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I have the impression that asset pricing models such as the CAPM or Fama & French 3 factor model typically concern nominal rather than real (inflation-adjusted) prices/returns. If this is indeed so, why is that?

Here is my guess. In cross-sectional asset pricing, there is no inherent time dimension (that is why it is called cross sectional), so the concept of inflation is irrelevant. Yet the models are estimated on data from multiple periods, so the time dimension is present in the data. Also, I suppose adjustment for inflation might not make a big difference when using daily data but it could become important when using monthly (or even lower frequency) data.

References to relevant texts would be appreciated.

Another question with a similar title but somewhat different content (more focus on continuous-time finance, risk-neutral measure and such) is this one.

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  • $\begingroup$ @Alper, good point. My real question is broader than that, though, as I am trying to get an overview of when to use nominal vs. real figures in asset pricing models. If I had to choose a specific model or two (or three), that would be the CAPM and Fama-French 3-factor or Carhart 4-factor models (thus not the ones concerned with smoothing consumption over time). I have edited the post accordingly. $\endgroup$ Commented Jun 1, 2023 at 12:55
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    $\begingroup$ "References to relevant texts would be appreciated" based on this it looks like you're wanting authoritative research, which may be difficult for a question like "why doesn't this model consider X). Are you looking for research you can cite, general curiosity, or something else? $\endgroup$
    – D Stanley
    Commented Jun 1, 2023 at 17:57
  • $\begingroup$ @DStanley, general curiosity. I hope this question has been discussed somewhere, as it seems like a fairly natural one to ask. Real vs. nominal is an essential distinction in many branches of finance, and I would be surprised if it has been overlooked in asset pricing. $\endgroup$ Commented Jun 1, 2023 at 18:25
  • $\begingroup$ Would this previous Q&A answer your question? "Discounting with inflation?" $\endgroup$
    – Alper
    Commented Jun 1, 2023 at 21:39
  • $\begingroup$ @Alper, that one is a basic question about discounting cash flows. I understand the logic there. Meanwhile, my question is specifically about certain cross-sectional asset pricing models. I think these are distinct enough questions. $\endgroup$ Commented Jun 2, 2023 at 6:46

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You can use nominal or real returns in the CAPM or Fama-French model. Both models have expressions for excess returns. As inflation will adjust nominal returns in the same way for different assets in the cross section, inflation cancels out.

More concretely, if $r^i_t = \log(P^i_t) - \log(P^i_{t-1})$ are nominal returns of asset $i$, $\pi_t = \log(\text{CPI}_t)-\log(\text{CPI}_{t-1})$ is inflation, and $\nu^i_t = r^i_t - \pi_t$ are real returns of asset $i$, then $r^i_t - r^j_t = \nu^i_t - \nu^j_t$. Excess returns will be equal if you use nominal or real returns.

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    $\begingroup$ I thought so, too. Good to get a confirmation. On the other hand, this does not work exactly for % returns in place of log-returns. In periods without low to modest inflation, the approximation is OK, but when inflation gets out of hand, this starts to matter. Any thoughts? Are log-returns the dominant sort of returns in cross-sectional asset pricing, or are % returns more widely used? $\endgroup$ Commented Jun 2, 2023 at 7:00
  • $\begingroup$ My original question included intertemporal asset pricing models, and I was thinking about how one aligns the inflation adjustment in them (which I think would make sense to have) with no adjustment for the cross-sectional models (this is my experience so far). Unfortunately, my original question was about to get closed as some users perceived it as being too broad, so I had to narrow down to cross-sectional models only... $\endgroup$ Commented Jun 2, 2023 at 7:00
  • $\begingroup$ We use log returns to allow algebraic manipulations such as Re = Ri - Rj, where Re are excess returns. We can say that all returns are defined as log returns. It is not an approximation of the true return; it is the definition used in the equations $\endgroup$
    – Andre
    Commented Jun 2, 2023 at 14:10
  • $\begingroup$ We can derive the CAPM and the FF model with excess returns defined as (1+Re)=(1+Ri)/(1+Rj) and so on. However, the formulas would not be so easy to understand and many analytical results would not be obtained. On the other hand, the implications in terms of intuition would be the same. So, there is no gain in using non-log returns. The first thing that is done when working with data is to take logs on prices and calculating returns as log returns $\endgroup$
    – Andre
    Commented Jun 2, 2023 at 14:13
  • $\begingroup$ Let me know if you need any other clarification. If the answer is fine, can you accept it? I might include the comments above in the answer. I will also complement the answer for the question of the link that you sent $\endgroup$
    – Andre
    Commented Jun 2, 2023 at 14:15

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