Question

Prices of zero-coupon, default-free securities with face values of $1,000 are summarized in the following table: Maturity (years) Price (per $1,000 face value) $971.52 $939.15 $904.51 Suppose you observe that a three-year, default-free security with an annual coupon rate of 10% and a face value of $1,000 has a price today of $1,182.85. Is there an arbitrage opportunity? If so, show specifically how you would take advantage of this opportunity. If not, why not?

Answer 1

YTM of the 3-year zero coupon bond= 3.401985% as follows:

E11 f =E10-1 A B C D Ε F 1 YTM of Zero coupon bond= ((F/P)^(1/n)-1 2 Where F= Face Value (Par Value) P= Price and n=term to maturity number of years 3 4 Bond 1 Bond 2 Bond 3 5 Face Value (F) $ 1,000.00 $ 1,000.00 $ 1,000.00 6 Price (P) $ 971.52 $ 939.15 $ 904.51 7 Term to maturity (n) 1 2 3 8 F/P= 1.02931489 1.0647926 1.105571 9 1/n= 0.5 0.3333333 10 (F/P)^(1/n)= 1.02931489 1.03188790 1.03401985 11 YTM= ((F/P)^(1/n)-1= 2.931489% 3.188790% 3.401985%| 17

YTM of 3-year coupon bond with similar risk profile of the above zero coupon bond is 3.4764% calculated using the RATE function of Excel as follows:

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