# October, what a month!

Last Friday was the 25th anniversary of the stock market crash on Black Monday, October 19, 1987. That event still stands as the most extreme negative event in the stock market going back to the 1950s. Exhibit 1 is a histogram showing the frequency of daily S&P 500 price changes in terms of standard deviations from the mean daily return (the data has been standardized with a mean of zero). As one might expect, roughly 95% of the S&P 500’s daily moves fall within +/- 2 standard deviations of the mean. But, look at those tails.

When shown as standard deviations, Black Monday was a 21-standard deviation event (the market fell 20.5% that day). What does that mean? Statistically, the probability of a 21-standard deviation event occurring on any particular day is 3.2793e-098 (i.e., very, very, very unlikely). We would expect to see such events no more than once every 8.3547e+094 years. How large is that number? An interesting paper by Kevin Dowd, John Cotter, Chris Humphrey and Margaret Woods (*How unlucky is 25-Sigma?*) calls such numbers “on truly cosmological scales” and compares them to the estimated number of particles in the universe. A 20-standard deviation event has an expected occurrence in years that is 10 times larger than the estimated number of particles in the universe.

The next day, October 20, 1987, the market experienced a positive 5.4-sigma event (the S&P 500 rose 5.33%). Statistically, we would expect to see a 5-sigma event once every 9,542 years. The thing is, the day after that the market experienced a positive 9-sigma event (on October 21, 1987 the S&P 500 rose 9.1%) – which we would expect to see only once every 355,120,000,000,000,000 years.

That’s three “once-in-a-lifetime” events, three days in a row.

In 2007, Goldman Sachs’ then CFO, David Viniar, famously attributed their flagship hedge fund’s dismal performance to “25-standard deviation moves, several days in a row” (FT, August 13, 2007). We know that is not very likely and, in fact, did not actually happen. In reality, the most extreme sigma event in 2007 was a 3.59-standard deviation decline on February 27, 2007 when the S&P 500 fell 3.5% (which we would expect to occur once every 16 years). On August 9, 2007 (the day considered the start of the global financial crisis), the market experienced a negative 3.04-sigma event – which we would expect to occur once **every two years**.

Getting back to the month of October, after the extreme event of Black Monday in October 1987, the next three largest sigma events all occurred in October 2008. October 13, 2008 saw the S&P 500 rise 11.6% – an 11.8-standard deviation move we would expect to see only once every 200,610,000,000,000,000,000,000,000,000 years. However, just **two days later** the S&P 500 fell 9% – a 9.3-standard deviation move we would expect to see only once every 355,130,000,000,000,000 years. Then, a mere **thirteen days after that** the S&P 500 rose 10.8% on October 28, 2008 – an 11-standard deviation move we would expect to see only once every 17,903,000,000,000,000,000,000,000 years.

Remember those days? They certainly occur more often than we’d expect. Three times each in two different months of October a quarter of a century apart. The next time you hear someone talking about “fat tails,” that’s the sort of thing they’re talking about.

# Index Performance Summary–December 2011

Here are a few exhibits from our recent Index Performance Monitor. Exhibit 1 shows the percentage change (in US Dollars) of global equities markets for various time periods as of 12/31/2011. The five regional index changes are price returns. The individual country index changes are total returns. Notable is that every region showed negative returns in 2011. Emerging markets suffered the most, losing nearly 20.5% (as a group, the BRICs were down roughly 26%, on average). However, the European and Pacific regions were not far behind. Within those regions, Japan, Germany, and France suffered almost as badly as the emerging markets. Despite the turmoil (and volatility – see Exhibit 2), US market performance seemed tame by comparison.

The longer-term picture, however, shows that emerging markets still rule the roost – with average annual price returns of 11.2% over the last 10 years despite 2011 losses. Emerging markets performance has fallen in the last two years, but not too far out of line with most of the developed markets.

Exhibit 2 shows asset mix total returns for selected (mostly US) assets over various time periods. US government bonds were the place to be in 2011. US corporates and REITs were not far behind. Anyone who dumped them early in the year, stayed out of them entirely, or (worse) shorted them, missed a significant opportunity or suffered losses.

