Question $2$

Horse PLC and Llama PLC are two companies whose shares are quoted on the Irish Stock Exchange. An analysis of these potential investments reveals the following information:

Expected return

E$($R$)$

Standard deviation of returns $(\backslash$sigma R$)$

Correlation with market returns $($rJ$,$M$)$

$0\mathrm{.}450\mathrm{.}81$

Horse PLC $9\mathrm{.}5\%11\%$

Llama PLC $10\mathrm{.}7\%$

$7\%$

The following additional information is also available:

$$The correlation between the returns on the two shares is $+0\mathrm{.}3.$

$$The risk$-$free rate of interest $($rF$)$ is $4\%.$

$$The expected return on the market portfolio E$($rM$)$ is $14\%.$

$$The standard deviation of the returns on the market portfolio $(\backslash$sigma M$)$ is $9\%.$

Required:

$($a$)$ An undiversified, rational, and risk$-$averse investor wishes to invest in the shares of one of the above companies. Explain $($with detailed reasons$)$ which company$$s shares should be preferred.

$(5$ marks$)$

$($b$)$ Calculate the beta of each of the two shares. Then, using the Capital Asset Pricing Model $($CAPM$),$ present calculations to:

$$ Show that the shares of Horse PLC are properly priced at their current valuation;

$$ Show that the shares of Llama PLC are not properly priced at their current valuation;

$$ Indicate the change which you would expect in the share price of Llama PLC$,$ assuming that

Llama$$s current share price is $5$ per share and its annual dividend is $0\mathrm{.}535$ per share.

$(12$ marks$)$

$($c$)$ An investor with $100,000$ to invest decides to form a two$-$security portfolio consisting of $40,000$ invested in shares of Horse PLC and $60,000$ invested in shares of Llama PLC$.$ Calculate the expected return and the standard deviation risk of this portfolio.

$(10$ marks$)($d$)$ Suppose instead the investor intends to invest the total fund of $100,000$ in a portfolio comprised of these two companies$$ shares, but wishes to minimise the portfolio$$s standard deviation. Determine

how much money should be invested in each company$$s shares in order to achieve this objective.

$(10$ marks$)$

$($e$)$ Assume that Horse PLC$$s shareholders are efficiently diversified, and assume also that the CAPM fully describes the market valuation process. In these circumstances:

$$ Discuss the relevance of the $$standard deviation of returns$$ as a measure of risk for the shareholders in Horse PLC$.$

$$ Explain how the senior managers in Horse PLC should evaluate capital investment proposals if their objective is to maximise shareholder wealth, and critically evaluate whether $($in practice$)$ senior managers are likely to adopt the approach which you recommend.