you are given four ETFs with their expected return, volatility and correlation as follows. Find out the weight to each ETF to achieve (1) Minimum Variance Portfolio and (2) Optimal Risky Portfolio (i.e. Portfolio to maximize Sharpe Ratio

Expected return and volatility

Exchange Traded Fund Name Ticker Expected Return (Annualized) Expected Volatility (Annualized)

Domestic Equity ETF HOME 8.5% 18%

Emerging Markets Equity ETF GROW 13.0% 30%

Domestic Debt ETF BOND 4.5% 8%

Global Commodities ETF MINE 6.0% 16%

Money Market ETF MMKT 2.0% 1%

Correlation Matrix

HOME GROW BOND MINE

HOME 1.00 0.70 0.40 0.10

GROW 0.70 1.00 0.28 0.07

BOND 0.40 0.28 1.00 0.04

MINE 0.10 0.07 0.04 1.00

Your Answer - % of each ETF

what is the Minimum Variance Portfolio of HOME? GROW? BOND ? MINE?

what is the Optimal Risky Portfolio of HOME? GROW? BOND ? MINE?