Option-adjusted effective duration (OAD)

Effective duration is measured by stressing the yield curve immediately by a fairly sizable step (say, 50 basis points) using the parallel pattern. Both assumptions are questionable. How likely can a 50 basis point shock occur on a single day? How often do we observe all points of the curve changing by an identical amount?

Let us not be distracted by the assumptions. The step selection actually matters a little. Duration assessment using the three-point stress test is fairly accurate — the error is due to the third derivative term (not even convexity). The purpose of shocks is not to simulate real-life dynamics, but to measure the price derivative. It is apparent that once the derivative is measured, it can serve for practical purposes well beyond dubious assumptions. One important statement is made below.

Fact 3. As trivial as it sounds, the product of OAD and interest rate volatility is equal to the corresponding price volatility. The same measure can serve as annualized volatility of total return measured over infinitesimal horizon.

If 100 bp/yr is the absolute volatility of interest rate, then a 4-yr duration MBS will have a 4% annualized price volatility. In the example that immediately follows Definition/Fact #1, the expected 1-yr return claims to be 3.5%. If we measure the return over a very short period of time and then annualize it, the total return can be expressed as 3.5% ± 4.0%.

OAD measurement convention that relies on parallel shocks can be easily modified to include durations to interest rate factors. The total volatility is produced by measuring volatility terms due to each factor and then adding them up via Pythagorean math.

Therefore, OAD and its possible modifications point to the total return uncertainty.

 

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