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 - Nov 2019)

Note: The time period was constrained by the available data for SPDR S&P 600 Small Cap ETF (SLY) [Dec 2005 - Nov 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	24.02%
SLY	SPDR S&P 600 Small Cap ETF	9.15%
EFA	iShares MSCI EAFE ETF	0.19%
EEM	iShares MSCI Emerging Markets ETF	0.54%
VNQ	Vanguard Real Estate ETF	1.91%
TLT	iShares 20+ Year Treasury Bond ETF	28.57%
LQD	iShares iBoxx $ Invmt Grade Corp Bd ETF	23.72%
GLD	SPDR Gold Shares	11.90%
Save portfolio »

Portfolio Returns

Portfolio Statistics
Portfolio	Expected Return	Expected Volatility	Sharpe Ratio
Provided Portfolio	8.40%	11.47%	0.63
Tangency Portfolio	8.33%	7.54%	0.95

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)	9.04%	10.14%	14.14%	0.635	0.00%	100.00%
2	SPDR S&P 600 Small Cap ETF (SLY)	9.57%	11.53%	18.82%	0.551	0.00%	100.00%
3	iShares MSCI EAFE ETF (EFA)	3.91%	5.47%	17.20%	0.251	0.00%	100.00%
4	iShares MSCI Emerging Markets ETF (EEM)	4.58%	7.19%	22.18%	0.272	0.00%	100.00%
5	Vanguard Real Estate ETF (VNQ)	7.79%	10.70%	22.78%	0.419	0.00%	100.00%
6	iShares 20+ Year Treasury Bond ETF (TLT)	6.56%	7.48%	13.36%	0.473	0.00%	100.00%
7	iShares iBoxx $ Invmt Grade Corp Bd ETF (LQD)	5.58%	5.86%	7.22%	0.651	0.00%	100.00%
8	SPDR Gold Shares (GLD)	7.32%	9.00%	17.77%	0.441	0.00%	100.00%
^*Expected return is annualized from historical monthly mean return. Ex ante Sharpe Ratio calculated using historical 1-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	0.91	0.89	0.79	0.71	-0.31	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	0.00
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	0.71	0.73	0.67	0.60	1.00	0.01	0.43	0.09
iShares 20+ Year Treasury Bond ETF	TLT	-0.31	-0.36	-0.24	-0.23	0.01	1.00	0.52	0.22
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	0.00	0.15	0.29	0.09	0.22	0.26	1.00
Based on monthly returns from Jan 2006 to Nov 2019

Efficient Frontier Points
#	SPY	SLY	EFA	EEM	VNQ	TLT	LQD	GLD	Expected Return^*	Standard Deviation^*	Sharpe Ratio^*
1	16.82%	0.90%	0.00%	0.00%	0.00%	12.88%	64.23%	5.18%	6.99%	6.84%	0.853
2	17.28%	1.02%	0.00%	0.00%	0.00%	13.38%	62.95%	5.38%	7.03%	6.84%	0.859
3	17.66%	1.19%	0.00%	0.00%	0.00%	13.86%	61.72%	5.57%	7.07%	6.84%	0.864
4	18.03%	1.37%	0.00%	0.00%	0.00%	14.35%	60.48%	5.77%	7.11%	6.84%	0.870
5	18.38%	1.55%	0.00%	0.01%	0.01%	14.84%	59.25%	5.96%	7.15%	6.85%	0.875
