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Posts Tagged ‘High Minus Low’

In yesterday’s post we discussed some informal analysis I’ve undertaken on the returns to the quantitative investment strategy known as “High Minus Low” or HML. The first step was an analysis of HML’s components, high and low BM stocks. I described the HML strategy in some detail and analysed the long-term diminution in the returns to those components. I think that the returns to both high BM and low BM stocks have been attenuating significantly over time. The phenomenon persisted over whichever recent period I analysed (since 1926 to the present day, or over the last 25, 20, 15 or 10 years). This suggested that it’s got harder over time to earn excess returns as a value investor employing a high BM strategy.

In today’s post, I analyse the returns to HML at the strategy level and ask whether the returns to HML are really just returns to a levered high BM strategy. In a Goldman Sachs Asset Management (GSAM) presentation, Maybe it really is different this time, GSAM argued that the returns to HML have diminished since August 2007 because too many investors are employing the same  strategy, a phenomenon GSAM describe as “overcrowding.” In summary, I agree with GSAM’s view that the returns to HML have indeed stagnated since late 2007. I’m not sure that this is attributable to “overcrowding” as GSAM suggests or just a function of the underlying market performance of the components of HML (i.e. everything has been and continues to be expensive, leaving little room for good returns). Interestingly, even accounting for the period of low attenuated performance between August 2007 and the present, the HML strategy has performed reasonably well over the last 10 years, which has been a period of diminished (or non-existent) returns for equities. The returns to a 130/30 HML strategy over the last 10 years significantly outpaced a high BM strategy and the market in general. Surprisingly (to me at least), the low BM short didn’t add much to HML returns. This is especially surprising give that the period analysed was one where the low BM stocks bore the brunt of the collapse. That observation requires some further analysis, but it’s a prima facie argument that most of the returns to HML are due to the leverage inherent in the strategy.

Returns to HML

Most hedge fund strategies being proprietary and, hence, closely guarded secrets, I’m not sure what the typical HML strategy looks like. For the sake of this argument, I’ve constructed three HML portfolios. The first is 30% short the low BM decile and 130% long the high BM decile, which is a not uncommon hedge fund strategy. The second is 100% short the low BM decile and 100% long the high BM decile, which highlights the low BM short and removes the effects of leverage from the high BM long. The third is 130% long the High BM decile and has no short, to remove the effect of the short and highlight the effect of the leverage. How would those strategies have fared over the last 10 years, which, as we saw yesterday, was a period of attenuated returns for equities?

The 130/30 HML strategy

“Low BM” is the lowest BM decile, marked in red. This is Decile 1 from the Average monthly returns to decile BM portfolios chart in yesterday’s post. “High BM” is the highest BM decile, marked in blue. This is Decile 1o from yesterday’s chart. The green “HML” line is -30% of the return on the low BM decile and 130% the return on the high BM decile. “Delta,” in purple, is the difference between the return on the low and high BM components of the HML strategy. Here’s the chart:

Several observations can be made about the chart. First, as at September 2009, the “Low BM” strategy (in red) is down 3%, which approximates the return on the market as a whole over the last 10 years. The “High BM” strategy (in blue) is up about 95%, which is not a great return over 10 years, but well ahead of the market in general and the Low BM portfolio. The HML portfolio is up around 124%, well ahead of both the Low BM and High BM portfolios. As recently as 2003, the 130/30 HML portfolio was underwater and it nearly accomplished this feat again in 2009. It performed almost in line with the High BM portfolio while the market was tanking, which is when I would have expected the Low BM short to protect the return on the HML, affording only a little protection. It seems that the return on the 130% long component of the High BM portfolio caused the HML strategy to tank with the High BM portfolio, although it also caused it to recover much faster. While GSAM is correct that HML returns have been reduced since late 2007, the 10-year return on the 130/30 HML is attractive.

The 100/100 HML strategy

In this chart the green “HML” line is -100% of the return on the low BM decile and 100% the return on the high BM decile:

The 100/100 HML chart illustrates several points. First, as at September 2009, the HML portfolio is up 98%, in line with the High BM portfolio. Where the Low BM portfolio falls, the 100% low BM short in the HML protects it. For the last 10 years, it has generally protected the HML return. Of course it hurts the HML’s performance when the low BM short rises, which, as we saw yesterday, has generally been the case since 1926.

