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.
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 » |
Ticker | Name | Allocation |
---|---|---|
SPY | SPDR S&P 500 ETF Trust | 24.63% |
SLY | SPDR S&P 600 Small Cap ETF | 10.12% |
EFA | iShares MSCI EAFE ETF | 0.01% |
EEM | iShares MSCI Emerging Markets ETF | 0.67% |
VNQ | Vanguard Real Estate ETF | 1.12% |
TLT | iShares 20+ Year Treasury Bond ETF | 32.08% |
LQD | iShares iBoxx $ Invmt Grade Corp Bd ETF | 19.72% |
GLD | SPDR Gold Shares | 11.65% |
Save portfolio » |
Portfolio | Expected Return | Expected Volatility | Sharpe Ratio |
---|---|---|---|
Provided Portfolio | 9.00% | 11.93% | 0.66 |
Tangency Portfolio | 9.09% | 7.87% | 1.01 |
# | Asset | CAGR | Expected Return | Standard Deviation | Sharpe Ratio | Min. Weight | Max. Weight |
---|---|---|---|---|---|---|---|
1 | SPDR S&P 500 ETF Trust (SPY) | 9.80% | 11.05% | 15.07% | 0.658 | 0.00% | 100.00% |
2 | SPDR S&P 600 Small Cap ETF (SLY) | 9.86% | 12.17% | 20.34% | 0.543 | 0.00% | 100.00% |
3 | iShares MSCI EAFE ETF (EFA) | 4.33% | 6.01% | 17.76% | 0.275 | 0.00% | 100.00% |
4 | iShares MSCI Emerging Markets ETF (EEM) | 5.87% | 8.56% | 22.36% | 0.332 | 0.00% | 100.00% |
5 | Vanguard Real Estate ETF (VNQ) | 6.92% | 9.85% | 22.92% | 0.380 | 0.00% | 100.00% |
6 | iShares 20+ Year Treasury Bond ETF (TLT) | 7.02% | 7.96% | 13.40% | 0.510 | 0.00% | 100.00% |
7 | iShares iBoxx $ Invmt Grade Corp Bd ETF (LQD) | 5.94% | 6.23% | 7.42% | 0.686 | 0.00% | 100.00% |
8 | SPDR Gold Shares (GLD) | 8.62% | 10.30% | 17.65% | 0.519 | 0.00% | 100.00% |
Results based on historical returns. Ex ante Sharpe Ratio calculated using 3-month treasury bill returns as the risk-free rate (1.13% annualized). |
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 | 0.72 | -0.32 | 0.34 | 0.06 |
SPDR S&P 600 Small Cap ETF | SLY | 0.91 | 1.00 | 0.81 | 0.74 | 0.74 | -0.37 | 0.30 | 0.02 |
iShares MSCI EAFE ETF | EFA | 0.89 | 0.81 | 1.00 | 0.88 | 0.70 | -0.27 | 0.41 | 0.14 |
iShares MSCI Emerging Markets ETF | EEM | 0.79 | 0.74 | 0.88 | 1.00 | 0.62 | -0.25 | 0.38 | 0.29 |
Vanguard Real Estate ETF | VNQ | 0.72 | 0.74 | 0.70 | 0.62 | 1.00 | -0.01 | 0.47 | 0.10 |
iShares 20+ Year Treasury Bond ETF | TLT | -0.32 | -0.37 | -0.27 | -0.25 | -0.01 | 1.00 | 0.47 | 0.21 |
iShares iBoxx $ Invmt Grade Corp Bd ETF | LQD | 0.34 | 0.30 | 0.41 | 0.38 | 0.47 | 0.47 | 1.00 | 0.27 |
SPDR Gold Shares | GLD | 0.06 | 0.02 | 0.14 | 0.29 | 0.10 | 0.21 | 0.27 | 1.00 |
Based on monthly returns from Jan 2006 to Dec 2020 |
