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When Modern Portfolio Theory was originally developed, one of the first models for stock market returns was called the Capital Asset Pricing Model (CAPM). Under the CAPM, a single risk factor β (Greek letter beta) was used, which denoted a securities volatility relative to the market portfolio.
There were empirical problems with this model, notably that low-beta stocks had a higher return than expected under the CAPM model.
Later, Eugene Fama and Kenneth French observed that small stocks and value stocks both had higher returns than the market as a whole. So in 1992, Fama and french added two more factors to the CAPM and proposed a 3-Factor model to explain stock returns. The three factors are β, SMB and HML. β is the market risk factor, the same as for CAPM. SMB stands for Small-Minus-Big, referring to size as market capitalization; HML stands for High-Minus-Low referring to the ratio book-value/market-cap.
Today, numerous investors “tilt” their stock portfolios toward small-cap and value stocks. There are mutual funds that invest in the various combinations of size and value.
In this article, I’ll look at smallcap and largecap stocks, both large value and growth, to see if the small risk premium has born out. I’ll be using Vanguard Index Funds for the comparison.
The Funds
First lets get a look at the Vanguard funds that are standing in for the various parts of the stock market.
The Large-Cap Funds
The large-value fund is Vanguard Value Index Fund (VIVAX). The top ten holdings of VIVAX as of 7/31/2011 are:
- Exxon Mobil Corp.
- Chevron Corp.
- General Electric Co.
- Johnson & Johnson
- AT&T Inc.
- Procter & Gamble Co.
- JPMorgan Chase & Co.
- Pfizer Inc.
- Wells Fargo & Co.
- Intel Corp
All are big, multinational companies. Big oil (Exxon, Chevron), consumer staples (P&G, J&J, big telecom (Verizon, AT&T) and big banks (JP Morgan, Wells Fargo). One huge semi-conductor manufacturer (Intel). They sound like the bluest of the blue chips.
The large-growth fund is Vanguard Growth Index Fund (VIGRX). The top ten holdings of VIGRX are:
- Apple Inc
- International Business Machines Corp
- Google Inc
- Coca-Cola Co/The
- Microsoft Corp
- Philip Morris International Inc
- Oracle Corp
- Schlumberger Ltd
- Wal-Mart Stores Inc
- PepsiCo Inc/NC
Big tech companies (Apple, IBM, Microsoft, Google, Oracle), big consumer products (Philip Morris, Coke, Pepsi, and a big retailer (Wal-Mart). This list is just the kind of high-tech companies I would have expected in growth stocks.
The Small-Cap Funds
The small-value fund is Vanguard Small Cap Value Index (VISVX). The top ten holdings of VISVX are:
- American Capital Agency Corp
- Camden Property Trust
- Essex Property Trust Inc
- BE Aerospace Inc
- Corn Products International Inc
- BRE Properties Inc
- First Niagara Financial Group Inc
- Senior Housing Properties Trust
- Cooper Cos Inc/The
- Aptargroup Inc
Looks like insurance companies, regional bank, real estate. I wouldn’t say they are household names. Honestly, I never heard of any of them. Sounds risky to me.
The small-growth fund is Vanguard Small Cap Growth Index (VISGX). The top ten holdings of VISGX are:
- Tempur-Pedic International Inc
- Polycom Inc
- Varian Semiconductor Equipment Associates Inc
- Gardner Denver Inc
- TransDigm Group Inc
- Gentex Corp
- MICROS Systems Inc
- Solera Holdings Inc
- Rockwood Holdings Inc
- Deckers Outdoor Corp
Some maufacturers (Varian, Gardner-Denver)). I’ve heard of a few of them, but most I’m not familiar with. These stocks also sound risky to me.