6	18.69%	1.76%	0.00%	0.01%	0.03%	15.33%	58.02%	6.16%	7.19%	6.85%	0.880
7	18.97%	1.97%	0.01%	0.01%	0.04%	15.81%	56.82%	6.35%	7.23%	6.86%	0.885
8	19.23%	2.21%	0.01%	0.02%	0.06%	16.30%	55.63%	6.54%	7.26%	6.87%	0.889
9	19.46%	2.46%	0.02%	0.02%	0.08%	16.78%	54.44%	6.73%	7.30%	6.88%	0.893
10	19.69%	2.70%	0.02%	0.03%	0.11%	17.24%	53.28%	6.92%	7.34%	6.89%	0.898
11	19.91%	2.95%	0.03%	0.03%	0.15%	17.70%	52.12%	7.11%	7.38%	6.90%	0.902
12	20.11%	3.21%	0.03%	0.04%	0.18%	18.15%	50.97%	7.30%	7.42%	6.92%	0.905
13	20.29%	3.47%	0.04%	0.05%	0.23%	18.61%	49.82%	7.49%	7.46%	6.93%	0.909
14	20.46%	3.73%	0.05%	0.06%	0.27%	19.07%	48.67%	7.69%	7.49%	6.95%	0.912
15	20.65%	3.99%	0.05%	0.08%	0.32%	19.53%	47.50%	7.88%	7.53%	6.96%	0.916
16	20.84%	4.25%	0.06%	0.09%	0.36%	19.99%	46.33%	8.08%	7.57%	6.98%	0.919
17	21.03%	4.51%	0.06%	0.10%	0.42%	20.45%	45.15%	8.28%	7.61%	7.00%	0.922
18	21.22%	4.77%	0.07%	0.11%	0.48%	20.91%	43.96%	8.48%	7.65%	7.02%	0.925
19	21.41%	5.02%	0.07%	0.13%	0.54%	21.38%	42.77%	8.68%	7.69%	7.04%	0.928
20	21.60%	5.27%	0.08%	0.15%	0.61%	21.85%	41.56%	8.88%	7.73%	7.07%	0.930
21	21.79%	5.52%	0.08%	0.17%	0.67%	22.32%	40.36%	9.08%	7.77%	7.09%	0.933
22	21.97%	5.77%	0.09%	0.20%	0.75%	22.78%	39.16%	9.29%	7.81%	7.12%	0.935
23	22.16%	6.02%	0.09%	0.22%	0.82%	23.25%	37.95%	9.49%	7.85%	7.14%	0.937
24	22.35%	6.27%	0.10%	0.25%	0.89%	23.72%	36.73%	9.69%	7.89%	7.17%	0.939
25	22.53%	6.53%	0.11%	0.27%	0.97%	24.19%	35.52%	9.89%	7.93%	7.20%	0.941
26	22.70%	6.78%	0.11%	0.30%	1.05%	24.66%	34.31%	10.09%	7.97%	7.23%	0.943
27	22.88%	7.03%	0.12%	0.32%	1.13%	25.13%	33.10%	10.28%	8.01%	7.26%	0.944
28	23.05%	7.29%	0.13%	0.35%	1.21%	25.61%	31.88%	10.48%	8.05%	7.29%	0.945
29	23.21%	7.55%	0.14%	0.38%	1.29%	26.07%	30.68%	10.68%	8.09%	7.32%	0.947
30	23.38%	7.81%	0.14%	0.41%	1.38%	26.52%	29.48%	10.88%	8.13%	7.36%	0.948
31	23.54%	8.08%	0.15%	0.43%	1.47%	26.96%	28.30%	11.08%	8.17%	7.39%	0.949
32	23.69%	8.34%	0.16%	0.46%	1.57%	27.38%	27.13%	11.28%	8.21%	7.43%	0.950
33	23.83%	8.61%	0.17%	0.49%	1.67%	27.80%	25.96%	11.48%	8.25%	7.46%	0.950
34	23.93%	8.89%	0.18%	0.51%	1.78%	28.19%	24.83%	11.69%	8.29%	7.50%	0.951
35	24.02%	9.15%	0.19%	0.54%	1.91%	28.57%	23.72%	11.90%	8.33%	7.54%	0.951
36	24.09%	9.42%	0.20%	0.57%	2.05%	28.92%	22.65%	12.11%	8.36%	7.58%	0.950
37	24.13%	9.70%	0.21%	0.60%	2.19%	29.25%	21.59%	12.33%	8.40%	7.63%	0.950
38	24.18%	9.98%	0.22%	0.63%	2.33%	29.56%	20.56%	12.54%	8.44%	7.67%	0.950
39	24.21%	10.27%	0.23%	0.66%	2.48%	29.86%	19.54%	12.76%	8.48%	7.71%	0.949
