This article is one in a long series which I hope will help explain the ins and outs of DFA – Dimensional Fund Advisors. NOTE: This is my interpretation and explanation only. For the final word, please refer to the DFA Canada Website.
Risk and Return Revisited
If we are looking at the long term numbers of a diversified portfolio of value stocks outperforming growth stocks, and small cap outperforming large cap, then we should see increased risk in the form of increased standard deviation if risk and return are truly related. After all, one of the main beliefs of DFA is that “markets work” and risk and return are related – so if there is more return to be had, it MUST come with additional risk.
Here are the return numbers presented again, but this time with the standard deviation numbers added as well:
You can see that the Value stocks and the Small stocks carry much higher standard deviations to go along with their higher annualized returns. The data showing Value stocks having higher returns and higher risk than Growth stocks may be against the conventional wisdom – most people assume growth stocks are riskier, but the long term data shows otherwise.
Let’s Take Another Step…
Now, let’s take a look at the Value effect WITHIN Large Cap stocks and WITHIN Small Cap Stocks. In other words, we are going to see if Large Cap Value outperforms Large Cap Growth, and we are going to see if Small Cap Value outperforms Small Cap Growth – and again we will toss in the standard deviations to serve as the main proxy for risk.
Data and Chart sourced from DFA Canada
Compounded Returns versus Average Return
First thing to note is that you actually see two sets of returns for each item we are looking at. It is important to note the distinction as pointed out by Michael James on Money in a comment in the last part in the series. The “Annualized Compound Return” is more meaningful since it allows you to figure out what your experience would’ve been if you had (and could have) actually invested in these indices (we’re not taking into account transaction costs, or the fact that you couldn’t really invest in anything that could track these indices since their inception). The “Annual Average Return” is simply taking all the annual returns and dividing by the number of years to get the average return you would expect for any year. (You can visit Michael James’ blog by clicking here)
Nonetheless, we see that for Large Cap stocks, there is again a Value premium in that Large Cap Value outperformed Large Cap Growth. We also see that within Small cap stocks the Value premium still shows up in that Small Cap Value outperformed Small Cap Growth. (However, we do also notice that the standard deviation on Small Cap Growth is not as low as we would expect relative to Small Cap Value. This indeed one of the very few anomalies with the Fama-French Three Factor Model [which I have yet to explain in detail!] since the data implies that the risk and return relationship in the value premium does not really show up for Small Cap stocks. This is acknowledged by Fama and French.)
I’ll end there since we’ve again covered a lot of ground. In Part X, we will finally see the Fama-French Three Factor Model formula and then start comparing this to the Capital Asset Pricing Model.