On robust estimation of the location parameter

This paper incorporates a time-varying intensity of disasters in the Rietz-Barro hypothesis that risk premia result from the possibility of rare, large disasters. During a disaster, an asset’s fundamental value falls by a time-varying amount. This in turn generates time-varying risk premia and thus volatile asset prices and return predictability. Using the recent technique of linearity-generating processes (Gabaix 2007), the model is tractable, and all prices are exactly solved in closed form. In the “variable rare disasters” framework, the following empirical regularities can be understood qualitatively: (i) equity premium puzzle (ii) risk-free rate-puzzle (iii) excess volatility puzzle (iv) predictability of aggregate stock market returns with price-dividend ratios (v) value premium (vi) often greater explanatory power of characteristics than covariances for asset returns (vii) upward sloping nominal yield curve (viiii) a steep yield curve predicts high bond excess returns and a fall in long term rates (ix) corporate bond spread puzzle (x) high price of deep out-of-the-money puts. I also provide a calibration in which those puzzles can be understood quantitatively as well. The fear of disaster can be interpreted literally, or can be viewed as a tractable way to model time-varying risk-aversion or investor sentiment. (JEL: E43, E44, G12)

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Variable Rare Disasters: An Exactly Solved Framework for Ten Puzzles in Macro-Finance

This review article tries to answer four questions: (i) what are the stylized facts about uncertainty over time; (ii) why does uncertainty vary; (iii) do fluctuations in uncertainty matter; and (iv) did higher uncertainty worsen the Great Recession of 2007-2009? On the first question both macro and micro uncertainty appears to rise sharply in recessions. On the second question the types of exogenous shocks like wars, financial panics and oil price jumps that cause recessions appear to directly increase uncertainty, and uncertainty also appears to endogenously rise further during recessions. On the third question, the evidence suggests uncertainty is damaging for short-run investment and hiring, but there is some evidence it may stimulate longer-run innovation. Finally, in terms of the Great Recession, the large jump in uncertainty in 2008 potentially accounted for about one third of the drop in GDP.

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Fluctuations in Uncertainty

Why is the equity premium so high, and why are stocks so volatile? Why are stock returns in excess of government bill rates predictable? This paper proposes an answer to these questions based on a time-varying probability of a consumption disaster. In the model, aggregate consumption follows a normal distribution with low volatility most of the time, but with some probability of a consumption realization far out in the left tail. The possibility of this poor outcome substantially increases the equity premium, while time-variation in the probability of this outcome drives high stock market volatility and excess return predictability. THE MAGNITUDE OF THE expected excess return on stocks relative to bonds (the equity premium) constitutes one of the major puzzles in financial economics. As Mehra and Prescott (1985 )s how, the fl uctuations observed in the consumption growth rate over U.S. history predict an equity premium that is far too small, assuming reasonable levels of risk aversion. 1 One proposed explanation is that the return on equities is high to compensate investors for the risk of a rare disaster (Rietz (1988)). An open question has therefore been whether the risk is sufficiently high, and the rare disaster sufficiently severe, to quantitatively explain the equity premium. Recently, however, Barro (2006) shows that it is possible to explain the equity premium using such a model when the probability of a rare disaster is calibrated to international data on large economic declines. WhilethemodelsofRietz(1988)andBarro(2006)advanceourunderstanding

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Can Time-Varying Risk of Rare Disasters Explain Aggregate Stock Market Volatility?

This paper quanties how variation in real economic activity and ination in the U.S. inuenced the market prices of level, slope, and curvature risks in U.S. Treasury markets. To accomplish this we develop a novel arbitrage-free DTSM in which macroeconomic risks{ in particular, real output and ination risks{ impact bond investment decisions separately from information about the shape of the yield curve. Estimates of our preferred macro-DTSM over the twenty-three year period from 1985 through 2007 reveal that unspanned macro risks explained a substantial proportion of the variation in forward terms premiums. Unspanned macro risks accounted for nearly 90% of the conditional variation in short-dated forward term premiums, with unspanned real economic growth being the key driving factor. Over horizons beyond three years, these eects were entirely attributable to unspanned ination. Using our model, we also reassess some of Chairman Bernanke’s remarks on the interplay between term premiums, the shape of the yield curve, and macroeconomic activity.

