The Determination of Stock Prices
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The Determination of Stock Prices

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    The Determination of Stock Prices The Determination of Stock Prices Presentation Transcript

    • The Determination of Stock Prices The price of an asset reflects the value of both future payouts earned by holding that asset and possible increases in the price of that asset. The importance of the future price of an asset for its current price introduces a dynamic element into asset pricing equations. In fact, a typical asset price equation takes the form of a first-order linear difference equation. To illustrate this, we consider a model of stock prices. Define pt as the time-t price of one share of a stock. The return on the stock is the sum of two components. A stock pays a dividend in period t 1 for holding the stock during period t, and we denote the expected value of this dividend as de 1. Another source of return to a stock is the t price at which it can be sold in the next period. During period t people expect the price of the stock in period t 1 to be pe 1. The expected return from holding a share of a t stock must equal the return from holding a bond in an asset market when investors can choose between either asset and when there is no difference in riskiness or liquidity between stocks and bonds. If the money spent on a share of stock were instead invested in a one-period bond paying an interest rate r, the return would be (1 r)pt. The expected return on the stock is equated to the return on a bond if (1 r)pt pte 1 dte 1. We assume that pe t 1 pt 1 for all t. We then have the first-order linear difference equation (1 r)pt pt 1 dte 1, which can be solved with methods discussed earlier. Rearranging terms, we have 1 1 pt pt 1 dte 1. 1 r 1 r The solution (13.11) shows that this equation has the forward solution 1 i dte 1 i pt . (13.13) i 0 1 r 1 r
    • This solution assumes that the terminal value de is finite since, then, 1 t . de lim 0. t→ 1 r 1 r The solution (13.13) predicts that the period-t price of a stock equals the present dis- counted value of its expected future stream of dividends. In particular, if the expected dividend is constant and equal to d, then the current stock price equals 1 i d pt i 0 1 r 1 r 1 d 1 (1 (1 r)) 1 r d , r which is the present discounted value of the stream of constant dividend payments. The solution (13.13) implies that anything that affects the dividend payment in the future affects the current price of the stock. The effect is larger for a given change that is closer to the present. Stock prices move in response to news about dividend pay- ments, and, thus, we would expect stock prices to be volatile. In fact, actual stock prices appear to be too volatile to be consistent with this model. Robert Shiller shows that the time path of the prices of composite stock market indices are much more volatile than the time path predicted by this model when actual dividend payments are used for the sequence {de}n 0. Work by Robert Barsky and J. t t Bradford DeLong, however, suggests that this model of the stock market may prove consistent with the data if investors must estimate the path of dividends since this introduces more volatility into the stock price sequence.6