Question

Today you buy 1 share of ABC Inc. at $100 per share. A year from now ABC will pay a dividend of $3 per share for sure. The price of ABC a year from now is uncertain and depends on the state of the economy. A year from now the economy will either be in a recession, a state of “normal" growth, or a boom with probabilities of 30%, 40%, and 30% respectively. After analyzing ABC you determine that the price of ABC a year from now in these various states of the economy will be:

State of the Economy Price of ABC

Recession $80

Normal Growth $110

Boom $130

What is the expected return (percent) over the next year from your investment in ABC? Return includes the dividend. What is the standard deviation of that return?

Answer 1

The answer is given below.

We use the normal formulae to calculate the Expected Value (10%) and the Standard Deviation (1.95%).

Given's Price of ABC share - $100 Dividend = $3 = State of Economy Price of ABC Recession o $80 Normal Growth for $110 Boom $130 Probabilite 0.3 or 30% 0.4 or 40% 0.3 or 30% en Aus) State of Fommy Recession Normal Boom Price of ABC 80 110 130 Dividends Returns 3 -17 3 13 3 0133 % Reburons Bobability 0.17« 17% 0.30 0.13 0.13% 0.4 0.33 or 33% 0.3 Expected Value of % Returns & = { / Returns) (Probability) - = -17%Xo3 + 13%x0.4 331.40.3 TEC%), 104 191 = aanw les 6 Standard Deviation of % Refuny = Variance of - wer % Returns Var (% Rebume) = ECKER - ECAR) - E (1%83) - Ê (%RS2 E(%R²) = { %R) ² (Bobability) 52 (170)x D:3 + (13%) x 0.4 + (33%8x 0.3 = 2.89% x 0.3 +1.69% 0.4 +10.89%x03 - EllbR3) = 4,81%

Var (% Returns) = 4.81% Var (% Returns) = 4.81% - 40% ² 1% Var (% Returns) = 3.81% i Sto. Der (%R) - War (%R) 3:81% 3.81 100 10 13.81 Xtoo % 10 Std. Der (% Retun) = 1.95 %