Question

Your friend has a stock portfolio that they know nothing about (it was a gift).  They know that you have been taking a finance course at GCC and they assume that you are an expert when it comes to financial matters.  Your friend is thinking about selling one stock and they have asked for your opinion: If all things remain equal, which stock would you sell and which stock would you definitely keep.

There are four stocks in the portfolio:

       

You have recently read an article in the Globe and Mail denoting that the likelihood of a market expansion next year is 30%, while the likelihood of a market decline is only 10%.  You trust the journalist and you assume that the probability of a normal market would be the remaining 60%.  Based on this article and some research, you conclude the expected performance of each stock will be:

       

You also find the Beta for each stock: Charlie’s = 1.5; Shiloh = 1; Taiya = 0.7; Zoe = 0.5.  In addition, a GIC has a rate of 3% and the market risk premium is 10%.

Assume that the portfolio is properly diversified.  Also assume that you like your friend and you want to give them the best information possible.

Required:  To fully answer your friend’s question you will need to comment on:

1. What is the expected return of EACH stock and the portfolio?
2. What is the total risk for each stock – showing the values for both systematic and unsystematic risk and commenting on which risk can be eliminated?
3. Based on 1 & 2, which stock would you suggest should be sold and which stock should be kept – assume that any selection that you make will not affect the diversification of the portfolio.

Answer 1

Ans - Part (A):

Er Charlie = Rf + b(Rm - Rf)

Where Rf (GCC) = risk free rate

B = beta of the stock

Rm - Rf = market premium

Therefore by equation:

= 3 +1.5(10)

= 3+15

=18%

Er (shiloh) = Rf + b(Rm - Rf)

= 3+1 (10)

=13%

Er(Taiya) = Rf + b(Rm - Rf)

= 3 + 0.7(10)

10%

Er(Zoe) =  Rf + b(Rm - Rf)

= 3 +0.5(10)

= 8%

Part (B)

In this we assume the volatility is 10% of the market, so we can calculate risk of each stock i,e total risk

charlie = 1.5(10%)= 15%

shiloh = 1(10%) = 10%

taiya = 0.7(10%) = 7%

zoe = 0.5(10%) = 5%

The systematic risk is calculated by this equation

systematic risk = beta * standard deviation of market

as beta of market is always 1

= 1*10%

= 10%

so unsystematic risk of each stock

Total risk = systematic + unsystematic

or

unsystematic = Total risk - systematic

charlie = 15-10 = 5%

shiloh = 10-10= 0

taiya= 7- 10 = -3%

zoe = 5 - 10 = -5%

we cannot diversifies systematic risk as it is consist of market, we can only diversifies our unsystematic risk because it consist of particular company. we can diversifies this by selecting stocks having negative correlation or zero correlation.

Part (C) There are more chances of market being stable or expansion instead of decline, so we should buy stocks having higher beta than market because if market return say 10% and charlie beta has 1.5 i.e it would give 1.5x return (15%) and we should sell zoe as it gives lesser return than market.

In case of worst scenario we can do opposite even.