“The Rate of Return on Everything“

This is the title of a new paper by Oscar Jorda, Katharina Knoll, Dmitry Kuvshinov, and Moritz Schularick (original paper, voxeu article). The paper is the result of a research project to calculate the rates of return on four major asset categories – equities, bonds, bills, and real estate – in 16 major developed economies going back as far in time as reasonable. (Quibble: Is that really everything? What about gold? currencies? commodities? paintings? vintage cars?)

The paper does nothing but compute long-run averages and standard deviations and draw graphs. No regressions, no econometric witchcraft, no funny stuff. Yet its findings are fascinating.

Bildschirmfoto 2018-01-08 um 09.46.21

Some of the results confirm what „everyone already knew, kind of“:

  1. Risky investments like equities and real estate yield 7% per year in real terms.
  2. The risk premium (equities/housing vis-a-vis short term bond rates) is usually between 4 to 5%.
  3. There is no clear long-run trend (either up or down) in rates of return. (Take this, Karl Marx!)

Some of the results are interesting, but not particularly puzzling:

  1. The return on total wealth (average of the rates of return on all assets weighted by their share in the economy’s aggregate portfolio) exceeds the rate of growth of GDP. This confirms Piketty’s claim that r > g. In terms of the Solow model it means we are living in a dynamically efficient regime: we cannot make both present and future generations better off by saving less. Perhaps the most interesting aspect of this finding is its robustness: it holds for every sub-period and for every country. It really seems to be a „deep fact“ about modern economies.
  2. The return on risk-free assets is sometimes higher, sometimes lower than the growth rate of GDP. For instance, before the two World Wars, the differential between the risk-free rate and growth was mostly positive, so that governments had to run primary surpluses to keep debt stable. Post-1950, the differential was mostly negative.
  3. Negative returns on safe assets are not unusual. Safe rates were negative during the two World Wars as well as during the crisis of the 1970s. In recent times safe rates went negative again in the aftermath of the global financial crisis. These findings don’t disprove the „secular stagnation“ hypothesis of Summers et al. but they do put it in historical perspective. It seems that rates were unusually high during 1980s and the recent downward trend could just be a reversion to the mean.

But some results are really puzzling – even shocking from the point of view of standard finance theory:

  1. The return on risk-free assets is more volatile than the return on risky ones. I haven’t yet digested this fact fully. Does this mean that “risk-free asset” is a total misnomer? No, because „risk-free“ refers to the unconditional nature of the payoff of an asset, not the variability of its return. A bond is „risk-free“ because it promises a fixed cash flow irrespective of the state of the economy. Stocks are called risky, not because their returns are volatile, but because the dividends they pay are conditional on the performance of the company. So does this mean that people’s time discount rate varies a lot? Why? It can’t be consumption growth variability – because consumption is quite smooth. What’s going on?
  2. Housing offers the same yield as equities, but is much less volatile. Jorda et al refer to this as the housing puzzle. I’m not sure how puzzled I should be by this. I surely found the high average yield of real estate assets surprising. However, from what I know about house price indices and the myriad measurement issues surrounding them, I feel that one should be very cautious about the housing returns. I definitely would like someone who knows more about this look carefully at how they calculated the returns (paging Dr. Waltl!). One potential solution to the puzzle I can see would be differences in liquidity. Housing is super illiquid, equities are quite liquid. Couldn’t the high return on housing just be an illiquidity premium?

There is much, much more in the paper, but those were the points that I found most striking. I’m sure this will be one of the most important papers of the past year and will be a crucial source for researchers in finance, growth, and business cycle theory. Plenty of food for thought.

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Intro to Econ: Third Lecture – Efficiency, Fairness, Trade, and a bit about Free Trade Agreements

In the third lecture, after a review of the second lecture, I talk about (bilateral) trade and more general exchange, efficiency, and fairness. I do this in the context of a kids’ birthday party and follow to some extent chapter 3 of Ariel Rubinstein’s “Economic Fables”. I don’t know how this is done in other areas in the world, but in Graz there seem to be certain specific norms that one should follow when you host a kid’s birthday party. You invite roughly as many children as your child’s age in years. Children bring presents, but each child also goes home from the party with some little bag of goodies. As concerned parents we do not want to give the children too many sweets so we give them little presents such as little Lego or Playmobil figures or a car or something like this. We did this twice this year (we have two kids) and in both cases the first thing that happens after the kids finally find the treasure (there is often a sort of treasure hunt) is this: the kids start to trade. So, I ask the students what is going on when kids are trading their presents.

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Me, Myself and Economics: Disequilibrium

I considered to choose ‘A Non-Equilibrium Approach’ as a subtitle of my dissertation thesis. About at the same time a colleague of mine stated that ‘disequilibrium economics’ are a ‘logic implausibility’ as an equilibrium in economics is not much more than a consistency condition – different to the notion in physics where it mainly refers to a state where the described system is at rest. I have to disagree with this maybe unintentional attempt to whitewash a bunch of approaches which are – as probably every other approach – criticized for good reason.

Just think of basic micro or macro and the definition of a market or an economy in equilibrium. There the term is not used to describe consistency in the derivation of the outcome, but mainly refers its characteristics – for example that supply and demand are balanced. Go further in the curriculum and think of an equilibrium in game theory. While it is also derived in a way which is consistent with the stated assumptions, its description states more than that – for example that it is a combination of strategies for which no individual has an incentive to unilaterally deviate.

Therefore, equilibrium approaches in my opinion go beyond detecting an outcome that is logically implied by assumptions and step-by-step analytics. They also tend to presume an outcome of a certain type and thereby risk the neglect of other outcomes, strategies, behaviour, and thereby even whole issues that may be highly relevant in reality.

