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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.

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closed as unclear what you're asking by Alex C, Attack68, LocalVolatility, skoestlmeier, Helin Oct 10 '18 at 1:11

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ Have you considered using the Fama/French market factor as a reference? It‘s calculation is based on the (almost) entire US-stock universe and the S&P500 is just a certain (sub-)portfolio of US-stocks. $\endgroup$ – skoestlmeier Oct 8 '18 at 14:42
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    $\begingroup$ @skoestlmeier Do you mean using market premium (Rm-Rf) of Fama and French and use it in the Equation to calculated expected return on S&P 500? --- Exp.Return (SP5) = rf + Beta(SP5) * Market Risk Premium (Fama and French) $\endgroup$ – riskfree Oct 8 '18 at 15:53
  • $\begingroup$ Maybe you should first figure out what do you mean by market. As you point out yourself, for a lot of people S&P500 is the market. $\endgroup$ – LazyCat Oct 8 '18 at 16:39
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    $\begingroup$ I thought exactly was @Achyut mentioned. Please point out what your research question is - what are you trying to do? $\endgroup$ – skoestlmeier Oct 8 '18 at 17:06
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    $\begingroup$ FYI I voted to close this questions since it it causing much confusion try to decipher what you are doing. I think it best to clearly define your terms, how you are proposing to do what you are doing and then ask the question. $\endgroup$ – Attack68 Oct 8 '18 at 18:45
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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.

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  • $\begingroup$ Thanks a lot! I will use spread estimator that was developed by Corwin and Schultz and see how ETFs impact the spread. $\endgroup$ – riskfree Oct 15 '18 at 21:27

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