8.91%	8.20%	0.943
50	24.09%	14.95%	0.10%	0.62%	3.83%	30.84%	9.34%	16.22%	8.94%	8.25%	0.941
51	23.98%	15.20%	0.11%	0.65%	4.05%	30.69%	8.82%	16.50%	8.97%	8.30%	0.938
52	23.86%	15.44%	0.13%	0.67%	4.28%	30.51%	8.33%	16.78%	9.00%	8.36%	0.935
53	23.74%	15.69%	0.14%	0.69%	4.50%	30.30%	7.87%	17.07%	9.03%	8.41%	0.932
54	23.63%	15.93%	0.15%	0.72%	4.73%	30.04%	7.42%	17.38%	9.05%	8.47%	0.929
55	23.49%	16.18%	0.16%	0.74%	4.97%	29.76%	7.00%	17.70%	9.08%	8.53%	0.926
56	23.37%	16.41%	0.17%	0.77%	5.22%	29.46%	6.58%	18.01%	9.11%	8.59%	0.922
57	23.24%	16.65%	0.18%	0.79%	5.47%	29.13%	6.20%	18.33%	9.14%	8.66%	0.919
58	23.06%	16.92%	0.20%	0.82%	5.73%	28.79%	5.85%	18.65%	9.16%	8.72%	0.915
59	22.87%	17.18%	0.21%	0.85%	5.99%	28.42%	5.51%	18.98%	9.19%	8.79%	0.911
60	22.67%	17.44%	0.22%	0.88%	6.26%	28.03%	5.20%	19.30%	9.21%	8.86%	0.907
61	22.46%	17.71%	0.23%	0.91%	6.53%	27.63%	4.91%	19.62%	9.24%	8.92%	0.903
62	22.26%	17.97%	0.24%	0.94%	6.80%	27.21%	4.63%	19.94%	9.27%	8.99%	0.899
63	22.04%	18.25%	0.25%	0.98%	7.07%	26.78%	4.36%	20.27%	9.29%	9.07%	0.894
64	21.81%	18.52%	0.26%	1.02%	7.35%	26.35%	4.10%	20.59%	9.32%	9.14%	0.890
65	21.58%	18.78%	0.26%	1.07%	7.64%	25.93%	3.85%	20.89%	9.34%	9.21%	0.885
66	21.34%	19.04%	0.27%	1.12%	7.93%	25.50%	3.62%	21.17%	9.36%	9.29%	0.881
67	21.08%	19.28%	0.28%	1.19%	8.25%	25.06%	3.42%	21.45%	9.39%	9.37%	0.876
68	20.81%	19.52%	0.29%	1.25%	8.57%	24.60%	3.24%	21.72%	9.41%	9.44%	0.871
69	20.52%	19.75%	0.30%	1.32%	8.89%	24.15%	3.06%	21.99%	9.43%	9.52%	0.866
70	20.21%	20.00%	0.31%	1.40%	9.22%	23.72%	2.88%	22.25%	9.45%	9.60%	0.861
71	19.90%	20.24%	0.32%	1.47%	9.55%	23.28%	2.71%	22.52%	9.47%	9.68%	0.856
72	19.59%	20.45%	0.33%	1.57%	9.90%	22.84%	2.55%	22.77%	9.49%	9.76%	0.851
73	19.28%	20.66%	0.33%	1.66%	10.25%	22.38%	2.39%	23.03%	9.51%	9.85%	0.846
74	18.95%	20.89%	0.34%	1.75%	10.61%	21.92%	2.23%	23.30%	9.53%	9.93%	0.841
75	18.58%	21.15%	0.35%	1.84%	10.98%	21.46%	2.08%	23.56%	9.55%	10.02%	0.835
76	18.21%	21.39%	0.35%	1.94%	11.36%	20.99%	1.94%	23.82%	9.57%	10.11%	0.830
77	17.82%	21.65%	0.34%	2.04%	11.77%	20.50%	1.81%	24.07%	9.59%	10.20%	0.824
78	17.41%	21.94%	0.33%	2.14%	12.18%	20.00%	1.69%	24.31%	9.62%	10.30%	0.819
79	16.99%	22.24%	0.32%	2.24%	12.60%	19.49%	1.57%	24.55%	9.64%	10.40%	0.813
80	16.54%	22.57%	0.31%	2.34%	13.02%	18.98%	1.46%	24.78%	9.66%	10.50%	0.807
81	16.08%	22.89%	0.30%	2.44%	13.46%	18.50%	1.35%	24.97%	9.68%	10.60%	0.802
82	15.63%	23.21%	0.29%	2.56%	13.90%	18.01%	1.25%	25.15%	9.70%	10.70%	0.796
83	15.17%	23.51%	0.29%	2.69%	14.34%	17.54%	1.15%	25.32%	9.72%	10.81%	0.790
84	14.68%	23.83%	0.28%	2.83%	14.78%	17.08%	1.05%	25.47%	9.74%	10.91%	0.785
85	14.17%	24.14%	0.28%	3.01%	15.23%	16.59%	0.97%	25.62%	9.76%	11.02%	0.779
86	13.68%	24.42%	0.27%	3.19%	15.73%	16.13%	0.88%	25.70%	9.78%	11.13%	0.773
87	13.07%	24.75%	0.31%	3.37%	16.25%	15.69%	0.80%	25.77%	9.80%	11.24%	0.766
88	12.39%	25.11%	0.32%	3.58%	16.79%	15.26%	0.72%	25.83%	9.82%	11.36%	0.760
89	11.69%	25.47%	0.32%	3.80%	17.34%	14.86%	0.65%	25.86%	9.83%	11.48%	0.754
90	10.95%	25.87%	0.33%	4.02%	17.91%	14.45%	0.58%	25.89%	9.85%	11.60%	0.747
91	10.18%	26.26%	0.34%	4.24%	18.50%	14.08%	0.51%	25.89%	9.87%	11.72%	0.741
92	9.41%	26.61%	0.35%	4.47%	19.13%	13.77%	0.44%	25.81%	9.88%	11.84%	0.735
93	8.65%	26.92%	0.36%	4.68%	19.85%	13.47%	0.38%	25.69%	9.90%	11.96%	0.728
94	7.86%	27.23%	0.37%	4.90%	20.59%	13.17%	0.32%	25.57%	9.91%	12.09%	0.722
95	7.10%	27.44%	0.35%	5.12%	21.40%	12.90%	0.27%	25.42%	9.92%	12.22%	0.716
96	6.38%	27.44%	0.27%	5.39%	22.39%	12.64%	0.21%	25.27%	9.94%	12.35%	0.709
97	5.74%	27.12%	0.20%	5.75%	23.49%	12.37%	0.16%	25.17%	9.94%	12.49%	0.702
98	5.13%	26.40%	0.14%	6.16%	24.96%	12.17%	0.11%	24.93%	9.94%	12.64%	0.693
99	4.57%	25.37%	0.07%	6.59%	26.47%	12.07%	0.05%	24.80%	9.93%	12.78%	0.685
100	4.00%	24.50%	0.00%	7.00%	27.50%	12.00%	0.00%	25.00%	9.92%	12.87%	0.679
^*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 (1.18% 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 2019
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