The Levered High BM strategy

This chart shows the High BM portfolio levered at the same rate as the 130/30 HML strategy (i.e.130%), but without the low BM short:

The Levered High BM portfolio tracks (visually) almost identically to the 130/30 HML strategy (Levered High BM closed up 123%, HML closed up 124%). This suggests to me that most of the additional gains in the 130/30 HML strategy over the High BM strategy are simply attributable to the leverage in the HML, and not out of any protection afforded by the low BM short.

Recent returns to HML depressed

A casual perusal of any chart above illustrates that HML has not progressed since August 2007. GSAM argues that this is a secular phenomenon due to overcrowding. I’m not convinced that it’s a secular phenomenon, but it’s certainly noteworthy. I’m also not entirely convinced that it’s due to overcrowding. It could just as easily be a function of the high price for equities in August 2007 and again now. GSAM argues that your view on the phenomenon as being either cyclical or secular is key to how you position yourself for the future. If you believe it’s cyclical, you’re a “Sticker,” and, if you believe it’s secular, you’re an “Adapter”. The distinction, according to Zero Hedge, is as follows:

The Stickers believe this is part of the normal volatility of such strategies

• Long-term perspective: results for HML (High Book-to-Price Minus Low Book-to-Price) and WML (Winners Minus Losers) not outside historical experience

• Investors who stick to their process will end up amply rewarded

The Adapters believe that quant crowding has fundamentally changed the nature of these factors

• Likely to be more volatile and offer lower returns going forward

• Need to adapt your process if you want to add value consistently in the future

I’m in the cyclical camp, but it may be other players withdrawing from the field that causes the cycle to turn.

Conclusion

Despite GSAM’s protestations to the contrary, and despite the diminution of equity returns at both the value and glamour ends of the market, HML remains an attractive strategy. Over a 10-year period of attenuated equity returns, a 130/30 HML strategy performed very well. It seems, however, that most of the returns to the 130/30 strategy are attributable to the leverage in the high BM portfolio, rather than any protection in the low BM short. As we saw yesterday, the low BM decile, while generating a lower return than the high BM decile over time, has mainly generated positive returns. This means that the low BM short will generally hurt the HML strategy’s performance.

My vast preference remains a leverage-free, long-only, ultra-high BM portfolio for a variety of reasons not connected with the chronic underperformance of the short, most notably that it’s the lowest risk portfolio available (despite what Fama and French say). In my opinion, the diminution in returns to the high BM strategy we observed yesterday is a cyclical phenomenon. 25 years is a long time for a cycle to turn, but I’m reasonably confident that the high BM strategy will again generate average monthly returns in line with the long-run average on yesterday’s chart, which means average monthly returns in the vicinity of 1.2% to 1.4%. I don’t foresee this occurring any time soon, and I think dwindling returns are the order of the day for the next 5 or 10 years. If I had to be anywhere in equities, however, I’d start in the cheapest decile of the market on a price-to-book basis and work my way through to those with the highest proportion of current assets. That’s a proven strategy that served Graham and Schloss very well, and, as far as I can see, there’s no reason why it shouldn’t continue to work.

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Recently we discussed a Goldman Sachs Asset Management (GSAM) presentation, Maybe it really is different this time, in which GSAM argued that High Minus Low or HML, a quantitative investment strategy that seeks to profit from the performance differential between high and low book value-to-market value (BM) stocks, had underperformed since August 2007 due to “overcrowding.” Robert Litterman, Goldman Sachs’ Head of Quantitative Resources, was quoted as saying that “strategies such as those which focus on price rises in cheaply-valued stocks…[have] become very crowded” since August 2007 and therefore unprofitable. The GSAM presentation included a variety of slides showing the reduction in the returns to HML and the growth in the number of practitioners in the space (See my summary of the GSAM presentation and Zero Hedge’s take on it).

Over the last week I’ve run my own informal analysis of the returns to HML and its components, high and low BM stocks. The resulting post has metastasised into an epic (by my standards), so I’ve broken it into two parts, Component returns (Part 1) and HML returns (Part 2). In today’s post, Component returns, I describe the HML strategy in some detail and analyse the long-term diminution in the returns to the components of HML, namely, high BM (low P/B) stocks and low BM (high P/B) stocks. The results are stunning. The returns to the high BM and low BM stocks have been attenuating significantly over time. Further, the phenomenon persists over whichever recent period we elect to choose (since 1926, or the last 25 years, 20 years, 15 years or 10 years). This suggests that it’s got harder over time to earn excess returns as a value investor employing a high BM strategy.

