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Risk numbers

Why are risk numbers used in attribution?

Historically, risk numbers have been widely used in attribution as they can be used as a proxy for a pricing function.

To see how a change in a security’s yield affects its price, one can either reprice it at two different yields and calculate its return from these two prices, or use the equation

r = y · δy − MD · δy

which gives the return in terms of the yield, the change in yield, and the modified duration. This is typically much simpler than having to provide pricing code for every security type the attribution system will have to handle.

When is it a bad idea to use risk numbers for attribution?

Unfortunately, supplying daily risk numbers can be a surprisingly difficult (and expensive) problem. It can take many man-months to set up reliable, robust feeds for risk numbers. In addition, risk numbers for some security types may not be available at all.

Attribution systems are also brittle. This means that if one risk number is wrong, it can skew the entire analysis. This applies especially to bond futures, which can have substantial weights in managed portfolios.

Many millions of dollars have been wasted on attribution systems that depend on sources of accurate, timely risk numbers. Be very careful before you commit to an attribution system that is designed on this principle.

FIA allows the use of both risk numbers and first-principles pricing, so it is not subject to this risk.

Raw pricing functions or risk numbers: which are better?

It depends. In some circumstances, raw pricing functions are ideal. All you need to supply are daily yield curve files; then all other analytics are calculated internally.

In others, you may prefer to use risk numbers for some or all of your holdings. For instance, you may have securities requiring a complex pricing model, or a requirement to use specific yields. In this case a pricing model may not be available or appropriate.

Note that both approaches can be used in the same portfolio.

Which is best: modified duration, Fisher-Weil duration, or DV01?

Modified duration, Fisher-Weil duration and DV01 are all measures of price (and hence return) sensitivity with respect to changes in the underlying yield of a security.

  • Modified duration measures the sensitivity of a security’s price to a parallel change in the yield curve.
  • Fisher-Weil duration measures the sensitivity of a security’s price to movement up or down in the entire yield curve. This can give quite different results to the returns calculated using modified duration.
  • DV01 is the dollar value of a one basis point decrease in interest rates. It is therefore similar to modified duration, but is used to measure dollar changes in the value of a portfolio, rather than its return. It is therefore of limited use in attribution.

Of the three, modified duration should always be used for attribution.

Where and why should I use key rate durations?

Only when you really need to.

Key rate durations measure the effect on a security’s yield of a change at a particular maturity. To measure the sensitivity of a security’s price to movements at ten different maturities on the yield curve requires ten values, for each security, for each date. The data requirements for KRD attribution can therefore become overwhelming.

FIA performs KRD attribution by perturbing the underlying risk-free yield curve, and repricing each security after each curve movement. The program can therefore generate detailed KRD reports without any additional data.