Financial Market Commentary

by Larry Gorman, Steven Sapra and Rob Weigand.

I recently teamed up with Steven Sapra from Analytic Investors and Larry Gorman from Cal Poly San Luis Obispo on a research paper that investigates the relation between stock market volatility, alpha and the information ratio. We find that measures of market volatility provide forecasts of when alpha-capture opportunities in U.S. equity markets improve or worsen. This article will present an executive summary of our findings; readers interested in the technical details can download the complete paper from SSRN.

Investors are apparently interested in the connection between volatility and the availability of alpha. For example, in his August 6 post on alpha/beta separation, Chris Holt mentions an article by Janet Rabovsky of Watson Wyatt  that explores the proper balance between indexing and active management. In particular, Rabovsky’s article makes note of a connection between expected market volatility (measured via the VIX) and the effectiveness of active management:

Not surprisingly, the higher the volatility of the market, the more likely it was for active managers to perform better than the index.

Before presenting our findings, we’ll clarify a few terms. Volatility refers to the standard deviation of stock returns around their time-series mean from the previous year. Dispersion refers to the cross-sectional standard deviation of stock returns around their mean on a particular day. The VIX, of course, is the CBOE implied volatility measure, computed from the implied volatilities of various S&P 500 index options.

It makes intuitive sense that alpha-capture opportunities should improve with higher market volatility — particularly as the dispersion of stock returns around their daily, weekly, or monthly average expands. When active managers predict which stocks are likely to perform better than others, they are essentially forecasting the cross-sectional dispersion of returns. For a given level of skill, there should be a greater opportunity to add value as the return differential between high- and low-performing stocks becomes larger. This is true for both long-only and long-short strategies.

To formally test this idea, we first compute the daily alphas of every stock in the S&P 500 from 1980-2008 vs. a Fama-French 4-factor model. This means that our alphas are measured net of the risk-free rate of interest and 4 betas (market, size, value and momentum). We then document how the supply of alpha varies with the volatility measures mentioned above. Noteworthy results include:

The dispersion of returns is positively related to time-series volatility (correlation = +0.73)

and the VIX (correlation = +0.76).

Moreover, the dispersion of alpha is positively related to return dispersion:

The upshot of this finding is that the alpha spread, or opportunity to add value vs. a benchmark, is expanding and contracting in sync with return dispersion and the VIX (due to its positive correlation with dispersion).

Even better, this relation is not just contemporaneous — dispersion and the VIX provide forecasts of the dispersion of alpha over 3-month and 1-year horizons (3-month results, reported as annualized returns, are shown below). Active managers can calculate dispersion — or observe the VIX at zero cost — and obtain reliable signals of when the dispersion of alpha will expand and contract. The table below divides all the trading days from 1980-2008 into quintiles based on the daily value of cross-sectional dispersion (from low to high), and shows the median annualized alpha from the 10th, 50th and 90th percentiles over the next 3 trading months.

As dispersion increases, the performance in the 10th percentile worsens (from -52% to -76%) and the performance in the 90th percentile improves (from +53% to +86%). This means that the expected alphas from shorting stocks in the 10th percentile and going long stocks in the 90th percentile get larger as dispersion increases.

Grouping trading opportunities by quintiles of the VIX provides an even more powerful alpha signal.

Active managers can anticipate tighter alpha spreads over the next 3 months when the VIX is in its lower two quintiles (comprising 40% of the trading days from 1991-2008, a shorter time period than the dispersion results because the CBOE began publishing the VIX in 1991), and wider alpha spreads when the VIX is in its top two quintiles (comprising another 40% of the trading days over that time period).

The signals do not identify opportunities to earn higher information ratios, however. We find that active risk (tracking error) expands and contracts proportionately with market volatility. The volatility signals are therefore most likely to be useful to absolute return alpha-hunters or relative return investors simply trying to outperform a benchmark, but less useful to relative return investors who measure performance using the information ratio.

Our findings partially explain why active managers, as a group, have such a difficult time outperforming their benchmarks. The best time for skilled managers to hunt alpha is often during periods of declining equity values (because volatility is higher during bear markets) — exactly when investors desire to decrease their equity allocations and reduce their overall risk exposure.

On the other hand, active managers are not underperforming their benchmarks due to an inadequate supply of alpha. In the presence of skill, the alphas that can be earned in U.S. equity markets are large and economically significant. Our analysis shows that a manager who is skilled at going long stocks in the 75th alpha percentile and short stocks in the 25th alpha percentile could earn average gross alphas of approximately 28-30%. Skill is apparently the commodity that is in short supply.

Posted by Rob Weigand.  I expect that, in light of the recent sharp declines in the value of U.S. and global equities, the pundits will begin playing their version of the classic game “Where’s Waldo,” except in this case the prized object they seek is the elusive concept known as the “market bottom.” There is a lot riding on their quest. ”Market timers” who can call a bottom and direct clients to make aggressive asset allocation changes out of bonds (and other safer assets) and back into equities can earn large excess returns. Even more importantly, these excess returns measure up as alpha (the type of outperformance for which managers can charge hefty performance fees). Let’s take a trip down memory lane and see how far the value of equities have fallen in previous bear markets.

