CFA Practice Question

CFA Practice Question

A 3-year bond with an annual coupon of 6% is selling at 100.55%. The treasury spot yield curve is given below.

Spot rate: Year 1 - 5.9%; Year 2 - 5.85%; Year 3 - 5.83%

What is the arbitrage-free value of the bond? If there is an arbitrage opportunity, how can it be exploited?
A. 100.55. There is no arbitrage opportunity.
B. 100.45. Buy the coupon and principal strips for 100.45 and sell them as a reconstituted bond for 100.55.
C. 100.60. Buy the bond for 100.55 and sell the coupon and principal strips for 100.60.
Explanation: The arbitrage-free value of the bond can be estimated by discounting each cash flow at its corresponding spot rate.

V0 = 6/(1.059) + 6 /(1.0585)2 + 106/(1.0583)3 = 100.45

Since the bond is selling for 100.55, there is an arbitrage opportunity. A trader can buy the strips of coupon and principal for 100.45 and sell them as a reconstituted bond for 100.55 for an immediate gain of 0.10 (= 100.55 - 100.45).

User Contributed Comments 5

User Comment
Dinosaur what does the spot rate mean?
twotwo Spot rate/Zero-coupon interest rate - The interest rate that would be earned on a zero-coupon bond
shiva5555 I bet the devil invests in bonds.
will080912 I answer B but, I think the bond is overvalued now and doesn´t make sense to buy it. If in the market it is selling at 100.55 why would someone buy it at a lower price?
I don't see the adbitrage advantage. If the the would be for example 100.35 I will buy it because I will expect the bond to raise and that I think would be an adbitrage advantage.
will080912 I mean why somebody would sell it at a lower price*
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