Question

A. What price should a 3 year semi-annual 10% coupon bond with $1000 face value be trading at if the prices of similar risk zero coupon of ($100 face value) bonds are given below:

Term (In Years) Price (In $)
0.5 100
1 97
1.5 96
2 93
2.5 92
3 91
4 89

b. How would you arbitrage the opportunity if you found out that the bond in Part A above was trading at par? Specifically, explain which bond/s will you buy and which one/s will be sell today and in how much quantities?

Answer 1

A) the current price of the bond is:

($50 x 1) + ($50 x 0.97) + ($50 x 0.96) + ($50 x 0.93) + ($50 x 0.92) + ($1,050 x 0.91) = $1,194.50

B) assuming that the bond is trading at par, you have a great opportunity to make money:

maturity zero coupon return of coupon

bond's price bond

0 $1,000 $0

0.5 $1,000 $50

1 $970 $100

1.5 $960 $150

2 $930 $200

2.5 $920 $250

3 $910 $300

You can buy 10 coupon bonds = -$10,000

Sell short 1 One-year zero coupon bond = $970

Sell short 1 Two-year zero coupon bond = $930

Sell short 11 Three-year zero coupon bond = $10,010

Positive cash flow = $1,910

At the end of year 1, you can pay the One-year zero coupon bond with the coupons received = $1,000 (cash flows = $0)

At the end of year 2, you can pay the Two-year zero coupon bond with the coupons received = $1,000 (cash flows = $0)

At the end of year 3, you can pay the Three-year zero coupon bonds with the coupons + maturity value received = $11,000 (cash flows = $0)

If the coupon bonds are selling at par, you could earn today $1,910 for every 10 bonds that you buy.