Q$1.)$ Suppose ONEX Corp. issued a zero$-$coupon bond that will mature exactly one year from today.

The bond will pay $$1000$ in a weak economy, and $$1100$ in a strong economy. The bond is AA

rated $($meaning it$$s not risk free, but fairly safe.$)$ The appropriate risk premium for AA rated

bonds is $3\mathrm{.}0\%($effective annual rate$).$ The current riskless rate is $5\mathrm{.}0\%($EAR$).$ The probabilities

of a weak or strong economy are equal.

What is the current fair market value of the bond?

a$)$ What are the payoffs of a portfolio of one share of security A and one share of security B$?$

b$)$ What is the market price of this portfolio? What is the risk$-$free rate?

c$)$ What is the no$-$arbitrage price of security C $?$

$($Hint: replicate the payoffs using security A $\backslash$& security B$)$

d$)$ What is the expected return of security C if both states are equally likely? What is its risk premium?