Friday, March 7, 2014

Is the value premium a liquidity premium?

 The "High minus low" strategy: Source 

If you haven't read Clifford Asness and John Liew's recent article on market efficiency, you should. There's plenty of meat in the article, but the one sinew I want to chew on is this above chart.  It shows the cumulative returns to a strategy called HML, or "high-minus-low."

This strategy involves going long cheap U.S. stocks (as measured by their price-to-book ratio) and simultaneously going short expensive stocks. Over the last eighty-five years or so, cheap stocks have roundly beat out expensive ones. This is called the value premium. A large part of Asness and Liew's investing effort revolves around exploiting this premium for their clients at AQR Capital Management.

Now as the authors point out, this outperformance could be due to a combination of two things. The behavioural explanation is that people are irrational, subject to various psychological tics that drive aberrations in prices. Perhaps investors are fickle and would rather plunge into sexy and expensive concept stocks than purchase boring but cheap stocks. Asness and Liew propose the idea that investment committees don't have sufficiently long windows for evaluating the performance of their investments. Whatever the explanation, by trading against the various behavioural tics, investors can earn superior profits.

The other explanation is that the value premium has a very rational underpinning. Those who buy cheap stocks and sell expensive ones need to earn a higher return because they must be compensated for bearing some sort of inconvenience, or because they are providing the market with some extra service.

What is that something? My guess is that if you were to adjust the HML strategy's results to account for the superior liquidity return provided by stocks that seem expensive, you'd probably see the returns on cheap and expensive stocks converge. What appears to be an anomaly on the chart is just the shadow of a liquidity premium. Asness and Liew aren't exploiting an irregularity, they're producing liquidity—and getting paid a fair rate for doing so.

Take two companies that are identical except that the shares of the first are more liquid than the second (yep, I've been down this road before). Given a choice of buying either of the two, investors will always prefer the more liquid share. Owning a stock with low bid-ask spreads and plenty of depth provides investors with the comfort of knowing that should some unpredictable event arise, they can easily sell their shares in order to mobilize the necessary resources to cope with the event.

We can think of people "consuming" the comfort provided by liquid shares, much like they consume the peace of mind provided by a fire extinguisher stored away in a closet. If we want more peace of mind, we need to buy a better quality fire extinguisher and/or shares with a higher degree of liquidity. If we can do with less, then we can buy a smaller fire extinguisher and/or switch into illiquid shares.

We can decompose the price of a share into two parts—the price people pay for the share's earnings, and the premium they are willing to cough up to consume the peace of mind that its liquidity provides. Since the earnings on our two shares are the same, the portion of each share's overall price that is explained by earnings will be equal. However, people will put a small premium on the consumption value of the services provided by the illiquid shares and a large premium on the superior consumption yield provided by liquid shares. The difference in premiums means that the market price of the liquid share will be higher than the illiquid one.

Because of this price discrepancy, people will typically say that the liquid share is "expensive" and the illiquid one "cheap", but these are misnomers. The liquid shares provide a stream of valuable services that the illiquid shares fail to provide, and therefore logic dictates that they must trade at a higher price. They might seem expensive relative to underlying earnings, but only if we intentionally ignore the very real flows of consumption that they provide.

By selling "expensive" stocks and buying "cheap" ones, Asness and Liew are really just selling liquidity while taking on illiquidity. In short, in exploiting the HML line they are acting as liquidity providers. Just like Kidde (a major manufacturer of fire extinguishers) provides the world with a worthy service—peace of mind—Asness and Liew are producing and selling that very same good. They are willingly holding the illiquid long positions that others would prefer not to hold, thus forgoing the peace of mind enjoyed by others. And in borrowing and selling liquid shares, they are feeding liquidity into the market that would otherwise be stranded in someone's account at a depository.

Just like Kidde should be well-compensated for its product, Asness and Liew should be appropriately rewarded for their sacrifices. As compensation, their illiquid long position will typically appreciate at a faster rate than an equivalent liquid long position. And their liquid short position will appreciate at a slower than an equivalent illiquid short position.

