Question

Today you bought 100 shares of ABC Inc. at $100 per share. A year from now ABC will pay a dividend of $2 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? What is the standard deviation of that return?

Answer 1

Expected Return from ABC stock =Pr(State=Recession)*(Return in Recession)+Pr(State=Normal*(Return in Normal)+Pr(State=Boom)*(Return in Boom)

Return for a Stock =Capital Gain/Loss + Dividend Gain

Return in Recession = (80-100)/100+2/100=-18%

Return in Normal = (110-100)+2/100=12%

Return in Boom = (130-100+2)/100=32%

Expected Return= 0.3(-18%)+0.4(12%)+0.3(32%)=-5.4%+4.8%+9.6%=9%

Std. Dev(Return)= E(r^2)-(E(r))^2

E(Return^2)=Pr(State=Recession)*(Return in Recession)^2+Pr(State=Normal*(Return in Normal)^2+Pr(State=Boom)*(Return in Boom)^2=0.3(-18%)^2+0.4(12%)^2+0.3(32%)^2=-97.2+57.6+307.2=267.6

Std Dev(return)=Square root(267.6-81)=Sqrt(186.6)=13.67%