The graph shows that, as far as bear markets go, “we ain’t seen nuthin’ yet” in the 2007-2008 bear. The S&P 500 is only down 13% since its high in July 2007. The bear market declines of the 1930s, 1940s, 1970s and early 2000s were all far worse (-85%, -39%, -40% and -43% respectively). What’s more disturbing to me is, when we look a little longer term, we see that today’s value of the S&P 500 is 10% lower than its high in August 2000. That means we’ve been in a no-gain trading range for 8 years. As the chart shows, this is not uncommon historically. For example, after almost 20 years of gains, stocks meandered around a big trading range from 1961-1972, then rose and fell sharply from 1972-1974.

Why do stocks get mired in low-return trading ranges following big run-ups? Let’s look at the next chart and consider an answer to this question.

Notice that big stock price increases are usually accompanied by expansion of the market P/E ratio (we use a 10-year moving average of earnings in the denominator to smooth out the short-term volatility in earnings — let’s call it the P/E10). In other words, big bull markets are not only driven by increases in corporate earnings and dividends, but also by how much per dollar of earnings investors are willing to pay to own stocks (what the P/E10 ratio measures). In this regard the market P/E10 ratio can be thought of as a measure of investors’ long-term optimism about the future. It only makes sense to pay more to own stocks if you think future earnings will grow faster than they’re growing now.

Unfortunately, the chart shows that investors get more than a little euphoric during these bull market periods, and the market P/E10 ratio eventually reverts to the mean (usually significantly overshooting on the downside), bringing stock values back down with it. In 1929 the market P/E10 hit 32, then bottomed out at 5.6 by 1932. In the extended bull market from 1942-1961, the market P/E10 expanded from 8.5 to 22. One of the reasons stock returns were stuck in a trading range from 1961-1972 is that the P/E10 stayed mainly above 20 from 1961-1969 (similar to today’s high P/E10). In 1974 the market P/E10 bottomed out at 8.3 and stayed low until 1982, when it fell as low as 6.6. These were some pretty bleak years in the stock market. But from 1982-1999 the P/E10 expanded all the way to 44, symptomatic of a phenomenal bubble.

This gives us an interesting framework for understanding what drives bull and bear markets.  The best bull market returns have been driven, at least in part, by expansion of the market P/E10 ratio. Unfortunately, as the P/E10 expands, it sucks some of the future expected return out of equities. It used to be the case that expected returns got reset as the P/E10 contracted to ridiculously low values (8 in the 1930s and 6 in the early 1980s). Apparently, it really is “darkest before the dawn” in terms of relative equity valuation. Investors’ despair over the stock market, reflected in super-low P/E10s, sets the stage for future bull runs.

Now here’s the problem — during the 2000-2002 bear market, the market P/E10 never fully corrected. Despite a 43% decline in stock values over this period, at the market bottom the P/E10 remained high, at 21. The current market P/E10 ratio is stuck in a range (25-29) that’s higher than we’ve ever seen (the long-term average is about 15). This means that the stock market might suffer from a dual problem. In addition to going nowhere for 8 years, the stock market has still not finished repricing equities to have the sort of long-term expected returns that get people profoundly excited about owning stocks. When you hear people like George Soros and Jeremy Grantham say that we are in the midst of the greatest global bubble of all time (real estate, commodities, US and global equities), this is what they’re talking about. The value of all investable assets is higher, relative to fundamentals, than ever before — which means that the expected returns for these asset classes are lower than ever before. And all this is playing out just as investors are reawakening to the harsh reality of what a risky world it is. Thus risk is getting re-priced into the value of US and global equities (and real estate, with commodities likely to follow), and prices will keep falling until investors believe the risk premia are sufficiently enticing to warrant a new wave of buying.

 Now, all this does not mean that we are NOT at the market bottom — but it does mean that there’s not much (rational) upside from here, either. In conclusion, let’s take a peek at an experiment I’ve been keeping track of for several years now. It’s not a very scientific one, but I’m sure you’ll agree that it’s interesting. In the chart below, I’ve overlayed graphs of the Nikkei 225 leading up to and following the Japan bubble of the 1980s with the S&P 500 leading up to and following the US stock market bubble of 2000 (in logarithms so that percentage changes in the indexes are visually comparable). Notice any similarities? The point is, based on this chart and the ones above, it would not be unprecedented for post-bubble economies to earn crummy, below-average returns for 10-20 years following the unwinding of bubbles. And we’ve got bubbles that aren’t even close to being fully unwound yet. Lots to think about there.

You can write to Rob Weigand at profweigand@yahoo.com or find him on the web at Rob Weigand’s Home Page.