In tomorrow’s post, I analyse the returns to HML at the strategy level and ask whether the returns to HML are really just returns to a levered high BM strategy. In summary, the returns to HML have indeed stagnated since late 2007. I’m not sure that this is attributable to “overcrowding” as GSAM suggests or just a function of the underlying market performance of the components of HML (i.e. everything has been and continues to be expensive, leaving little room for good returns). Interestingly, GSAM’s argument that HML is dead as of August 2007 aside, the HML strategy has performed reasonably well over the last 10 years, which has been a period of diminished (or non-existent) returns for equities. The returns to a 130/30 HML strategy over the last 10 years significantly outpace a high BM strategy and the market in general. Surprisingly (to me at least), the low BM short didn’t add much to HML returns. This is especially surprising give that the period analysed was one where the low BM stocks bore the brunt of the collapse. That observation requires some further analysis, but it’s a prima facie argument that most of the returns to HML are due to the leverage inherent in the strategy.

A primer on HML

As I mentioned above, HML is a quantitative investment strategy that seeks to profit from the performance differential between high and low book value-to-market value stocks. It’s interesting to me because it appears to be a value-based strategy. In actuality, it finds its roots in the Fama and French Three-Factor Model, which is an attempt to explain the excess returns attributable to value stocks within an efficient markets context. HML also owes an intellectual debt to the various studies demonstrating the relative outperformance of low price-to-value stocks over higher price-to-value stocks – Roger Ibbotson’s Decile Portfolios of the New York Stock Exchange, 1967 – 1984 (1986), Werner F.M. DeBondt and Richard H. Thaler’s Further Evidence on Investor Overreaction and Stock Market Seasonality (1987), Josef Lakonishok, Andrei Shleifer, and Robert Vishny’s Contrarian Investment, Extrapolation and Risk (1994) as updated by The Brandes Institute’s Value vs Glamour: A Global Phenomenon (2008) – but it is most closely associated with Fama and French.

Fama and French observed in their 1992 paper, The Cross-Section of Expected Stock Returns, that there is “striking evidence” of a “strong positive relation between average return and book-to-market equity” [“BE” is book equity and “ME” is market equity, so “BE/ME” is just BM, the inverse of P/B]:

Average returns rise from 0.30% for the lowest BE/ME portfolio to 1.83% for the highest, a difference of 1.53% per month.

Note also that the strong relation between book-to-market equity and average return is unlikely to be a [beta] effect in disguise.*

[Although] BE/ME has long been touted as a measure of the return prospects of stocks, there is no evidence that its explanatory power deteriorates through time. The 1963-1990 relation between BE/ME and average return is strong, and remarkably similar for the 1963-1976 and 1977-1990 subperiods. Second, our preliminary work on economic fundamentals suggests that high-BE/ME firms tend to be persistently poor earners relative to low-BE/ME firms.

Ibbotson (1986), DeBondt and Thaler (1987), Lakonishok, Shleifer, and Vishny (1994) and The Brandes Institute (2008) all make similar findings. Low P/B stocks outperform higher P/B stocks in the aggregate, and in rank order, the cheapest decile, quintile, quartile etc outperforming the next cheapest and so on. This phenomenon obviously presents a problem for the efficient markets crowd because the historic excess returns of value stocks over glamour stocks cannot be explained by the traditional CAPM model. Fama and French’s solution is the Three-Factor Model.

Fama and French attribute the variation in average returns between high and low BM stocks to “relative distress,” arguing that value strategies (i.e. high BM stocks) produce abnormal returns because they are fundamentally riskier. This observation is the impetus for the inclusion of “value” as a factor in Fama and French’s Three-Factor Model, where it is accounted for as “HML”. (It was also the impetus for Piotroski’s F_SCORE, which seeks to use “context-specific financial performance measures to differentiate strong and weak firms” within the universe of high BM stocks.)

