1
$\begingroup$

For bonds I've newly seen the measure DTS, spread duration times spread. The pnl is then approximated

$$ V = -DTS \frac{\Delta S}{S}$$

where $S$ the current spread and $\Delta S$ the spread change. My question is, what is the unit of this? Assume a spread duration of 10, and $S=3\%$. My DTS is then $DTS = 10*0.03 = 0.3$. Now using only the spread duration, for a change of $0.1\%$ this yields a value change of $10*0.001=0.01$, hence I lost $1\%$. Note here the spread move is entered in numercis $(0.001)$ and the result is also in numerics! Lets assume for $DTS$ that spread widen $10\%$. My value change $0.3*0.1 = 0.03$. Although I'm almost certain, here the $0.03$ are in $\%$, i.e. in numerics $0.0003$. But I can't see why this is the case mathematically. It must be simple still don't get it :)

$\endgroup$

1 Answer 1

3
$\begingroup$

Assume $[s]$ to be the unit of the rate or rate spread, e.g. percentage points or basis points. Then

$$ \begin{matrix} dPV&\approx \frac{\partial PV}{\partial S} dS & \frac{\\\$}{s}s\\ &=\frac{S}{S}\frac{\partial PV}{\partial S} dS& \frac{s}{s}\frac{\\\$}{s}s\\ &=\partial PV\left/\frac{\partial S}{S}\right.\frac{dS}{S}& \frac{\\\$}{\%}\%\\ &=DTS \frac{dS}{ S} & \frac{\\\$}{\%}\% \end{matrix} $$

so DTS should be in Dollar-per-percent-change.

$\endgroup$
2
  • $\begingroup$ many thanks for your answer. What do you exactly mean by "in" dollar-per-percent-change? I do see that $dS/S$ is a percentage change, but what confuses me is, although I translate % into numerics I still get % for $dPV$ $\endgroup$
    – swissy
    Nov 22, 2023 at 7:20
  • $\begingroup$ I've added the dimensions. $\endgroup$ Nov 22, 2023 at 7:45

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.