Tag: quant

The Low Volatility Anomaly

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More returns for less risk

Our previous post on Momentum highlighted the inherent cliff-risk in the “buy-high, sell-higher” strategy. But even before Fama French published their 3-Factor paper, researchers had found that the “high risk = high reward” relationship is quite fragile. In 1972, Haugen, Robert A., and A. James Heins, studying the period from 1926 to 1971, came out with a working paper – On the Evidence Supporting the Existence of Risk Premiums in the Capital Market (ssrn) – that concluded that over the long run stock portfolios with lesser variance in monthly returns have experienced greater average returns than their ‘riskier’ counterparts (wikipedia).

Basically, a portfolio of low-volatility stocks will out-perform the market. More returns for less risk.

What Explains the Anomaly?

There are two main trains of thought on why this anomaly persists.

  1. It is difficult to short high-beta stocks and buy low-beta stocks. Because, if it were easy, one could construct a zero-beta portfolio with positive expected returns… and this anomaly would vanish.

  2. Stocks of companies with predictable earnings exhibit low-volatility. So, low-volatility is essentially high-quality – a known investment factor.

Historical Performance

While low-volatility has out-performed market indices, it is magic wand that makes drawdowns disappear.

India

US

Risks

The biggest risk in a portfolio of low-volatility stocks is that a large proportion of it could be held by weak hands – investors who are drawn to it primarily because of its low-volatility. And when faced with a drawdown that is steeper than historical experience, they can simultaneously head for the exits, resulting in a cascading drop in price. The triggers could be a missed earnings estimate, an industrial accident, etc. While momentum investors are used to being routinely hit in the head, a small shove can push low-volatility investors down a cliff.

Portfolio Construction

A portfolio of low-volatility stocks vs. a low-volatility portfolio of stocks.

While initial research focused on stocks that had low-volatility, a collection of low-volatility stocks can result in a portfolio with high-volatility if the correlations among them are high. To illustrate, consider two low-volatility stocks who’s volatility varies through time like this:

If you put them in the same portfolio, what happens to the portfolio volatility?

Now, what if you picked two stocks whose volatility were inversely correlate? In theory, you can mix to high-volatility stocks and get a low-volatility portfolio.

Resulting in:

Source: Low Volatility: Stock vs. Portfolio, StockViz

Min-Vol vs. Low-Vol

A Min-Vol portfolio tries to optimize the overall portfolio volatility. A completely different approach to having a portfolio of Low-Vol stocks. In the US, there are two large ETFs that track these different approaches: USMV – the iShares Edge MSCI Min Vol USA ETF, and SPLV – the Invesco S&P 500 Low Volatility ETF.

It appears that Min-Vol has an edge over Low-Vol in most scenarios.

Conclusion

While Momentum of Min/Low Volatility can appear to be diametrically different strategies, there are ways to mix them up in the same portfolio to achieve a lower-volatility momentum or a higher-return-low-vol outcomes.

However, at the end of the day, retail investors will forever be at the mercy of market beta. So, irrespective of which flavor of jam you like, the kind of bread you eat makes the biggest difference!

Enjoy the discussion:

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Factors, The Famous 5

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Moar!

In our post on Intro to Factors, we showed how Fama and French added value (HML) and small-caps (SMB) to the original market-risk model to account for the relative out-performance of small-cap/value investment strategies. The genesis of their idea was basically that certain portfolio returns deviated significantly from the market-risk-only model and they wanted to see if they could account for it systematically.

In 2014, they updated their model by adding 2 more factors: profitability (RWM) and investment (CMA) – stocks with a high operating profitability perform better and stocks of companies with the high total asset growth have below average returns.

No Free Lunch

Investors can construct long-only portfolios with a single leg of any one of these factors to exploit it.

For example, one can rank stocks by high book-to-price ratio, take the first 100 of them and create a value portfolio. Such a portfolio will have a high factor loading (ß) for HML.

But just because you can do something like this, should you do it? Depends on your motivations. Factor returns ebb and flow. To visualize the cumulative effect of their spreads, you can plot them as a return series:

As you can see, single factors can spend years in negative territory. During that time, plain-old, low-cost market-beta would be racing ahead while a factor portfolio will be an expensive drag.

This leads us to posit that single factor portfolios are not buy-and-hold-forever investments. For example, during the final phases of a bull market, everything is expensive. So a portfolio of “pure value” stocks will be basically junk that no investor cares about. If you were to invest in such a portfolio, then when the market turns, these stocks are likely to drawdown way more than the rest of the market. If they were unloved in a bull, they will be massacred at the turn.

So unless you thoroughly understand the dynamics of how different factors behave in different market environments, you should stick to market beta.

The Factor Zoo

Fama and French opened the flood-gates for factor research. Academics rushed to discover and publish increasingly esoteric and often overlapping factors. At last count, there were over 400 factors published in various academic journals.

While some of them are a result of p-hacking and not all of them result in lasting alpha, there are a couple that have confounded academics and practitioners alike with their persistence: momentum and low-volatility.

Stay tuned.

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Factors, Intro

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First came the market, then came the factors…

The Efficient Market Hypothesis

Two economists walk down a road and they see a twenty dollar bill lying on the side-walk. One of them asks “is that a twenty dollar bill?” Then the other one answers “It can’t be, because someone would have picked it up already,” and they keep walking. (source)

In 1965, Eugene Fama published his dissertation arguing for the random walk hypothesis. i.e., stock market prices evolve according to a random walk (so price changes are random) and thus cannot be predicted. This was followed by Paul Samuelson, who published a proof showing that if the market is efficient, prices will exhibit random-walk behavior. (source)

Together, they form the basis of the efficient market hypothesis (EMH).