Also, notable is the substantial increase in volatility, as measured by the VIX. Although volatility fell in the last few months of 2011, it was up overall for the year.

# The Bigger Picture: S&P 500 Rolling 10-Year Annual Returns

It’s useful to expand our horizons on a regular basis and take a look at the longer-term picture when it comes to the equities markets. It helps put recent events in perspective. Exhibit 1 shows the rolling 10-year average annual total return and the rolling 10-year average annual income return of the S&P 500 from 1926 through the end of 2011. As we can see, recent returns have been downright dismal and most closely resemble the period following the Great Depression in the 1930s. The recent rolling 10-year low was reached in February 2009.

Exhibit 1 also shows the importance of dividends. Although the S&P 500 yield is near it’s all-time low, in the current environment it supplies the lion’s share of total return.

The picture changes a bit when we look at real returns – total returns adjusted for inflation. Exhibit 2 shows the rolling 10-year average annual inflation adjusted total return for the S&P 500 from 1926 through the end of 2011. On a real basis, we can see that the recent market lows are the worst on record since, and including, the Great Depression – bottoming at –5.86% in February 2009. S&P 500 rolling real returns then remained negative until February 2011.

# Correlation of US Equity Market with Global Regions

Exhibit 1 is a table showing monthly correlations of the US equity market with various global equity markets as of 12/11/2011. The first five columns show average monthly correlations for various time periods. The next ten columns show average monthly correlations by year for the ten years 2002 – 2011. The final column shows the trend of monthly correlations over the last ten years.

(Click on image to enlarge.)

Several things stand out:

1. As has been widely reported, global markets have generally become more correlated over the last decade. For most regions, the highest correlations with the US market have occurred within the last three years – with India being the lone exception in this data set. The lowest correlations generally occurred early in, or in the middle of, the last decade.

2. Japan, Russia, and India have tended to be the least correlated markets over the last ten years, with China not far behind.

3. Those looking for diversification outside US equity markets have very few choices among relatively developed markets these days. Japan and India are currently the markets least correlated with the US equity market. US market correlations with China and Russia are quite high recently.

# “Sell in May” Part Deux

May 2011 once again saw a negative price return on the S&P 500; although, this year’s –1.35% pales next to last year’s price return of –8.20%. Since everyone is looking at June’s expected performance, I thought I’d update last year’s “Sell in May” charts (“They sold in May. Will they stay away?”).

The Reformed Broker has a post up (“June Swoon”) with a chart showing the average monthly gain of the Dow Jones Industrial Average since 1950. Exhibit 1 below updates our chart from last year showing the average price return by month for the S&P 500 for the period January 1945 through May 2011.

After last year’s miserable June performance, which saw a –5.39% return, the average monthly price return in June since 1945 has turned slightly negative at –0.02% – further cementing it’s standing as one of the worst performing months for the S&P 500.

Exhibit 2 shows the S&P 500 price return for the month of June for the prior 11 years (2000 – 2010). In eight of the last eleven years, the S&P 500 price return has either been roughly zero or negative. Last year’s performance caused the 11-year average return to fall even further to –1.83%.

If you haven’t made your vacation plans, yet, June looks like a fine month to hedge your positions, take some time off, and forget about the market.

**UPDATE [6/5/2011)**

A discussion with a client prompted me to create a few additional charts – three of which I’ve posted below.

Exhibit 3 shows the average monthly price return (since 1945) for the S&P 500 for the six-month period May through October, and for the six-month period November through April. There certainly seems to be something to the “Halloween Indicator.”

Exhibit 4 shows the S&P 500 average compounded price return (since 1945) for the six-month periods shown. As expected, the S&P 500 has done much better from November through April.

Exhibit 5 shows the S&P 500 average monthly price return by quarter. Since 1945, you wouldn’t have missed much – on average – had you taken the entire summer off each year.

