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 - Jun 2021)

Note: The time period was constrained by the available data for SPDR S&P 600 Small Cap ETF (SLY) [Dec 2005 - Jun 2021].

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	26.06%
SLY	SPDR S&P 600 Small Cap ETF	9.85%
EFA	iShares MSCI EAFE ETF	0.04%
EEM	iShares MSCI Emerging Markets ETF	0.65%
VNQ	Vanguard Real Estate ETF	1.47%
TLT	iShares 20+ Year Treasury Bond ETF	30.99%
LQD	iShares iBoxx $ Invmt Grade Corp Bd ETF	19.84%
GLD	SPDR Gold Shares	11.10%
Save portfolio »

Portfolio Returns

Portfolio Statistics
Portfolio	Expected Return	Expected Volatility	Sharpe Ratio
Provided Portfolio	9.19%	11.76%	0.66
Tangency Portfolio	9.00%	7.88%	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	Expected Return	Standard Deviation	Sharpe Ratio	Min. Weight	Max. Weight
1	SPDR S&P 500 ETF Trust (SPY)	11.71%	14.91%	0.673	0.00%	100.00%
2	SPDR S&P 600 Small Cap ETF (SLY)	13.32%	20.14%	0.570	0.00%	100.00%
3	iShares MSCI EAFE ETF (EFA)	6.44%	17.52%	0.295	0.00%	100.00%
4	iShares MSCI Emerging Markets ETF (EEM)	8.76%	22.01%	0.333	0.00%	100.00%
5	Vanguard Real Estate ETF (VNQ)	10.93%	22.66%	0.411	0.00%	100.00%
6	iShares 20+ Year Treasury Bond ETF (TLT)	7.16%	13.45%	0.435	0.00%	100.00%
7	iShares iBoxx $ Invmt Grade Corp Bd ETF (LQD)	5.91%	7.39%	0.631	0.00%	100.00%
8	SPDR Gold Shares (GLD)	9.49%	17.71%	0.452	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	0.91	0.89	0.78	0.72	-0.32	0.34	0.05
SPDR S&P 600 Small Cap ETF	SLY	0.91	1.00	0.81	0.74	0.74	-0.38	0.27	0.01
iShares MSCI EAFE ETF	EFA	0.89	0.81	1.00	0.88	0.69	-0.27	0.40	0.14
iShares MSCI Emerging Markets ETF	EEM	0.78	0.74	0.88	1.00	0.61	-0.25	0.38	0.29
Vanguard Real Estate ETF	VNQ	0.72	0.74	0.69	0.61	1.00	-0.02	0.46	0.10
iShares 20+ Year Treasury Bond ETF	TLT	-0.32	-0.38	-0.27	-0.25	-0.02	1.00	0.49	0.21
iShares iBoxx $ Invmt Grade Corp Bd ETF	LQD	0.34	0.27	0.40	0.38	0.46	0.49	1.00	0.27
SPDR Gold Shares	GLD	0.05	0.01	0.14	0.29	0.10	0.21	0.27	1.00
Based on monthly returns from Jan 2006 to Jun 2021

Efficient Frontier Points
#	SPY	SLY	EFA	EEM	VNQ	TLT	LQD	GLD	Expected Return^*	Standard Deviation^*	Sharpe Ratio^*
1	13.61%	1.17%	0.01%	0.00%	0.00%	13.81%	65.68%	5.72%	7.14%	7.08%	0.823
2	14.26%	1.26%	0.00%	0.00%	0.00%	14.31%	64.30%	5.86%	7.20%	7.08%	0.830
3	14.86%	1.38%	0.00%	0.00%	0.00%	14.82%	62.93%	6.01%	7.25%	7.08%	0.837
4	15.42%	1.52%	0.00%	0.00%	0.00%	15.32%	61.57%	6.16%	7.31%	7.08%	0.844
