Handbook of the Economics of Finance

We propose a new model of exchange rates, which yields a theory of the forward premium puzzle. Our explanation combines two ingredients: the possibility of rare economic disasters, and an asset view of the exchange rate. Our model is frictionless, has complete markets, and works for an arbitrary number of countries. In the model, rare worldwide disasters can occur and affect each country’s productivity. Each country’s exposure to disaster risk varies over time according to a mean-reverting process. Ri sky countries command high risk premia: they feature a depreciated exchange rate and a high interest rate. As their risk premium mean reverts, their exchange rate appreciates. Therefore, currencies of high interest rate countries appreciate on average. To make the notion of disaster risk more implementable, we show how options prices might in principle uncover latent disaster risk, and help forecast exchange rate movements. We then extend the framework to incorporate two factors: a disaster risk factor, and a business cycle factor. We calibrate the model and obtain quantitatively realistic values for the volatility of the exchange rate, the forward premium puzzle regression coefficients, and near-random walk exchange rate dynamics. Finally, we solve a model of stock markets across countries, which yields a series of predictions about the joint behavior of exchange rates, bonds, options and stocks across countries. The evidence from the options market appears to be supportive of the model. (JEL: E43, E44, F31, G12, G15)

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Rare Disasters and Exchange Rates

We estimate an empirical model of consumption disasters using new data on consumption for 24 countries over more than 100 years, and study its implications for asset prices. The model allows for par tial recoveries after disasters that unfold over multiple years. We find that roughly half of the drop in consumption due to disasters is subsequently reversed. Our model generates a sizable equity premium from disaster risk, but one that is substantially smaller than in simpler models. It implies that a large value of the intertemporal elasticity of substitution is necessary to explain stock-market crashes at the onset of disasters. (JEL E21, E32, E44, G12, G14)

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Crises and Recoveries in an Empirical Model of Consumption Disasters

Paul Samuelson (1969) was once asked by a physicist for a law in economics that was both nontrivial and true. This is a difficult challenge, as many (roughly) true results are in the end rather trivial (for example, demand curves slope down), while many nontrivial results in economics in fact require too much sophistication and rationality on the part of the agents to actually hold true in practice. 1 Samuelson answered, “the law of comparative advantage.” The story does not say whether the physicist was satisfied. The law of comparative advantage is a qualitative law, and not a quantitative one as is the rule in physics. Indeed, many of the insights of economics seem to be qualitative, with many fewer reliable

https://pubs.aeaweb.org/doi/pdfplus/10.1257/jep.30.1.185

Power Laws in Economics: An Introduction

There is an unmet need for greater investment in preparedness against major epidemics and pandemics. The arguments in favour of such investment have been largely based on estimates of the losses in national incomes that might occur as the result of a major epidemic or pandemic. Recently, we extended the estimate to include the valuation of the lives lost as a result of pandemic-related increases in mortality. This produced markedly higher estimates of the full value of loss that might occur as the result of a future pandemic. We parametrized an exceedance probability function for a global influenza pandemic and estimated that the expected number of influenza-pandemic-related deaths is about 720 000 per year. We calculated that the expected annual losses from pandemic risk to be about 500 billion United States dollars - or 0.6% of global income - per year. This estimate falls within - but towards the lower end of - the Intergovernmental Panel on Climate Change's estimates of the value of the losses from global warming, which range from 0.2% to 2% of global income. The estimated percentage of annual national income represented by the expected value of losses varied by country income grouping: from a little over 0.3% in high-income countries to 1.6% in lower-middle-income countries. Most of the losses from influenza pandemics come from rare, severe events.

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Pandemic risk: how large are the expected losses?

confidence interval of 2 to 4. The results are robust to uncertainty about the values of the disaster probability and the equity premium, and can accommodate seemingly paradoxical situations in which the equity premium may appear to be infinite.

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On the size distribution of macroeconomic disasters

In the rare-disasters setting, a key determinant of the equity premium is the size distribution of macroeconomic disasters, gauged by proportionate declines in per capita consumption or GDP. The long-term national-accounts data for up to 36 countries provide a large sample of disaster events of magnitude 10% or more. For this sample, a power-law density provides a good fit to the distribution of the ratio of normal to disaster consumption or GDP. The key parameter of the size distribution is the upper-tail exponent, `alpha`, estimated to be near 5, with a 95% confidence interval between 3-1/2 and 7. The equity premium involves a race between `alpha` and the coefficient of relative risk aversion, `gamma`. A higher `alpha` signifies a thinner tail and, therefore, a lower equity premium, whereas a higher `gamma` implies a higher equity premium. The equity premium is finite if `alpha-1>gamma`. To accord with the observed average unlevered equity premium of around 5%, we get a point estimate for `gamma` close to 3, with a 95% confidence interval of roughly 2 to 4.

On the Size Distribution of Macroeconomic Disasters

https://www.nber.org/system/files/working_papers/w21871/w21871.pdf

Rare events and long-run risks.

China's real estate market rebounded sharply after a temporary slowdown in 2014-2015. This paper uses city-level data to estimate the range of house price overvaluation across city-tiers and assesses the main risks of a sharp housing market slowdown. If house prices rise further beyond "fundamental" levels and the bubble expands to smaller cities, it would increase the likelihood and costs of a sharp correction, which would weaken growth, undermine financial stability, reduce local government spending room, and spur capital outflows. Empirical analysis suggests that the increasing intensity of macroprudential policies tailored to local conditions is appropriate. The government should expand its toolkit to include additional macro-prudential measures and push forward reforms to address the fundamental imbalances in the residential housing market.

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The Residential Real Estate Market in China: Assessment and Policy Implications

Rare events (RE) and long-run risks (LRR) are complementary elements for understanding asset-pricing patterns, including the average equity premium and the volatility of equity returns. We construct a model with RE (temporary and permanent parts) and LRR (including stochastic volatility) and estimate this model with long-term data on aggregate consumption for 42 economies. RE typically associates with major historical episodes, such as the world wars and the Great Depression and analogous country- specific events. LRR reflects gradual and evolving processes that influence long-run growth rates and volatility. A match between the model and observed average rates of return requires a coefficient of relative risk aversion, γ, around 6. Most of the explanation for the equity premium derives from RE, although LRR makes a moderate contribution. We think the required γ will decline (and, thereby, become more realistic) if we allow for incomplete information about the underlying shocks, including the breakdown of RE into temporary and permanent parts. We thought that the addition of LRR to the RE framework would help to match the observed volatility of equity returns. However, the joint model still substantially understates this volatility. We think this aspect of the model will improve if we allow for stochastic evolution of the disaster probability.Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

/pdf/rare-events-and-long-run-risks-4t5qgjipok.pdf

Tao Jin

Papers

On the size distribution of macroeconomic disasters

On the Size Distribution of Macroeconomic Disasters

Rare events and long-run risks.

The Residential Real Estate Market in China: Assessment and Policy Implications

Rare Events and Long-Run Risks