Interest Rate Risk Measures Beyond Duration and Convexity

Summary

The document surveys practical ways to measure interest rate risk beyond duration and convexity, emphasizing that the right measure depends on the portfolio and use case. It describes scenario impacts on fair value, economic value of equity, or net interest income, as well as reverse stress measures that ask how large a rate move would trigger an unacceptable loss. Parallel shifts are a simple starting point, while key-rate or tenor-bucket sensitivities show exposure to localized curve moves. IR01, DV01, PV01, and PVBP express value changes for a one-basis-point shift; hedge equivalents can translate sensitivity into approximate swap or futures positions.

For nonlinear or complex books, the response recommends full revaluation under hypothetical and historical curve scenarios, potentially including curve twists, principal-component moves, spread shocks, and cross-currency interactions. Convexity can improve small-move approximations, but may not capture large shocks accurately. The document offers a menu rather than one universal metric; scenario design, likelihood assumptions, accounting treatment, and local rate volatility affect interpretation, and a one-basis-point shock may be too small in high-rate markets.

Key ideas

• Choose interest rate risk measures according to the portfolio and whether it belongs to a banking or trading book.
• IR01 and tenor-bucket sensitivities measure value changes under parallel or localized one-basis-point rate moves.
• Reverse stress measures can express the rate move needed to reach an unacceptable impact.
• Full revaluation across hypothetical and historical scenarios is useful when exposures are nonlinear.
• Curve shape, spreads, currency interactions, and market-specific rate volatility can require additional scenarios.

Tags

# Trying to replicate the Beta of Yahoo in R but am getting an answer that is way off


# Trying to replicate the Beta of Yahoo in R but am getting an answer that is way off












Yahoo calculates the Beta by using 3 years of monthly returns and using the S&P 500 as a market proxy but I cannot seem to replicate this or even get close using R. I downloaded the data from Yahoo from 12/01/2014 to 12/01/2017 for NKE and GSPC and take the adjusted closing price (either that or just closing price they both should at least be fairly close to the beta if the calculation is done correctly). Then I do the following

```
>nike = read.csv("NKE.csv")
>sp = read.csv("^GSPC.csv")
>nikeAC = nike$Adj.Close
>spAC = sp$Adj.Close
> niker = rep(0,36)
> 
> for (i in 1:36){
+     niker[i] = (nikeAC[i+1]-nikeAC[i])/nikeAC[i]
+ }
> 
> spr = rep(0,36)
> 
> for (i in 1:36){
+     spr[i] = (spAC[i+1]-spAC[i])/spAC[i]
+ }
> cov(spr,niker)/var(spr)
```

and get an output of -1.21 when the Beta is supposed to be around .54. I would also like to add that they don't use an adjusted Beta so I should be getting something close to .54 as I've checked other sites and they seem to be within the .54 -.64 range generally.

## Answer by Andrew (score 4, accepted)

https://quant.stackexchange.com/a/37453

You need returns for 36 months, in particular data from 37 months. Yahoo also uses unadjusted closing prices for the reference index as far as i know. The data from 8/1/2015 got to be an error, I checked multiply data sources and found no similarities. After interpolating that point i got a beta of 0.48.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.