# | SPY | SLY | EFA | EEM | VNQ | TLT | LQD | GLD | Expected Return* | Standard Deviation* | Sharpe Ratio* |
---|---|---|---|---|---|---|---|---|---|---|---|
1 | 14.17% | 0.63% | 0.00% | 0.00% | 0.00% | 14.71% | 64.72% | 5.76% | 7.42% | 7.09% | 0.887 |
2 | 14.77% | 0.69% | 0.00% | 0.00% | 0.00% | 15.19% | 63.43% | 5.91% | 7.47% | 7.09% | 0.894 |
3 | 15.31% | 0.78% | 0.00% | 0.00% | 0.00% | 15.68% | 62.18% | 6.05% | 7.52% | 7.09% | 0.900 |
4 | 15.81% | 0.91% | 0.00% | 0.00% | 0.00% | 16.16% | 60.94% | 6.18% | 7.56% | 7.10% | 0.906 |
5 | 16.27% | 1.05% | 0.00% | 0.00% | 0.00% | 16.64% | 59.73% | 6.32% | 7.60% | 7.10% | 0.911 |
6 | 16.69% | 1.22% | 0.00% | 0.00% | 0.00% | 17.11% | 58.53% | 6.45% | 7.65% | 7.11% | 0.917 |
7 | 17.08% | 1.41% | 0.00% | 0.01% | 0.00% | 17.59% | 57.33% | 6.58% | 7.69% | 7.11% | 0.922 |
8 | 17.45% | 1.62% | 0.00% | 0.01% | 0.01% | 18.08% | 56.12% | 6.72% | 7.74% | 7.12% | 0.927 |
9 | 17.80% | 1.84% | 0.00% | 0.02% | 0.01% | 18.56% | 54.91% | 6.85% | 7.78% | 7.13% | 0.932 |
10 | 18.15% | 2.05% | 0.00% | 0.03% | 0.02% | 19.05% | 53.71% | 7.00% | 7.82% | 7.14% | 0.937 |
11 | 18.48% | 2.28% | 0.00% | 0.04% | 0.03% | 19.53% | 52.49% | 7.14% | 7.87% | 7.15% | 0.942 |
12 | 18.77% | 2.55% | 0.00% | 0.04% | 0.05% | 20.03% | 51.27% | 7.29% | 7.91% | 7.16% | 0.947 |
13 | 19.04% | 2.82% | 0.00% | 0.05% | 0.06% | 20.52% | 50.06% | 7.44% | 7.96% | 7.18% | 0.951 |
14 | 19.31% | 3.09% | 0.00% | 0.06% | 0.08% | 21.01% | 48.85% | 7.60% | 8.00% | 7.19% | 0.955 |
15 | 19.57% | 3.37% | 0.00% | 0.07% | 0.10% | 21.49% | 47.64% | 7.75% | 8.05% | 7.21% | 0.959 |
16 | 19.83% | 3.65% | 0.00% | 0.08% | 0.13% | 21.98% | 46.43% | 7.91% | 8.09% | 7.22% | 0.963 |
17 | 20.09% | 3.92% | 0.00% | 0.10% | 0.15% | 22.47% | 45.20% | 8.07% | 8.14% | 7.24% | 0.967 |
18 | 20.35% | 4.20% | 0.00% | 0.11% | 0.17% | 22.97% | 43.97% | 8.22% | 8.18% | 7.26% | 0.971 |
19 | 20.61% | 4.49% | 0.00% | 0.13% | 0.20% | 23.46% | 42.73% | 8.38% | 8.23% | 7.28% | 0.974 |
20 | 20.86% | 4.78% | 0.00% | 0.14% | 0.22% | 23.96% | 41.49% | 8.55% | 8.27% | 7.30% | 0.978 |
21 | 21.11% | 5.08% | 0.00% | 0.16% | 0.25% | 24.45% | 40.24% | 8.71% | 8.32% | 7.33% | 0.981 |
22 | 21.36% | 5.37% | 0.01% | 0.18% | 0.28% | 24.95% | 38.98% | 8.88% | 8.37% | 7.35% | 0.984 |
23 | 21.61% | 5.67% | 0.01% | 0.20% | 0.30% | 25.45% | 37.72% | 9.05% | 8.41% | 7.37% | 0.987 |
24 | 21.85% | 5.97% | 0.01% | 0.22% | 0.33% | 25.95% | 36.45% | 9.22% | 8.46% | 7.40% | 0.990 |
