Hi, I am looking at measurement of sensitivity of bond prices to interest rates. eg. Macaulay's Duration, Modified Duration, and Convexity. I am wondering are there problems that are associated with such measures, as in disadvantage or weakness. And can u please discuss the eventual complications engendered by embedded options. Thank you very much.

Hi korchamp, I assume you'd let us know if this is a homework question (out of courtesy)? It's pretty broad query, sort of like asking, what are the drawbacks of P/E ratio (ie, where to start??), but as it is very thematic to FRM and highly testable, I'll gladly offer a start to an idea that took me a long time to grasp. Setting aside Mac duration, they (duration and convexity) have in common: they are are single-factor analytical sensitivity measures [i.e., Taylor Series in the bond asset class. Almost all of our analytical approximations are Taylor. Duration is just the name it gets in bonds!]; i.e., they reduce a complex bond price dependence into a single measure, simplifying for convenience but distorting, based on a single factor, YIELD (most commonly). In short, they suggest, bond price change = f[yield]. While convexity overcomes the key weakness of duration (linear approximation), it nevertheless participates in the reduction of the entire term structure of rates into a single (effectively flat) yield. So, their weakness stems from the fact that a bond reacts to the entire set of rates along the term structure, the behavior of which does not realistically reduce to a single (yield) number. Here is Tuckman on the implication of this single-factor approach (how to overcome? multi-factor approaches, which is why the FRM goes to KEY RATES next, which is the most obvious graduation from single to multi-factor). There are two closely-related assumptions, single-factor and parallel shift, that IMO it's okay to treat as one idea for an initial understanding: