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Journal of Economics and Finance

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01-01-2013

Uncertainty and risk premium puzzle

Author: Heeho Kim

Published in: Journal of Economics and Finance | Issue 1/2013

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Abstract

This paper provides a theory and evidence that the risk premium puzzle may be viewed mainly as a phenomenon pertaining to the unstable foreign exchange market. In an unstable market, errors uncompensated by an initial risk premium accrue due to consumer expectation revision about the ex ante uncertainty of the exchange rate. These revision errors are different from the forecasting errors, depending on the frequency of the consumer expectation revision and the degree of risk aversion. A simulation was discussed on how the risk premium actually deviates from an initial premium in the unstable market. Using the monthly data of the U.K., Japan, Australia, Korea, Malaysia, and Thailand from January 1994 to December 2008, it is shown that revision errors for risk premium were statistically significant and were non-trivial in magnitude and that the degree of absolute risk aversion went up during the Asian currency crisis as well as the recent financial crisis periods.

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See Engel (1992), Domowitz and Hakkio (1985), Hodrick and Srivastava (1986), Bekaert and Hodrick (1992), Dutton (1993) for determination of risk premium in a general equilibrium model.

The DA function weighs more on the probability of downside risk. See also Segal and Spivak (1997), Gul (1991) for a few examples of the preference with the first-order risk aversion.

See Engel (1996) for Jensen’s Inequality. Jensen’s inequality could exist regardless of Siegel’s paradox.

The second-order conditions are satisfied when the utility function is strictly concave and u″<0.

Mark (1988) expresses premium as \( \frac{{{f_{{t = 1|t}}} - {E_t}{s_{{t + 1}}}}}{{{f_{{t + 1|t}}}}} \), and Cumby (1988) defined it as real term \( \frac{{({E_t}{s_{{t + 1}}} - {f_{{t + 1|t}}}){P_t}}}{{{s_t}{P_{{t + 1}}}}}. \)

Hansen and Hodrick (1980) and Engel (1992) show that premium is influenced by real and nominal shocks

Refer to Dutton (1993) for the income effect of real and nominal shocks on premium.

See Koutmos (1998) and Domowitz and Hakkio (1985) for works on forecasting error in risk premium.

See Mehra and Prescott (1985), Dutton (1993), Bekaert (1994), Bekaert and Hodrick (1992) for premium puzzle. They showed that an actual degree of risk aversion should be 40.0 ∼ 50.0 in order to explain the premium evaluated at the real market.

In matching sampling data of the futures rate with those of the spot rate, we may lose lots of information on data. See Bekaert and Hodrick (1992).

When futures rate data were not available at the end of the month, these rates were sampled the day before the end of the month.

Using a survey data, Cavaglia and Wolff (1996) examined the movements of risk premium.

Use of a log variable instead of a level variable for the risk premium can eliminate Jensen’s inequality, which can arise from Siegel’s paradox.

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Title: Uncertainty and risk premium puzzle
Author: Heeho Kim
Publication date: 01-01-2013
Publisher: Springer US
Published in: Journal of Economics and Finance / Issue 1/2013
Print ISSN: 1055-0925
Electronic ISSN: 1938-9744
DOI: https://doi.org/10.1007/s12197-010-9170-7

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