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Problem 1 You are given the following information about stock X and the market port - folio, M : E ( r ) sigma

Problem 1 You are given the following information about stock X and the market port-
folio, M :
E(r)\sigma
Riskless Asset (f )0.03(3%)0.00
Stock X 0.10.60
Market Portfolio (M )?0.30
The market portfolio includes all stocks in the economy (including X). You are not given the
expected return of the market portfolio. The correlation between the returns on the stock X and the
market portfolio is equal to 0.5. Assume that CAPM holds.
a) What is the expected return on the market portfolio M ?
b) Construct a portfolio with \beta =1.5 that is efficient.1 What is the standard deviation
and expected return of this portfolio?
c) Consider a portfolio that has correlation of 0.6 with the market portfolio. What
is the idiosyncratic risk of this portfolio if its standard deviation is 50%? Use the
standard deviation of the non-systematic component of returns as the measure of
idiosyncratic risk.
d) You have $1000 to invest in a combination of the risk-free asset, stock X, and the
market portfolio. You are thinking about investing $300 in the riskless asset, $400
in stock X, and $300 in the market portfolio. What are the overall expected return,
standard deviation, and beta of this portfolio?
e) You seem to dislike the portfolio obtained in (d). You understand that you can
tolerate the overall risk of your portfolio up to \sigma P =30%. Thus, you are willing
to invest your $1000 in any combination of the risk-free asset, the stock X, and
the market portfolio that gives you the highest expected return, given a standard
deviation of 30%. How much money do you invest in each of the three securities,
and what expected return and beta does your portfolio have?
1To construct (or to find) a portfolio, its sufficient to describe its weights on all assets that are used to
build this portfolio.

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