This difference in expected price appreciation emerges because in equilibrium, an illiquid share needs to provide the same total expected return as a liquid share. Liquid shares already provide an outsized non-pecuniary return (their ability to act as fire extinguishers). In order to counterbalance this, the illiquid share must provide an outsized pecuniary return, or a faster rate of price appreciation. I'm ignoring dividends here. (Again, see this post).

So the HML line charted above illustrates the financial compensation that flows to folks like Asness and Liew who go out of their way to fabricate financial fire extinguishers. (I don't doubt there are also behavioural reasons for it.) Or, conversely, it represents the financial return that people are willing to forgo in order to consume the services provided by liquid shares.

To some degree, Asness and Liew's HML strategy reminds me of the strategy used by Long Term Capital Management. LTCM did a lot of convergence trades in treasury markets. It shorted "on-the-run" bonds, the most recent vintage of debt issued by the government, while purchasing "off-the-run" bonds. On-the-run bonds attract more liquidity than an equivalent off-the-run bonds, and therefore trade at a premium. Thus we see different prices for what are otherwise two identical securities. After a few weeks go by, the current on-the-run bond is replaced by the next issue and suddenly loses its liquidity premium. As long as the short position in on-the-run bonds is held until the next treasury auction, it yields a guaranteed gain when offset against the long position.

Source

I don't think that the profits that LTCM enjoyed by exploiting the on-the-run convergence trade should be thought of as arbitrage gains accruing as a result of other people's irrationality. Much like Asness & Liew and Kidde, LTCM was fabricating peace of mind for others; it held the illiquid securities others didn't want while borrowing and supplying the market with the liquid securities that others preferred. The "excess" return that LTCM enjoyed was the market's fair reward for providing this service.

The service that Asness and Liew provides also reminds me of what a bank does. A bank purchases illiquid personal IOUs issued by families and businesses while selling highly liquid deposits. The bank needn't offer much of an interest rate on deposits because deposits already provide a high liquidity yield. It requires a high interest rate on the IOUs it purchases because it must be compensated for absorbing their illiquidity. The spread the bank earns by holding illiquid assets and providing liquid assets is similar in nature to the HML spread earned by Asness and Liew, and the on-the-run/off-the-run spread earned by LTCM.

Of course LTCM eventually bit the dust. But that didn't have anything to do with the demise of the convergence trade, it had to do with leverage. When its debtors proved unwilling to roll over LTCM's funding, the fund was forced to liquidate at a loss before its positions had converged. If LTCM had been less aggressive, it could have easily held its positions until payoff. The firm might still be in the business of producing fire extinguishers for the financial community, just like Asness and Liew are doing by participating in the HML trade.

41 comments:

  1. The only thing is I would expect value to provide more liquidity in the form of less volatility, after all they do have lower beta.

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    1. This is entirely contingent on how one defines liquidity. Small caps are less liquid than large and do provide higher returns. Value stocks are less volatile than growth but offer (or offered) higher returns. Lower volatility can be considered higher liquidity because they hold their value better across a recession where liquidity is at a premium. Liquidity as ease of selling or as maintaining its value. If greater swings in price are liquidity, then liquidity is to be avoided, not to pay a premium for. Growth with its higher volatility offers less liquidity and less return.

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  2. Good post JP.

    The fire extinguisher analogy doesn't work 100%. (Few analogies do). Some people need liquidity more than others. It doesn't make sense to buy something if you don't need it (as you have said before).

    But this may create a positive feedback loop. The people who buy and sell less will buy the less liquid stocks, but because they buy and sell them less, that reduces liquidity further?

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    1. Neat, it's the inverse of the liquidity-creates-liquidity argument. If liquidity breeds liquidity and illiquidity breeds illiquidity, and people want one or the other, why don't we see one infinitely liquid stock and a bunch of entirely illiquid stocks?

      A few quick thoughts. Exchanges pay specialists or market makers to provide liquidity, limiting the feedback loop to the downside. The huge benefits a firm might enjoy by competing away another firm's much large liquidity premia might limit it to the upside.

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  3. I like your LTCM comment. BTW, if the return on value strategies is determined by liquidity differences, one would guess that with an increase in passive investing (ETFs), that liquidity differences would be reduced and going forward, value strategies should underperform. Time to short BRK vs SPY?

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    1. Before I put on my short position...

