The EAFE is the international index comprising markets in Europe, Australia, and the Far East. Consider the following annualized stock return data: Average U. S. index return: 14% Average EAFE index return: 13% Volatility of the U. S. return: 15.5% Volatility of the EAFE return: 16.5% Correlation of U. S return and EAFE return: 0.45 (i) What would be the return and risk of a portfolio invested half in the EAFE and half in the U. S. market? Show your solution procedure in detail. (ii) Compare volatility of portfolio and the volatility of the U. S. return as well as the volatility of the EAFE return.

a) i) 13.5% ii) risk on portfolio = 13.63%

b) Volatility of the portfolio (13.65%) is < Volatilities of the individual indexes

Explanation:

A) Determine the return and risk of the portfolio

i) Return [ E(r^p) ]  = ∑ wi*ri ---- (  1 )

where : wi = weight of stocks ,  ri = rate of return ( estimated ) N = number of stocks

Back to equation 1

E(r^p)  =  (0.5*14% ) +  (0.5*13% ) = 13.5%

ii) risk of portfolio

we can determine the risk of portfolio using the equation below

Vol [ r( t + 1 , $ ) + s ( t + 1 ) ]   ( volatility on Japanese equity ) = 13.63%

attached below is the remaining solution

b) comparing the Volatilities

Volatility of the portfolio (13.65%) is < Volatilities of the individual indexes ( i.e. volatility of US return ( 15.5% ) , Volatility of EAFE return ( 16.5% ) )

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