Question

The YTM of 1,000 bond with a 10% coupon rate, semiannual coupons, and two years to maturity is 6.5 APR, compounded semiannually.

b.Suppose the market price of this bond curretly is $980. Is there an arbitrage opportunity ?

Answer : Yes / No

c. Is this bond undervalued or overvalued by the market ?

Answer : I don't know / Undervalued / Overvalued

d. Should you long or short this bond ?

Answer : Long / Short / Do nothing

e. How much will be your arbitrage profit ?

Answer : 31.79 / 83.72 / 84.66 / 7.31 / 0.00

Answer 1

b. Yes, there is an arbitrage opportunity.

first we calculate current value of the bond. we can use financial calculator for the same.

coupons are semi-annual. so, maturity and YTM will also be semi-annual.

N = semi-annual maturity = 2*2 = 4; I/Y = semi-annual YTM = 6.5%/2 = 3.25%; PMT = semi-annual coupon = $1,000*10%/2 = $50; FV = face value = $1,000 > CPT = compute > PV = current value = $1,064.66

calculator will display PV as neagtive value as it's a cash outflow.

current market price of the bond is $980 which is lower than current value of the bond of $1,064.66. so, there's an arbitrage opportunity.

c. this bond is undervalued by the market.

d. You should long this bond.

e. Answer is 84.66.

arbitrage profit = current value of the bond - current market price of the bond = $1,064.66 - $980 = 84.66

your arbitrage profit will be 84.66.