      "one would guess that with an increase in passive investing (ETFs), that liquidity differences would be reduced..."

      Why is that?

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    2. For example, stocks usually go up/down when they get added/subtracted to/from a index. This is the liquidity effect and ETF investors generally buy/sell indices. There are ETFs/Indices that now cover every imaginable niche (sector ETFs). I see this in my own behavior; usually I buy a country/asset/sector ETF as a top-down decision, then I quickly scan through the reports on the top 3-5 holdings as a sanity check, then buy/sell. Honestly, I have no idea what I'm buying below the top 5. I rarely buy individual stocks unless it is cheaper than buying the corresponding ETF. The bottom line is I buy/sell a lot of assets that I would not have as a single share buyer. I think my behaviour is reducing the liquidity differences between stocks, but maybe I misunderstood your post.

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    3. Ok, I get it. Interesting point. I agree that if liquidity differences are flattening, folks like Warren Buffet won't see such high returns. (Of course, I'm not sure if ALL differences in value are driven by liquidity, there could be behavioural biases too).

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    4. Not every stock is in a popular index. Oddly enough one of the requirements of index membership for most indexes is a minimum level of liquidity. It may be that the juiciest opportunity will come from buying stocks outside indexes, and selling them when they are added to indexes.

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  4. It is important to note that if there is any inefficiency in the market whatsoever it would be captured by the value anomaly - inefficiently underpriced stocks would have lower P/B's than their inefficiently overpriced counterparts. It's interesting to think of this mispricing as a liquidity service... what do you make of the recent flatness of the past decade? do you think that liquidity is deepening across the market, diminishing the return to producing it?

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    1. I'm not sure if I'd attribute the flatness of markets over the last decade to liquidity per se. Things are probably more complex than that. But you're right that as an asset is made more liquid, its price rises, but once liquidity improvements can no longer be produced then its price will plateau.

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    2. Ah sorry, I meant the flatness of the returns to the strategy (the picture makes it seem as though it's stopped producing alpha since around 2003)

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    3. Ok, I see. Interesting. Similar to jt26's point, I think? If the liquidity profile of stocks is deepening, and stocks that were historically illiquid are now more liquid relative to historically liquid stocks, then yes, the returns to creating selling liquidity/buying illiquidity will diminish.

      If every asset has the exact same liquidity, then there would no longer be any relatively illiquid shares that Asness & Liew could be paid to hold.

      Is that sort of what you're getting at?

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    4. "It is important to note that if there is any inefficiency in the market whatsoever it would be captured by the value anomaly - inefficiently underpriced stocks would have lower P/B's than their inefficiently overpriced counterparts."

      Low P/B is a signal for cheapness that has worked historically, but it isn't cheapness itself. If low P/B investing got to be a mindless fad, then low P/B stocks could become expensive, and high P/B stocks cheap.

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    5. Imagine 2 companies with the same book value and the same intrinsic value. If there is inefficiency in the market, just as a fact of arithmetic the low p/b stock will be the undervalued one rand the high p/b stock will be overly valued, leaving the low p/b one to return more. If the inefficiency were to be gotten rid of by he low p/b method being mindless, it would be reflected in those stocks being priced higher and thus making them not low p/b stocks. The same thing is true for the SMB phenomenon. That's what's interesting about these phenomena, is that they will be better or equal but rarely ever a worse strategy than the market portfolio. If inefficiency is whittled away to 0, that will be the cause of HML or SMB becoming ineffective strategies, not their mindlessness

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    6. "If the inefficiency were to be gotten rid of by he low p/b method being mindless, it would be reflected in those stocks being priced higher and thus making them not low p/b stocks."

      Growth stocks *should* have high P/Bs. It would be an anomaly if they didn't. The anomaly is that they are too high.

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    7. Even among growth stocks there are those with higher and lower book-to-market values. Imagine the two companies I was talking about were both growth stocks, and the argument holds. The research shows that as you go further down the rung on p/b's, performance improves, it's not simply that the high decile underperforms and the low decile outperforms.

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  5. "By selling "expensive" stocks and buying "cheap" ones, Asness and Liew are really just selling liquidity while taking on illiquidity."

