1. Assume that the risk-free interest rate is 2.50 percent per year and the yearly expected returns for Large-Cap stocks (SPY), Small-Cap stocks (IWM), non-US stocks (EAFE), and Gold are

E( R!Larg eCap)=8.00% E( R!SmallCap)=10.10% E(R!EAFE)=7.50% E(R!IAU)=-1.00%

with annual standard deviations for returns on the respective asset classes of

LargeCap=17.5%SmallCap=21.2%

EAFE=19.5%IAU=14.2%

and with estimated correlation matrix for the returns for these four asset classes given by

Correlation Matrix for S&P 500, Ishares Russell 2000,

EAF, and Gold

SPY IWM IEF IAU

1.000 -0.050

1.000

SPY

1.000 0.770 0.670 -0.070

IWM

1.000

0.600 -0.110

IEF IAU

1. determine the expected return and standard deviation for an equally weighted portfolio of the four assets classes summarized above,
2. determine the portfolio weights for the unconstrained portfolio (negative portfolio weights/short positions allowed) having the maximum Sharpe Ratio (see the note below),
3. determine the expected return for the portfolio with the maximum possible Sharpe Ratio,
4. determine the standard deviation for the portfolio with maximum possible Sharpe Ratio
5. determine the portfolio weights along with the expected portfolio return and standard deviation for the minimum variance portfolio.