Indexation
Indexation:
Arnott is a smart man. Finally got a chance to read through his unabridged articles and they contain some real gems. For instance, this is something to really sink your teeth into: "An efficient market in the pricing of individual assets, with pricing errors relatiz}e to true fair value, requires an inefficient market in the capiveighted indexes—and vice versa."
If one makes the assumption that there is some-- any-- deviation of stock prices from their true value, then it can be shown mathematically that market cap weighted indices will underperform other methods.
Interestingly enough, I'm going to see if I can take an opposing viewpoint to Arnott. I am not quite so sure that we necessarily must give up a valuation-based weighting schema for indices, unless the empirical mean reversion in the valuation component of company valuation is super duper strong. I think there might be ways to construct a more efficient index under this alternative schema.
I'm sorry if this entry doesn't make sense. Ask and I'll send the reference papers. One word of warning though, they are slightly complicated. Below is the commentary I've written up thus far.
----------------------------
Rob Arnott wrote an interesting paper in the March/April edition of the Financial Analysts Journal and I think he brings up some good ideas. I had some thoughts regarding his paper and a possible extension.
Arnott adds another layer of insight into the question of just what 'the market return' really is in finance literature. He cites CAPM as a somewhat valid economic theory which relies very heavily on what the assumed market return is. Some people posit that it's the S&P 500 return or some weighted average of past S&P 500 returns. His paper and subsequent articles dig into why some current assumptions (and Bill Sharpe!) are a bit silly. This is an important question because if the assumed market portfolio differs from the real market portfolio, our risk/return benchmark statistics will all be wrong, which is a bad thing.
Here are a couple key points I got from the paper, which may or may not be 100% accurate (please let me know if anything doesn't sound right).
To be completely theoretically accurate, the CAPM market index should be a measure of (1) the fair value of (2) pretty much all things which are able to be invested in, so that it's representative of the market as a whole. Finally, the CAPM market index is by definition mean-variance efficient.
Under the above definition, the S&P 500 return is a fundamentally flawed measure of the market return on two levels. First off, the S&P doesn't satisfy (2) above: "the simple fact is, the capital asset pricing model works if your market portfolio spans everything: every stock, every bond, every house, every office building, everything you could invest in on the planet including human capital, including the NPV of all your respective labors going into the future. There's no such thing as an index like that, it doesn't exist. So right off the bat you can say that the S&P 500 is not the market, and anyone who says that it's efficient because it is the market is missing the point: it's not the market." Second and perhaps more importantly, the S&P also doesn't necessarily satisfy (1) above either, because the S&P 500's weighting of stocks by capitalization maximizes the chance of having a 'fair value flawed' portfolio. Unless one believes that stocks do not fluctuate (even randomly and unknown to investors) from their fair value sometimes, then it can be more or less proven that cap-weighted indices will underperform over time. Below are a couple important points.
Price inefficiency, or deviation of stock prices from fair value, need not immediately suggest arbitrage! Suppose we merely know that some companies are overvalued and others are undervalued. We have no simple way to trade away this idiosyncratic noise in prices because we do not know which stock is currently overvalued and which stock is undervalued. Therefore this assumption is not all that crazy.
The cap weighting return drag thesis in my mind comes down to the following really cool statement: " An efficient market in the pricing of individual assets, with pricing errors relative to true fair value, requires an inefficient market in the cap weighted indexes—and vice versa."
The cap weighting return drag thesis may also at least partially explain the relative outperformance of value over growth, and of small caps over large caps.
It is valid to create a market portfolio indexed by more "fundamental" metrics instead of market cap if the alternative metrics can in some way remove the biases inherent in cap weighting schemes without introducing new risks or problems of their own. For example, one may weight stocks by some measure of historical free cash flow instead of market cap.
The kicker: a very robust sampling of 'more valid' valuation metrics consistently outperforms the S&P 500 in both returns and in risk control!
A number of points merit mentioning before I bring up one possible extension.
A market index is more 'valid' as a suitable CAPM market index if it can correct the S&P by underweighting the components which are most statistically likely to be overvalued and overweighting the stocks which are most statistically likely to be undervalued.
Rydex's equal-weight S&P touches in some way on this notion, but not entirely. Equally weighing all S&P components corrects for some of the bias inherent in the S&P's cap weighting, but it isn't perfect because it is in some ways blind to the "real" value of the S&P stocks.
Arnott brings up some interesting statistics regarding the performance of highest market cap companies as well as the performance of the top 10% of all companies on the basis of market cap in the S&P 500, and finds that there is a large and seemingly statistically significant probability that they will underperform the overall market over most time horizons. More than that, the expected underperformance is really big. He calls this a 'return drag,' and implies that this is what is causing the problems for cap weighted indices. He then offers valuation-agnostic metrics as a cure to the problem.
