The equity premium as a transaction costs artefact

The value, or mere existence, of the equity premium — the excess return of a passive holding of a representative basket of equities compared to corresponding, “risk free”, government bonds — is one of the most debated theme in economics.

The only consensus there is, is about history: the premium can be observed in the past, in the vicinity of five(ish) percentage points on top of the risk free rate (being a differential it applies similarly in real and nominal terms), at least for the main representative Western markets like the UK and US that have a long and relatively uninterrupted track record, long enough to smooth out short-term volatility.

There are various more or less convincing explanations, but none of them is overwhelming enough to have gathered a consensus, and the contradiction with efficient markets is one that is hard to get around. If there’s an easy way to make excess returns, by simply holding the market and being patient, why is not everybody doing it, diminishing or eliminating the premium in the process?

It could be that everybody is actually doing it, and that the premium seen in the past will not be observed in the future. Indeed merely looking at periods of the order of a decade in the past, in the West or in Japan, would not show that impressive a premium. The question is whether this is just volatility, which doesn’t contradict the premium hypothesis, or a permanent change.

But even if this is so, we still need to explain the past premium, and what has changed that would make it disappear? One part of the explanation could be that people were not conscious of it, and thus didn’t price equities correctly in the past. A problem with this explanation is that, in open pluralistic markets, price inefficiencies tend to attract custom even if the process by which they occur is not well understood. Researchers have analysed the price records of option-like financial instruments from a few centuries ago, well before our current sophisticated understanding of option pricing, and found that they were priced consistently enough with say what the Black-Scholes formula would predict, despite being traded long before Messrs. Black and Scholes were born.

A pet theory of mine is that a proportion of the equity premium could be explained by transaction costs.

The way we compute the equity premium is gross, net of friction costs because they are difficult to compute precisely, and because they should be negligible if the strategy being modelled is not trading-intensive. In the case of the equity premium, the thing it models is the difference in return an investor would have faced if they made the choice of buying and holding passively a representative basket of an equity market, compared to holding the corresponding government bonds. In modern terms, it compares buying and holding, for instance, a low-cost index ETF with straight government bond holdings or a matching bond ETF.

The minimal net costs assumption on bonds may be reasonably accurate, even historically, but it’s more questionable for the equity index. Today you can buy a mainstream index ETF for <10 basis point annual fee, and with transaction fees for long buy-and-hold that are truly negligible compared to the already small annual fee. But an enlightened investor wishing to buy the index in 1920 would have faced two headwinds.

First, low-cost index products were simply not available. The only solution they would have had is DIY: buy and hold, and maintain, a representative sample of the market themselves, constructed from individual shareholdings. This would have certainly cost more that 10 basis point per annum, and some hassle.

The second headwind is that the index investor would have needed to know that index investing was a good idea at the time nobody knew yet it was a good idea. This contradicts my proposition above that markets tend to find anomalies without necessarily the individual agents understanding them. When you add transaction costs though, the contradiction may be partially resolved: you can devise a variety of high churn investment strategies that in aggregate and over the long-term are equivalent to a passive index as we know it, net of transaction costs. Besides we are thinking about long periods here (decades or more) where the compounding effect of transaction costs is extremely adverse. If you pay 1% transaction cost this year, and reinvest the same pile for 50 years, you lose the compound value for that 1%; and future yearly losses will compound as well.

Unfortunately I have not seen any quantified estimate of the effect of transaction cost on a typical investor in say the 1920s. To know this we should find a way to estimate not the gross returns of a model equity investor, but the net of cost returns investors actually faced during the historical period. What is certain is that they did not get 1-basis point spreads on the SPY ETF and $5 all-inclusive online share trades. If you add the fact that those who might have been unknowingly applying high-churn variants of index investing got hit by the churn rate, it becomes pretty realistic that several percentage points of the historical equity premium, or perhaps all of it, could be explained by transaction costs. That is, if the theory is correct, historical investors have enjoyed a much smaller premium than the gross model shows.

A possible venue to quantify this would be to look at the historical revenue of the brokerage industry, perhaps the ratio of this revenue to market capitalisation would give a useful rough estimate of the costs faced by actual historical investors.

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