Question

An investor is bullish about metal prices and buys on margin shares of BHP Billiton Ltd. (BHP) currently trading at $78 per share. The initial margin requirement is 60%, and she has $4,450 to invest as initial margin. The expected return of the market is 10% and the volatility (std. deviation) of the market is 17%. The risk-free rate is 1% and BHP has a beta of 1.48. According to CAPM, what should be the expected return of the investor’s portfolio including the margin purchase? Enter your answer as a decimal (not as a percent).

Answer 1

Parameters provided in the question,

The current price of BHP Billiton Ltd = $78 per share.

The initial margin requirement is 60% and has $4,450.

The expected return of the market i.e E(Rm )= 10%

The risk-free rate, Rf =1%

Beta , = 1.48.

Now first calculating the expected return on the stock of BPH Billiton Ltd using CAPM(Capital Asset Pricing Model ),

Let the expected return be E(R)

E(R) = Risk free rate + Beta (Expected market return. - Risk free rate )

E(R) = Rf + ( E(RM)- Rf)

Substituting the values,

E(R) = 1 + 1.48( 10-1). = 1 + 1.48(9) = 1+13.32 = 14.32 %

Thus expected return without margin purchase is 14.32

Now, Considering the margin purchase. Buying stock on margin means buying stock with partially borrowed funds,

Now The initial investment is $ 4450(60% initial margin). However, an investor would be able to buy shares worth $ 7416.66(4450 / 0.6).

Since the market price is 78, the investor would be able to buy 95 (7416.66/78) shares.

Values of shares the investor is holding = 95 X 78 = $ 7410.

The appreciated value of holding = 7410 X ( 1+ E(R)) = 7410 (1.14) = $ 8447.4

Now, Expected return with margin purchase =((Appreciated holdings -Initial investment )/Initial investment )

Substituting the values,

Expected return with margin purchase = ((8447.4 - 4450 ) / 4450 ) = 0.8983

Thus Expected return with margin purchase = 0.8983