Question

Please answer the following 2 questions using the probabilities of different scenarios below.

Return of stocks	Boom (Prob. = 1/3)	Normal Economy (Prob. = 1/2)	Recession (Prob. = 1/6)
S&P 500 portfolio	25%	10%	-5%
Bond	3%	6%	8%

• What is the expected return and standard deviation of the S&P 500 portfolio and the Bond?

• Suppose AAPL has a beta of 0.8. If the risk-free rate is 3% and the market return is 9%, according to CAPM, the expected return for AAPL is? If the stock price for AAPL is $100 today, according to the expected return you calculate, what is the expected price for AAPL in a year if AAPL is not paying a dividend? What is the expected price if AAPL will pay a dividend of $3?

Answer 1

CAPM: CAPITAL ASSET PRICING MODEL

The CAPM describes the relationship between the expected return and risk of investing in an asset. i.e, it is used to calculate the expected returns of an asset. The factors required for assessing the expexcted rate of retun on an asset includes risk free rate of return, beta of the secuity and expected retun of the market at large.

Risk free rate of return: is the yield rate of government bonds.

Beta of the security: is the measure of the volatility of the secuity in the market. The fluctuations in the price in relation to the overall market.

Expected retun of the market : is the addtional expceted margin over and above the risk free rate of return. i.e the rate of government bonds.

Formula of CAPM: Ra = Rrf + [Ba x (Rm – Rrf) ] where, it denotes the following

Ra = Expected return on a security

Rrf = Risk-free rate

Ba = Beta of the security

Rm = Expected return of the market

Applying the above forumla in the given question we get,

Ra = ??, Rrf = 3% , Ba = 0.8, Rm = 9%

Ra = 3% + [0.8 x (9% – 3%) ]

Ra = 3% + 4.8%

Ra = 7.8%

So,According to CAPM, the expected return for AAPL is 7.8%.

Answer to second Part of the question,which is on expected price of equity.

The Excpected price of equity cas be acertained throught two models or methods depending upon the scenario of the Dividend. If No dividend is paid then the above CAPM model is apt and provides the result. But if the Company pays dividend then, Dividend capitalisation model shall be used.

So, if no Dividend is paid, the answe is same as above of CAPM model.

Now, if dividend is paid, Dividend capitalisation model shall be used. The formula for the same is

Re = (D1 / P0) + g

Where:

Re = Cost of Equity

D1 = Dividends/share next year

P0 = Current share price

g = Dividend growth rate***

***Dividend Growth = (Dt/Dt-1) – 1

Where:

Dt = Dividend payment of year t  

Dt-1 = Dividend payment of year t-1 (one year before year t)

Appying the above forumla in the questiion we get,

Re = (D1 / P0) + g

Re= ( 3 / 100) + [ ( 3 ) - 1 ]

Re = 0.03 + 2

Re = 2.03 %