Cautiousness in the Small and in the Large

27 Pages Posted: 27 Oct 2012 Last revised: 17 Dec 2012

See all articles by James Huang

James Huang

Lancaster University - Department of Accounting and Finance

Richard Stapleton

University of Manchester - Division of Accounting and Finance

Date Written: October 11, 2012

Abstract

In this paper we propose a new downside risk aversion measure, which is called cautiousness in the literature. Using a simple portfolio problem with a risk-free bond, a stock, and an option on the stock, we show that, an agent has higher cautiousness (i) if and only if she is always more likely to buy the option, (ii) if and only if she always demands more options per share. As an option's payoff is a convex function of the underlying stock price, increasing positions in the option increases the convexity of a portfolio's payoff and results in a strong increase in skewness which is defined by Van Zwet (Van Zwet, W. R. (1964). Convex Transformations of Random Variables, Mathematical Centre Tracts 7, Mathematisch Centrum, Amsterdam) and Chiu (Chiu, W. H. (2005). Skewness Preference, Risk Aversion, and the Precedence Relations on Stochastic Changes, Management Science 12, 1816-1828).

Keywords: cautiousness, convex transformation of random variables, demand for options, downside risk aversion, strong increases in skewness

JEL Classification: D81, G11

Suggested Citation

Huang, James Xiaoping and Stapleton, Richard, Cautiousness in the Small and in the Large (October 11, 2012). Available at SSRN: https://ssrn.com/abstract=2166790 or http://dx.doi.org/10.2139/ssrn.2166790

James Xiaoping Huang (Contact Author)

Lancaster University - Department of Accounting and Finance ( email )

The Management School
Lancaster LA1 4YX
United Kingdom
01 5245 93633 (Phone)
01 5248 47321 (Fax)

Richard Stapleton

University of Manchester - Division of Accounting and Finance ( email )

Crawford House
Oxford Road
Manchester M13 9PL
United Kingdom

HOME PAGE: http://rstapleton.com/

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