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Why do investors buy cum-dividend when mean dividend valuation ratios are greater than one? . ( The cum-dividend share purchase decision) Michael Cain and Lynn Hodgkinson
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Why do investors buy cum-dividend when mean dividend valuation ratios are greater than one? (The cum-dividend share purchase decision) Michael Cain and Lynn Hodgkinson Bangor Business School University of Wales Empirical Finance, Brunel University, May 2008
Introduction • This talk will consider the cum-dividend share purchase decision by statistically modelling the movement in share prices over the short holding period, after the dividend has been declared but before its payment, and expressing investor preferences by means of a utility function. The optimal solution is obtained for two particular utility functions.
Introduction (contd.) • It is shown that it is possible for investors to buy shares cum-dividend even if on average the share price is likely to fall by more than the dividend. The model is fitted to actual data and estimates of the level of risk-aversion of investors is obtained; this is used to forecast subsequent cum-dividend trading volume.
Preliminaries • In a risk-neutral world, without taxes, transaction costs and settlement costs, one might expect that the drop in share price when a share goes ex-dividend should be exactly equal to the dividend paid on that stock. • A considerable number of studies have reported that the price drop ratio (the drop in share price from the cum-dividend day to the ex-dividend day divided by the net dividend) is less than 1.
Literature • The seminal work was that of Campbell and Beranek (1955). Other work includes: Elton and Gruber (1970), Laknishok and Vermaelen (1986), Lasfer (1995), Bali and Hite (1998), Frank and Jagannathan (1998) and Bell and Jenkinson (2002); the latters’ results indicate that the ratio in fact exceeded one for large UK companies with high dividend yields when tax credits were available for tax-exempt institutions.
Aim and Plan • Analysis of other data also indicated a counter-intuitive ratio of more than 1 and the object is thus to attempt to model the economic decision making process involved and thereby explain the various outcomes. • Having satisfactorily modelled the situation the plan is to estimate the level of investor risk aversion and to consider the difficult problem of forecasting trading volume.
Model for price change • An investor considers how many (q) shares to purchase at current price, p, cum-dividend with a view to selling the shares and realising any gains or losses ex-dividend. • The dividend, d = rpwhere ris the dividend yield (0< r<1).
Model (contd.) • The share price ex-dividend is Xp where Xis the (random) multiplicative modifier of the price as it goes from cum-dividend to ex-dividend. If the price increases, then the realised value x of Xwill be >1 but if the price decreases, the realised value x of X will be <1.
Model (contd.) • With a positive dividend (d >0, r >0) it might be expected that the share price will decrease and perhaps to a level of approximately d below the current price; so that the realised value of Xmay be <1 and perhaps approximately 1 – r. The dividend valuation ratio (DVR) is:
Dividend valuation ratio (DVR) • DVR expresses the fall in the share price as a proportion of the dividend and provides a measure of the worth of the dividend; such receipt being worthwhile only if D<1. • It is assumed that any income or capital gains tax is taken into account in the definitions of r andp.
Price Model • Suppose that X has a gamma distribution with shape parameterkand scale parameter l(k>0, l > 0) • kandlencapsulate all current information about the market in so far as it affects the likely movement in the share price over the very short holding time.
Risk-Neutrality If the investor is risk-neutral: • he/she will not buy any shares if k/l < 1 – r, when E(D)>1, but • his/her demand will be unbounded if k/l >1 – r, that is when E(D)<1.
Utility and Risk • If E(D)=1, a risk-neutral investor will be indifferent between buying and not buying any shares. • Consider therefore other risk attitudes encapsulated by a utility of wealth function U(.) with U’(x)>0 for x>0.
Estimating Risk Aversion • Conditional on constant risk aversion, with these results it should be possible to consider hypotheses about the level of risk aversion of investors and to obtain a probability distribution of a, the constant measure of risk aversion.
Extension to E(D)>1 • It follows that, if E(D)=1, some investors will buy shares. • Invoking a continuity argument with regard to the general expression for the derivative of E, it also follows that even with E(D)>1, risk attitudes can make it possible for investors to optimally buy some shares.