Summary of Equity Characteristics
Table I summarizes the equity characteristics of the four stock funds.
| VIVAX LCV |
VIGRX LCG |
VISVX SGV |
VISGX SCG |
|
|---|---|---|---|---|
| Number of Stocks | 413 | 429 | 1016 | 952 |
| Median Market Cap | $50.2 billion | $34.5 billion | $1.7 billion | $1.7 billion |
| Price/Book Ratio, P/B | 1.6 | 3.6 | 1.4 | 3.1 |
| Price/Earnings Ratio, P/E | 13.7 | 17.9 | 19.1 | 28.9 |
| Return on equity, ROE | 16.1% | 23.9% | 8.5% | 11.7% |
| Earnings growth rate, g | -1.0% | 13.3% | -0.3% | 9.2% |
The large-cap companies are 20x to 30x the size, by market cap, of the small-cap companies. Do smaller companies with puny balance sheets present a greater risk for investors? That is what we want to find out.
The value companies have lower P/B and lower P/E than the growth companies. In other words, their valuations are lower, or you could say they are cheaper. But are they more of a bargain?
The growth companies have higher return on equity and earnings have grown faster. In fact, both large and small value stocks have negative earnings growth! So you get what you pay for. Or do you? These questions are what we intend to investigate.
Large versus Small Comparisons
First I’ll compare the large against the small.
Large-value versus Small-value
The first chart is for Vanguard Value Index Fund (VIVAX) and Vanguard Small Cap Value Index (VISVX). The chart shows the growth of $10,000 since the funds inception in 2001.
Clearly, the small-cap value fund has a higher return over the past 20 years than the large-cap value fund. Small-cap took an early lead over large-cap, which it held for the whole period.
Large-growth versus Small-growth
The second chart is for Vanguard Growth Index Fund (VIGRX) and Vanguard Small Cap Growth Index (VISGX). Again, the chart shows the growth of $10,000 since the funds inception in 2001.
Once again, the small-cap fund has a higher return over the past 20 years than the large-cap fund. At no time over the period did small-cap fall behind large-cap.
The same relationship holds for both the value and growth funds. This is evidence for a small-cap risk premium.
Value versus Growth Comparisons
Now I’ll repeat the comparison, except this time, the value stocks will go up against the growth stocks.
Large-value versus Large-growth
The third chart is for Vanguard Value Index Fund (VIVAX) and Vanguard Growth Index (VIGRX).
In the early 1990’s, large-growth fell behind large-value. But in the late 1990’s, large growth took the lead, culminating in the tech bubble which peaked in year 2000. The large growth fell more than large-value, but surprisingly, they ended up about the same place in 2003.
From 2003 to 2007, their fortunes were reversed. Now large-value took the lead. But then in the crash of 2008, large-value fell more, and once again they were even. Since the bottom in 2009, large-value has generally been ahead. That is until just recently, when large-value fell more.
It is hard to say which fund looks riskier. There were times when one or the other was ahead, but they both finished up at the same place.
Small-value versus Small-growth
What about small-value versus small-growth? The fourth and last chart is for Vanguard Small-Cap Value Index Fund (VISVX) and Vanguard Small-Cap Growth Index (VISGX).
Another interesting chart with no clear winner or loser. For the most part, both small-value and small-growth are about the same. Only in the past year or so has small-growth pulled out ahead of small-value.
Where is the Value Premium?
There is clearly empirical evidence in the Vanguard fund return data that shows evidence for a small-cap premium. It manifest itself in both the case of value and growth funds. This is logical. Most stock analysts and common sense would tell you that, in general, smaller companies are a riskier bet than larger companies.
Evidence for a value premium is dodgier. Between the large caps, there’s no decision either way for value or growth. The data goes back to 1992, just after the 3-Factor model was proposed. Did it stop working?
Between the small caps, there’s also no strong case for a value premium. The Vanguard funds only date from 1998, so about 13 years. But, if anything, there appears to be a weak case for a small-growth premium.
In another article, I’ll come back and look more closely at annual returns to see if we can find the elusive value risk premium. In the meantime, Mr. Eugene Fama, Mr. Kenneth French, what have you got to say for yourselves?
