Rub In Stein

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Great GreatMoments MomentsininFinancial FinancialEconomics Economics Copyright©2003 Mark Rubinstein Copyright©2003 Mark Rubinstein

C=f(S,t)

Great Moments in Financial Economics Mark Rubinstein Paul Stephens Professor of Applied Investment Analysis University of California at Berkeley www.in-the-money.com

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Great Moments in Financial Economics Copyright©2003 Mark Rubinstein

Great Moments in Financial Economics C=f(S,t)

1) Present value 2) Modigliani-Miller Theorem 3) Short-Sales

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Great Moments in Financial Economics Copyright©2003 Mark Rubinstein

Present Value C=f(S,t)

PV0(X1, X2, …, Xt, …) =

∞

Σ

t=1

Xt rt

■ The current stock price equals the present value of all future dividends. This view of stock prices supplies the context for “fundamental analysis”, which attempts to estimate (usually by some indirect method) the time series of future dividends. It implies that the current stock price is independent of its planned liquidation date. ■ Finite-lived annuity (T years):

PV0(X1, X2, …, Xt, …, XT) = (X/(r – 1))[1 – (1/r)T] ■ Perpetually growing cash flow (g < r): PV0(X1, X2, …, Xt, …) = X1/r + X1g/r2 + X1g2/r3 + · · · = X1/(r – g)

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Great Moments in Financial Economics Copyright©2003 Mark Rubinstein

Present Value C=f(S,t)

Fisher, Halley, de Witt, de Moivre

Irving Fisher, The Rate of Interest: Its Nature, Determination and Relation to Economic Phenomena (1907) Edmund Halley, “Of Compound Interest” (1761) Johan de Witt, “Value of Life Annuities in Proportion to Redeemable Annuities” (1671) Abraham de Moivre, Treatise on Annuities on Lives (1725)

PV0(X1, X2, X3, …, Xt, …) = X0x/(1 – x) where x ≡ g/r — John Burr Williams, The Theory of Investment Value, p. 88, equation 17a.

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Great Moments in Financial Economics Copyright©2003 Mark Rubinstein

Modigliani-Miller Theorem C=f(S,t)

Modigliani-Miller Theorem: In a perfect market, if the operating income of a firm is independent of its capital structure, then (present) value of a firm (the sum of the value of its debt and equity) is independent of its capital structure. Homemade leverage argument: don’t pay for someone else to make something you can make yourself for free. Value additivity argument: the present value of the sum of cash flows is the sum of their present values. Franco Modigliani and Merton Miller, “The Cost of Capital, Corporation Finance and the Theory of Investment,” American Economic Review 48, No. 3 (June 1958), pp. 261-297. [Taxes] Franco Modigliani and Merton Miller, “Reply to Heins and Sprenkle,” American Economic Review 59, No. 4, Part 1 (September 1969), pp. 592-595.

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Great Moments in Financial Economics Copyright©2003 Mark Rubinstein

C=f(S,t)

Modigliani-Miller Theorem “Law of the Conservation of Investment Value”

“If the investment value of an enterprise as a whole is by definition the present worth of all its future distributions to security holders, whether on interest or dividend account, then this value in no wise depends on what the company’s capitalization is. Clearly, if a single individual or a single institutional investor owned all the bonds, stocks, and warrants issued by a corporation, it would not matter to this investor what the company’s capitalization was (except for details concerning the income tax). Any earnings collected as interest could not be collected as dividends. To such an individual it would be perfectly obvious that total interest- and dividend-paying power was in no wise dependent on the kind of securities issued to the company’s owner. Furthermore, no change in the investment value of the enterprise as a whole would result from a change in its capitalization. Bonds could be retired with stock issues, or two classes of junior securities (i.e. common stock and warrants) could be combined into one, without changing the investment value of the company as a whole. Such constancy of investment value is analogous to the indestructibility of matter and energy; it leads us to speak of the Law of the Conservation of Investment Value, just as physicists speak of the Law of the Conservation of Matter, or the Law of the Conservation of Energy.” – John Burr Williams, The Theory of Investment Value (1938), pp. 72-73.

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Great Moments in Financial Economics Copyright©2003 Mark Rubinstein

Short-Sales and Stock Prices C=f(S,t)

Laundry List of “Anomalies”

■ overpricing of IPOs ■ “Monday effect” ■ momentum factor in stock returns ■ stocks with high turnover have lower returns ■ high beta stocks have too low returns ■ closed-end fund discounts ■ smirk in index option prices ■ excess volatility of stock returns ■ asymmetry of market crashes over market rises ■ recent Internet-based stock market “bubble”

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Great Moments in Financial Economics Copyright©2003 Mark Rubinstein

Short-Sales and Stock Prices C=f(S,t)

Williams-Miller Hypothesis

Edward Miller, “Risk, Uncertainty and Divergence of Opinion” (1977) “In multiple stock markets, each stock will be held only by those who like that particular stock issue better than any other, and those who prefer some other stock will not be owners of that particular stock, even though they may entertain an opinion on that one along with the opinions on all others. … In other words, in a multiple stock market there is a tendency for most people to think all stocks but their own too high. If most people are right in their opinion of the other fellow’s investments, then it would follow that stocks in general have a tendency to sell too high, because almost every other stock will enjoy some distinction of its own, and will tend to gather around itself its own special group of enthusiasts who will bid its price up too high. If every stock is somebody’s favorite, then every price should be viewed with skepticism.” – John Burr Williams, The Theory of Investment Value (1938), pp. 28-29.

Prediction: the greater the divergence of opinion and the higher the barriers to short-selling, the higher the prices of stocks

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Great Moments in Financial Economics Copyright©2003 Mark Rubinstein

Short-Sales and Stock Prices C=f(S,t)

Diamond-Verrechhia Hypothesis

Douglas Diamond and Robert Verrecchia, “Constraints on Short-Selling and Asset Price Adjustment to Private Information” (1987)

Rational Expectations: optimists take into account the pessimism of those that would have liked to have short-sold, so on average prices are not too high or too low How to Tell the Difference: announcements of increases in shortinterest push prices down immediately or with delay? Crash Asymmetry: when pessimistic information is unusually negative, it is not factored into prices

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Great Moments in Financial Economics Copyright©2003 Mark Rubinstein

Short-Sales and Stock Prices C=f(S,t)

Short-Selling Puzzles

Demand Puzzle: why is there not much more short selling? Supply Puzzle: why aren’t more investors willing to loan out their stock to short-sellers?