5	15.94%	1.69%	0.00%	0.00%	0.00%	15.82%	60.23%	6.32%	7.36%	7.09%	0.851
6	16.42%	1.88%	0.00%	0.00%	0.00%	16.33%	58.90%	6.47%	7.41%	7.10%	0.857
7	16.88%	2.08%	0.00%	0.01%	0.01%	16.84%	57.57%	6.62%	7.47%	7.10%	0.863
8	17.33%	2.29%	0.00%	0.02%	0.01%	17.34%	56.25%	6.77%	7.52%	7.11%	0.869
9	17.77%	2.50%	0.00%	0.02%	0.02%	17.84%	54.93%	6.92%	7.57%	7.12%	0.875
10	18.19%	2.72%	0.00%	0.03%	0.03%	18.34%	53.62%	7.07%	7.63%	7.13%	0.880
11	18.59%	2.96%	0.00%	0.03%	0.05%	18.85%	52.32%	7.22%	7.68%	7.15%	0.886
12	18.98%	3.20%	0.00%	0.04%	0.06%	19.35%	51.00%	7.37%	7.73%	7.16%	0.891
13	19.37%	3.44%	0.00%	0.04%	0.08%	19.86%	49.70%	7.52%	7.78%	7.17%	0.896
14	19.74%	3.68%	0.00%	0.05%	0.10%	20.37%	48.39%	7.67%	7.84%	7.19%	0.901
15	20.09%	3.93%	0.00%	0.07%	0.13%	20.87%	47.09%	7.82%	7.89%	7.21%	0.905
16	20.44%	4.18%	0.00%	0.08%	0.16%	21.38%	45.80%	7.96%	7.94%	7.23%	0.910
17	20.78%	4.44%	0.00%	0.10%	0.19%	21.88%	44.51%	8.11%	7.99%	7.25%	0.914
18	21.12%	4.69%	0.00%	0.11%	0.22%	22.39%	43.22%	8.25%	8.04%	7.27%	0.918
19	21.46%	4.94%	0.00%	0.13%	0.25%	22.90%	41.92%	8.40%	8.10%	7.29%	0.922
20	21.80%	5.20%	0.00%	0.15%	0.28%	23.41%	40.61%	8.54%	8.15%	7.31%	0.925
21	22.13%	5.46%	0.00%	0.17%	0.31%	23.93%	39.31%	8.69%	8.20%	7.34%	0.929
22	22.45%	5.72%	0.00%	0.20%	0.35%	24.44%	38.00%	8.84%	8.25%	7.36%	0.932
23	22.78%	5.97%	0.01%	0.22%	0.39%	24.96%	36.69%	8.98%	8.30%	7.39%	0.935
24	23.08%	6.24%	0.01%	0.25%	0.43%	25.47%	35.39%	9.13%	8.36%	7.42%	0.938
25	23.39%	6.50%	0.01%	0.27%	0.47%	25.98%	34.09%	9.28%	8.41%	7.45%	0.941
26	23.70%	6.76%	0.01%	0.30%	0.52%	26.48%	32.80%	9.43%	8.46%	7.48%	0.944
27	23.99%	7.03%	0.02%	0.33%	0.57%	26.95%	31.53%	9.59%	8.51%	7.51%	0.946
28	24.27%	7.30%	0.02%	0.36%	0.63%	27.42%	30.27%	9.75%	8.56%	7.54%	0.949
29	24.54%	7.57%	0.02%	0.39%	0.69%	27.89%	29.02%	9.90%	8.61%	7.57%	0.951
30	24.80%	7.84%	0.02%	0.41%	0.76%	28.34%	27.79%	10.05%	8.66%	7.61%	0.952
31	25.04%	8.10%	0.03%	0.44%	0.84%	28.79%	26.56%	10.19%	8.71%	7.64%	0.954
32	25.27%	8.38%	0.03%	0.48%	0.93%	29.22%	25.35%	10.34%	8.76%	7.68%	0.955
33	25.47%	8.66%	0.03%	0.51%	1.02%	29.63%	24.17%	10.50%	8.81%	7.72%	0.957
34	25.66%	8.95%	0.03%	0.54%	1.13%	30.04%	23.00%	10.65%	8.86%	7.76%	0.957
35	25.82%	9.24%	0.03%	0.58%	1.24%	30.41%	21.88%	10.80%	8.91%	7.80%	0.958
36	25.95%	9.55%	0.04%	0.61%	1.35%	30.72%	20.83%	10.95%	8.96%	7.84%	0.959
37	26.06%	9.85%	0.04%	0.65%	1.47%	30.99%	19.84%	11.10%	9.00%	7.88%	0.959
