Suppose that we have identified three important systematic risk factors given by exports,inflation,and industrial production.In the beginning of the year,growth in these three factors is estimated at -1%,2.5%,and 3.5% respectively.However,actual growth in these factors turns out to be 1%,-2%,and 2%.The factor betas are given by β_EX = 1.8,β_I = 0.7,and β_IP = 1.0. Calculate the stock's total return if the company announces that they had an industrial accident and the operating facilities will close down for some time thus resulting in a loss by the company of 7% in return.Assume expected return on the stock is 6%. A) -4.05% B) -2.05% C) 4.55% D) 0.40% E) 1.85%

Question

Quizplus · Accepted Answer

Firstly, we need to calculate the expected return from the three systematic risk factors using the given formula:
E(Ri) = Ri0 + βi1U1B1E(U1) + βi2U2B1E(U2) + βi3U3B1E(U3)

where,
Ri = expected return of the stock
Ri0 = expected return with zero systematic risk
βi1U1B1 = Beta for the first systematic factor (exports)
βi2U2B1 = Beta for the second systematic factor (inflation)
βi3U3B1 = Beta for the third systematic factor (industrial production)
E(U1) = expected return for the first systematic factor
E(U2) = expected return for the second systematic factor
E(U3) = expected return for the third systematic factor

Substituting the values we get:
E(Ri) = 0.06 + (1.8 x (-0.01)) + (0.7 x 0.025) + (1.0 x 0.035) = 0.0605 or 6.05%

Now, let's calculate the actual return with the given information:
Actual return = Expected return + Unexpected return
Unexpected return = Loss by the company due to the industrial accident = -7%
Actual return = 6.05% - 7% = -0.95%

Therefore, the stock's total return is -0.95%, which is option B.

Suppose That We Have Identified Three Important Systematic Risk Factors