HML in the Fama and French context measures the historic excess returns of value stocks over growth stocks, which break the traditional CAPM model. Here’s how they circumvent the problem: By splitting out HML from the market return and labelling the portion of the excess return attributable to HML as “riskier,” Fama and French can explain away those excess returns. They then simply apply an HML coefficient to a portfolio of value stocks and – abracadabra – the expected return is higher than the market return but explainable within the efficient markets world because of the additional risk attributable to value. The proponents of the efficient markets hypothesis breathe a sigh of relief and continue to believe that no one can make excess returns once those returns are adjusted for risk. (Don’t mention that value is not, per se, riskier, because such an observation would break the model all over again.) It’s worth noting that Lakonishok, Shleifer, and Vishny (1994) disagree with Fama and French’s assertion that the returns are due to financial distress, arguing instead that the returns to value are the result of a bias that leads investors to extrapolate past performance too far into the future, not fully appreciating the phenomenon of mean reversion.

Whatever the basis for the returns to value, the phenomenon has attracted a substantial following in the world of quantitative investing. So much so that GSAM thinks the field is now “overcrowded” and that explains the diminution in returns since August 2007. The attraction of the HML strategy to a quant is easy to understand: They’re agnostic to the reason for the excess returns, and more than happy to earn some and remain market neutral. The solution is to split out from the market return the excess return attributable to HML. How does one do that in practice? One simply buys the value stocks and sells the glamour stocks. This means buying high BM stocks and selling short low BM stocks. It’s extraordinary that, despite the tortured EMH reasoning, HML is a strategy that a value investor would recognize and (shorting, leverage and aggregation notwithstanding) probably approve of in its general terms. Before looking at the returns to the HML strategy, I think it’s useful to look under the hood and consider the “engine” of the strategy, which is the returns to the underlying components.

* One of the observations made by Fama and French (1992) is that “average returns for negative BE firms are high, like the average returns of high BE/ME firms. Negative BE (which results from persistently negative earnings) and high BE/ME (which typically means that stock prices have fallen) are both signals of poor earnings prospects.” This is very interesting. I’ve never heard of a negative BM strategy. While it makes me a little nervous to think about, it’s possible that negative BM stocks are an untapped source of returns. Perhaps it’s just the leverage at the company level, but it warrants a further investigation and a later post. Let me know if you’ve got any data or studies on the subject.

Returns to HML’s components: High BM and Low BM

There are two components to the HML strategy: The high BM long and the low BM short. The strategy seeks to remain market neutral by selling short low BM stocks, which are expected to fall back to the mean market BM value, and using leverage to buy high BM stocks, which are expected to rise to the mean market BM value. To see how each component performs, I’ve produced a chart of average monthly stock returns since 1926. Before I present the graph, a quick disclaimer: What follows does not amount to a formal academic study into the relative performance of high BM and low BM over time. It’s nothing more than me messing around with COMPUSTAT return data and plugging it into an Excel spreadsheet. Stocks were divided into ten deciles based on book value-to-market value. Average returns for each decile were calculated on a monthly basis over five different time periods:

  • “All” from July 1926 to September 2009
  • “25 Years”, from October 1984 to September 2009
  • “20 Years”, from October 1989 to September 2009
  • “15 Years”, from October 1994 to September 2009
  • “10 Years”, from October 1999 to September 2009

“Decile 10” is formed from the portfolio of stocks with the highest BM ratio (lowest P/B), “Decile 1” is the portfolio of stocks with the lowest BM ratio (highest P/B) and so on. Here’s the chart:

For me, three observations leap out from the chart. First, the relationship between high and low BM deciles is relatively unchanged over time. The relatively high BM stocks in deciles 10, 9, and 8 tend to outperform the relatively lower BM stocks in deciles 1, 2, and 3. With few exceptions, the higher the ratio of book to market, the better the performance.

Second, the returns to all deciles have attenuated significantly over time. This was one of the questions I had after reading The Brandes Institute’s Value vs Glamour: A Global Phenomenon update of the Contrarian Investment, Extrapolation and Risk. The Brandes Institute paper didn’t split out from Lakonishok, Shleifer, and Vishny’s paper the more recent returns to high BM stocks, but the blended return was lower in the later study, suggesting that returns had diminished in the intervening period. As far as this simple analysis goes, it seems to confirm that impression.

The third observation is that the low BM decile – Decile 1 – has for most of the time had a positive monthly return. It is only over the last 10 years that the monthly returns for the lowest BM decile have been negative. This is significant because this means that, the last 10 years aside, one employing the HML strategy would have lost money on the low BM short, and would have earned better returns without the short. Over the last 10 years, however, one would expect that the low BM short has paid off handsomely. As you’ll see tomorrow, this is not actually the case.

Hat tip to the Ox for the return data.

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