Over the full annual history of the size and value data in the U.S., the size premium has averaged 3.4 percent per year with 14 percent volatility, while the value premium has averaged 5.0 percent per year with 14.1 percent volatility. These equate to Sharpe Ratios of 0.24 and 0.36, respectively. This also means that it can be expected for these premiums to be flat in (very) roughly 20 percent of 10-year periods (or, more precisely, in about 20 percent of 10-year periods for the size premium and 15 percent for the value premium). While 10-year periods such as 2006–2015 shouldn’t happen frequently, one 10-year stretch like this within an investment lifetime is well within the realm of possibility. And it’s important to emphasize that periods like these don’t prove the premiums have disappeared precisely because they are well within the realm of possibility.

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I explore one methodology here by running Fama-French three-factor regressions for a large number of Vanguard and DFA funds and using the output to tease out how much additional expense ratio investors are paying on average for small-cap and value exposure, respectively. (Anyone who is interested in the exact methodology can email me. The details are too laborious to include in the blog post.)

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Examining the Early Period

From January 2003 through December 2012, a factor analysis shows the two funds had roughly comparable exposure to value, but DFSVX had markedly higher exposure to market risk (i.e., beta risk) and owned much smaller companies. Since both the equity market and small-cap stocks did exceedingly well during this period, with an average annual equity premium of 8.0 percent and a size premium of 4.3 percent, it’s not surprising to see that DFA Small Value had substantially higher performance than Vanguard Small Value.

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Expected inflation rates in the U.S. and elsewhere are very low. Figure 1 shows the average annual expected inflation rates in the U.S. over the next one, three, five, 10, 20 and 30 years.

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“We find, surprisingly, that rising equity glidepaths in retirement … have the potential to actually reduce both the probability of failure and the magnitude of failure for client portfolios.”

I initially suspected the basic claims might not hold up under analytic scrutiny and recently got the chance to dig into their data tables to find out. In my analysis, I focus on the success rates and 5th percentile shortfall results they report in Tables 2, 4 and 6 in their paper. These three tables contain results for 4 percent withdrawal rates under three different sets of capital market assumptions.

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The Size Premium in Growth and Value Stocks

While it’s true in aggregate that small-cap stocks have had similar risk-adjusted returns (or Sharpe Ratios) compared with large-cap stocks, a more nuanced picture emerges when we separately look at the performance of small-cap versus large-cap in growth stocks and then in value stocks. The figure below displays the difference in Sharpe Ratios comparing small-cap growth stocks with large-cap growth stocks and then comparing small-cap value stocks with large-cap value stocks.

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If bond fund prices (or, equivalently, net asset values) were fair on a day-to-day basis, you should generally see that a prior day’s return for a fund tells you nothing about what today’s return will be. In other words, past returns shouldn’t predict future returns. The good news is that this is a testable proposition.

I pulled daily returns data for five different large bond funds from two different fund families. The first three funds have the majority of their portfolios invested in less liquid securities like municipal bonds and high-yield corporate bonds. The last two tend to own fixed income securities with better trading liquidity.

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Focus on Correlation, Not Volatility

When evaluating whether an asset class effectively protects against inflation, the focus should be on the correlation between that asset class’s returns and inflation and not the relative volatility of the asset class’s returns when compared with the volatility of inflation. This misconception often leads to assumptions, such as commodities as an asset class cannot effectively hedge inflation because its returns are about 8–10 times more volatile than inflation. This is simply false.

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What Is HFT?

Larry Harris, professor of finance at the University of Southern California, has spent an academic career studying trading in equity markets, and he categorizes high-frequency traders into three areas:

1) Market makers
2) Fundamentally driven traders
3) Front-runners

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