    When you say "just" you seem to be saying that stocks sell dear (relative to book value) only because they're more liquid.

    Really?? Amazon is more liquid than Apple?

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    1. I'm riding my point pretty hard in this post for the sake of clarity, but I did give a nod to behavioural reasons for value differences... ie. "(I don't doubt there are also behavioural reasons for it.)"

      The proper way to measure liquidity across different stocks is to get market prices for the value that investors place on that liquidity.

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    2. If one could obtain that data, I would predict you'd find little or no correlation between the liquidity value and book-to-market "value." Liquidity undoubtedly has some effect on price, but I would suggest not on the order of magnitude that we see in book-to-market variations.

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    3. Though you might find a much larger correlation between short-term changes in liquidity value and changes in B-M values.

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    4. "...but I would suggest not on the order of magnitude that we see in book-to-market variations."

      That may be, but the HML return isn't very big to begin with. $1 invested in the strategy in 1927 is now worth just $4 or so. A weak force can explain a weak effect.

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    5. The HML is a self-financing portfolio, so it's not exactly true that $1 "invested" would quadruple. I'm not sure how to calculate the return to HML. The $1 is probably held as treasuries in a collateral account.

      Investing $1 in the long side only would be worth much, much more than $4

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    6. Ok, good point. Let me re-hone my argument ... If Asness and Liew are consistently reporting outsized returns relative to the market, I think that it's reasonable that some part (half, 3/4, 1/50, 100/100) may be due to them bearing illiquidity/providing liquidity.

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    7. Steve,

      There are surely other factors that explain the variance of price to book value (like expected growth for instance) which are neither behavioral nor liquidity related but these should not cause a difference in expected (risk adjusted) return. This difference in return between google and apple (at least in expectations) is likely much smaller and could be explained by liquidity. Though of course those are probably both pretty liquid (and they may have the same expected return).

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  6. LTCM would not have been in business in the first place if they hadn't used so much leverage. The liquidity premium that they could extract on an un-levered on-the-run vs. off-the-run strategy wouldn't provide much of a return on capital.

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    1. Yep, good point. The on-the-run/off-the-run spread doesn't seem to be a very big spread.

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  7. JP, O/T on one of your old posts, on your comment here in particular:
    http://jpkoning.blogspot.com/2013/09/separating-functions-of-moneythe-case.html?showComment=1379531534519#c1295798415247681926

    Does that imply that the concept of UOA in isolation sets up a self contained system of names and symbols and relates the names and symbols to each other internal to this system with numerical ratios, but that this self contained system is not tied to any value or anything at all in the outside world? It sounds like the "definition" (which I take to be the thing which gives the UOA value in terms of an MOA) you now consider to be part of the MOA. Am I correct?

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    1. Yep, that's right. (Funny you ask, my next post is on MOA. I'll try to clarify therein.)

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    2. Great, thanks JP. I've also asked Bill Woolsey to clarify where he stands too, but I haven't heard back yet:
      http://monetaryfreedom-billwoolsey.blogspot.com/2014/02/more-on-negative-interest-rates.html?showComment=1394484009721#c2472031652415480814
      I suspect that you and Bill might agree on UOA, but perhaps not on everything here. But I'm not sure, so that's why I'm asking. Looking forward to your next post.

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    3. I certainly hope Bill and I agree, since I learnt the terms from him!

      But you make a good point. The third category on your list doesn't have its own term. I've been folding it into the MOA. Maybe we can call it the "Tom Brown multiple"?

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    4. JP, in case you're wondering why the interest, there's been a thread going on this on themoneyillusion.com. I won't attempt to find the start of it for you, but here's one entry point (to give a little context):

      http://www.themoneyillusion.com/?p=26304&cpage=3#comment-322686

      I do like the "Tom Brown multiple" idea, but I'm guessing there's no need for that as Bill or this fellow: Jurg Niehans, have probably already nailed it down, don't you think (hope)?.

      I kind of joke about this, but I assume no two econ people agree on anything, especially about fundamental ideas like "money" or any other words for that matter. My philosophy has been to learn what each one means when they use various words. If this thread actually results in two or more people being on the same page, I'll be overjoyed!

