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 - Sep 2021)

Note: The time period was constrained by the available data for SPDR S&P 600 Small Cap ETF (SLY) [Dec 2005 - Sep 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	21.71%
SLY	SPDR S&P 600 Small Cap ETF	13.22%
EEM	iShares MSCI Emerging Markets ETF	0.87%
VNQ	Vanguard Real Estate ETF	1.72%
TLT	iShares 20+ Year Treasury Bond ETF	32.64%
LQD	iShares iBoxx $ Invmt Grade Corp Bd ETF	18.28%
GLD	SPDR Gold Shares	11.58%
Save portfolio »

Portfolio Returns

Portfolio Statistics
Portfolio	Expected Return	Expected Volatility	Sharpe Ratio
Provided Portfolio	8.94%	11.71%	0.64
Tangency Portfolio	8.88%	7.96%	0.94

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)	11.56%	14.87%	0.667	0.00%	100.00%
2	SPDR S&P 600 Small Cap ETF (SLY)	12.88%	20.02%	0.555	0.00%	100.00%
3	iShares MSCI EAFE ETF (EFA)	6.27%	17.40%	0.288	0.00%	100.00%
4	iShares MSCI Emerging Markets ETF (EEM)	8.02%	21.94%	0.304	0.00%	100.00%
5	Vanguard Real Estate ETF (VNQ)	10.81%	22.56%	0.409	0.00%	100.00%
6	iShares 20+ Year Treasury Bond ETF (TLT)	7.08%	13.40%	0.432	0.00%	100.00%
7	iShares iBoxx $ Invmt Grade Corp Bd ETF (LQD)	5.78%	7.36%	0.620	0.00%	100.00%
8	SPDR Gold Shares (GLD)	9.28%	17.60%	0.445	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	0.90	0.89	0.78	0.73	-0.31	0.34	0.06
SPDR S&P 600 Small Cap ETF	SLY	0.90	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	0.87	0.70	-0.26	0.41	0.15
iShares MSCI Emerging Markets ETF	EEM	0.78	0.74	0.87	1.00	0.61	-0.25	0.38	0.29
Vanguard Real Estate ETF	VNQ	0.73	0.74	0.70	0.61	1.00	-0.01	0.46	0.10
iShares 20+ Year Treasury Bond ETF	TLT	-0.31	-0.38	-0.26	-0.25	-0.01	1.00	0.49	0.22
iShares iBoxx $ Invmt Grade Corp Bd ETF	LQD	0.34	0.27	0.41	0.38	0.46	0.49	1.00	0.27
SPDR Gold Shares	GLD	0.06	0.01	0.15	0.29	0.10	0.22	0.27	1.00
Based on monthly returns from Jan 2006 to Sep 2021

Efficient Frontier Points
#	SPY	SLY	EFA	EEM	VNQ	TLT	LQD	GLD	Expected Return^*	Standard Deviation^*	Sharpe Ratio^*
1	12.74%	1.39%	0.00%	0.00%	0.00%	13.22%	66.41%	6.24%	6.99%	7.07%	0.806
2	13.29%	1.51%	0.00%	0.00%	0.00%	13.74%	65.12%	6.34%	7.04%	7.07%	0.813
3	13.79%	1.67%	0.00%	0.00%	0.00%	14.25%	63.84%	6.45%	7.09%	7.07%	0.819
4	14.23%	1.85%	0.00%	0.00%	0.00%	14.76%	62.59%	6.57%	7.14%	7.08%	0.825
5	14.60%	2.09%	0.00%	0.00%	0.00%	15.29%	61.34%	6.69%	7.19%	7.08%	0.831
