Question

Problem 1

Part 1

The expected return of Yahoo is 12% with standard deviation of 20% and the expected return

of Google is 15% with standard deviation of 25%. The correlation coefficient of Yahoo and Google

is -1. What should be the risk free rate if there is no arbitrage opportunity?

Part 2:

Suppose that 1 year zero rate is 1% and 2 year zero rate is 2%. Consider a risk free bond with

maturity of two years and a face value of $100 that has an annual coupon rate of 3%. Let Y denote

the yield to maturity for this bond. Write down an equation whose solution provides you the yield to

maturity for the bond (you do not need to solve the equation). All rates including the yield are

continuously compounded.

Answer 1

1.

standard deviation of protfolio=weight of google*standard deviation of google - weight of yahoo*standard deviation of yahoo

risk free rate has standard deviation of zero

=>0=weight of google*standard deviation of google-weight ofyahoo*standard deviation of yahoo

=>weight of google*25%=weight of yahoo*20%

=>weight of google*25%=(1-weight of google)*20%

therefor, weight of google=0.444

weight of yahoo=0.556

hence, riskfree rate=4/9*15%+5/9*12%=13.33%

2.

3%*1000/1.01+3%*1000/1.02^2+1000/1.02^2=3%*1000/(1+ytm)+3%*1000/(1+ytm)^2+1000/(1+ytm)^2