# A Tale of Two Fund Managers, Part 2

In Part 1 of this “series,” I looked at Bill Miller’s Legg Mason Value Trust to see if Miller really was a “value” guy and whether or not he had added any “value” as a stock picker. Using a Fama-French Three-Factor Analysis (3FM), the answers were “no” and “no” for the time periods examined (through May 2008).

This time, I’m going to look at Ken Heebner’s CGM Focus Fund (CGMFX) to see if he’s really a "”growth” guy and whether or not he has added any “value” as a stock picker. Exhibit 1 shows a chart of the daily price of the fund (adjusted for dividends) since inception on October 1, 1997 through the end of October 2010. The chart shows that CGMFX had a great run until mid-2008 – handily outpacing the S&P 500. According to Bloomberg Businessweek, Heebner’s fund had average annual returns of 32% from 2000 through 2007, while the S&P 500 returned 1.7% annually. Then things got very ugly very fast. From it’s peak on June 23, 2008 to the subsequent low on March 9, 2009, the fund lost 67% of its value.

Despite his relatively abysmal performance since 2008 (see Exhibit 2), Heebner’s long-term record tops all other mutual funds, according to Morningstar, and his CGMFX fund has outperformed the S&P 500 by nearly 15% per year over the last decade. While this is a notable achievement, we’ll see below that the S&P 500 might not be the most appropriate benchmark for CGMFX.

So, let’s get to it. Using daily data and the same methodology described in Part 1, I regressed the daily risk-adjusted returns of CGMFX against the factors in the 3FM (data from Kenneth French’s web site): the excess return of the total market (CRSP 1-10) over the T-bill return (Mkt-RF), the return of small company stocks minus that of big company stocks (small minus big, or SmB), and the return of the cheapest third of stocks sorted by price/book minus the most expensive third (high minus low, or HmL). Exhibit 3 shows the results of the regressions over various time periods.

Interpreting the results, we find:

1. Over the life of the fund, the 3FM explains roughly half of the variation in the fund’s daily returns – not a great fit. More recently, however, the three factors explain roughly 90% of the fund’s returns – a pretty decent fit.

2. Looking at the Alpha, we see that Heebner has outperformed the regression-based benchmark over the longer term by about 7% per year (columns 1 and 2), but more recently he has underperformed by nearly 6% annually (columns 4 and 5). He’s also on track to underperform in 2010. Note, however, that the t-statistics and p-values tell us that his alpha is not statistically significant.

3. The fund’s long-term beta (Mkt-RF) is just under 1.0 (columns 1 and 2) – so basically the fund moves with the market. More recently, however, the fund has become more volatile and beta has risen to about 1.3.

4. The SmB coefficients tell us that the fund is basically a large cap fund (SmB <= 0.0).

5. The HmL coefficients tell us that the fund is a *value* fund – the statistically significant coefficients are either well above 0.3 (columns 1 and 2) or slightly below (column 6). Just as with Miller’s LMVTX, Morningstar classifies CGMFX as a “Blend” fund – a hybrid of growth and value. If you consider only the more recent HmL factors loadings you might reach the same conclusion.

So, once again the 3FM analysis tells a slightly different story than the “conventional” wisdom. Ken Heebner’s CGM Focus Fund is a large cap *value* fund that is recently more volatile than the market and generates no statistically significant alpha.

# They sold in May. Will they stay away?

The S&P 500 price return in May 2010 was –8.20% (total return was –7.99%) — much worse than the historical average for the month of May. Exhibit 1 shows the historical average price return by month for the S&P 500 for the period January 1945 through May 2010.

As we see in Exhibit 1, the month of June has historically been one of the worst performing months for the S&P 500 – with price return averaging 0.1%. However, more recently S&P 500 performance in the month of June has been downright dismal. Since 2000, June S&P 500 price return has been negative five times (see Exhibit 2). The average monthly price return for June over the last nine years is –1.48%. Over the last five years (June 2005 – June 2009) the average monthly price return in June has been –2.36%.

They sold in May this year. Will they stay away in June?

