Topic $11$ Risk vs Reward

Exercise $1$: Rewards

An investor thinks that the share price of company ABC is going to increase in the

next few days. The current market price of ABC is $$60$ per share. The investor has

$$15,000$ of cash which he can use to invest in the stock. The investor also has the

possibility of borrowing an additional $$5,000$ from a broker to purchase the stock

on margin. If the share price of ABC increases to $$70$:

a$)$ What would be the profit or loss of the investor if he$/$she invests all his$/$her

cash in ABC?

b$)$ What would be the profit or loss of the investor if$,$ apart from the cash, he$/$she

also invests the borrowed $$5,000?$

c$)$ Compare your results between $($a$)$ and $($b$).$

d$)$ What are the assumptions that you took into account when arriving at results

$($a$)$ and $($b$)?$

e$)$ How would your results in $($a$),($b$)$ and $($c$)$ change if the share price of ABC

went down to $$50?$

Exercise $2$: Risk and Reward

Suppose we have the following scenarios.

Bear market Normal market Bull market

Probability $0\mathrm{.}30\mathrm{.}40\mathrm{.}3$

Stock X $-20\%12\%25\%$

Stock Y $-10\%5\%15\%$

Based on the scenario analysis described above:

a$)$ What are the expected rates of return for Stocks X and Y$?$

b$)$ What are the standard deviations of returns on Stocks X and Y$?$

c$)$ Based on the results obtained in $($a$)$ and $($b$),$ which stock is the riskiest?

d$)$ Assume that you hold a portfolio of $$20,000$ and that you invest $$12,000$ in

stock X and $$8,000$ in stock Y$.$ What would be the expected return on your

portfolio?

Exercise $3$: Expected Return of a portfolio

Consider a risky portfolio. The end$-$of$-$year cash flow derived from the portfolio will

be either $$80,000$ or $$200,000$ with equal probabilities of $0\mathrm{.}5$ each. The alternative

risk$-$free investment in Treasury Bills $($Government bonds$)$ earns $5\%$ per annum.

a$)$ If the investor requires a risk premium of $8\%,$ how much will he be willing to

pay for the portfolio?

b$)$ Suppose that the investor is able to purchase the portfolio for the amount

found in $($a$),$ what will be the rate of return on the portfolio?

c$)$ Now suppose that the risk premium required amounts to $11\%,$ what will be

the price that the investor is willing to pay for the portfolio?