My possible extension:
Going Deeper Into Some of the Implications
Below are some of the implications which I think might be important but weren't satisfactorily covered in his articles (in my opinion at least).
First off the return drag he mentions is very striking but isn't 'clean' in my opinion. Market cap can be broken down into a more fundamental component like earnings or EBITDA and a multiple component like PE or EV/EBITDA. To say that high market cap implies mean reversion over some time horizon is equivalent to saying that high (PE and/or earnings) or high (EV/EBITDA and/or EBITDA) implies mean reversion—so which piece is it? To be cleaner, wouldn't it be better to analyze each component individually? Is it the earnings which mean reverts, or the PE? I bring up this specific way of decomposing market cap because Arnott's proposed solution implies the multiple component of market cap is the dominant mean reverter, because it is clear that all he is doing is weighting entirely off of the more fundamental component—earnings, EBITDA, cash flow, head count… these are all fundamental components. So why not do out the actual statistics on how much mean reversion there was in the components??? Doing them on market cap is nice looking but it isn't focused and 100% relevant to his proposed solution.
It seems that Arnott doesn't really attempt to correct for the implied mean reversion in the multiple. Instead, he throws out multiples completely and uses valuation-agnostic metrics, stating that his indices outperform the S&P. Does all this imply that it is not possible (or not economically worthwhile) to correct the market index for mean reversion in the multiple component? Where are the numbers?
So overall, I think that Arnott's papers are amazing and house some really crucial ideas. I also think that his proposed solutions are great, and correct for a lot of the inherent bias in the S&P 500. Furthermore the strategies used are extremely simple, which adds to the credibility of the underlying theory.
But that being said, it seems like he might be jumping the gun slightly by throwing out all information contained by multiples. By going straight off fundamentals, he seems to imply that multiples are irrelevant. But this is an inherent contradiction with his findings on market cap mean reversion. For example: suppose you have two companies, A and B, spitting out the same free cash flow this quarter. However A is valued at 50 and B at 150, implying that the multiple of FCF is higher for B than for A. Arnott's schema considers these two companies equal to one another. But Arnott himself admits that there is mean reversion in the multiple, so we could adjust for that by allocating more to A and less to B.
Arnott is a smart man. Finally got a chance to read through his unabridged articles and they contain some real gems. For instance, this is something to really sink your teeth into: "An efficient market in the pricing of individual assets, with pricing errors relatiz}e to true fair value, requires an inefficient market in the capiveighted indexes—and vice versa."
If one makes the assumption that there is some-- any-- deviation of stock prices from their true value, then it can be shown mathematically that market cap weighted indices will underperform other methods.
Interestingly enough, I'm going to see if I can take an opposing viewpoint to Arnott. I am not quite so sure that we necessarily must give up a valuation-based weighting schema for indices, unless the empirical mean reversion in the valuation component of company valuation is super duper strong. I think there might be ways to construct a more efficient index under this alternative schema.
I'm sorry if this entry doesn't make sense. Ask and I'll send the reference papers. One word of warning though, they are slightly complicated. Below is the commentary I've written up thus far.
----------------------------
Rob Arnott wrote an interesting paper in the March/April edition of the Financial Analysts Journal and I think he brings up some good ideas. I had some thoughts regarding his paper and a possible extension.
Arnott adds another layer of insight into the question of just what 'the market return' really is in finance literature. He cites CAPM as a somewhat valid economic theory which relies very heavily on what the assumed market return is. Some people posit that it's the S&P 500 return or some weighted average of past S&P 500 returns. His paper and subsequent articles dig into why some current assumptions (and Bill Sharpe!) are a bit silly. This is an important question because if the assumed market portfolio differs from the real market portfolio, our risk/return benchmark statistics will all be wrong, which is a bad thing.
Here are a couple key points I got from the paper, which may or may not be 100% accurate (please let me know if anything doesn't sound right).
To be completely theoretically accurate, the CAPM market index should be a measure of (1) the fair value of (2) pretty much all things which are able to be invested in, so that it's representative of the market as a whole. Finally, the CAPM market index is by definition mean-variance efficient.
