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Assume that the market risk-free interest rate is 12.00%. Assume that a zero-coupon risk free bond,...

Assume that the market risk-free interest rate is 12.00%. Assume that a zero-coupon risk free bond, with maturity 2 years and 100 face value, is trading at 75. Which of the following is true?

(a) By lending today for two years at the market rate, and short-selling the bond, you have an arbitrage.

(b) By borrowing today for two years at the market rate, and buying the bond, you have an arbitrage.

(c) By buying the bond today and investing the proceeds forward after two years, you have an arbitrage.

(d) There is no arbitrage opportunity.

(e) I choose not to answer.

I would love an explanation to this. As I know the correct answer, but does not understand. :)

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Answer #1

b)By borrowing today for two years at the market rate which is 12% and buying the bond you have an arbitrage. Because the bond has yield to maturity at the rate 15.47 % which is higher than the market interest rate. So it is profitable to borrow fund at market rate ,b the bond and there will be an arbitrage

Bonds yield to maturity = ((F/PV)(1/n))-1

=((100/75)0.5)-1 =15.47%

F=face value=100

PV=present value=75

n=number of years to maturity

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