That ETF’s Expense Ratio Stole My Alpha

Expense ratios matter in ways some investors don't think much about.

A few weeks ago, I published a blog called "'Smart Beta' 5: No Alpha Here."

My findings—no statistically significant alpha in outperformance-claiming U.S. large-cap funds—made some folks hopping mad.

A few attacked my character, but others had something substantial to say. Here are a few of the latter comments:

"There are back-tested index results for something like SPLV [the PowerShares S&P 500 Low Volatility Portfolio (SPLV | A-47)] that go back 20 years or so." —Nick Carver

"In my research of 'smart beta' indexes (not the ETFs), specifically the Russell Fundamental Indexes, I have seen huge alpha over the long run. I will concede that the Russell fundamental indexes aren't the actual ETFs." —MC

MC, you are wise. The indexes are not the ETFs.

ETFs are miracles of modern financial engineering. ETFs allow anyone to hold a diversified basket of securities, often for mere pennies. But they're not made of fairy dust. They hold, and trade, actual stocks, bonds, currencies, commodity futures, etc.

These real-life portfolios aren't free. They have management fees, and tracking error, in addition to trading costs. Those costs can kill a fund's alpha.

It's entirely possible that an index can have statistically significant alpha, but an ETF tracking that index doesn't.

That's exactly what happened to two funds I analyzed in that provocative blog: Nick Carver's example SPLV and the WisdomTree LargeCap Dividend Fund (DLN | A-95).

I revisited the 11 funds from the "no alpha" blog to measure alpha slippage between fund and index. I had to drop two funds for lack of clean index data.

This time, I used the S&P 500 Index as my bogey, because, unlike ETF.com's chosen U.S. Large Cap segment benchmark, the S&P 500 has ETFs that track it—three, in fact. I chose the iShares Core S&P 500 ETF (IVV | A-97) as the most efficient S&P 500 ETF with at least five years of performance history.

I ran two sets of regressions: fund versus fund (NAVs), and index versus index. For example, I compared SPLV's returns with IVV's, and, separately, the S&P 500 Low Volatility Index to the S&P 500 index (total return versions, in all cases). I covered one-, three- and five-year periods ending on March 31, 2014.

The results were similar in all time frames. The most interesting—the three-year set—is below; you can find the other two at the end of this blog.

Three takeaways for comparing the index versus index regressions to the fund versus fund ones:

1. The goodness of fit (R squared) and betas are virtually identical. Clearly, these funds track their indexes quite tightly. Moreover, the high goodness of fit results confirm that the S&P 500 is an appropriate benchmark for these large-cap U.S. indexes.
2. The index alphas are higher than the fund alphas, with the difference almost entirely explained by the expense ratio. Again, these funds track their indexes well, and the expenses of operating the funds have a real effect. This is not news.
3. As the difference in alphas moved away from zero, alpha significance increased. In some cases, the significance crossed a threshold. And to statisticians, this is a make-it-or-break-it leap from indeterminacy to fame.

Let me explain.

Alphas have a margin of error. This matters, because like all statistics, regression alphas are an estimate. Alphas come with error bars.

An alpha's significance is the probability that its error bars don't encompass the number zero. Alpha's significance depends on its magnitude and of the width of its error bands. The wider the bands, the more likely the number zero will fall between them. If the "true" value of your alpha could actually be zero, or the opposite sign, it isn't real. It's noise.

DLN's index's alpha significance versus the S&P 500 is 95.53 over our three-year period. For most statisticians, anything over 95 is the real deal.

Remember, you can't buy DLN's index; you have to buy the ETF. And when you compare the ETF against IVV, the alpha significance drops to 93.69 percent. A minor shift, for sure, but a jump across the 95 percent significance line. To statisticians, that's like crossing the international date line.

SPLV is even a more dramatic case. The index versus index-alpha significance comes in at 90.11 percent, a whisker over the generous 90 percent relevance boundary. But the fund versus fund significance of 88.36 percent lands on the wrong side of the tracks.

There's a technical explanation for this. In a case like this, where U.S. large-cap funds track their indexes tightly, the width of the alpha error bands should be the same, whether you're working with the indexes or the funds. In this case, the difference in alpha's magnitude makes or breaks its significance.

The expense ratio is the clear culprit. It reduces every index alpha, across the board. Check out the tables.

Any positive-index alphas will get closer to zero as you account for expense ratios, while negative ones will grow more negative. On an absolute value basis, positive-index alphas' significance ratio numerators will drop, while negative ones will increase. The bigger the expense ratio, the bigger the significance shift.

So yes, the expense ratio can eat your alpha.

The significance situation gets more complicated with indexes that are harder to track, generally ones that rebalance frequently or include small-caps and emerging market securities. In those cases, the standard error of alpha might actually increase from an index-on-index to a fund-on-fund regression.

But the expense ratio effect won't go away.

A fund is not an index. The real-world costs of operating a fund can kill your alpha.

At the time this article was written, the author held a long position in IVV. Contact Elisabeth Kashner, CFA, at [email protected].