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

Excess Return Frontier

Benchmark

Benchmark Ticker

Geometric Mean

Min Variance Frontier

Chart from Origin

Efficient Frontier Results (Jan 2006 - Apr 2022)

Note: The time period was constrained by the available data for SPDR S&P 600 Small Cap ETF (SLY) [Dec 2005 - Apr 2022].

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 »

Max Sharpe Ratio Portfolio
Ticker	Name	Allocation
SPY	SPDR S&P 500 ETF Trust	27.54%
SLY	SPDR S&P 600 Small Cap ETF	11.80%
EFA	iShares MSCI EAFE ETF	0.09%
EEM	iShares MSCI Emerging Markets ETF	0.19%
VNQ	Vanguard Real Estate ETF	2.90%
TLT	iShares 20+ Year Treasury Bond ETF	29.21%
LQD	iShares iBoxx $ Invmt Grade Corp Bd ETF	9.32%
GLD	SPDR Gold Shares	18.95%
Save portfolio »

Portfolio Returns

Portfolio Statistics
Portfolio	Expected Return	Standard Deviation	Sharpe Ratio
Provided Portfolio	8.15%	11.76%	0.58
Max Sharpe Ratio Portfolio	8.61%	8.71%	0.83

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)	10.97%	15.04%	0.626	0.00%	100.00%
2	SPDR S&P 600 Small Cap ETF (SLY)	11.87%	19.93%	0.513	0.00%	100.00%
3	iShares MSCI EAFE ETF (EFA)	5.38%	17.33%	0.243	0.00%	100.00%
4	iShares MSCI Emerging Markets ETF (EEM)	6.72%	21.69%	0.253	0.00%	100.00%
5	Vanguard Real Estate ETF (VNQ)	10.74%	22.54%	0.408	0.00%	100.00%
6	iShares 20+ Year Treasury Bond ETF (TLT)	5.71%	13.55%	0.333	0.00%	100.00%
7	iShares iBoxx $ Invmt Grade Corp Bd ETF (LQD)	4.61%	7.58%	0.459	0.00%	100.00%
8	SPDR Gold Shares (GLD)	9.45%	17.37%	0.462	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	0.76	0.73	-0.25	0.37	0.07
SPDR S&P 600 Small Cap ETF	SLY	0.90	1.00	0.81	0.74	0.74	-0.34	0.30	0.03
iShares MSCI EAFE ETF	EFA	0.89	0.81	1.00	0.87	0.70	-0.23	0.42	0.15
iShares MSCI Emerging Markets ETF	EEM	0.76	0.74	0.87	1.00	0.60	-0.22	0.39	0.28
Vanguard Real Estate ETF	VNQ	0.73	0.74	0.70	0.60	1.00	-0.00	0.46	0.11
iShares 20+ Year Treasury Bond ETF	TLT	-0.25	-0.34	-0.23	-0.22	-0.00	1.00	0.52	0.21
iShares iBoxx $ Invmt Grade Corp Bd ETF	LQD	0.37	0.30	0.42	0.39	0.46	0.52	1.00	0.27
SPDR Gold Shares	GLD	0.07	0.03	0.15	0.28	0.11	0.21	0.27	1.00
Based on monthly returns from Jan 2006 to Apr 2022

