9.26 The Slope of the Price/Yield Curve* and Duration
Refer to the Price/Yield curve to illustrate the following characteristics (a new graph is presented on the next page).
Note:
For large changes in yield, the price change as predicted by Duration will lead to increasing errors. (See also Malkiel’s Theorems – below, especially the fourth theorem.)
Remember:
There are 100 basis points (b.p.s or “beeps”) to one percent, i.e., (.01) (.01) = .0001
| Change in Yield (b.p.s) | Dollar Price Change6 Predicted by Modified Duration (Percent of Par) | Actual Dollar Price Change (Percent of Par) |
|---|---|---|
| + 150 | – 10.20 | – 9.55 |
| + 100 | – 6.80 | – 6.50 |
| + 50 | – 3.40 | – 3.32 |
| 0 | 0.00 | 0.00 |
| – 50 | + 3.40 | + 3.47 |
| – 100 | + 6.80 | + 7.11 |
| – 150 | + 10.20 | + 10.90 |
Notes:
- The above mathematical errors in the Duration-based estimate versus the actual price change is due to the slope/curvature, i.e., Convexity, of the Price/Yield curve. As yields diverge from the point of tangency, the Duration-based “error” increases.
- Further, the actual price goes up more than it goes down, given an equal move in YTM basis points (but obviously in different directions). The error will be greater when yields decline. This is so because the slope steepens to the left – Malkiel’s fourth theorem (see below). Prices increase more than they decrease for the same yield change.
