3. (15 points) You have recently been hired by a wealth management firm and are in charge of designing optimal portfolios for several high-net worth clients. The firm had chosen three ETFs that invest in Domestic Equity (asset A), Foreign Equity (asset B) and Long-Term Bonds (asset C) as well as a Money Market Mutual Fund which will serve as the risk-free asset. For these asset classes the research department has provided you with the following assumptions.

Also the Money Market Mutual Fund expected return is 0.5% (your risk free-rate)

And you get the tangency portfolio arrangement (portfolio weights and standard deviation):

Suppose one of your clients is interested in investing $200 million in a portfolio with an expected return of 12%. What investment would you recommend in each of the asset classes? Give a specific recommendation about what amount your client should invest in the Money Market Mutual Fund, Domestic equities, Foreign equities and Long-Term bonds. What is the standard deviation of the portfolio that you recommend?

Asset Class Correlation with Expected Returns Standard Deviation Domestic Equity Foreign Equity Long-Term Bonds 9.3 % 18.5 % 10.77% 20.4 % 0.77 Domestic Equity (A) Foreign Equity (B) Long-Term Bonds (C) 5.2 % 6.8 % 0.37 Tangency: W(A) -0.05 w(B) 0.20 0.85 1.00 0.0051 w(C) Sum Portfolio Variance Portfolio Standard Deviation Portfolio Expected Return Sharpe Ratio (Target) 7.14% 6.11% 0.79 Asset Class Correlation with Expected Returns Standard Deviation Domestic Equity Foreign Equity Long-Term Bonds 9.3 % 18.5 % 10.77% 20.4 % 0.77 Domestic Equity (A) Foreign Equity (B) Long-Term Bonds (C) 5.2 % 6.8 % 0.37 Tangency: W(A) -0.05 w(B) 0.20 0.85 1.00 0.0051 w(C) Sum Portfolio Variance Portfolio Standard Deviation Portfolio Expected Return Sharpe Ratio (Target) 7.14% 6.11% 0.79