6	14.92%	2.35%	0.00%	0.01%	0.00%	15.81%	60.11%	6.80%	7.23%	7.09%	0.837
7	15.21%	2.63%	0.00%	0.01%	0.01%	16.33%	58.90%	6.91%	7.28%	7.09%	0.842
8	15.47%	2.93%	0.00%	0.02%	0.01%	16.85%	57.70%	7.02%	7.33%	7.10%	0.847
9	15.73%	3.22%	0.00%	0.03%	0.02%	17.36%	56.49%	7.14%	7.37%	7.11%	0.853
10	15.99%	3.52%	0.00%	0.04%	0.02%	17.87%	55.29%	7.26%	7.42%	7.12%	0.857
11	16.23%	3.82%	0.00%	0.05%	0.03%	18.38%	54.09%	7.39%	7.47%	7.13%	0.862
12	16.47%	4.13%	0.00%	0.07%	0.05%	18.89%	52.89%	7.51%	7.51%	7.14%	0.867
13	16.69%	4.44%	0.00%	0.08%	0.06%	19.40%	51.69%	7.64%	7.56%	7.16%	0.871
14	16.91%	4.76%	0.00%	0.10%	0.07%	19.92%	50.47%	7.77%	7.61%	7.17%	0.876
15	17.12%	5.08%	0.00%	0.12%	0.09%	20.43%	49.26%	7.90%	7.66%	7.19%	0.880
16	17.33%	5.40%	0.00%	0.14%	0.11%	20.95%	48.03%	8.04%	7.70%	7.20%	0.884
17	17.53%	5.72%	0.00%	0.15%	0.14%	21.47%	46.80%	8.18%	7.75%	7.22%	0.888
18	17.74%	6.04%	0.00%	0.17%	0.18%	21.99%	45.56%	8.33%	7.80%	7.24%	0.892
19	17.94%	6.36%	0.00%	0.19%	0.21%	22.51%	44.32%	8.47%	7.85%	7.26%	0.896
20	18.14%	6.67%	0.00%	0.21%	0.25%	23.04%	43.07%	8.61%	7.90%	7.28%	0.899
21	18.35%	6.99%	0.00%	0.24%	0.29%	23.56%	41.83%	8.75%	7.94%	7.30%	0.903
22	18.55%	7.31%	0.00%	0.26%	0.33%	24.09%	40.57%	8.89%	7.99%	7.33%	0.906
23	18.75%	7.63%	0.00%	0.28%	0.38%	24.61%	39.32%	9.04%	8.04%	7.35%	0.909
24	18.95%	7.95%	0.00%	0.30%	0.42%	25.12%	38.08%	9.18%	8.09%	7.38%	0.912
25	19.16%	8.27%	0.00%	0.33%	0.46%	25.64%	36.82%	9.32%	8.14%	7.40%	0.915
26	19.37%	8.59%	0.00%	0.35%	0.50%	26.15%	35.57%	9.46%	8.19%	7.43%	0.918
27	19.57%	8.91%	0.00%	0.38%	0.55%	26.66%	34.32%	9.61%	8.24%	7.46%	0.920
28	19.78%	9.22%	0.00%	0.41%	0.60%	27.17%	33.07%	9.76%	8.29%	7.49%	0.923
29	19.98%	9.53%	0.00%	0.44%	0.65%	27.67%	31.83%	9.90%	8.33%	7.52%	0.925
30	20.17%	9.85%	0.00%	0.47%	0.71%	28.16%	30.61%	10.04%	8.38%	7.55%	0.927
31	20.34%	10.17%	0.00%	0.50%	0.77%	28.63%	29.41%	10.19%	8.43%	7.58%	0.929
32	20.51%	10.49%	0.00%	0.53%	0.84%	29.10%	28.21%	10.33%	8.48%	7.62%	0.931
33	20.68%	10.79%	0.00%	0.56%	0.91%	29.57%	27.02%	10.47%	8.52%	7.65%	0.932
34	20.84%	11.10%	0.00%	0.59%	1.00%	30.02%	25.85%	10.60%	8.57%	7.69%	0.933
35	21.00%	11.39%	0.00%	0.63%	1.09%	30.46%	24.68%	10.75%	8.62%	7.73%	0.935
36	21.16%	11.68%	0.00%	0.66%	1.18%	30.87%	23.55%	10.89%	8.66%	7.76%	0.935
37	21.30%	11.98%	0.00%	0.70%	1.28%	31.26%	22.45%	11.03%	8.71%	7.80%	0.936
38	21.43%	12.27%	0.00%	0.74%	1.38%	31.64%	21.36%	11.17%	8.75%	7.84%	0.937
