Question

1. What is the standard deviation of the returns on the Fly-by-Night Airlines stock and Feet-on-the Ground Bus Company, with the same return outcomes and probabilities described above? Of these two stocks, which is riskier?

• Suppose that Fly-by-Night stock has a return of 15% half of the time and 5% the other half of the time, making its expected return 10%, while stock in Feet-on-the-Ground has a fixed return of 10%.

• Fly-by-Night stock has uncertainty associated with its returns and so has greater risk than stock in Feet-on-the- Ground, whose return is a sure thing.

Answer 1

P1 = probability of occurrence of return 1 = 0.5

P2 = probability of occurrence of return 2 = 0.5

R1= Return in state 1 = 15%

R2= Return in state 2 = 5%

Expected return (Re) = 10%

Standard deviation of Fly by night stock:

σ = ( P1 (R1 - Re)² + P2 (R2 - Re)² ) ^1/2

= ( 0.5 (0.15 - 0.1)² + 0.5 (0.05 -0.1)² ) ^1/2

= 0.05 or 5%

Standard deviation of Feet on the ground:

P1 = probability of occurrence of return 1 = 1

R1= Return in state 1 = 10%

σ = ( P1 (R1 - Re)² ) ^1/2

= ( 1 (0.1 - 0.1)² ) ^1/2

=0

Fly-by-Night stock standard deviation = 5%

Feet-on-the Ground Bus Company standard deviation = 0%