25 | 22.08% | 6.27% | 0.01% | 0.25% | 0.36% | 26.45% | 35.18% | 9.39% | 8.51% | 7.43% | 0.993 |
26 | 22.31% | 6.57% | 0.01% | 0.28% | 0.40% | 26.94% | 33.92% | 9.57% | 8.55% | 7.46% | 0.995 |
27 | 22.54% | 6.87% | 0.02% | 0.31% | 0.44% | 27.43% | 32.66% | 9.74% | 8.60% | 7.48% | 0.998 |
28 | 22.77% | 7.16% | 0.02% | 0.33% | 0.48% | 27.93% | 31.39% | 9.92% | 8.65% | 7.52% | 1.000 |
29 | 23.00% | 7.46% | 0.02% | 0.36% | 0.52% | 28.41% | 30.13% | 10.09% | 8.69% | 7.55% | 1.002 |
30 | 23.23% | 7.75% | 0.02% | 0.39% | 0.56% | 28.88% | 28.89% | 10.27% | 8.74% | 7.58% | 1.004 |
31 | 23.43% | 8.05% | 0.02% | 0.42% | 0.62% | 29.33% | 27.69% | 10.45% | 8.78% | 7.61% | 1.005 |
32 | 23.62% | 8.35% | 0.01% | 0.46% | 0.67% | 29.77% | 26.49% | 10.63% | 8.83% | 7.65% | 1.006 |
33 | 23.81% | 8.66% | 0.01% | 0.49% | 0.73% | 30.20% | 25.30% | 10.81% | 8.87% | 7.68% | 1.008 |
34 | 23.99% | 8.96% | 0.01% | 0.52% | 0.79% | 30.60% | 24.14% | 10.99% | 8.92% | 7.72% | 1.009 |
35 | 24.17% | 9.24% | 0.01% | 0.56% | 0.87% | 30.99% | 23.00% | 11.16% | 8.96% | 7.76% | 1.009 |
36 | 24.33% | 9.53% | 0.01% | 0.59% | 0.95% | 31.37% | 21.88% | 11.33% | 9.00% | 7.79% | 1.010 |
37 | 24.48% | 9.83% | 0.01% | 0.63% | 1.03% | 31.75% | 20.78% | 11.49% | 9.04% | 7.83% | 1.010 |
38 | 24.63% | 10.12% | 0.01% | 0.67% | 1.12% | 32.08% | 19.72% | 11.65% | 9.09% | 7.87% | 1.010 |
39 | 24.74% | 10.42% | 0.01% | 0.72% | 1.21% | 32.40% | 18.67% | 11.83% | 9.13% | 7.91% | 1.010 |
40 | 24.83% | 10.72% | 0.01% | 0.77% | 1.31% | 32.70% | 17.64% | 12.01% | 9.17% | 7.96% | 1.010 |
41 | 24.93% | 11.02% | 0.01% | 0.82% | 1.42% | 32.98% | 16.63% | 12.20% | 9.21% | 8.00% | 1.009 |
42 | 24.98% | 11.34% | 0.01% | 0.87% | 1.53% | 33.22% | 15.68% | 12.38% | 9.24% | 8.04% | 1.008 |
43 | 25.01% | 11.67% | 0.01% | 0.92% | 1.65% | 33.42% | 14.77% | 12.56% | 9.28% | 8.09% | 1.007 |
44 | 25.03% | 11.99% | 0.00% | 0.97% | 1.79% | 33.59% | 13.90% | 12.74% | 9.32% | 8.14% | 1.006 |
45 | 25.01% | 12.32% | 0.00% | 1.02% | 1.93% | 33.72% | 13.08% | 12.92% | 9.35% | 8.18% | 1.005 |
46 | 24.96% | 12.67% | 0.00% | 1.07% | 2.07% | 33.80% | 12.31% | 13.11% | 9.39% | 8.23% | 1.003 |
47 | 24.87% | 13.02% | 0.00% | 1.13% | 2.22% | 33.84% | 11.61% | 13.31% | 9.42% | 8.28% | 1.001 |
48 | 24.76% | 13.37% | 0.00% | 1.19% | 2.37% | 33.82% | 10.97% | 13.51% | 9.45% | 8.33% | 0.998 |
49 | 24.64% | 13.72% | 0.00% | 1.25% | 2.54% | 33.79% | 10.35% | 13.71% | 9.48% | 8.38% | 0.996 |
50 | 24.49% | 14.07% | 0.00% | 1.32% | 2.70% | 33.74% | 9.77% | 13.92% | 9.51% | 8.43% | 0.993 |