The efficient market hypothesis (EMH), is a hypothesis that states that share prices reflect all information and consistent alpha generation is impossible. According to the EMH, stocks always trade at their fair value on exchanges, making it impossible for investors to purchase undervalued stocks or sell stocks for inflated prices. Therefore, it should be impossible to outperform the overall market through expert stock selection or market timing, and the only way an investor can obtain higher returns is by purchasing riskier investments. (source)

Inefficiencies are opportunities

Any market practitioner knows that this is not entirely true. There are numerous hurdles in the way of pure efficiency:

  1. Information is not free.

  2. Liquidity is not unlimited.

  3. Prices are not continuous.

  4. Market statistics are forever in flux.

  5. Investors have different goals and pursue different outcomes.

  6. Taxes, rules and regulations.

According to EMH, a portfolio’s return could be fully explained by the market (source):

r = rf+ ß(rm – rf) + α

Where:

  • r = Expected rate of return

  • rf = Risk-free rate

  • ß = Beta

  • (rm – rf)= Market risk premium

This is a single-factor model. i.e., portfolio returns are only explained by market risk (rm – rf: market risk premium.) Whatever cannot be explained by the market is α, or the portfolio manager’s skill.

However, if you setup a portfolio in certain ways, you consistently ended up with higher returns, implying that there was something about the market, something systematic, that was not being captured by this equation. So, if you were rewarding a portfolio manager only on the basis of α calculated from the above equation, then you were probably over-paying the PM for harvesting something that the market offered for “free.”

In 1992, Eugene Fama and Kenneth French designed a model to fix this – the Fama–French three-factor model.

The Fama-French model aims to describe stock returns through three factors: (1) market risk (rm – rf: market risk premium,) (2) the outperformance of small-cap companies relative to large-cap companies (SMB: Small Minus Big,) and (3) the outperformance of high book-to-market value companies versus low book-to-market value companies (HML: High Minus Low.) The rationale behind the model is that high value and small-cap companies tend to regularly outperform the overall market. (source)

Where:

  • r= Expected rate of return

  • rf = Risk-free rate

  • ß = Factor’s coefficient (sensitivity)

  • (rm – rf)= Market risk premium

  • SMB(Small Minus Big) = Historic excess returns of small-cap companies over large-cap companies

  • HML(High Minus Low) = Historic excess returns of value stocks (high book-to-price ratio) over growth stocks (low book-to-price ratio)

  • ↋= Risk, or α

Think of SMB and HML as “base-rates.” A portfolio’s returns can now be explained by the degree of tilt (factor cofficients, ßs) it has towards value (HML) and small-caps (SMB). Furthermore, you can set up incentives for the portfolio manager that incorporates these factors so that he is rewarded only if he can out-perform a generic small-cap/value portfolio.

The academic definition of value (HML) and small-caps (SMB) is quite different from what investors are used to colloquially. Fama and French were interested in the decomposition of portfolio returns into sub-components (factors) and the persistence of these factors over many years/decades. They did this by constructing SMB and HML as long-short portfolios and analyzing the spread. It is very different from what the media refers to by these terms. It is useful to think of these as spreads and not as typical long-only “value” portfolio.

No pain, No gain

Just because these factors are persistent, doesn’t mean that they are always positive. A simple way to visualize this is to see the cumulative returns of the market risk premium (MKT = rm – rf) over SMB and HML.

There are periods of both out-performance and under-performance. In fact, one of the theories proposed to explain the persistence of these factors is behavioral: investors herd into value or small-caps based on recent out-performance. Thus, setting them up for subsequent under-performance. Upon which, they will exit en masse, allowing the factors to out-perform once again.

The real world is messy

Most investors are long-only. Whey we buy a value fund, for example, we are not really buying a Fama-French HML long-short portfolio. Our portfolios have a market beta and a bunch of other things affecting it besides high book-to-price ratio.

To visualize this, if we decompose the iShares Russell 1000 Value ETF, IWD, to its 3-factors, we get:

rf + 0.92*(rm – rf) – 0.06*SMB + 0.35*HML + α

Compared to iShares Russell 1000 Growth ETF, IWF:

rf + 1.03*(rm – rf) – 0.05*SMB – 0.27*HML + α

Conclusion

The Fama-French 3-Factor model is a useful tool to analyze investment portfolios. It allows us to decompose returns to different factors so that we can better understand the drivers of returns.

Coming up next: The Fama-French 5-Factor model.

Enjoy our discussion:

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Fat Tails

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Introduction

Years of returns can get wiped out in a month in the markets. While investors mostly focus on the average, the tails end up dictating their actual returns. (Introduction)

Sampling and Measurement

Typically, a uniform sample is taken. The problem with this is it under-represents the tails. This leads to models that work on average but blow up on occasion. One way to overcome this problem is through stratified sampling. (Sampling)

Expected shortfall (ES) is a risk measure that can be used to estimate the loss during tail-events. (Measuring)

Acceptance

All assets have fat tails. It is a feature, not a bug. (Historical)

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Fat Tails, Everywhere

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There is no asset free of extreme tail losses. If an asset produces any sort of return, it is going to be exposed to some sort of tail event.

One can try to find uncorrelated assets so that those losses don’t occur at the same time. However, correlations between asset returns are not stable – they change over time and behave quite erratically during market panics.

In the end, to be an investor is to accept the fact that large losses occasionally happen.

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