Efficient Frontier Points
#	SPY	SLY	EFA	EEM	VNQ	TLT	LQD	GLD	Expected Return^*	Standard Deviation^*	Sharpe Ratio^*
1	10.24%	1.56%	0.04%	0.00%	0.00%	10.10%	71.07%	6.99%	5.80%	7.32%	0.630
2	10.82%	1.66%	0.03%	0.00%	0.00%	10.51%	69.73%	7.24%	5.86%	7.32%	0.638
3	11.39%	1.76%	0.02%	0.00%	0.00%	10.95%	68.40%	7.49%	5.92%	7.32%	0.645
4	11.92%	1.88%	0.02%	0.00%	0.00%	11.38%	67.08%	7.72%	5.98%	7.32%	0.653
5	12.44%	2.02%	0.01%	0.00%	0.00%	11.83%	65.76%	7.95%	6.04%	7.33%	0.660
6	12.96%	2.16%	0.01%	0.00%	0.00%	12.28%	64.42%	8.17%	6.10%	7.33%	0.667
7	13.46%	2.31%	0.00%	0.00%	0.00%	12.74%	63.09%	8.40%	6.15%	7.34%	0.674
8	13.94%	2.46%	0.00%	0.00%	0.01%	13.19%	61.77%	8.63%	6.21%	7.34%	0.681
9	14.41%	2.63%	0.00%	0.00%	0.02%	13.64%	60.45%	8.86%	6.27%	7.35%	0.687
10	14.85%	2.80%	0.00%	0.00%	0.03%	14.09%	59.14%	9.09%	6.33%	7.36%	0.694
11	15.28%	2.98%	0.00%	0.00%	0.05%	14.54%	57.83%	9.31%	6.38%	7.38%	0.700
12	15.71%	3.16%	0.00%	0.00%	0.07%	14.99%	56.52%	9.54%	6.44%	7.39%	0.706
13	16.14%	3.35%	0.00%	0.00%	0.09%	15.46%	55.20%	9.77%	6.50%	7.40%	0.712
14	16.55%	3.54%	0.00%	0.00%	0.12%	15.92%	53.87%	10.00%	6.56%	7.42%	0.718
15	16.96%	3.74%	0.00%	0.00%	0.14%	16.39%	52.53%	10.23%	6.61%	7.43%	0.724
16	17.36%	3.95%	0.00%	0.00%	0.16%	16.87%	51.19%	10.47%	6.67%	7.45%	0.729
17	17.76%	4.16%	0.00%	0.00%	0.18%	17.34%	49.85%	10.70%	6.73%	7.47%	0.735
18	18.17%	4.37%	0.00%	0.01%	0.21%	17.81%	48.51%	10.93%	6.79%	7.49%	0.740
19	18.56%	4.58%	0.00%	0.01%	0.24%	18.28%	47.16%	11.17%	6.85%	7.51%	0.746
20	18.96%	4.79%	0.00%	0.01%	0.27%	18.76%	45.81%	11.40%	6.91%	7.53%	0.751
21	19.36%	5.00%	0.00%	0.01%	0.30%	19.24%	44.45%	11.64%	6.96%	7.55%	0.756
22	19.75%	5.22%	0.00%	0.01%	0.33%	19.72%	43.09%	11.87%	7.02%	7.58%	0.761
23	20.13%	5.44%	0.00%	0.01%	0.37%	20.21%	41.73%	12.11%	7.08%	7.60%	0.766
24	20.51%	5.67%	0.00%	0.01%	0.40%	20.69%	40.36%	12.35%	7.14%	7.63%	0.770
25	20.89%	5.89%	0.00%	0.01%	0.44%	21.18%	38.99%	12.60%	7.20%	7.66%	0.775
26	21.26%	6.12%	0.01%	0.01%	0.48%	21.67%	37.61%	12.84%	7.26%	7.69%	0.779
27	21.63%	6.34%	0.01%	0.02%	0.52%	22.15%	36.25%	13.09%	7.32%	7.72%	0.783
28	21.99%	6.57%	0.01%	0.02%	0.56%	22.63%	34.89%	13.33%	7.38%	7.75%	0.787
29	22.35%	6.80%	0.02%	0.02%	0.61%	23.10%	33.53%	13.57%	7.44%	7.78%	0.791
30	22.70%	7.03%	0.02%	0.02%	0.66%	23.57%	32.19%	13.81%	7.50%	7.81%	0.795
31	23.05%	7.26%	0.02%	0.03%	0.71%	24.04%	30.84%	14.06%	7.56%	7.85%	0.798
32	23.38%	7.49%	0.03%	0.03%	0.76%	24.51%	29.50%	14.30%	7.62%	7.88%	0.802
33	23.72%	7.72%	0.03%	0.04%	0.82%	24.96%	28.18%	14.54%	7.67%	7.92%	0.805
34	24.05%	7.95%	0.03%	0.04%	0.89%	25.41%	26.86%	14.77%	7.73%	7.95%	0.808
35	24.38%	8.17%	0.04%	0.05%	0.95%	25.85%	25.55%	15.01%	7.79%	7.99%	0.811
36	24.68%	8.40%	0.04%	0.06%	1.03%	26.27%	24.27%	15.25%	7.85%	8.03%	0.814
37	24.97%	8.63%	0.04%	0.06%	1.11%	26.67%	23.03%	15.48%	7.90%	8.07%	0.816
38	25.24%	8.86%	0.05%	0.07%	1.20%	27.04%	21.83%	15.71%	7.96%	8.11%	0.818
39	25.50%	9.09%	0.05%	0.08%	1.30%	27.40%	20.64%	15.94%	8.01%	8.15%	0.820
