Question

You observe following three securities in the market.

(1)Zero-coupon bond: Maturity = 5 years, Face value = $500, Current price = $332.52.

(2)Regular coupon bond: Maturity = 5 years, Face value = $1,500, Coupon rate = 8%, Current price = $1477.16.

(3)Regular Annuity: Maturity = 5 years, Annual payments in arrears = $240, Current price = $974.20.

Suppose that, you are convinced that the prices of zero-coupon and regular coupon bonds are done correctly in the market. Then, as per you, what should be the fundamental price of the regular annuity? Do you think that there is an arbitrage opportunity? If yes, what should be your arbitrage strategy at t=0? What is the arbitrage profit at t=0? And show the net cash flows for t=1 t=2,….. t=5 years. Assume that you can buy/sell only integer quantity of financial securities.

Answer 1

if the price of the zero coupon bond is correct the Interest rate= (maturity value/current price)(1/5) -1

= (500/332.52)(1/5)  -1

= 1.085 - 1

= 8.5%

formulas used:-

Fundamental Price of Regular Annuity =PV(8.5%,C3,C4)

Arbitrage profit=C2+C5

to earn the arbitage profit we will sell regular annuity today and earn arbitrage profit of $28.45.

yearly cashflow=

year 0 = 974.2

Year -1 = 240

Year -2 = 240

Year -3 = 240

Year -4 = 240

Year -5 = 240.

i hope my efforts will be fruitful to you.....