Explaining why things happen using models is an important part of finance. It helps investors to manage risk and build investment portfolios to suit their needs. In this post I wanted to give a brief rundown of a couple of explanatory models as a precursor to a post about why we use Dimensional Fund advisors as opposed to the more popular Vanguard or Blackrock offerings.
Capital Asset Pricing Model (CAPM)
The capital asset pricing model was developed independently in the 1960’s by Jack Treynor, William Sharpe, John Lintner and Jan Mossin. It is used to describe the expected return for assets based on their relationship to systematic (market) risk (Kenton, 2021). The formula for the CAPM is as follows:
Where:
Without going into too much detail, as there are plenty of articles that talk about CAPM, what this model says is that historically, the expected return of an investment portfolio is correlated with the risk-free rate, asset price volatility and the market risk premium. In other words, investors holding assets that are riskier than government bonds should be compensated with higher returns. According to the CAPM, assets that have historically had higher volatility of returns are considered to be riskier than assets with lower volatility of returns, this is noted by the Greek letter beta. By definition the market beta is equal to 1, so an asset with a beta of 2 is historically twice as volatile as an asset the market.
Fama and French 3 factor model
The original CAPM was a sensible model for explaining why certain stock market portfolios would outperform others. However, since it’s inception, portfolio returns have been shown to have little correlation with beta alone (Fama and French 1992). This indicates that there are reasons, other than volatility, that explain the differences in portfolio returns.
In their 1992 paper entitled “The Cross Section of Expected Stock Returns” Eugene Fama and Kenneth French proposed that ‘size’ (SMB) and ‘value’ (HML) premiums be added to the original CAPM, in now what is known as the Fama and French 3 factor model:
Where in addition to the original CAPM:
The paper ranks portfolios based on size; book-to-market value; and volatility; and assesses correlations between these risk factors and average monthly returns. What it shows is that:
- Diversified portfolios consisting of small stocks, as measured by market capitalization, tended to outperform large stocks over long periods
- Diversified portfolios consisting of value stocks, as measured by the price-to-book ratio, tendered to outperform, growth stocks over long periods
What this means is that small cap stocks are riskier than large cap stocks and stocks with a higher book-to-market value (value stocks) are riskier than stocks with lower book-to-market value (growth stocks). In essence the 3-factor model is able to explain much of the variation in returns between diversified portfolios which represents a significant improvement over the original CAPM.
Possible reasons for increased risk
Small companies face significantly higher idiosyncratic risk when compared to larger companies. Small companies tend to have lower budgets for performing market research and promoting their business. They also benefit less from economies of scale. However, can be more flexible with their product offerings and move quickly to capture emerging trends.
Consider the risk and reward scenarios for a small burger shop with 1 outlet looking to expand to 2 outlets vs a large chain with 1,000 outlets looking to open 100 new outlets. For the small outlet, the funding requirements for this expansion are huge when compared with equity of the business but the potential reward could be a doubling of profits and shareholder value. For the large chain, opening 100 new outlets would probably only raise profits by 10% but given that the funding requirements compared with the overall value of the business is small, the risk is minimal.
Growth companies represent the companies that have a high market value relative to the value of their assets. For example, if company G has assets worth $1M and a market capitalization of $5M then it’s price-to-book ratio is $5M/$1M = 5. If company V also has assets worth $1M but a market cap of $2M then it’s price-to-book ratio is $2M/$1M = 2. Essentially, company G has a higher book-to-market value than company V. The reason for these different book-to-market values is often because the market believes that company G has more favorable prospects, such as potential game changing technology, that could enable them to achieve a high growth rate in the future.
One reason for, so called ‘growth’ companies, being outperformed by ‘value’ companies is likely due to the market being overly exuberant about growth companies’ future prospects and overly skeptical about value companies. One, current example of this is Tesla which has a price-to-book ratio of 26.20 vs Toyota which has a price-to-book value of 1.1 (Marcrotends 2021). Here we see the market is valuing (pricing in) Tesla’s future growth prospects very highly compared to that of Toyota which puts a huge amount of expectation on Tesla to perform as a company; but if Tesla is unable to perform as expected the stock price growth will likely suffer.
Further to this, value stocks are said to be riskier than growth stocks because there is often a good reason for why the market has given them a low valuation, such as competition eroding their market share. This means that while there is a very real possibility that they may continue to perform poorly there is also the opportunity for them turn their fortunes around.
What does this mean for investors?
The original CAPM and 3-factor model identify key stock market investing risk factors, namely market, size and value. Smart investing is about creating portfolios that expose investors to their desired and tolerable risk factors at the appropriate levels in order to give them the best chance at producing their required rate of return. Exposure to the risk factors of value and size are likely to increase returns in the long run but investors need to also be aware that periods of underperformance are almost guaranteed.
References
Kenton, W, 2021, Capital Asset Pricing Model (CAPM), Investopedia, available from: <https://www.investopedia.com/terms/c/capm.asp>
Fama. E, French. K, 1992, The Cross-Section of Expected Stock Returns, Journal of Finance, Vol 47 Issue 2 pp 427 – 465
Macro trends, 2021, Tesla Price to Book Ratio 2009-2021 | TSLA, available from: <https://www.macrotrends.net/stocks/charts/TSLA/tesla/price-book>
Macro trends, 2021, Toyota Price to Book Ratio 2006-2021 | TM, available from: <https://www.macrotrends.net/stocks/charts/TM/toyota/price-book>
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