Size Matters, If You Control Your Junk

The first stock market trading strategy ever discovered was the size anomaly. Banz (1981) found that small stocks outperform large stocks, even after taking into account their higher risk. This finding has had profound implications, such as the creation of small stock indices (since the returns of small stocks shouldn’t be compared to large stocks) and the classification of mutual funds into small or large. It also has implications beyond purely trading. If small companies are underpriced, then they can create value simply by merging with each other.

But, the size effect has since gone out of favor, since it:

  1. Seems to have disappeared since its discovery in 1981, as investors started to exploit the effect
  2. Is driven by extremely small stocks (microcaps and penny stocks)
  3. Is confined to January
  4. Is predominantly a proxy for liquidity
  5. Is weak internationally

Instead, trading strategies since have focused on other dimensions such as value and momentum. But, Toby Moskowitz of Chicago Booth and AQR Capital Management, a former winner of the Fischer Black Prize for outstanding contributions to finance research by someone under 40, presented his new paper at LBS on Thursday, resurrecting the size effect. It’s entitled “Size Matters, If You Control Your Junk”, and co-authored with Cliff Asness, Andrea Frazzini, Ronen Israel, and Lasse Pedersen of AQR. It shows that the size effect still holds if you do a simple twist – control for the quality of a firm (or its opposite, junk).

Quality is any desirable characteristic of a firm. There are four dimensions, which can each be measured in different ways:

  1. Profitability, e.g. gross profits, margins, earnings, accruals, cash flows
  2. Growth: five-year growth in each profitability measure
  3. Safety: low beta, low leverage, low credit risk, low volatility
  4. Payout: dividends, buybacks (net of new equity issuance).

(See the bottom of this post for a simple theoretical justification of these above measures).

Of course, in an efficient market, all of these desirable characteristics will already be in the stock price. But, the crux of active investment strategies is that the market is not efficient. Asness, Frazzini, and Pedersen previously showed that quality stocks outperform junk stocks. And this explains the fragility of the size effect. Small stocks tend to be very junky (i.e. low-quality). Thus, any premium that you earn, as a result of small stocks outperforming large stocks on average, in eaten away by these stocks also being low-quality. So the solution is simple – control for quality. I.e. capture the size premium not just by buying small stocks in general, but buying small stocks that are also high quality.

The results are impressive. The alpha (risk-adjusted annual return) to a strategy of buying small stocks and shorting large ones, ignoring quality, is 1.7%/year (t-stat of 1.23). This becomes 5.9%/year (t-stat of 4.89) controlling for quality. Moreover, this result is immune to the standard ways in which the pure size effect is fragile:

  1. It is stable through time
  2. It is not driven by microcaps, but true for small stocks in general
  3. It is consistent across seasons, and not only driven by January
  4. Is robust to controlling for illiquidity
  5. Is more consistent internationally.

What could be going on here? Why do small stocks outperform large stocks, but only when you control for quality? The authors are still investigating potential explanations, but I punted on one during the seminar (note, this is only my interpretation, not the authors’). Small stocks typically outperform large stocks because they are not noticed by investors: the media and stock analysts typically cover large stocks. As a result, they’re underpriced. But, “junk” (low-quality) stocks attract attention because they are lottery-like. Highly risk stocks (e.g. a pharma start-up) have the potential for huge returns. This may explain why junk typically underperforms quality – investors bid up junk stocks due to their lottery-like characteristics. Thus, while small stocks in general don’t get much attention, junk stocks do – a start-up that’s potentially discovering a cancer cure will indeed be covered by the media. Thus, it’s only small, quality stocks which will exhibit the “inattention discount”, and so they earn the highest returns.


This is the justification of the authors’ quality measures. The simple stock valuation formula is

P = Div / (r – g)

where P = stock price, Div = dividend, r = required rate of return, g = growth rate

Divide through by B (book value) gives

P/B = (Profit / B * Div / Profit) / (r  – g)

which yields

P/B = (Profitability * Payout) / (r – g)

where Profitability = Profit / Book Value,  and Payout = Dividend / Profit

So, a company has a high P/B (high price relative to its book value), if it has

  1. High profitability
  2. High growth (g)
  3. High safety (and thus investors require a low rate of return, r)
  4. High payout

which are indeed the four dimensions of quality studied by the authors.