38	26.16%	10.15%	0.04%	0.68%	1.60%	31.24%	18.87%	11.26%	9.04%	7.93%	0.959
39	26.23%	10.46%	0.04%	0.72%	1.72%	31.46%	17.94%	11.42%	9.09%	7.97%	0.959
40	26.29%	10.78%	0.05%	0.76%	1.85%	31.66%	17.03%	11.58%	9.13%	8.01%	0.958
41	26.33%	11.10%	0.05%	0.80%	1.98%	31.85%	16.13%	11.75%	9.17%	8.06%	0.958
42	26.35%	11.44%	0.05%	0.84%	2.12%	32.03%	15.26%	11.92%	9.22%	8.10%	0.957
43	26.39%	11.76%	0.05%	0.88%	2.25%	32.15%	14.44%	12.08%	9.26%	8.15%	0.956
44	26.40%	12.08%	0.06%	0.93%	2.40%	32.24%	13.66%	12.25%	9.30%	8.20%	0.955
45	26.40%	12.39%	0.06%	0.97%	2.55%	32.30%	12.92%	12.42%	9.34%	8.25%	0.954
46	26.40%	12.69%	0.07%	1.01%	2.72%	32.34%	12.19%	12.59%	9.37%	8.30%	0.953
47	26.41%	12.99%	0.07%	1.05%	2.89%	32.31%	11.51%	12.77%	9.41%	8.35%	0.951
48	26.43%	13.28%	0.08%	1.10%	3.07%	32.23%	10.86%	12.95%	9.45%	8.40%	0.949
49	26.42%	13.57%	0.08%	1.14%	3.26%	32.16%	10.23%	13.13%	9.49%	8.46%	0.947
50	26.39%	13.85%	0.08%	1.19%	3.47%	32.06%	9.63%	13.32%	9.53%	8.52%	0.945
51	26.35%	14.13%	0.09%	1.24%	3.68%	31.91%	9.08%	13.51%	9.56%	8.57%	0.942
52	26.30%	14.41%	0.09%	1.28%	3.90%	31.73%	8.56%	13.72%	9.60%	8.63%	0.939
53	26.25%	14.69%	0.10%	1.33%	4.11%	31.53%	8.06%	13.94%	9.63%	8.69%	0.937
54	26.19%	14.98%	0.10%	1.37%	4.33%	31.29%	7.59%	14.15%	9.67%	8.75%	0.934
55	26.13%	15.26%	0.09%	1.41%	4.56%	31.03%	7.14%	14.37%	9.70%	8.82%	0.931
56	26.09%	15.53%	0.09%	1.46%	4.79%	30.74%	6.70%	14.60%	9.74%	8.88%	0.927
57	26.03%	15.81%	0.09%	1.50%	5.02%	30.45%	6.29%	14.81%	9.77%	8.95%	0.924
58	25.98%	16.08%	0.09%	1.54%	5.25%	30.14%	5.89%	15.03%	9.81%	9.02%	0.920
59	25.92%	16.34%	0.09%	1.58%	5.51%	29.80%	5.51%	15.23%	9.84%	9.09%	0.917
60	25.88%	16.58%	0.09%	1.63%	5.79%	29.44%	5.15%	15.44%	9.87%	9.16%	0.913
61	25.84%	16.82%	0.10%	1.66%	6.07%	29.07%	4.79%	15.65%	9.91%	9.24%	0.909
62	25.78%	17.06%	0.10%	1.70%	6.36%	28.68%	4.46%	15.87%	9.94%	9.31%	0.904
63	25.74%	17.29%	0.10%	1.73%	6.65%	28.23%	4.16%	16.10%	9.97%	9.39%	0.900
64	25.72%	17.50%	0.10%	1.76%	6.94%	27.78%	3.86%	16.33%	10.01%	9.47%	0.895
65	25.70%	17.71%	0.11%	1.80%	7.24%	27.31%	3.59%	16.55%	10.04%	9.56%	0.891
66	25.65%	17.94%	0.11%	1.83%	7.55%	26.82%	3.32%	16.77%	10.07%	9.64%	0.886
67	25.60%	18.18%	0.11%	1.86%	7.86%	26.28%	3.09%	17.02%	10.11%	9.73%	0.881
68	25.51%	18.41%	0.11%	1.90%	8.19%	25.74%	2.87%	17.26%	10.14%	9.82%	0.876
69	25.41%	18.64%	0.11%	1.94%	8.53%	25.19%	2.67%	17.50%	10.17%	9.92%	0.871
70	25.31%	18.87%	0.12%	1.98%	8.88%	24.63%	2.49%	17.73%	10.20%	10.01%	0.865