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Risk Premiums in Dynamic Term Structure Models with Unspanned Macro Risks

We show that bond risk-premia rise with uncertainty about expected inflation and fall with uncertainty about expected growth; the magnitude of return predictability using these two uncertainty measures is similar to that by multiple yields. Motivated by this evidence, we develop and estimate a long-run risks model with time-varying volatilities of expected growth and inflation. The model simultaneously accounts for bond return predictability and violations of uncovered interest parity in currency markets. We find that preference for early resolution of uncertainty, time-varying volatilities, and non-neutral effects of inflation on growth are important to account for these aspects of asset markets.

A Long-Run Risks Explanation of Predictability Puzzles in Bond and Currency Markets

https://repository.upenn.edu/cgi/viewcontent.cgi?article=1216&context=fnce_papers

Good and bad uncertainty: Macroeconomic and financial market implications ☆

We show that bond risk premia rise with uncertainty about expected inflation and fall with uncertainty about expected growth; the magnitude of return predictability using these uncertainty measures is similar to that by multiple yields Motivated by this evidence, we develop and estimate a long-run risks model with timevarying volatilities of expected growth and inflation The model simultaneously accounts for bond return predictability and violations of uncovered interest parity in currency markets We find that preference for early resolution of uncertainty, time-varying volatilities, and non-neutral effects of inflation on growth are important to account for these aspects of asset markets The Author 2012 Published by Oxford University Press on behalf of The Society for Financial Studies All rights reserved For Permissions, please e-mail: journalspermissions@oupcom, Oxford University Press

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We show that volatility movements have first-order implications for consumption dynamics and asset prices. Volatility news affects the stochastic discount factor and carries a separate risk premium. In the data, volatility risks are persistent and are strongly correlated with discount-rate news. This evidence has important implications for the return on aggregate wealth and the cross-sectional differences in risk premia. Estimation of our volatility risks based model yields an economically plausible positive correlation between the return to human capital and equity, while this correlation is implausibly negative when volatility risk is ignored. Our model setup implies a dynamics capital asset pricing model (DCAPM) which underscores the importance of volatility risk in addition to cash-flow and discount-rate risks. We show that our DCAPM accounts for the level and dispersion of risk premia across book-to-market and size sorted portfolios, and that equity portfolios carry positive volatility-risk premia.

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Volatility, the Macroeconomy, and Asset Prices

The paper examines equilibrium models based on Epstein–Zin preferences in a framework in which exogenous state variables follow affine jump diffusion processes. A main insight is that the equilibrium asset prices can be computed using a standard machinery of affine asset pricing theory by imposing parametric restrictions on market prices of risk, determined inside the model by preference and model parameters. An appealing characteristic of the general equilibrium setup is that the state variables have an intuitive and testable interpretation as driving the consumption and dividend dynamics. We present a detailed example where large shocks (jumps) in consumption volatility translate into negative jumps in equilibrium prices of the assets as agents demand a higher premium to compensate for higher risks. This endogenous “leverage effect,” which is purely an equilibrium outcome in the economy, leads to significant premiums for out-of-the-money put options. Our model is thus able to produce an equilibrium “volatility smirk,” which realistically mimics that observed for index options.

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Ivan Shaliastovich

Papers

A Long-Run Risks Explanation of Predictability Puzzles in Bond and Currency Markets

Good and bad uncertainty: Macroeconomic and financial market implications ☆

A Long-Run Risks Explanation of Predictability Puzzles in Bond and Currency Markets

Volatility, the Macroeconomy, and Asset Prices

An equilibrium guide to designing affine pricing models