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    5. So far I don't have a response from Bill: I emailed him too, and left a msg for him at Nick Rowe's (where he'd left a comment). I'd love to see you address this separate "definition" concept in your MOA post... :D

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  8. I wonder how you would measure the liquidity of a stock? I would think you could use bid/ask spread. If this is the case, one could buy stocks with a high spread and short those with a low spread and this would capture the gains from liquidity preference.

    This whole line of reasoning raises the question of why some stocks are more liquid than others though. If two stocks were "equal" in other respects, shouldn't doing this cause the bid/ask spreads (and therefore the returns from creating liquidity) to converge? I suspect there may be a risk premium bound up in this somehow (the two things seem often difficult to disentangle to me).

    For what it's worth, your account of what banks do here is entirely in line with my view.

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    1. In my opinion, the best way to measure liquidity is to find out how much people are willing to pay to own it. I have a bunch of posts on this, this one for instance:

      http://jpkoning.blogspot.ca/2014/01/different-goods-are-differently-liquid.html

      We don't measure the value of a pear by measuring its sweetness, but by asking people what they'd be willing to pay for it. It should be the same with liquidity.

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    2. Yes of course, that's the definition of "value." What I mean by "measured" is "observed." Specifically, can it be separated out from any other kind of premium (like risk premium) when looking at prices of stocks? Otherwise, you can call any otherwise unexplained difference in return a "liquidity premium." If not bid/ask spread, how about average volume or the price of shares (this seems to be the explanation which gets thrown out for a stock split for instance)?

      P.S. That was the first post of yours I ever read. It was good :)

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    3. Glad you liked it.

      "...when looking at prices of stocks?"

      We can't really do this yet.

      But you might be able to observe a pure liquidity premium that has been stripped of any risk premium by offering an investor a synthetic asset that entirely replicates a position in, say, MSFT. The only difference would be that the synthetic asset would be entirely illiquid for, say, 1 year. The discount that the market applies to the synthetic MSFT position relative to the outright MSFT position would indicate the dollar value of the 1-year liquidity services they are forgoing by choosing the synthetic asset. The party offering the synthetic asset needs to be as close to a risk-free institution as possible, like a clearinghouse, say the CME, or a depository of some sort like DTCC.

      Another way to think of it is that a risk-free institution is offering investors the ability to deposit MSFT for a fixed term. Whatever interest rate investors require will be the liquidity premium.

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  9. Presumably you would also argue that the size premium and other risk premiums are also due to provision of liquidity to the market! At least with the size premium I think the argument would be on more solid ground, given the tendency for smaller stocks to have wider bid-ask spreads and lower turnover than large cap stocks.

    Consider the following thought experiment: an investor decides to buy and sell companies based on their P/B ratio and finds that, on average, she achieves a higher return from those companies purchased at a low P/B ratio. Since all companies are highly illiquid (I.e. they never trade expect at purchase or sale time) the excess return can't be due to liquidity provision.

    In terms of exchange traded markets, simply undertake a double sort experiment: sort stocks into deciles according to liquidity (whatever your preferred measure is) and then within each of these groups look at the returns experienced by stoxks with low P/B ratios compared to those with high P/B ratios. You will find that the value risk premium remains, and since we have already sorted for liquidity, this risk premium can't be explained by liquidity provision.

    Others have posited that the risk premium arises from financial distress and it's correlation with overall equity market returns (I.e. that the value premium often generates negative returns at times when investors strongly dislike such returns and so need to be compensated for that "non-beneficial timing of returns"). This argument is akin to saying that tail risk events are priced, and there is some recent research that supports such a theory.

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    1. " You will find that the value risk premium remains..."

      Hmmm, it sounds like you've crunched the numbers on this?

      Note: I have no problem admitting that liquidity probably doesn't explain everything, but it might explain some portion of the various premia. I'm not an extremist on this.

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  10. Agree with the comments above regarding the size premium. A compensation for liquidity risk - if there is such a thing, and I believe there is - is more associated with SMB than with HML. Plenty of extremely liquid, cheap (e.g. low market-to-book, low P/E) names. Think AAPL. I'm sure there is plenty of work out there running liquidity against HML, and guessing the correlations are much lower than liquidity against SMB.

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