39	21.55%	12.57%	0.00%	0.79%	1.49%	32.01%	20.29%	11.31%	8.80%	7.88%	0.937
40	21.63%	12.89%	0.00%	0.83%	1.60%	32.34%	19.26%	11.44%	8.84%	7.92%	0.937
41	21.71%	13.22%	0.00%	0.87%	1.72%	32.64%	18.28%	11.58%	8.88%	7.96%	0.937
42	21.78%	13.53%	0.00%	0.91%	1.84%	32.91%	17.32%	11.71%	8.92%	8.01%	0.937
43	21.86%	13.85%	0.00%	0.95%	1.96%	33.15%	16.39%	11.83%	8.97%	8.05%	0.937
44	21.93%	14.17%	0.00%	0.99%	2.09%	33.37%	15.50%	11.95%	9.01%	8.09%	0.937
45	21.98%	14.50%	0.00%	1.03%	2.22%	33.54%	14.66%	12.07%	9.05%	8.14%	0.936
46	22.01%	14.82%	0.00%	1.06%	2.37%	33.66%	13.87%	12.20%	9.09%	8.18%	0.935
47	22.05%	15.14%	0.00%	1.10%	2.52%	33.74%	13.11%	12.34%	9.13%	8.23%	0.934
48	22.06%	15.47%	0.00%	1.15%	2.67%	33.76%	12.41%	12.47%	9.16%	8.28%	0.933
49	22.04%	15.80%	0.02%	1.20%	2.84%	33.75%	11.74%	12.61%	9.20%	8.33%	0.931
50	22.00%	16.13%	0.04%	1.24%	3.02%	33.72%	11.11%	12.75%	9.24%	8.38%	0.930
51	21.95%	16.46%	0.06%	1.29%	3.20%	33.66%	10.50%	12.88%	9.27%	8.44%	0.928
52	21.87%	16.81%	0.07%	1.34%	3.39%	33.57%	9.92%	13.03%	9.31%	8.49%	0.925
53	21.77%	17.16%	0.09%	1.38%	3.59%	33.46%	9.36%	13.18%	9.34%	8.55%	0.923
54	21.67%	17.51%	0.11%	1.43%	3.79%	33.32%	8.82%	13.35%	9.37%	8.60%	0.920
55	21.56%	17.87%	0.14%	1.47%	3.99%	33.16%	8.30%	13.51%	9.41%	8.66%	0.918
56	21.47%	18.21%	0.16%	1.51%	4.19%	32.99%	7.79%	13.67%	9.44%	8.72%	0.915
57	21.37%	18.56%	0.17%	1.56%	4.41%	32.81%	7.30%	13.83%	9.48%	8.79%	0.912
58	21.27%	18.91%	0.18%	1.60%	4.62%	32.60%	6.81%	14.01%	9.51%	8.85%	0.909
59	21.18%	19.27%	0.19%	1.65%	4.83%	32.37%	6.33%	14.18%	9.55%	8.92%	0.906
60	21.05%	19.63%	0.20%	1.70%	5.04%	32.10%	5.91%	14.37%	9.58%	8.98%	0.903
61	20.93%	19.99%	0.19%	1.74%	5.27%	31.80%	5.51%	14.57%	9.61%	9.05%	0.899
62	20.81%	20.35%	0.19%	1.79%	5.49%	31.50%	5.11%	14.77%	9.65%	9.12%	0.896
63	20.70%	20.71%	0.18%	1.84%	5.71%	31.16%	4.73%	14.97%	9.68%	9.19%	0.892
64	20.58%	21.07%	0.18%	1.89%	5.94%	30.80%	4.38%	15.17%	9.72%	9.27%	0.888
65	20.46%	21.41%	0.17%	1.94%	6.18%	30.43%	4.05%	15.36%	9.75%	9.34%	0.885
66	20.34%	21.74%	0.17%	1.99%	6.41%	30.04%	3.74%	15.57%	9.78%	9.42%	0.881
67	20.20%	22.07%	0.16%	2.05%	6.66%	29.64%	3.44%	15.77%	9.81%	9.49%	0.876
68	20.06%	22.39%	0.16%	2.11%	6.92%	29.22%	3.16%	15.97%	9.84%	9.57%	0.872
69	19.91%	22.72%	0.15%	2.18%	7.19%	28.77%	2.91%	16.16%	9.87%	9.66%	0.867
70	19.77%	23.05%	0.15%	2.25%	7.47%	28.30%	2.67%	16.35%	9.90%	9.74%	0.863
