Question

Grubb, an analyst at the Oracle Consulting has forecasted next years returns for IBM stock and the overall market under the following three plansible scenarios.

State of the world Probability Return On IBM Return on Market Portfolio

Long drawn war 0.1 -20% -6%

Short War 0.7 10% 12%

No war 0.2 30% 16%

a) compute expected return, and the standard deviation the IBM stock and the market portfolio

b) If the esstimated beta for the IBM is 1.2 and the risk-free rate is 4%, what is the required rate of return using CAPM model?

c) In view of your answers to a and b above what is the indicated investment strategry. Give arguments supported by your analysis

Answer 1

a) Expected Return of IBM Stock = (0.1*20)+(0.7*10)+(0.2*30) = 15%

Expected Return of Market = (0.1*6)+(0.7*12)+(0.2*16) = 12.2%

Standard deviation of IBM Stock = Square root of P*(R-)² = square root of (20-15)²*0.1+(10-15)²*0.7+(30-15)²*0.3 = square root of 65 = 8.0623 %

Standard deviation of market = Square root of P*(R-)² = square root of (6-12.2)²*0.1+(12-12.2)²*0.7+(16-12.2)²*0.3 = square root of 6.76 = 2.60 %

b) Using CAPM, Required rate = R_f + Beta (R_m - R_f)

Required rate = 4 + 1.2* (12.2 - 4) = 13.84%

c) From a and b above, we see that the IBM stock gives us a return of 15% with the risk of 8.0623% while the market gives us 12.2% return with a risk of 2.6% . The required rate of return is 13.84% i.e. the IBM stock provides the investor with return more than his expectation which is good.