In case my concern is not clear, a discussion of Rubinstein’s famous e-mail game may help. The e-mail game may be described as the following: A couple wants to meet and prefers being together over being separated. However, if it rains they prefer to meet inside, otherwise the prefer to meet outside. Whether it rains or not is determined by nature and only one person, let’s assume the woman, knows the weather for sure. If it will rain, she sends an e-mail to the man. Every received e-mail is read and automatically triggers a response, but every e-mail also gets lost with a certain small probability. That means that the e-mail conversation may last for a long time and even forever, but the probability for the latter case tends to be zero.

Because of the small but nevertheless positive probability for an e-mail to get lost, both parties will never know for sure how many e-mails have been sent. The woman knows whether she sent an e-mail or not, but she is confused about the state where one or two e-mails were sent (captured by the partition Pw). While it may be that the second e-mail – sent by automatic response from the man’s account – got lost, it also may be the case that her e-mail did not pass through in the first place. The moment the second e-mail passes through, the third e-mail is triggered automatically and she can distinguish that state from the ones before. However, she again cannot distinguish between the state of three and four e-mails sent – because if she would know about the fourth e-mail, she would have automatically sent the fifth, being in another state. The man faces a similar incompleteness of information (captured by the partition Pm). He in turn is confused about whether none or one e-mail was sent, just like he is confused about whether two or three e-mails were sent and so on.

Rubinstein thereby shows that the strictly formal approach does not lead to an equilibrium in which they meet outside in the nearby game even if there is a high probability for the information to pass on. In fact, the formal result of the game described above is that none of the two will risk to go outside as there is no state (described in terms of e-mails sent) about whose appearance exists common knowledge. However, the example not only shows how easy simple games may get complicated in formal term, but also shows how misleading the strictly formal conclusion can be with regard to an underlying issue. It was about a couple who wants to meet, inside on rainy days, outside otherwise. They both know their preferences. They differ only in the information they have – first about the state of nature and second about how many e-mails are sent. The second issue however should not be the one of primary interest. Instead a social scientist and therefore economist should just ask: how many e-mails have to be sent that they both know that they both know about the weather and therefore human beings of these days will coordinate for the preferred equilibrium.

One e-mail sent just states that it is rainy and the woman knows about it. Two e-mails sent means that the man received this important information, but the women does not know that yet. Three e-mails sent means that the woman knows that the man knows. Four e-mails sent means that the man now knows that the woman knows that he knows. Five e-mails mean that the woman now knows that the man knows that the women knows that the man knows. At the latest after the sixth and seventh e-mail both know that they reached the aspired situation where both know that they both know.

While they can never be sure that their last e-mail passed through, they reach a state where human beings of these and thereby the economic agents of interest will not care about it. Agents may differ with regard to the number of e-mails they require in order to believe in a successful coordination, but I claim that there are not much of them who require more than the five to seven e-mails.

So, while the formal equilibrium approach provides some insights in favour of a theoretical statement about mutual and common knowledge, it risks to draw too much attention towards the wrong issue or at least away from non-equilibrium outcomes that may be highly probable in reality. I think that this is a general issue of equilibrium economics, which are worthwhile and helpful in many regards, but always have to be done as well as interpreted with caution.

Intro to Econ: Second Lecture – Financial Derivative Pricing

The final bit of the second lecture is an introduction to financial engineering. Assuming the absence of arbitrage is all one needs to price financial derivatives. A financial derivative, perhaps a bit narrowly defined, is a financial product – that is a risky investment possibility – with payoffs that depend exclusively on other “basic” financial products such as bonds and stocks. Students may want to google what bonds and stocks are if they do not yet know. For our purposes all we need to know is that a stock of a company has a value or price that substantially varies over time. The future price of a stock is uncertain today and this uncertainty can be quite large.

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Intro to Econ: Second Lecture – Arbitrage with Sports Bets

In this part of the second lecture I turn to another area in which the absence of arbitrage – due to people preferring more money over less – implies severe restrictions: sports betting. I begin by giving the students potentially fictional betting odds on three football (soccer) games, given in the following table.

 \begin{tabular}{c|ccc} & Game 1 & Game 2 & Game 3 \\ \hline A & 1,1 & 4,75 & 1,9 \\ x & 11 & 3,6 & 4,2 \\ B & 21 & 1,78 & 5 \\ \end{tabular}

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Intro to Econ: Second Lecture – Arbitrage with Exchange Rates

I begin the second lecture by reminding the students about the key insights of the first class: that people pursue goals, that this leads to systematic patterns of behavior, and that these patterns are somewhat understandable, perhaps even somewhat predictable to an analyst. The particular goal we talked about in the first class was that people try to avoid wasting time. In the end I talked about queuing behavior that can be understood as a consequence of this goal: for example, we expect roughly equally long queues at supermarket checkout points and roughly equally fast queues in traffic jams.

In the second lecture I then take up another goal most people share: people, “ceteris paribus”, tend to prefer more money over less. The expression “ceteris paribus” means “all else equal”. I might be reluctant to accept extra money if this means someone is allowed to hit me on the head. But I generally will be happy to receive extra money if this does not come with any extra obligations.

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Intro to Econ: First Lecture – People pursue Goals

In this second half of my first lecture, I start with making the students do some work and then asking them a few questions. The purpose of all this is to demonstrate to the students that human behavior is not entirely unpredictable and that in some cases there are some very simple principles that can explain a fair amount of behavior. Continue reading