51 | 24.34% | 14.42% | 0.00% | 1.38% | 2.88% | 33.66% | 9.21% | 14.12% | 9.54% | 8.49% | 0.991 |
52 | 24.17% | 14.77% | 0.00% | 1.44% | 3.06% | 33.54% | 8.69% | 14.32% | 9.56% | 8.54% | 0.988 |
53 | 24.01% | 15.10% | 0.00% | 1.51% | 3.25% | 33.40% | 8.19% | 14.54% | 9.59% | 8.59% | 0.984 |
54 | 23.87% | 15.43% | 0.00% | 1.57% | 3.44% | 33.22% | 7.71% | 14.77% | 9.62% | 8.65% | 0.981 |
55 | 23.73% | 15.75% | 0.00% | 1.64% | 3.63% | 33.02% | 7.24% | 14.99% | 9.65% | 8.71% | 0.977 |
56 | 23.59% | 16.08% | 0.00% | 1.70% | 3.82% | 32.80% | 6.78% | 15.22% | 9.67% | 8.77% | 0.974 |
57 | 23.47% | 16.41% | 0.00% | 1.77% | 4.01% | 32.54% | 6.36% | 15.45% | 9.70% | 8.83% | 0.970 |
58 | 23.36% | 16.73% | 0.00% | 1.83% | 4.21% | 32.24% | 5.96% | 15.67% | 9.73% | 8.90% | 0.966 |
59 | 23.22% | 17.05% | 0.00% | 1.90% | 4.41% | 31.93% | 5.58% | 15.91% | 9.75% | 8.96% | 0.962 |
60 | 23.07% | 17.39% | 0.00% | 1.96% | 4.63% | 31.58% | 5.23% | 16.15% | 9.78% | 9.03% | 0.957 |
61 | 22.93% | 17.72% | 0.00% | 2.03% | 4.84% | 31.21% | 4.90% | 16.38% | 9.80% | 9.10% | 0.953 |
62 | 22.83% | 18.02% | 0.00% | 2.09% | 5.06% | 30.82% | 4.57% | 16.61% | 9.83% | 9.17% | 0.948 |
63 | 22.74% | 18.30% | 0.00% | 2.15% | 5.30% | 30.40% | 4.26% | 16.85% | 9.85% | 9.25% | 0.943 |
64 | 22.67% | 18.56% | 0.00% | 2.22% | 5.54% | 29.95% | 3.97% | 17.09% | 9.88% | 9.32% | 0.938 |
65 | 22.60% | 18.82% | 0.00% | 2.28% | 5.79% | 29.49% | 3.69% | 17.33% | 9.90% | 9.40% | 0.933 |
66 | 22.53% | 19.07% | 0.00% | 2.35% | 6.04% | 29.00% | 3.45% | 17.57% | 9.93% | 9.48% | 0.927 |
67 | 22.45% | 19.31% | 0.00% | 2.41% | 6.29% | 28.49% | 3.22% | 17.82% | 9.95% | 9.56% | 0.922 |
68 | 22.38% | 19.55% | 0.00% | 2.47% | 6.55% | 27.97% | 3.00% | 18.08% | 9.97% | 9.65% | 0.916 |
69 | 22.29% | 19.79% | 0.00% | 2.54% | 6.81% | 27.44% | 2.81% | 18.32% | 9.99% | 9.73% | 0.911 |
70 | 22.18% | 20.06% | 0.00% | 2.61% | 7.08% | 26.89% | 2.63% | 18.56% | 10.02% | 9.82% | 0.905 |
71 | 22.07% | 20.31% | 0.00% | 2.68% | 7.36% | 26.32% | 2.47% | 18.79% | 10.04% | 9.91% | 0.899 |
72 | 21.94% | 20.58% | 0.00% | 2.74% | 7.64% | 25.75% | 2.32% | 19.02% | 10.06% | 10.00% | 0.893 |
73 | 21.81% | 20.83% | 0.00% | 2.80% | 7.95% | 25.18% | 2.18% | 19.25% | 10.08% | 10.09% | 0.887 |
74 | 21.68% | 21.08% | 0.00% | 2.86% | 8.26% | 24.60% | 2.05% | 19.47% | 10.10% | 10.19% | 0.880 |
75 | 21.53% | 21.36% | 0.00% | 2.92% | 8.56% | 24.02% | 1.93% | 19.67% | 10.12% | 10.28% | 0.874 |
76 | 21.34% | 21.68% | 0.00% | 2.98% | 8.87% | 23.44% | 1.82% | 19.86% | 10.14% | 10.38% | 0.868 |