40	25.75%	9.32%	0.05%	0.09%	1.40%	27.71%	19.51%	16.17%	8.07%	8.20%	0.822
41	25.96%	9.55%	0.06%	0.10%	1.52%	28.01%	18.40%	16.40%	8.12%	8.24%	0.824
42	26.14%	9.80%	0.06%	0.11%	1.64%	28.28%	17.34%	16.62%	8.17%	8.28%	0.825
43	26.33%	10.04%	0.06%	0.12%	1.77%	28.53%	16.30%	16.85%	8.22%	8.33%	0.827
44	26.52%	10.27%	0.07%	0.13%	1.90%	28.76%	15.27%	17.08%	8.27%	8.37%	0.828
45	26.71%	10.51%	0.07%	0.14%	2.03%	28.94%	14.29%	17.32%	8.32%	8.42%	0.829
46	26.89%	10.73%	0.07%	0.15%	2.16%	29.09%	13.35%	17.57%	8.37%	8.47%	0.830
47	27.05%	10.95%	0.08%	0.15%	2.30%	29.20%	12.44%	17.83%	8.42%	8.51%	0.831
48	27.19%	11.17%	0.08%	0.16%	2.44%	29.28%	11.58%	18.09%	8.47%	8.56%	0.831
49	27.32%	11.38%	0.08%	0.17%	2.59%	29.31%	10.77%	18.37%	8.52%	8.61%	0.831
50	27.43%	11.60%	0.09%	0.18%	2.74%	29.29%	10.02%	18.65%	8.56%	8.66%	0.832
51	27.54%	11.80%	0.09%	0.19%	2.90%	29.21%	9.32%	18.95%	8.61%	8.71%	0.832
52	27.65%	11.97%	0.09%	0.20%	3.06%	29.06%	8.70%	19.28%	8.65%	8.76%	0.832
53	27.74%	12.15%	0.09%	0.21%	3.22%	28.86%	8.12%	19.61%	8.69%	8.81%	0.831
54	27.83%	12.30%	0.10%	0.22%	3.39%	28.63%	7.58%	19.95%	8.74%	8.86%	0.831
55	27.90%	12.46%	0.10%	0.22%	3.57%	28.34%	7.09%	20.31%	8.78%	8.92%	0.830
56	27.94%	12.61%	0.11%	0.23%	3.76%	28.02%	6.65%	20.68%	8.82%	8.97%	0.829
57	27.98%	12.76%	0.12%	0.24%	3.95%	27.68%	6.22%	21.05%	8.86%	9.03%	0.828
58	28.00%	12.92%	0.12%	0.25%	4.15%	27.34%	5.80%	21.42%	8.90%	9.09%	0.827
59	28.02%	13.08%	0.13%	0.26%	4.35%	26.99%	5.40%	21.79%	8.94%	9.14%	0.825
60	28.04%	13.23%	0.13%	0.27%	4.55%	26.62%	5.00%	22.16%	8.98%	9.20%	0.824
61	28.05%	13.37%	0.14%	0.27%	4.76%	26.23%	4.63%	22.54%	9.02%	9.26%	0.822
62	28.08%	13.51%	0.14%	0.28%	4.96%	25.82%	4.28%	22.92%	9.05%	9.33%	0.821
63	28.12%	13.64%	0.15%	0.29%	5.17%	25.39%	3.94%	23.30%	9.09%	9.39%	0.819
64	28.16%	13.76%	0.15%	0.31%	5.39%	24.95%	3.61%	23.67%	9.13%	9.46%	0.817
65	28.19%	13.88%	0.16%	0.33%	5.61%	24.48%	3.31%	24.03%	9.17%	9.52%	0.815
66	28.20%	14.02%	0.16%	0.35%	5.84%	24.00%	3.03%	24.40%	9.21%	9.59%	0.813
67	28.20%	14.15%	0.17%	0.37%	6.07%	23.49%	2.76%	24.78%	9.25%	9.66%	0.810
68	28.18%	14.30%	0.18%	0.40%	6.30%	22.97%	2.51%	25.17%	9.28%	9.74%	0.808
69	28.15%	14.44%	0.18%	0.42%	6.54%	22.45%	2.26%	25.56%	9.32%	9.81%	0.805
70	28.11%	14.59%	0.19%	0.44%	6.78%	21.92%	2.02%	25.95%	9.36%	9.89%	0.803
71	28.05%	14.75%	0.19%	0.46%	7.02%	21.40%	1.81%	26.32%	9.39%	9.96%	0.800
72	27.97%	14.92%	0.20%	0.48%	7.25%	20.87%	1.63%	26.68%	9.43%	10.03%	0.797
73	27.87%	15.08%	0.20%	0.51%	7.51%	20.34%	1.46%	27.02%	9.46%	10.11%	0.794
74	27.76%	15.25%	0.21%	0.55%	7.77%	19.83%	1.31%	27.33%	9.49%	10.18%	0.791
75	27.66%	15.41%	0.21%	0.59%	8.03%	19.31%	1.18%	27.60%	9.52%	10.26%	0.788
76	27.54%	15.57%	0.22%	0.65%	8.30%	18.80%	1.06%	27.87%	9.55%	10.33%	0.785
77	27.39%	15.74%	0.22%	0.70%	8.58%	18.30%	0.93%	28.14%	9.58%	10.41%	0.782
78	27.22%	15.94%	0.23%	0.75%	8.86%	17.81%	0.82%	28.37%	9.61%	10.49%	0.779
79	26.99%	16.14%	0.23%	0.80%	9.15%	17.34%	0.72%	28.62%	9.63%	10.56%	0.776
