Business Economics 271
John W. Sell
DURATION PROBLEM SET
Duration has many uses in financial analysis. It, in turn, is affected by several factors including: time remaining until maturity, coupon rates, and market interest rates. Examine the effects of these factors on duration by filling in the table below. Use semi-annual compounding and let December 31, 2001 be the settlement date. Assume that the maturity date is December 31 of the year indicated.
|
Year of Maturity |
Yield (%) |
Coupon Rate (%) |
Duration |
|
2005 |
11.58 |
10.00 |
? |
|
2007 |
11.58 |
10.00 |
? |
|
2012 |
11.58 |
10.00 |
? |
|
2027 |
11.58 |
10.00 |
? |
|
|
|
|
|
|
2009 |
8.00 |
10.00 |
5.827 |
|
2009 |
10.00 |
10.00 |
? |
|
2009 |
12.00 |
10.00 |
? |
|
2009 |
15.00 |
10.00 |
? |
|
|
|
|
|
|
2009 |
11.58 |
8.00 |
? |
|
2009 |
11.58 |
10.00 |
? |
|
2009 |
11.58 |
12.00 |
? |
|
2008 |
11.58 |
15.00 |
? |
Can you verify in the chart that duration increases as time until maturity increases? Can you show also that duration decreases as market yields rise and as coupon rate rise? What rows in the chart confirm this?
You might wish to construct an EXCEL spreadsheet to do these calculations. This can be done as follows:
· Type the labels, “Settlement”, “Maturity”, ”Coupon”, “Yield”, and “Par” in cells A3 to A7 respectively.
· Type the label, “McCauley’s Duration” in cell D3.
· In cell D4, type the following formula, “=DURATION(B3,B4,B5,B6,2,0)”.
· The coupon rate and yield in cells B5 and B6 should be entered as decimal numbers. For example, 5.8% should be entered as 0.058.
You should calculate at least one duration value by hand in order to
confirm the calculation.
Problem: A freshman entering the College of Wooster in 2002 is planing to attend graduate school when she leaves the College. Which of the following bonds (all yielding 9%) would be the most conservative investment for her (assume that the relevant market rate of interest is 12%)? Let the settlement date be April 30, 2002 and the maturity date be April 30 of the years indicated. Use annual interest payments.
Newell 12s06
Newell 7.25s11
Newell 13s09
Newell 18s10
Newell 9s07
Problem: Show that a zero-coupon bond has a duration equal to its time until maturity no matter what the market rate of interest or the time remaining until maturity. Give several examples to make your point.
Updated March 2002, by Jws.