9.10 Volatility: Introduction to Convexity
How much will dollar price move up as yields move down? If we are to believe what we have seen in the Price / Yield Curve (PYC), dollar prices should move up increasingly.
Below we see a small set of numbers for a bond; the numbers represent just a few points along the PYC for a given bond. Let’s assume that:
Maturity: 30 Years
Coupon: 6% (Annual)
Questions
- How much does the dollar price rise when the YTM decreases (from 8% to 7% in comparison to moving from 5% to 4%)?
- What is the percentage price increase (i.e., similar to the first derivative)?
| YTM | Price (% of Par) | Percentage Price Increase |
| .08 | 77.487 | + 0.1304 |
| .07 | 87.594 | |
| ∆ Price = | + 10.107 |
| .05 | 115.375 | + 0.1664 |
| .04 | 134.582 | |
| ∆ Price = | + 19.207 |
Observations
- As yields decrease (go to the left), prices increase.
- As we go further to the left, prices increase at an increasing rate. The curve gets steeper.
- The Price / Yield Curve demonstrates that at low market yields (YTM), volatility is greater.
- This is because the PYC steepens to the left. Price goes up (and down) more for a given change in yield at lower rates.
