What is the formula for the present value of a basis point?

The formula for calculating the present value of a basis point is indeed derived from the concept of dollar duration, which measures the sensitivity of the price of a bond or fixed-income security to a change in interest rates.

When we discuss the present value of a basis point, we are considering a one-basis-point change in yield (which is 0.01%). To quantify the monetary effect of this small change in yield on the price of a bond, we take the dollar duration of the bond and multiply it by the decimal equivalent of a basis point, which is 0.0001.

By applying this multiplication, we obtain the dollar value change associated with a 1 basis point change in yield. This outcome reflects how sensitive the bond's price will be in relation to small changes in interest rates, thereby providing a clear measure that investors can use to assess their interest rate risk.

In summary, the present value of a basis point calculated by multiplying dollar duration with 0.0001 accurately captures the impact of small fluctuations in interest rates on the value of fixed-income securities.