Why Measuring S&P 500 Inefficiency Requires an Asset Pricing Model
Summary
The discussion explains why a time-varying measure of S&P 500 mispricing cannot be defined independently of a model for what prices or expected returns should be. Market efficiency tests are joint tests of efficiency and an asset pricing model, so labeling the index overvalued or undervalued requires defending the chosen benchmark and its assumptions. The questioner's proposed comparison of ex post and ex ante CAPM returns is problematic because the S&P 500 itself is often used as a market proxy.
The answer notes that CAPM is not generally considered a strong empirical model and that the S&P 500 may have little unexplained alpha under multifactor models using a broad market proxy. It suggests that liquidity could be a more measurable research outcome, though liquidity itself is difficult to define. The discussion offers conceptual guidance rather than a tested proxy or empirical procedure; claims of index mispricing therefore remain difficult to validate and depend on model choice.
Key ideas
- A market efficiency test is jointly a test of efficiency and the selected asset pricing model.
- A claim that the S&P 500 is mispriced requires a defensible estimate of its correct price or expected return.
- Using the index as both the subject and market proxy makes a CAPM-based inefficiency measure problematic.
- Multifactor models may leave little unexplained S&P 500 return relative to a broad market benchmark.
- Liquidity may be a more measurable research target than inefficiency, though it is also hard to quantify.
Tags
Full text
# Is there a proxy for S&P 500 market/pricing inefficiency? # Is there a proxy for S&P 500 market/pricing inefficiency? I need a variable or tool which can proxy for S&P 500's inefficiency (whether pricing efficiency or market inefficiency). Initially, I intended to use CAPM and consider the difference in ex-post and ex-ante required rate of return as a proxy for inefficiency; however this does not seem to work as S&P 500 is itself a proxy for market. Exp.Return (SP5) = rf + beta(SP5)(Return on Market - rf) where, S&P500 = SP5 Is there a way I can model market/price inefficiency of S&P500 (which will be my dependent variable) so that I can see the impact on S&P when a new financial product is introduced. ## Answer by Matthew Gunn (score 6) https://quant.stackexchange.com/a/42112 #### Mispricing can only be measured relative to some asset pricing model Fama (1970) famously defined an efficient market as, "a market in which prices always 'fully reflect' all available information." A perhaps less widely understood point of Fama is that any test of market efficiency is a joint test of: (1) market efficiency and (2) an asset pricing model! To say prices are wrong (i.e. inefficient) given available information you must say something about what prices should be given available information. #### A core problem with what you're proposing To have some time-varying measure of S&P 500 inefficiency, you'll have to say, at various points in time, something about what the price or expected returns of the S&P 500 instead should be! It'll be a tough row to hoe though to justify statements of the form, "the price of the S&P 500 is 2% too high" or "the expected return of the S&P 500 is 2% too low." Can you convincingly argue you know when the price of the S&P 500 is correct and when it's wrong? I'm not arguing this is impossible: you have periods such as the 90s tech boom where such inefficiency is plausible. It's a bold claim though, and you're inviting the snarky question of, "so where's your successful hedge fund?" #### Other comments The CAPM does not work and is not a reasonable asset pricing model to use in academic finance. Empirically, average returns are if anything declining in market beta rather than rising as predicted by the CAPM. You correctly recognize that under various factor and multi-factor models, the S&P 500 will most likely be priced correctly as it'll have a beta of near 1 with respect to the CRSP value weight index (which is the typical proxy for the market portfolio in factor models), a near zero loading on other factors, and no significant alpha leftover. Is there any chance you instead want to measure liquidity? Liquidity is a somewhat nebulous concept that while being difficult to measure, is perhaps more measurable than inefficiency.
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.