- almostcutmyhair
**Posts:**197**Joined:**

Why do we use simple return--of yield to maturities--instead of log-returns?

We (whoever that is) do not quote continuously compounded returns because that is not a market convention (with perhaps one or two outlier exceptions).

We (whoever that is) do not quote continuously compounded returns because that is not a market convention (with perhaps one or two outlier exceptions).

- almostcutmyhair
**Posts:**197**Joined:**

I was asking a simple question: Why do "WE" use simple or absolute returns (i.e. bps changes) of rates, instead of their log-returns, when calculating historical VaR for bonds, besides the fact that rates can be negative? QuoteOriginally posted by: bearishWho are "we" and what do you mean?

OK - let me try. Rates don't have returns, but the underlying bonds do. In my current world, we actually calculate tracking errors (as close to VaR as I would care to get) on bond portfolios based on the log returns of the underlying bonds. But one reasonable way to approximate that is to add up the product of the basis point change in a set of key rates and the corresponding key rate durations. So this may be the reason why you have come across the basis point change approach to interest rate risk. More generally, if you do your VaR calculations based on a full fledged interest rate model (as opposed to based on key rate durations and some sort of principal components), you should let the model dynamics guide your interest rate shocks. If the model is lognormal (which I would not necessarily recommend), then you should focus on the relative interest rate moves, although I still wouldn't refer to them as "returns".

you have 2 methods when computing perturbations to create hypothetical scenarios for Historical Simulation.for Interest rates the underlying model is the classic random walk.for example ,the n-th sample (hypothetical tomorrow ) is given by the following Xn = Xmtm + ( Xn -Xn-1 ), where Xmtm is the MTM value ,this has the benefit of respecting the stationarity historicallyobserved for interest rates and it is simple in terms of use and computation,it can lead to negative hypothetical future interest rates,in a low interest rate environment (like now ) ,it is best to use the other method which is the percent return method.in the latter modelsuch representaion is the classical exponential of a random walk where the log price is a random walk

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