Question

1)Find the Macaulay duration and the modified duration of a15​-year,11.5​%corporate bond priced to yield9.5​%.According to the modified duration of this​ bond, how much of a price change would this bond incur if market yields rose to10.5​%?Using annual​ compounding, calculate the price of this bond in one year if rates do rise to10.5​%.How does this price change compare to that predicted by the modified​ duration? Explain the difference.

2) An investor is considering the purchase of​ a(n)6.75%​,​18-year corporate bond​ that's being priced to yield8.75%.She thinks that in a​ year, this bond will be priced in the market to yield 7.75%. Using annual​ compounding, find the price of the bond today and in 1 year.​ Next, find the holding period return on this​ investment, assuming that the​ investor's expectations are borne out.

Answer 1

MD = modified duration

YTM (Y) = 9.5% = 0.095

Maturity (n) = 15 years

Coupon rate (c) = 11.5% = 0.115

  

  

  

  

   Years

Modified duration =   

=   

=

= 7.556

Macaulay duration = modified duration * ( 1 + Y)

= 7.556 * (1+0.095)

= 7.556 * 1.095 = 8.274

Calculation of CMP if face value = $1000.

Current market price = [coupon amount * PVIFA(9.5%, 15 years) ] + [redemption value * PVIF (9.5%, 15 years)

= ( 115 * 7.828) + (1000 * 0.2563)

= 900.24 + 256.3 = $1156.54

Using modified duration change in market price, if yield change by 1%

Change in yield = 10.5% - 9.5% = 1%

change in market price = current market price * change in yield * (Modified duration/100)

= 1156.54 * 1 * (7.556/100)

= 1156.54 * 0.07556

= 87.388

expected market price = 1156.54 - 87.388 = $1069.152

Using macaulay duration change in market price, if yield change by 1%

Change in yield = 10.5% - 9.5% = 1%

change in market price = current market price * change in yield * (Macaulay duration/100)

= 1156.54 * 1 * (8.274/100)

= 1156.54 *0.08274

= 95.69

Expected market price = 1156.54 - 95.69 = $1060.85

When yield increases, market price decreases and vice versa. The macaulay duration has more volatility when compared to modified duration. So, expected market price will be less for macaulay duration. The greater the duration, the more volatile the bond.