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Arith vs. geo average, Survivorship Bias, Trans Costs, Taxes, Etc.

falkenblog writes:


Monday, July 13, 2009
One of the most important constants in finance is the Equity Risk premium, that expected return on the signature risk asset, equities, over the risk free alternative (usually, long-term Treasuries). It's the one risk premium that is generally considered positive, too large even, which is a relief because in most areas the returns are decidedly negative for taking more risk. Estimates in the early 1990s were about 8%, now, around 3% annually.

In today's WSJ Jason Zwieg goes over a flaw in Jeremey Siegel's famous stock return estimate going back to 1802. As one would expect, stock indices prior to 1871 have a lot of survivorship bias issues. He suspects Siegel's index accounts for only 5% of equity investments actually available, and so could be severely biased, because the difference between the winners, and the average, is usually quite large. This highlights the many subtle biases in historical asset returns.

I have found that on average industry stratistics are maintained by biased parties, because those who do the work collecting such data invariably have a vested interest in the asset class, and incentives matter. Little things like selection biases in historical reconstructions, corporate actions, can get very detailed and matter a great deal. I have seen performance records where I had inside knowledge of the guy's strategy, and every time their performance was exaggerated. People exaggerate with a rather straightforward, self-interested bias on things that can help them, and index creators invariably have a rooting interest in the asset class they are 'merely monitoring'.

Is the equity premium really zero? I think for the average investor, yes it is, and it's a central issue in my book, Finding Alpha. As that old classic noted, the question 'where are all the customer's yachts?' answers itself.

Consider the following annualized adjustments that mainstream economists apply piecemeal, though when considered in total take the current estimate of 3% well below zero:

The bottom line is these are all individually very modest adjustments, and so the current 3% equity risk premium is well below the total 13% adjustment. Like the OJ evidence, you can throw out ANY ¾ of the evidence and the equity premium is zero! Caveat Emptor.
  • Geometric vs. Arithmetic averaging: 2% (See Dimson, Marsh, and Staunton). This is where a stock going from 100, to 200, back to 100 has an arithmetic return of +25%, the geometric lower, at zero. Geometric is relevant to the long-term investor, and most investors have a much greater volatility than the indices, making this estimate conservative.
  • Survivorship Bias/Peso Problems: 3% (see Rietz, Jorion and Goetzmann, Barro) The US is the best market in the 20th century, so not a good datapoint for an 'average' going forward.
  • Taxes: 3% (see Gannon and Blum, 2006). Since 1960, the after-tax equity premium is reduced to about 60 basis points is you assume 20% turnover and a top tax rate.
  • Adverse market Timing: 3% (See Dichev, 2005). Alas, most inflows are at peaks, outflows in troughs. The average dollar invested has experienced a much lower return than the annual averages.
  • Transaction Costs: 2%. historically, commissions were about 60 cent/share until the 1975 deregulation, and are currently w about 2 cents a share (about 0.1%) on average. Plus, mutual funds often had 8.5% fees. Trade impact is rarely mentioned, but for an institution it is unavoidable, at least 0.2% one-way. Lastly, the bid-ask spread will cost you about 0.25% on average if you cross it, much more historically. It doesn't matter than some passive funds have negative expenses, because we are talking about a hundred year average for your average or marginal investor.