71	25.16%	19.13%	0.12%	2.02%	9.23%	24.07%	2.33%	17.95%	10.23%	10.11%	0.860
72	24.96%	19.43%	0.12%	2.07%	9.58%	23.50%	2.17%	18.16%	10.26%	10.20%	0.854
73	24.76%	19.75%	0.13%	2.11%	9.93%	22.93%	2.04%	18.37%	10.29%	10.30%	0.849
74	24.54%	20.09%	0.13%	2.15%	10.28%	22.34%	1.91%	18.57%	10.32%	10.41%	0.843
75	24.32%	20.42%	0.13%	2.19%	10.64%	21.76%	1.80%	18.74%	10.35%	10.51%	0.837
76	24.09%	20.77%	0.14%	2.24%	10.99%	21.18%	1.68%	18.91%	10.38%	10.62%	0.832
77	23.82%	21.12%	0.14%	2.29%	11.36%	20.62%	1.57%	19.07%	10.41%	10.72%	0.826
78	23.55%	21.47%	0.15%	2.35%	11.73%	20.07%	1.46%	19.21%	10.44%	10.83%	0.820
79	23.25%	21.82%	0.15%	2.43%	12.13%	19.52%	1.36%	19.34%	10.47%	10.94%	0.814
80	22.92%	22.15%	0.16%	2.53%	12.55%	18.98%	1.26%	19.45%	10.50%	11.06%	0.808
81	22.58%	22.50%	0.16%	2.65%	12.99%	18.44%	1.17%	19.52%	10.52%	11.17%	0.802
82	22.23%	22.84%	0.17%	2.76%	13.44%	17.92%	1.08%	19.56%	10.55%	11.29%	0.795
83	21.91%	23.16%	0.17%	2.87%	13.91%	17.39%	0.99%	19.59%	10.58%	11.41%	0.789
84	21.57%	23.50%	0.18%	2.97%	14.38%	16.85%	0.91%	19.63%	10.60%	11.54%	0.783
85	21.16%	23.92%	0.18%	3.08%	14.85%	16.30%	0.83%	19.68%	10.63%	11.67%	0.776
86	20.71%	24.38%	0.16%	3.21%	15.32%	15.76%	0.76%	19.71%	10.66%	11.80%	0.770
87	20.21%	24.87%	0.14%	3.34%	15.78%	15.23%	0.69%	19.73%	10.69%	11.93%	0.764
88	19.61%	25.45%	0.12%	3.49%	16.25%	14.70%	0.62%	19.76%	10.72%	12.07%	0.757
89	18.90%	26.12%	0.10%	3.70%	16.70%	14.19%	0.56%	19.74%	10.75%	12.21%	0.750
90	18.20%	26.78%	0.08%	3.89%	17.15%	13.67%	0.50%	19.73%	10.78%	12.36%	0.744
91	17.43%	27.47%	0.06%	4.07%	17.65%	13.17%	0.44%	19.71%	10.81%	12.51%	0.737
92	16.65%	28.25%	0.04%	4.25%	18.17%	12.67%	0.38%	19.60%	10.84%	12.67%	0.730
93	15.82%	29.06%	0.02%	4.49%	18.70%	12.17%	0.32%	19.43%	10.88%	12.84%	0.723
94	14.81%	29.84%	0.00%	4.76%	19.35%	11.68%	0.26%	19.30%	10.91%	13.01%	0.715
95	13.84%	30.54%	0.00%	5.01%	20.00%	11.23%	0.21%	19.16%	10.93%	13.18%	0.708
96	12.89%	31.11%	0.00%	5.30%	20.70%	10.85%	0.17%	18.99%	10.95%	13.34%	0.701
97	11.94%	31.61%	0.00%	5.62%	21.50%	10.47%	0.12%	18.74%	10.97%	13.51%	0.693
98	11.02%	31.93%	0.00%	6.01%	22.35%	10.12%	0.08%	18.49%	10.98%	13.68%	0.685
99	9.94%	32.48%	0.00%	6.39%	23.15%	9.78%	0.04%	18.21%	11.00%	13.85%	0.678
100	8.00%	34.00%	0.00%	7.50%	23.00%	9.50%	0.00%	18.00%	11.01%	14.03%	0.670
^*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:

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 Jun 2021
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