77 | 21.13% | 22.01% | 0.00% | 3.04% | 9.18% | 22.87% | 1.71% | 20.06% | 10.16% | 10.48% | 0.861 |
78 | 20.94% | 22.31% | 0.00% | 3.11% | 9.50% | 22.29% | 1.60% | 20.25% | 10.18% | 10.58% | 0.855 |
79 | 20.74% | 22.60% | 0.00% | 3.19% | 9.82% | 21.70% | 1.50% | 20.45% | 10.20% | 10.68% | 0.849 |
80 | 20.56% | 22.87% | 0.00% | 3.27% | 10.17% | 21.11% | 1.41% | 20.62% | 10.22% | 10.79% | 0.842 |
81 | 20.39% | 23.13% | 0.00% | 3.35% | 10.50% | 20.52% | 1.32% | 20.79% | 10.24% | 10.89% | 0.836 |
82 | 20.18% | 23.42% | 0.00% | 3.44% | 10.85% | 19.99% | 1.21% | 20.91% | 10.25% | 11.00% | 0.829 |
83 | 19.89% | 23.78% | 0.00% | 3.53% | 11.19% | 19.48% | 1.10% | 21.02% | 10.27% | 11.11% | 0.823 |
84 | 19.49% | 24.21% | 0.00% | 3.65% | 11.56% | 18.98% | 1.01% | 21.11% | 10.29% | 11.22% | 0.816 |
85 | 19.08% | 24.62% | 0.00% | 3.78% | 11.94% | 18.50% | 0.92% | 21.16% | 10.30% | 11.33% | 0.809 |
86 | 18.67% | 25.05% | 0.00% | 3.93% | 12.32% | 18.02% | 0.84% | 21.18% | 10.32% | 11.45% | 0.802 |
87 | 18.24% | 25.49% | 0.00% | 4.07% | 12.70% | 17.55% | 0.77% | 21.19% | 10.33% | 11.56% | 0.796 |
88 | 17.73% | 25.96% | 0.00% | 4.25% | 13.10% | 17.09% | 0.69% | 21.18% | 10.35% | 11.69% | 0.789 |
89 | 17.10% | 26.45% | 0.00% | 4.51% | 13.51% | 16.66% | 0.62% | 21.15% | 10.36% | 11.81% | 0.781 |
90 | 16.39% | 26.98% | 0.00% | 4.80% | 13.97% | 16.23% | 0.54% | 21.10% | 10.37% | 11.94% | 0.773 |
91 | 15.53% | 27.55% | 0.00% | 5.10% | 14.46% | 15.84% | 0.47% | 21.04% | 10.38% | 12.08% | 0.765 |
92 | 14.50% | 28.23% | 0.00% | 5.42% | 14.99% | 15.47% | 0.41% | 20.98% | 10.39% | 12.22% | 0.757 |
93 | 13.45% | 28.91% | 0.00% | 5.78% | 15.50% | 15.10% | 0.35% | 20.91% | 10.39% | 12.36% | 0.749 |
94 | 12.46% | 29.60% | 0.00% | 6.15% | 16.01% | 14.76% | 0.28% | 20.74% | 10.40% | 12.51% | 0.741 |
95 | 11.49% | 30.22% | 0.00% | 6.51% | 16.57% | 14.45% | 0.23% | 20.54% | 10.41% | 12.66% | 0.733 |
96 | 10.53% | 30.73% | 0.00% | 6.85% | 17.20% | 14.17% | 0.18% | 20.32% | 10.41% | 12.80% | 0.725 |
97 | 9.60% | 31.09% | 0.00% | 7.25% | 17.85% | 13.93% | 0.14% | 20.14% | 10.41% | 12.93% | 0.718 |
98 | 8.66% | 31.32% | 0.00% | 7.62% | 18.80% | 13.62% | 0.09% | 19.89% | 10.40% | 13.09% | 0.708 |
99 | 7.75% | 31.42% | 0.00% | 7.99% | 19.89% | 13.53% | 0.05% | 19.37% | 10.39% | 13.24% | 0.699 |
100 | 6.50% | 32.00% | 0.00% | 8.50% | 20.50% | 13.50% | 0.00% | 19.00% | 10.38% | 13.37% | 0.692 |
*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 (1.13% annualized). |