80	26.70%	16.34%	0.24%	0.86%	9.46%	16.88%	0.65%	28.88%	9.66%	10.63%	0.772
81	26.42%	16.55%	0.24%	0.91%	9.77%	16.41%	0.57%	29.13%	9.68%	10.71%	0.769
82	26.09%	16.80%	0.24%	0.97%	10.09%	15.94%	0.50%	29.37%	9.71%	10.79%	0.766
83	25.70%	17.10%	0.25%	1.03%	10.40%	15.48%	0.44%	29.60%	9.73%	10.86%	0.762
84	25.24%	17.42%	0.25%	1.09%	10.76%	15.04%	0.38%	29.81%	9.76%	10.95%	0.758
85	24.77%	17.76%	0.25%	1.15%	11.14%	14.57%	0.33%	30.03%	9.78%	11.03%	0.755
86	24.19%	18.13%	0.26%	1.22%	11.57%	14.12%	0.27%	30.23%	9.80%	11.12%	0.751
87	23.50%	18.58%	0.27%	1.29%	12.04%	13.67%	0.23%	30.43%	9.83%	11.21%	0.746
88	22.71%	19.06%	0.27%	1.36%	12.56%	13.24%	0.18%	30.60%	9.85%	11.31%	0.742
89	21.87%	19.53%	0.28%	1.44%	13.10%	12.84%	0.15%	30.79%	9.87%	11.40%	0.737
90	20.95%	20.08%	0.29%	1.51%	13.65%	12.44%	0.12%	30.97%	9.89%	11.50%	0.733
91	20.02%	20.64%	0.29%	1.59%	14.18%	12.03%	0.10%	31.15%	9.91%	11.60%	0.728
92	18.96%	21.31%	0.30%	1.66%	14.73%	11.65%	0.08%	31.30%	9.93%	11.70%	0.723
93	17.83%	22.00%	0.31%	1.74%	15.27%	11.31%	0.06%	31.49%	9.95%	11.80%	0.719
94	16.59%	22.68%	0.31%	1.81%	15.88%	10.96%	0.04%	31.73%	9.97%	11.90%	0.714
95	15.28%	23.34%	0.32%	1.87%	16.55%	10.64%	0.03%	31.97%	9.98%	12.00%	0.709
96	14.02%	23.87%	0.33%	1.89%	17.28%	10.35%	0.02%	32.25%	10.00%	12.09%	0.705
97	12.81%	24.15%	0.33%	1.85%	18.10%	10.08%	0.01%	32.67%	10.01%	12.18%	0.701
98	11.58%	24.41%	0.22%	1.78%	19.01%	9.90%	0.01%	33.10%	10.02%	12.25%	0.697
99	9.93%	25.05%	0.11%	1.66%	19.90%	9.87%	0.00%	33.49%	10.03%	12.33%	0.694
100	7.00%	25.50%	0.00%	1.50%	22.00%	10.00%	0.00%	34.00%	10.03%	12.45%	0.687
^*Annualized 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:

IMPORTANT: The projections or other information generated by Portfolio Visualizer regarding the likelihood of various investment outcomes are hypothetical in nature, do not reflect actual investment results and are not guarantees of future results. Results may vary with each use and over time.
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. All use is subject to terms of service.
Investing involves risk, including possible loss of principal. Past performance is not a guarantee of future results.
Asset allocation and diversification strategies do not guarantee a profit or protect against a loss.
Hypothetical returns do not reflect trading costs, transaction fees, commissions, or actual taxes due on investment returns.
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.
Refer to the related documentation sections for more details on terms and definitions, methodology, and data sources.
Portfolio optimization is a process of choosing the proportions of various assets to be held in a portfolio in such a way as to make the portfolio better than any other combination according to the selected objective function such as maximizing risk-adjusted return. 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 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 Apr 2022
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