Question

You own stock with an overall expected return of 18.32 percent. The economy is expected to either boom or be normal. There's a 65 percent chance the economy will boom. If the economy booms, the stock is expected to return 23 percent. What's the expected return on the stock if the economy is normal?

A. 8.51%

B. 9.63%

C. 11.84%

D. 10.25%

Please show work.

Answer 1

Solution:

As per the information given in the question we have

A stock has an overall expected return of 18.32 %

Chance / Probability that the economy will boom : 65 % = 0.65

Expected Return on the stock if the economy booms = 23 %

Chance / Probability that the economy will be normal : ( 100 % - 65 % ) = 35 % = 0.35

Expected Return on the stock if the economy is normal = To find

The overall expected return can be calculated using the formula

Overall Expected Return = ( P₁ * R₁ ) + ( P₂ * R₂ )

Where

P₁ = Chance the economy will boom ; R₁ : Expected Return on the stock if the economy Booms

P₂ = Chance the economy will be normal    ; R₂ : Expected Return on the stock if the economy is normal

As per the information given in the question we have:

Overall expected return = 18.32 %    ;   P₁ = 0.65 ; R₁ = 23 %   ; P₂ = 0.35    ; R₂ = To find

Applying the above values in the formula we have

18.32 = ( 0.65 * 23 ) + ( 0.35 * R₂ )

18.32 = 14.95 + ( 0.35 * R₂ )

18.32 – 14.95 = ( 0.35 * R₂ )

3.37 = ( 0.35 * R₂ )

R₂ = 3.37 / 0.35

= 9.63 %

Thus the expected return on the stock if the economy is normal is 9.63 %

The solution is Option B. 9.63 %