Under the above definition, the S&P 500 return is a fundamentally flawed measure of the market return on two levels. First off, the S&P doesn't satisfy (2) above: "the simple fact is, the capital asset pricing model works if your market portfolio spans everything: every stock, every bond, every house, every office building, everything you could invest in on the planet including human capital, including the NPV of all your respective labors going into the future. There's no such thing as an index like that, it doesn't exist. So right off the bat you can say that the S&P 500 is not the market, and anyone who says that it's efficient because it is the market is missing the point: it's not the market." Second and perhaps more importantly, the S&P also doesn't necessarily satisfy (1) above either, because the S&P 500's weighting of stocks by capitalization maximizes the chance of having a 'fair value flawed' portfolio. Unless one believes that stocks do not fluctuate (even randomly and unknown to investors) from their fair value sometimes, then it can be more or less proven that cap-weighted indices will underperform over time. Below are a couple important points.
Price inefficiency, or deviation of stock prices from fair value, need not immediately suggest arbitrage! Suppose we merely know that some companies are overvalued and others are undervalued. We have no simple way to trade away this idiosyncratic noise in prices because we do not know which stock is currently overvalued and which stock is undervalued. Therefore this assumption is not all that crazy.
The cap weighting return drag thesis in my mind comes down to the following really cool statement: " An efficient market in the pricing of individual assets, with pricing errors relative to true fair value, requires an inefficient market in the cap weighted indexes—and vice versa."
The cap weighting return drag thesis may also at least partially explain the relative outperformance of value over growth, and of small caps over large caps.
It is valid to create a market portfolio indexed by more "fundamental" metrics instead of market cap if the alternative metrics can in some way remove the biases inherent in cap weighting schemes without introducing new risks or problems of their own. For example, one may weight stocks by some measure of historical free cash flow instead of market cap.
The kicker: a very robust sampling of 'more valid' valuation metrics consistently outperforms the S&P 500 in both returns and in risk control!
A number of points merit mentioning before I bring up one possible extension.
A market index is more 'valid' as a suitable CAPM market index if it can correct the S&P by underweighting the components which are most statistically likely to be overvalued and overweighting the stocks which are most statistically likely to be undervalued.
Rydex's equal-weight S&P touches in some way on this notion, but not entirely. Equally weighing all S&P components corrects for some of the bias inherent in the S&P's cap weighting, but it isn't perfect because it is in some ways blind to the "real" value of the S&P stocks.
Arnott brings up some interesting statistics regarding the performance of highest market cap companies as well as the performance of the top 10% of all companies on the basis of market cap in the S&P 500, and finds that there is a large and seemingly statistically significant probability that they will underperform the overall market over most time horizons. More than that, the expected underperformance is really big. He calls this a 'return drag,' and implies that this is what is causing the problems for cap weighted indices. He then offers valuation-agnostic metrics as a cure to the problem.
My possible extension:
Going Deeper Into Some of the Implications
Below are some of the implications which I think might be important but weren't satisfactorily covered in his articles (in my opinion at least).
First off the return drag he mentions is very striking but isn't 'clean' in my opinion. Market cap can be broken down into a more fundamental component like earnings or EBITDA and a multiple component like PE or EV/EBITDA. To say that high market cap implies mean reversion over some time horizon is equivalent to saying that high (PE and/or earnings) or high (EV/EBITDA and/or EBITDA) implies mean reversion—so which piece is it? To be cleaner, wouldn't it be better to analyze each component individually? Is it the earnings which mean reverts, or the PE? I bring up this specific way of decomposing market cap because Arnott's proposed solution implies the multiple component of market cap is the dominant mean reverter, because it is clear that all he is doing is weighting entirely off of the more fundamental component—earnings, EBITDA, cash flow, head count… these are all fundamental components. So why not do out the actual statistics on how much mean reversion there was in the components??? Doing them on market cap is nice looking but it isn't focused and 100% relevant to his proposed solution.
It seems that Arnott doesn't really attempt to correct for the implied mean reversion in the multiple. Instead, he throws out multiples completely and uses valuation-agnostic metrics, stating that his indices outperform the S&P. Does all this imply that it is not possible (or not economically worthwhile) to correct the market index for mean reversion in the multiple component? Where are the numbers?
So overall, I think that Arnott's papers are amazing and house some really crucial ideas. I also think that his proposed solutions are great, and correct for a lot of the inherent bias in the S&P 500. Furthermore the strategies used are extremely simple, which adds to the credibility of the underlying theory.
But that being said, it seems like he might be jumping the gun slightly by throwing out all information contained by multiples. By going straight off fundamentals, he seems to imply that multiples are irrelevant. But this is an inherent contradiction with his findings on market cap mean reversion. For example: suppose you have two companies, A and B, spitting out the same free cash flow this quarter. However A is valued at 50 and B at 150, implying that the multiple of FCF is higher for B than for A. Arnott's schema considers these two companies equal to one another. But Arnott himself admits that there is mean reversion in the multiple, so we could adjust for that by allocating more to A and less to B.
posted by Dan McCarthy at
9:51 AM
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