*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 andÂ 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)

# More Support…

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.

Patrick

Hi Preet,

This is fascinating. Let me see if I understand the 14.03% annualized compound return of the “Small Value” index: you start in January 1927 by investing equal dollar amounts in each of the companies with both low market caps and high BtM ratios. At the end of the year, you rebalance your holdings so again you have an equal dollar amount in each company that qualifies as of January 1928, and repeat until the end of 2007. At the end of 2007, you’d find your investment has grown by a factor of 1.1403^80. Is that right?

Preet

@Patrick – actually I believe it is based on market cap within those parameters and not equal dollar amounts. I’ll try to get clarification on that. But otherwise, if you could invest in such an index with no costs or taxes, then yes you are correct about the growth. Rebalancing was annual.

Patrick

@Preet – seems slightly ironic that a fund targeting small-cap stocks would be market cap-weighted. :-)

Preet

@Patrick – To be clear – the data in this post is not a fund’s performance, but rather is the back-tested performance of a certain criteria of market constituents. In the case you are referring to: Small stocks with high BtMs. The stocks that fit this criteria could be weighted by a fund on an equal weight basis, or on a market capitalization basis or any other way. While I’m still trying to find out if these data are market-cap or equal weighted, I see your point about the irony! :)

Michael James

Preet: Thanks for the link. For anyone who wants to work out compound returns from average returns, the difference is roughly half the standard deviation squared. So, an average return of 12% with a 20% standard deviation gives a compound return of 10% (0.12-(1/2)(.2)*(.2)=0.10).

Patrick

I wonder if my pension should be invested in IJS…

Preet

@Patrick – I wouldn’t be too hasty on that! While the chart looks good it is worth noting that there can be very long periods of underperformance. You’ll note that in a previous blog post, it was indicated that the equity premium takes maybe over 30 years to reliably show up with statistical confidence – same sort of story with small and value. You can “tilt” towards small and value to differing degrees with DFA instead of going all out – but it won’t be apparent until later the effects of momentum on small cap mandates which can be crippling if they aren’t ‘immunized’ – which you can’t get with regular index tracking ETFs.