Question

Q5.23. (Strange) Stock A always alternated between +20% and
–10% in the past. Stock B earned 4.5% per annum.

1. What was the average rate of return for stock A?
2. What was the average rate of return for stock B?
3. On a 1-year basis, would a risk-neutral investor prefer +20% or –10% with equal probability, or 4.5% for sure?
4. How much would each dollar invested 10 years ago in stock A have earned?
5. How much would each dollar invested 10 years ago in stock B have earned?
6. What is going on here?

Answer 1

1. Average return of stock A=(20-10)/2=5%

2.Average Return of Stock B=4.5%

3.Risk Neutral Investors do not considered the risk involved in the decision. They are interested in returns and invest where there is possibility of higher return

Hence Risk Neutral investor will prefere investment in Stock A where there is possibility of higher return

4.Expected Return of stock A=0.5*20%+0.5*(-10%)=5%

Future Value (FV)=Present Value (PV)*((1+r)^N)

r=Return

rate =5%=0.05

N=Number of years=10

PV=$1

FV=1*(1+0.05)^10=$1.63

Amount Earned for $ 1 investment in 10 Years=(1.63-1)=$0.63

5.Future Value (FV)=Present Value (PV)*((1+r)^N)

r=Return rate =4.5%=0.045

N=Number of years=10

PV=$1

FV=1*(1+0.045)^10=$1.53

Amount Earned for $ 1 investment in 10 Years=(1.53-1)=$0.53