September 2008
CFP® Student
Newsletter
Predicting Bond Price Changes
On the CFP® Examination, application of concepts is important. In the area of fixed income securities, you know from your studies that if interest rates rise, outstanding marketable bond prices will fall, because new investors will demand a higher yield. For example, assume that a 15-year Government of Canada (GOC) marketable bond was issued 10 years ago with a 3% coupon rate (fixed interest rate), but today a 4% return is competitive on new issues of 5-year GOC marketable bonds. Therefore, a new investor will demand a 4% yield (return) on the outstanding GOC bond and its price will fall. To predict how far the price of a marketable bond will fall given a specified increase in interest rates or will rise given a specified decrease in interest rates, we can use concepts called Macaulay Duration, modified duration and convexity.
Example of the use of Macaulay duration, modified duration, convexity and predicting changes in bond prices.
| Example: |
An investor purchases a Telus 8% bond maturing in exactly 15 years. |
Assume the Macaulay duration of the bond is 10 years (on average it will take the investor 10 years to get their cash back on their investment).
Question One: What is the modified duration on the bond?
| Answer: Modified Duration = |
Macaulay Duration |
| |
1 + Semi-Annual Yield to Maturity |
Assume the annual yield to maturity on the bond is 12%. The semi-annual yield to maturity is 6% or 0.06.
| Modified Duration on the Telus Bond |
= |
10 |
| |
|
1 + 0.06 |
| |
= |
10 |
| |
|
1.06 |
| |
= |
9.434 or 9.43 |
Question Two: Assume the bond price is $72.48. What percentage change would there be in the bond price if yields increase or decrease by 1%?
Answer: The bond price should change by the modified duration, 9.43, for a 1% change in yield. This equals:
If interest rates fall 1%, the bond price should rise to $79.32 ($72.48 + $6.84). If interest rates rise 1%, the bond price should fall $6.84 to $65.64 ($72.48 – $6.84).
Note that modified duration predicts an equal change in the bond price for a 1% change in interest rates (but in the opposite direction).
Convexity – In fact, the change in the price of a bond is not equal for a 1% rise or 1% fall in yields. There is a bias for the bond price to rise more than it falls for a 1% change in interest rates.
This bias is due to convexity. The yield/price change on a bond is not symmetrical; it is convex. There is curvature in the yield/price movement that is not captured by modified duration. This curvature is captured by convexity.
Example: Assume that on the Telus 8% bond, convexity accounts for a 0.40% (40 basis points) change in the bond price, for each 1% change in yield.
Question Three: When combining modified duration and convexity, how much should the Telus 8% bond rise in price, for a 1% decrease in the yield? Also, what should be the new price of the bond?
Answer: The bond price should rise 9.83% (9.43 + 0.40) for a 1% decrease in yields.
|
This equals:
|
|
|
$7.12 ($72.48 x 0.0983)
|
|
The price of the bond should rise to:
|
|
|
$79.60 ($72.48 + $7.12)
|
Question Four: When combining modified duration and convexity, how much should the Telus 8% bond fall in price for a 1% increase in yields?
Answer: The bond price should fall 9.03% (9.43 – 0.40) for a 1% increases in yields.
| This equals: |
|
$6.54 ($72.48 x 0.0903) |
| The price of the bond should fall to: |
|
$65.94 ($72.48 – $6.54) |
It is likely that on the CFP® examination, you will be tested on the concepts described above, not necessarily on the numbers. It is important that you are aware that modified duration measures interest rate risk and predicts a price change in the bond price. Also, modified duration is not a perfect predictor due to convexity.
Ron Foran, CFA, CFP, CLU, FCSI
President,
Foran Financial Institute
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The Financial Advisors Association of Canada