Question

(1) A: The stocks of Apple and Amazon have the following expected returns: State of Economy Probability of State of Economy Apple's Return if State Occurs Amazon's Return if State Occurs Recession 55% -9% -12% Normal 30% 8% 11% Boom 15% 17% 14% Which company's stock is riskier, based on standard deviation?  

B: If you have 120 shares of Apple's common stock ($171.05 per share) and 90 shares of Amazon's common stock ($1162.35 per share) in your portfolio, what is the expected return on your portfolio?

(2) Stock Y has a beta of 1.30 and an expected return of 15.3%. Stock Z has a beta of 0.70 and an expected return of 9.3%. If the risk-free rate is 5.5% and the market risk premium is 6.8%, are these stocks correctly priced?

(3) You have one million USD and want to create a portfolio equally as risky as the market. Given this information, fill in the rest of the following table: Asset Investment Beta Stock A $195,000 beta 0.90 Stock B $340,000 beta 1.15 Stock C ? 1.29 Risk-free asset ?

(4) Suppose you observe the following situation: Security Beta Expected Return Pete Corp. 1.15 12.90% Repete Co. 0.84 10.20% Assume the two securities are correctly priced. Based on CAPM, what is the expected return on the market? What is the risk-free rate?  

(5) Explain the CAPM. [hint: we need to discuss systematic and unsystematic risks, diversification, assumptions CAPM makes, SML line, the model, things CAPM can't explain, etc. ]

Answer 1

1

A) The information gives is as under :

State of Economy	Probability of State of Economy	Apple's Return if State Occurs	Amazon's Return if State Occurs
Recession	55%	-9%	-12%
Normal	30%	8%	11%
Boom	15%	17%	14%

. The information given in this case is various probabilistic scenarios and their corresponding returns .

In such a case , we apply the following formulas for Expected return and Expected Standard Deviation

  

where pi represents the individual probabilities in different scenarios

Ri represents the corresponding returns in different scenarios and

represents the expected return calculated as above.

Therefore , Expected Return of Apple = 0.55*(-9%)+ 0.3*8%+ 0.15*17%= 0.00%

Similarly, Expected Return of Amazon = 0.55*(-12%) +0.3* 11%+ 0.15*14% = -1.20%

and Expected Standard Deviation of Apple = sqrt [ 0.55* (-0.09-0)2 + 0.3* (0.08-0)2 + 0.15* (0.17-0)2 ]

= sqrt (0.004455+0.001920+0.004335 )

= sqrt (0.010710) = 0.103489 or 10.35%

Expected Standard Deviation of Amazon = sqrt [ 0.55* (-0.12+0.012)2 +0.30* (0.11+0.012)2 + 0.15* (0.14+0.012)2 ]

=sqrt (0.014346) = 0.119775 or 11.98%

Amazon's stock is more riskier as its standard deviation is higher

B.

Total amount invested in Apple = 120 shares * $171.05/share = $20526

Total amount invested in Amazon = 90 shares * $1162.35/share = $104611.50

% invested in Apple = 20526/(20526+104611.50) = 0.16403

% invested in Amazon = 104611.5/(20526+104611.50) = 0.83597

As return of a portfolio is the weighted average return

Return of the portfolio = 0.16403* 0%+ 0.83597 * (-1.20%) = -0.01 or -1%

The expected return of the portfolio is -1%