71	19.62%	23.37%	0.14%	2.32%	7.76%	27.82%	2.43%	16.54%	9.93%	9.83%	0.858
72	19.47%	23.70%	0.14%	2.39%	8.05%	27.35%	2.20%	16.71%	9.97%	9.92%	0.853
73	19.34%	24.03%	0.13%	2.46%	8.33%	26.86%	1.99%	16.85%	10.00%	10.01%	0.848
74	19.19%	24.35%	0.13%	2.53%	8.64%	26.37%	1.80%	16.99%	10.03%	10.11%	0.843
75	19.01%	24.68%	0.12%	2.60%	8.95%	25.87%	1.63%	17.12%	10.06%	10.20%	0.838
76	18.81%	25.00%	0.12%	2.69%	9.27%	25.39%	1.47%	17.25%	10.08%	10.30%	0.832
77	18.61%	25.32%	0.11%	2.79%	9.59%	24.88%	1.32%	17.37%	10.11%	10.40%	0.827
78	18.39%	25.65%	0.11%	2.90%	9.94%	24.35%	1.17%	17.49%	10.14%	10.50%	0.821
79	18.15%	25.99%	0.10%	3.01%	10.30%	23.82%	1.04%	17.59%	10.17%	10.61%	0.815
80	17.91%	26.33%	0.10%	3.12%	10.67%	23.28%	0.91%	17.68%	10.19%	10.72%	0.809
81	17.61%	26.65%	0.09%	3.26%	11.10%	22.76%	0.80%	17.73%	10.22%	10.83%	0.803
82	17.32%	26.97%	0.09%	3.40%	11.57%	22.20%	0.71%	17.75%	10.24%	10.95%	0.796
83	17.00%	27.31%	0.08%	3.54%	12.06%	21.63%	0.62%	17.75%	10.27%	11.08%	0.789
84	16.68%	27.67%	0.08%	3.68%	12.56%	21.06%	0.55%	17.73%	10.30%	11.21%	0.782
85	16.36%	28.02%	0.08%	3.82%	13.06%	20.48%	0.47%	17.71%	10.32%	11.34%	0.775
86	16.03%	28.40%	0.07%	3.95%	13.55%	19.89%	0.41%	17.68%	10.35%	11.48%	0.768
87	15.66%	28.83%	0.07%	4.10%	14.04%	19.30%	0.36%	17.64%	10.38%	11.61%	0.761
88	15.21%	29.33%	0.07%	4.24%	14.53%	18.73%	0.31%	17.59%	10.41%	11.75%	0.754
89	14.64%	29.92%	0.07%	4.38%	15.01%	18.16%	0.27%	17.57%	10.44%	11.90%	0.747
90	13.99%	30.53%	0.07%	4.52%	15.51%	17.62%	0.24%	17.53%	10.46%	12.04%	0.741
91	13.31%	31.19%	0.06%	4.66%	16.06%	17.05%	0.20%	17.47%	10.49%	12.20%	0.733
92	12.52%	31.83%	0.06%	4.85%	16.63%	16.51%	0.17%	17.42%	10.52%	12.35%	0.726
93	11.63%	32.56%	0.06%	5.04%	17.27%	15.96%	0.14%	17.34%	10.54%	12.52%	0.718
94	10.78%	33.23%	0.06%	5.26%	18.01%	15.37%	0.11%	17.18%	10.57%	12.70%	0.710
95	9.93%	33.95%	0.06%	5.48%	18.79%	14.75%	0.09%	16.94%	10.60%	12.91%	0.701
96	9.12%	34.47%	0.05%	5.74%	19.69%	14.12%	0.07%	16.72%	10.63%	13.11%	0.692
97	8.24%	35.01%	0.05%	5.95%	20.71%	13.49%	0.06%	16.50%	10.65%	13.32%	0.682
98	7.38%	35.34%	0.05%	6.11%	21.92%	12.76%	0.04%	16.41%	10.68%	13.54%	0.673
99	6.40%	35.29%	0.03%	6.22%	23.58%	12.05%	0.02%	16.41%	10.70%	13.77%	0.663
100	5.50%	36.00%	0.00%	6.00%	24.50%	11.50%	0.00%	16.50%	10.73%	13.93%	0.658
^*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 Sep 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