40	24.23%	10.56%	0.24%	0.69%	2.63%	30.12%	18.56%	12.98%	8.51%	7.76%	0.948
41	24.21%	10.84%	0.25%	0.72%	2.80%	30.34%	17.64%	13.20%	8.55%	7.80%	0.947
42	24.18%	11.12%	0.26%	0.75%	2.98%	30.53%	16.75%	13.42%	8.58%	7.85%	0.946
43	24.15%	11.39%	0.27%	0.79%	3.15%	30.71%	15.89%	13.65%	8.61%	7.89%	0.945
44	24.11%	11.66%	0.28%	0.83%	3.33%	30.86%	15.07%	13.87%	8.65%	7.94%	0.943
45	24.06%	11.93%	0.29%	0.87%	3.52%	30.97%	14.27%	14.10%	8.68%	7.99%	0.942
46	24.00%	12.19%	0.30%	0.91%	3.71%	31.07%	13.50%	14.33%	8.71%	8.04%	0.940
47	23.92%	12.45%	0.30%	0.95%	3.90%	31.12%	12.76%	14.58%	8.74%	8.08%	0.938
48	23.83%	12.72%	0.31%	0.99%	4.10%	31.16%	12.05%	14.83%	8.77%	8.13%	0.936
49	23.76%	12.98%	0.32%	1.03%	4.30%	31.17%	11.37%	15.08%	8.80%	8.19%	0.934
50	23.67%	13.23%	0.33%	1.07%	4.51%	31.16%	10.70%	15.33%	8.83%	8.24%	0.931
51	23.57%	13.48%	0.34%	1.11%	4.72%	31.12%	10.06%	15.60%	8.86%	8.29%	0.929
52	23.47%	13.73%	0.36%	1.16%	4.93%	31.05%	9.44%	15.87%	8.89%	8.34%	0.926
53	23.35%	13.97%	0.38%	1.20%	5.16%	30.95%	8.86%	16.13%	8.91%	8.40%	0.923
54	23.22%	14.21%	0.41%	1.25%	5.38%	30.83%	8.31%	16.40%	8.94%	8.45%	0.920
55	23.10%	14.42%	0.43%	1.30%	5.62%	30.69%	7.78%	16.66%	8.96%	8.51%	0.917
56	22.98%	14.62%	0.46%	1.36%	5.85%	30.51%	7.29%	16.95%	8.99%	8.57%	0.914
57	22.85%	14.81%	0.48%	1.41%	6.09%	30.29%	6.84%	17.24%	9.01%	8.63%	0.910
58	22.73%	15.00%	0.50%	1.46%	6.33%	30.04%	6.40%	17.53%	9.03%	8.69%	0.907
59	22.61%	15.18%	0.52%	1.52%	6.59%	29.78%	5.99%	17.81%	9.06%	8.75%	0.903
60	22.50%	15.35%	0.54%	1.58%	6.84%	29.51%	5.58%	18.09%	9.08%	8.81%	0.899
61	22.37%	15.53%	0.55%	1.64%	7.10%	29.24%	5.20%	18.37%	9.10%	8.87%	0.895
62	22.22%	15.70%	0.57%	1.70%	7.37%	28.96%	4.83%	18.65%	9.12%	8.93%	0.892
63	22.00%	15.90%	0.58%	1.76%	7.66%	28.66%	4.51%	18.92%	9.14%	9.00%	0.887
64	21.78%	16.10%	0.60%	1.83%	7.95%	28.33%	4.21%	19.21%	9.16%	9.06%	0.883
65	21.55%	16.29%	0.62%	1.90%	8.23%	27.98%	3.94%	19.50%	9.18%	9.13%	0.879
66	21.33%	16.46%	0.63%	1.97%	8.52%	27.62%	3.69%	19.77%	9.20%	9.20%	0.875
67	21.13%	16.62%	0.65%	2.05%	8.81%	27.26%	3.45%	20.04%	9.22%	9.26%	0.870
68	20.90%	16.79%	0.67%	2.13%	9.11%	26.87%	3.21%	20.33%	9.24%	9.34%	0.865
69	20.65%	16.96%	0.68%	2.21%	9.41%	26.47%	3.00%	20.61%	9.25%	9.41%	0.861
70	20.42%	17.13%	0.69%	2.29%	9.73%	26.06%	2.81%	20.87%	9.27%	9.48%	0.856
71	20.17%	17.28%	0.70%	2.38%	10.06%	25.64%	2.63%	21.13%	9.29%	9.55%	0.851
