In page 174 of tuckmam's new book, it attempts to find out the 'beta' of a real yield change vs nominal yield change to enhance the effectiveness of a dv01 hedge between a nominal treasury and a TIPS. The idea is that the real yield and nominal yield change are not 1 for 1, e.g. When a yield change is 5bp in the real market, the nominal market can exhibit a change of 2-8bps. Hence a regression equation was proposed:Delta nominal-yield = alpha + beta * delta real-yield + errorI was thinking.. Shouldn't it be instead a regression between the LEVEL of the yields as opposed to the CHANGE of the yield? Imagine this data set below Nominal:1, 2, 3Real yield: 1.1, 1.2, 1.3The level regression will have a beta which say that for a 10 bps change in real yield corresponds to a 100bps change of nominal yield. Where as if we do a regression of the CHANGEDelta nominal: 1, 1, 1Delta real yield: 0.1, 0.1, 0.1The regression here would fail as we can't really tell as there is no change in the delta value.If anyone has read any book or familiar with regression hedges.. Please take a look thank you in advance...

Actually.. Level regression and difference regression will produce the same beta. But if anyone wants to discuss or comment to this that woud be good too...

Quote I was thinking.. Shouldn't it be instead a regression between the LEVEL of the yields as opposed to the CHANGE of the yield? Imagine this data set below Nominal:1, 2, 3Real yield: 1.1, 1.2, 1.3 You may fit regression on this data..........nobody perhaps going to stop you, however your inference may be wrong. In this case, the growth of a particular series may be completely driven by it's own momentum (i.e. due to auto-correlation), without any outside help (i.e. cross-correlation, hence Regression).Just for your information, there is entirely one literature exists on such issue, called the Spurious regression.HTH

The nominal yield equals the real yield plus expected inflation. Therefore the Beta of either a level regression or a difference regression would be 1 except for any relation between expected inflation and real rates.If you believe changes in inflation expectations are related to changes in real rates, then you would do a difference regression.If you believe inflation levels are related to real rate levels, then you would do a level regression.Of course, the truth is that inflation expectations are related to both the level of and change in real rates. But the market will work hard to erase any level effect. For example, you might argue that high real rates depress economic activity, which will lead to reduced price pressure and therefore less inflation. But the market should take this into account so that inflation expectations are a random walk. That's not completely true, of course, but it means the difference regression is likely to be more useful than the level regression.You might do best with a mixed model, say change in nominal interest rates regressed on both change in real rates and level of real rates times change in real rates. This might tell you to use a different hedge ratio at times of high or low real rates.