Monthly Archives: March 2012

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.


MK Chen’s amazing paper about the effect of language features on economic behaviour has been making the rounds. In a nutshell, by doing some kind of regression of savings rate and other similar metrics of economic prudence, from surveys and various data sources, against whether the mother tongue (or group thereof) of the groups surveyed expresses the future tense weakly or strongly, he finds that there is a fairly convincing correlation. And it seems to resist controls for incidental factors. It’s not a definite proof, but within the limits of statistical methods it seems fairly solid — many studies in finance or medicine get publicity with much weaker statistical significance.

While such effects have been long thought about — see the Sapir Whorf hypothesis — this instance, if further confirmed, is particularly striking in its amplitude and simplicity.

The correlation is, at least for my sense of intuition, inverted: that is speakers of languages with a strong future tense, such as English, make for poor savers unlike those of languages with a weak future, where you can use the present tense plus context or markers for future actions. But it can make sense: it’s easier to delay things to tomorrow when you have the linguistic tools to do so, although that explanation sounds possibly a bit too simple to be the only truth.


If you take it to policy it may mean, among other things, that some countries may be natural deficit countries and other natural bankers. So in the end lamenting trade imbalances may be totally pointless, and we should just accept them as cultural differences and try to make them manageable.

It made me reflect on the nature credit. The American literature and folklore often takes credit for granted, and you read things like that people “cannot” buy a car or a house, or go to university, when credit is tight or not available. This is a trivial fallacy. You can save for a car, and buy it outright when you get enough cash to pay for it. And same for everything else someone can afford within the limits of their lifetime income and the choices they make. An absence of credit just delays consumption. In a steady state where everybody is delayed by the same and relatively constant amount, this shouldn’t have much interesting impact. Some would still argue that this delay means less consumption, but even that is, basically, false.

Let’s for a moment assume that we have a perfect credit model, where credit is available and where everybody repays within their lifetime according to the agreed conditions. If we compare the total consumption on the lifetime of otherwise identical individuals, with the same income, who both plan their affairs wisely so as to end up with exactly zero net assets on the day they die; basically the borrower can consume his income less interest, while the saver can consume more plus interest if he saves early in an interest bearing vehicle, with the proviso that they must stop saving later in life to achieve the zero ending asset condition.

If this world was a village with just this 2 people, we’d have the accounting identity:

  • C(saver) = W + I
  • C(borrower) = W – I

where C is lifetime consumption of each party, W is wages which we assumed equal for both parties, and I is the interest which the borrower pays to the saver given this is a two-person world.

So basically the saver is 2I ahead in the amount he actually consumes. It’s just an intertemporal choice for both of them. To what level it is a good idea is another question but economically it is both possible, and sustainable.

Does the model fall down if we introduce more than two people and default? Not particularly, if the savers set I, of which they are price makers, at the right value to include the default rate of the borrowers, we can still have a fully stable and sustainable system, which caters for varying intertemporal choices.

I’m a bit more fuzzy on if and how this generalizes to a full blown world, but the intuition is that it will be naturally stable. Basically if savers want to save too much, the value of I will become temporarily unsustainable and become below the default rate, and the imbalance corrected with default sooner or later. In other words, there might not be much to do about this problem from a policy perspective, beyond trying to smooth out volatility induced by temporary mispricing of credit produced by imbalanced preferences between saver and borrower groups.


The other, unrelated, point it brings to me is that most of what we understand as national character may just be due to language artefacts. This could explain consistency of some traits of characters — Roman writers were already finding Germans dour and fiscally prudent two thousand years ago — in a much more convincing way than the classic explanations like fizzy blood theories, which fall down in any region with loose borders and lots of population mix along them and through economic or wartime population movements, or the quasi-mystical appeal to the nation state, basically a nineteenth century invention, where somehow random events like place of birth and passport are supposed to have way more influence on identity than their minimal factual relevance warrants.

This opens a myriad of questions: could we find other factors that explain this or other things with greater precision than this single factor? For instance do languages that requires you to construct most of your sentence before you can start it, or require the listener to wait for the end of the message to have it complete (like German again) imply something on behaviour? Do some more obscure constructs that are not so easy to acknowledge also have an impact?

And what happens if you teach multiple languages early enough? Will the next generation of Chinese, if they are taught English early enough, will rush to their credit cards once adults, settle on running a well balanced book, or keep on saving? (and inversely if American kids learned Chinese or German.)