Question

Mickey is the manager of a portfolio of equities as shown below.
Stock
Investment
Beta
A
$300,000
2.0
B
$300,000
1.2
C
$400,000
0.6
The risk free rate is 3% and the market risk premium is 7%.
Mickey’s best friend, Donald, calls him and asks him to help evaluate the bonds of Goofy Limited as there may be a window of opportunity for arbitrage. The bonds have face value of $1,000 and pay 5% annual coupons. The bonds mature in 3 years with redemption at par. The yield to maturity is 15%.
(a) Compute the beta and expected return of the portfolio.

(b) Propose one (1) possible method that Mickey can rebalance his portfolio if he expects the stock markets to rise in the next 6 months.

(c) Infer one (1) possible reason for Goofy Limited’s bonds to trade at yield to maturity of 15%.

Answer 1

Stock	Investment	as % of investment(W)	Beta
A	$300,000	30%	2
B	$300,000	30%	1.2
C	$400,000	40%	0.6
Total Value	$1,000,000	100%

a)

Portfolio Beta = W_A x β_A + W_B x β_B + W_C x β_C

Portfolio Beta = 0.3 x 2 + 0.3 x 1.2+ 0.4 x 0.6

Portfolio Beta = 0.6 + 0.36 + 0.24 => 1.2

Risk free rate = 3% , Market risk premium = 7%

Using CAPM

expected return = risk free rate + Beta x market risk premium

Expected return = 3% + 1.2 x 7% => 3% + 8.4% = 11.4%

b)

If mickey is expecting rise in the market in next 6 months, then he should rebalance his portfolio in such a manner so that his portfolio beta rises from current level of 1.2, since there is a direct relationship of portfolio beta with market return, higher the beta of portfolio, higher will be the return. One such way is to increase the investment in Stock A from current 300,000 to 400,000 which will increase the beta of portfolio from 1.2 to (0.4 x 2 + 0.3 x 1.2 + 0.3 x 0.6) = 1.34, and its return will increase from 11.4% to 12.38% immediately and if stock rises in future then by this market proportion.

c)

Bonds FV = 1000, N = 3, coupon = 1000*5% = 50, Rate(I) = 15% using financial calculator, we determine price(pv) = 771.68

So we can see the relationship between Price of bonds and yield of bond, there is inverse relationship between YTM vs Price, if Price of the bond goes down from its face value its YTM increases or Price goes up, its YTM goes down, So it can be the reason of trading at 15% YTM that Goofy sold its bonds at higher discount, so that to increase the YTM on its bonds.