# What’s the Big Deal With Short Selling?

On July 15th, the SEC issued an emergency order limiting “naked” short selling of 19 selected financial stocks. The rule went into effect on July 21st, and was initially intended to last for two weeks — with a possible extension of up to 30 days. On July 29th, the SEC extended the rule until August 12. I won’t go into a discussion of short selling, or try to get inside the SEC’s head here. What I do want to do, however, is take a look at short interest data for some of the companies on the SEC’s list and compare that data to other well-known companies that are not on the list. I wanted to know if there was an “obvious” reason to selectively limit the short selling of certain companies’ shares — something that might jump out at you from the data? In short, I wanted to know if there was any “there” there?

So, I fired up Excel and had a chartfest. The results are shown below. The first chart is a rather busy-looking thing that shows short interest for the last 10 years (as a percentage of shares outstanding) for nine US companies on the SEC’s list (warning: PDF file). As is obvious from the chart, short interest for LEH, FNM, and FRE (and to a lesser extent, MER) rose rather dramatically in the last 12 months and was at 10-year highs as of March 31, 2008. It’s also clear that short interest for the remaining companies, while perhaps higher recently, is not “unusually” high. Note that Goldman Sachs’ (GS) short interest was much higher in the ’02-’03 time frame than it is today — it even exceeded MER’s current level by a relatively substantial amount.

The following panel shows individual charts for each of the nine companies. From these charts, we can again see that the only companies with “abnormally” high short interest (as of 3/31/2008) were LEH, FNM, and FRE (and, to a lesser extent, MER).

Now, let’s compare the financial company short interest data to that of a few non-financial companies. I’ve added short interest data for the following companies to the busy chart to make it even busier:

- General Motors (GM)
- Crocs (CROX)
- Overstock.com (OSTK)
- Yahoo! (YHOO)
- DuPont (DD)
- Advanced Micro Devices (AMD)
- Disney (DIS)

One look at this chart and it’s obvious that almost none of the selected financial companies can hold a candle to the non-financial companies when it comes to short interest levels. That mess of thick lines hugging the bottom of the chart is the financial company data. Pretty dramatic difference, huh?

Here, again, are individual charts for each of the non-financial companies showing how their short interest levels changed over the last ten years. In the case of YHOO and DIS, we can see that historically they have tended to have higher short interest levels than all of the financial firms on the SEC’s list. Oh, and that last chart in the panel (BSC)…I threw that one in for grins. Notice that BSC’s short interest was much higher than any of the current SEC-listed companies as far back as August 2007 (when it exceeded 10% of shares out).

# A Tale of Two Fund Managers, Part 1

There’s been a lot of chatter lately about various mutual funds – primarily because of their “celebrity” managers and recent performance (or lack, thereof). On his blog, Humble Student of the Markets, Cam Hui recently performed a simple factor analysis of the Legg Mason Value Trust (LMVTX), run by Bill Miller, and the CGM Focus Fund (CGMFX), run by Ken Heebner. I’m going to look at those two funds, too, only from a slightly different perspective. Miller’s fund is a “value” fund — it must be because it says so in the name, right? Heebner’s fund is supposedly a growth fund. Is this really true? Has this been true over time? Well, I’m going to do the infamous Fama-French Three-Factor analysis (3FM) on each of these funds over various time periods to see just exactly how much value and growth each pursued.

For the first part of this tale, I’m going to focus on Bill Miller’s fund. Bespoke Investment Group highlighted the recent struggles of his “value” fund so far this year. Morningstar’s QuickTake report shows just how ugly it has been for LMVTX in the 21st Century:

Miller went from being a “rock star” who beat the S&P 500 every year for 15 years, to someone who has woefully underperformed the last few years. The market, with it’s “What have you done for me lately?” mentality seems to have written him off.

A quick glance at the price chart of the Legg Mason Value Trust over the life of the fund shows that it had a great run until about 1999-2000 (with a nasty blip in 1998). Then things got very volatile very fast. If you had bought the fund ten years ago and held on to it all this time, you wouldn’t have much to show today for your patience. As someone recently said, “You would have gotten bond-like returns with stock-like volatility.”

