Question

A risk-free zero coupon bond pays $1,000 at the end of six years. (a) The risk-free rate is currently 10% effective annual. What should the current price of the bond be? (b) Suppose the bond currently costs $500. Describe an arbitrage to take advantage of any discrepancy you see. What will you buy? What will you sell? What are your cashflows today and in the future? For the remaining sub-questions, assume that there are no arbitrage opportunities. (c) Joan buys the bond today after arbitrage by market participants has restored its price to what it should be. She intends to hold it till maturity, and to receive the payment of $1,000. What will her HPR be? What will her annualized HPR (AHPR) be?

Answer 1

a.) Current Price should be $564.47

b.) As the current market price of the bond is $500 and ideal value should be $564.47. There is an arbitrage opportunity. To take advantage of arbitrage one should borrow money at 10% and buy the bond with this money.

If someone wants to make through an arbitrage opportunity his/her cashflow be like...

Today He/she would borrow some money @10% - which is cash inflow for today.

Invest the borrowed money in the bond - which is cash outflow today.

At the time of bond maturity, He/she will receive a bond amount - Future Cash inflow

Pay their borrowed money from received money - Future cash outflow.

C.) HPR = 77.16%

D.) Annualized HPR = 10%

Calculation:

a.)

c.) Holding period return = ((Income + (end of period value - purchase value)) / purchase value) * 100

= ((0 +(1000 - 564.47))/564.47) *100

= 77.16%

d.) Annualized HPR = ((( 1 + (HPR/100) ) 1/time in year ) - 1) * 100

=( ((1+1.7716)1/6) - 1 ) *100

= (0.10) * 100

= 10%