72	19.94%	17.43%	0.71%	2.47%	10.40%	25.21%	2.46%	21.38%	9.31%	9.63%	0.846
73	19.72%	17.57%	0.72%	2.56%	10.74%	24.76%	2.29%	21.63%	9.32%	9.71%	0.841
74	19.47%	17.69%	0.74%	2.67%	11.12%	24.31%	2.14%	21.87%	9.34%	9.79%	0.836
75	19.20%	17.82%	0.75%	2.79%	11.50%	23.86%	1.99%	22.09%	9.35%	9.87%	0.830
76	18.94%	17.95%	0.76%	2.91%	11.88%	23.41%	1.84%	22.30%	9.37%	9.95%	0.825
77	18.68%	18.07%	0.77%	3.03%	12.28%	22.96%	1.70%	22.51%	9.38%	10.04%	0.820
78	18.32%	18.26%	0.79%	3.16%	12.67%	22.50%	1.57%	22.74%	9.40%	10.13%	0.814
79	17.88%	18.50%	0.80%	3.28%	13.10%	22.04%	1.44%	22.97%	9.42%	10.22%	0.808
80	17.36%	18.76%	0.81%	3.42%	13.54%	21.59%	1.32%	23.20%	9.43%	10.32%	0.802
81	16.78%	19.05%	0.82%	3.57%	14.01%	21.14%	1.20%	23.43%	9.45%	10.41%	0.796
82	16.22%	19.33%	0.83%	3.72%	14.47%	20.70%	1.07%	23.65%	9.47%	10.51%	0.790
83	15.57%	19.62%	0.84%	3.89%	14.94%	20.30%	0.96%	23.88%	9.48%	10.61%	0.784
84	14.91%	19.91%	0.85%	4.06%	15.42%	19.90%	0.85%	24.11%	9.49%	10.71%	0.778
85	14.25%	20.20%	0.86%	4.23%	15.90%	19.48%	0.77%	24.31%	9.51%	10.81%	0.772
86	13.55%	20.50%	0.87%	4.39%	16.41%	19.07%	0.70%	24.51%	9.52%	10.91%	0.767
87	12.86%	20.75%	0.87%	4.54%	16.94%	18.70%	0.63%	24.69%	9.53%	11.01%	0.761
88	12.14%	21.00%	0.89%	4.70%	17.50%	18.34%	0.57%	24.86%	9.54%	11.11%	0.755
89	11.39%	21.27%	0.90%	4.87%	18.05%	17.98%	0.50%	25.04%	9.56%	11.21%	0.749
90	10.58%	21.54%	0.91%	5.04%	18.65%	17.61%	0.43%	25.23%	9.57%	11.32%	0.743
91	9.74%	21.80%	0.93%	5.21%	19.28%	17.23%	0.38%	25.43%	9.58%	11.43%	0.737
92	8.91%	22.04%	0.92%	5.40%	19.94%	16.86%	0.33%	25.58%	9.59%	11.54%	0.731
93	8.07%	22.27%	0.87%	5.62%	20.62%	16.54%	0.28%	25.73%	9.60%	11.65%	0.725
94	7.24%	22.39%	0.82%	5.82%	21.34%	16.28%	0.23%	25.87%	9.61%	11.75%	0.720
95	6.43%	22.50%	0.75%	6.00%	22.05%	16.05%	0.19%	26.02%	9.62%	11.85%	0.714
96	5.56%	22.48%	0.65%	6.21%	22.90%	15.82%	0.15%	26.24%	9.63%	11.96%	0.709
97	4.74%	22.04%	0.61%	6.52%	23.81%	15.54%	0.11%	26.64%	9.63%	12.06%	0.702
98	3.95%	21.46%	0.57%	6.76%	24.88%	15.29%	0.07%	27.03%	9.62%	12.17%	0.696
99	3.17%	21.08%	0.54%	6.98%	25.79%	15.19%	0.03%	27.22%	9.62%	12.26%	0.690
100	2.50%	20.50%	0.50%	7.00%	27.00%	15.50%	0.00%	27.00%	9.62%	12.33%	0.686
^*Ex-ante values shown for portfolio return and volatility. Ex ante Sharpe Ratio calculated using historical 1-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 Nov 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 1-month treasury bill returns as the risk free rate