Quick test: can you figure out in which year Miller’s fund suffered it’s worst daily drop by eye-balling the price chart below?

ANS: See that drop, oh, about three-quarters of the way through…1987? LMVTX fell -16.67% on October 20, 1987.

Anyway…

So, is Bill Miller really a value guy, and has he added any, um, value as a stock picker? You know, has he generated any alpha? To answer these questions, I whipped up a bunch of regressions using price data from Yahoo! Finance for LMVTX and Fama/French Benchmark Factor data from Kenneth French’s web site.

The Three-Factor Model (3FM) data includes daily, weekly, and monthly data for the 30-day T-bill return (RF), the excess return of the total market (CRSP 1-10) over the T-bill return (Mkt-RF), the return of small company stocks minus that of big company stocks (small minus big, or SmB), and the return of the cheapest third of stocks sorted by price/book minus the most expensive third (high minus low, or HmL). I used daily data for this exercise, and I calculated Bil Miller’s risk adjusted return by subtracting the daily T-bill return from his fund’s daily return over the life of the fund (the Fama/French data actually goes back to the 1920’s; LMVTX started trading in 1986). The following table shows the results of the regressions over various time periods (I realize the table is very hard to read; click on it to see a slightly larger image):

So, what does all this mean? We can interpret the regression coefficients as follows:

1. Intercept = alpha (%/day)

2. Mkt-RF = beta

3. SmB = small cap (> 0.5) or large cap (<= 0.0)

4. HmL = value (> 0.3) or growth (<= 0.0)

Taking each in turn, we find:

1. From inception through the first quarter of 2008, on average, the fund has not generated any alpha (the t-stat and p-value tell us that alpha is no different than 0). The same applies for the 10-year period from 1998 to 2008. However, for the trailing twelve month period, the trailing 3-year period, and the trailing 5-year period, the fund has generated substantial *negative* alpha (on an annualized basis, approximately –**18.9%** on a TTM basis, **-11.09%** on a trailing 3-year basis, and **-6.55** on a trailing 5-year basis). Clearly, Miller’s performance has declined dramatically, recently.

2. The funds beta has varied between 0.86 and 1.1 — so basically the fund moves with the market.

3. The SmB coefficients tell us that, more recently, the fund is basically a large cap fund. Over the life of the fund, however, while still more large cap than small cap, it “leans” in the direction of small caps.

4. The HmL coefficients tell us that the fund is a *growth* fund — all HmL loadings are basically 0 (or, where statistically significant, closer to 0 than to .3). That is surprising, although, Morningstar does classify LMVTX as a “Blend” fund — a hybrid of growth/value (and, I suppose if we look sideways at the HmL loading for the time period 1986-2008, we could call it a blend…sort of).

Finally, we can see from the R-squared that over the life of the fund, the 3FM explains about three-quarters of the variation in the risk-adjusted daily returns (RAR). More recently, the 3FM explains well over 90% of the variation of the daily RAR.

So, our 3FM analysis has determined that Bill Miller’s Legg Mason Value Trust is actually a large cap *growth* fund — which moves with the market, and generates huge amounts of negative alpha.

In Part 2, we’ll look at Ken Heebner’s CGM Focus Fund.

# Recent ETF Trends

Here’s a look at how key ETFs have done recently.

Major themes:

1. Technology has held up a bit better than the general market. On a relative basis, the QQQQs have fared better than the general market (as represented by SPY), although they are both in negative territory for the last month.

2. Value has underperformed growth. On a relative basis, large-cap value (as represented by IVE) has fared worse than large-cap growth (IVW), but both are down for the past month. This same trend holds for mid-cap and small-cap growth and value – with value underperforming.

3. Financials continue to do poorly. Other than China (FXI) and India (INP), the Financials (XLF) have had the worst performance over the last month.

4. Commodities and energy are up, metals are down. Oil (USO) and natural gas (UNG) are each up more than 9% in the last month, while gold (GLD) and silver (SLV) are each down over 1%.

5. Global markets are down across the board over the last month, with declines ranging from roughly 2.5% (EWC – Canada) to more than 14% (INP – India).