Yield Duration Statistics: Price Value of a Basis Point (PVBP)

Incorrect. That is the change for a 1 bp change in yields.

An important measure of interest rate risk is the change in a bond price for a 1 basis point change in yield. This is referred to as the __price value of a basis point (PVBP)__. It is also sometimes called the present value of a basis point (PV01) or the discounted value of a basis point (DV01). PVBP can be computed by shifting the bond price one basis point in either direction. It can also be computed using modified duration.

Using bond prices, PVBP is computed as follows: $$\displaystyle PVBP = \frac{(PV_-) - (PV_+)}{2}$$ where $$\displaystyle PV_-$$ is the bond price if yields decrease by 1 bp and $$\displaystyle PV_+$$ is the bond price if yields increase by 1 bp. In the equation above, the price of the bond is computed for one basis point shifts above and below the current yield.

Correct! The bond price would be expected to change by 10 times the PVBP. For a 10 bps decrease in interest rates the price would be expected to increase by about 1.385 to 101.385.

What happens to PVBP as modified duration increases, other things unchanged?

Correct! An increase in modified duration causes PVBP to increases. Bonds with higher durations have more price volatility.

To summarize: [[summary]]

Incorrect. That is a bit too high. PVBP is the expected change for a 1 bp change in yields.

Based on this example, how much would the bond price be expected to change for a 10 bps decrease in interest rates?

Incorrect. An increase in modified duration will not cause PVBP to decrease.

Incorrect. PVBP will change if duration changes.

As an example, consider a 6.00%, 30-year bond, with semiannual coupons that is non-callable. The bond is priced with a yield-to-maturity of 6.00% at 100. If the yield is shifted down by 1 bp to 5.99%, the bond price is 100.138. If the yield is shifted up by 1 bp to 6.01%, the bond will price is 99.861. Therefore, the PVBP is calculated as $$\displaystyle PVBP = \frac{(100.138 - 99.861)}{2} = 0.1385$$. This means that a 1 bp change in yields changes the price of the bond by about 0.1385. You can see in this example the price increases by about that amount when yields are shifted down by 1 bp.

Increases

Decreases

Stays the same

0.1385

1.3850

3.1850

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