. A mutual fund newsletter advertises that“diversification is an important facto

Question

. A mutual fund newsletter advertises that“diversification is an important factor in long-terminvestment success. A well-diversified portfolio includesinvestments whose return rates have low correlations.” You review a table of correlations between return rates ofvarious classes of investments. You see that the correlationbetween municipal bonds and large-cap stocks is +.65. Youalso notice that the correlation between municipal bonds andsmall-cap stocks is +.15.

a. If my portfolio is already heavily invested inmunicipal bonds, and I wish to add an investment in accordance withthe diversification advice above, should I invest in large-cap orsmall-cap stocks? Explain why.

b. If I want to invest in something that will do wellwhen my municipal bonds are not doing well, in general, what kindof correlation would you suggest I look for?

c. What percent of the variation in large-cap stock returnrates can be accounted for by knowing the return rates formunicipal bonds?

Explanation / Answer

Var(X+Y) = Var(X)+Var(Y)+2correl(X,Y)*Var(X)*Var(Y)
since correlation of of small cap and municipal bonds islesser from diversification perspective it is advisable to addsmall cap stocks.
b)When municpal bonds don't do well then that something shoulddo well that means the correlation should be negative betweenmunicipal bonds and the new investment.
c) if we try to explain the rate of retuns of Large Caps(Y)using municipal bonds returns (X) by constructing a linearregression model Y =a+bX then % of variance of Y explained by X isR2 = Correl (X,Y)2 = 0.65*0.65 =42.25%
Hope it is useful. Feel free to ask for anyclarifications

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