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##### Shane Whelan

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**102 Years of Financial Economics**Shane Whelan**2002**1900**2002**Louis Bachelier: Theory of Speculation. 1900**2002**Fischer Black & Myron Scholes: The Pricing of Option Contracts and Corporate Liabilities. Robert Merton: Theory of Rational Option Pricing. 1973 Louis Bachelier: Theory of Speculation. 1900**2002**Fischer Black & Myron Scholes: The Pricing of Option Contracts and Corporate Liabilities. Robert Merton: Theory of Rational Option Pricing. 1973 1944 John von Neumann & Oskar Morgenstern: Theory of Games and Economic Behaviour. Louis Bachelier: Theory of Speculation. 1900**2002**Fischer Black & Myron Scholes: The Pricing of Option Contracts and Corporate Liabilities. Robert Merton: Theory of Rational Option Pricing. 1973 1944 John von Neumann & Oskar Morgenstern: Theory of Games and Economic Behaviour. Bulletin of A.M.S.: Posterity may regard this book as one of the major scientific achievements of the first half of the twentieth century. Louis Bachelier: Theory of Speculation. 1900**2002**Fischer Black & Myron Scholes: The Pricing of Option Contracts and Corporate Liabilities. Robert Merton: Theory of Rational Option Pricing. 1973 1944 John von Neumann & Oskar Morgenstern: Theory of Games and Economic Behaviour. Louis Bachelier: Theory of Speculation. 1900**2002**Fischer Black & Myron Scholes: The Pricing of Option Contracts and Corporate Liabilities. Robert Merton: Theory of Rational Option Pricing. 1973 Work of Probabilists: Levy, Cramér, Wiener, Kolmogorov, Doblin, Khinchine, Feller, Itô. John von Neumann & Oskar Morgenstern: Theory of Games and Economic Behaviour. 1944 Louis Bachelier: Theory of Speculation. 1900**2002**Fischer Black & Myron Scholes: The Pricing of Option Contracts and Corporate Liabilities. Robert Merton: Theory of Rational Option Pricing. 1973 • “Looking back it is difficult to understand why the approaches and solutions developed for today’s financial sector, which are clearly oriented towards mathematics, or to be more precise towards probability theory, did not originate from the breeding-ground of actuarial thinking.” • Bühlmann, H., The Actuary: the Role and Limitations of the Profession since the Mid-19th Century. • ASTIN, 27, 2, 165-171 Work of Probabilists: Levy, Cramér, Wiener, Kolmogorov, Doblin, Khinchine, Feller, Itô. Louis Bachelier: Theory of Speculation. 1900**Financial Economics: Three Prongs**• Market Efficiency • modelling how prices evolve in (near) efficient markets • e.g., quantifying mismatch risk; probability of market crashes • Asset Pricing • factors that drive individual security prices • e.g., comparative assessment of growth versus value indicators; pricing anomalies • Corporate Finance • optimum financial management of companies • e.g., capital structure; dividend policy; pension fund investment**Orthodox History**2002 Fischer Black & Myron Scholes: The Pricing of Option Contracts and Corporate Liabilities. Robert Merton: Theory of Rational Option Pricing. 1973 Louis Bachelier: Theory of Speculation. 1900**Orthodox History**2002 Fischer Black & Myron Scholes: The Pricing of Option Contracts and Corporate Liabilities. Robert Merton: Theory of Rational Option Pricing. 1973 Franco Modigliani & Merton Miller: The Cost of Capital, Corporation Finance and the Theory of Investments 1958 Louis Bachelier: Theory of Speculation. 1900**1900: Bachelier’s Theory of Speculation**• ‘It seems that the market, the aggregate of speculators, at a given instant, can believe in neither a market rise nor a market fall…’; ‘…the mathematical expectations of the buyer and the seller are zero’. • His research leads to a formula ‘which expresses the likelihood of a market fluctuation’. • Brownian Motion, Wiener Process; Random Walk.**1900: Bachelier’s Theory of Speculation**Price Future Period**Actuaries’ Role**• Main practical import of Bachelier’s model • s.d. of return distribution is directly proportional to elapsed time • “In order to get an idea of the real premium on each transaction, one must estimate the mean deviation of prices in a given time interval...the mean deviation of prices is proportional to the square root of the number of days” . • Émile Dormoy, Journal des Actuaries Français, (1873) 2, p. 53. • Was Bachelier original ideas influenced by actuaries? • Henri Lefèvre and his diagrams?**Actuaries’ Role**• Text-book for French actuaries in 1908 disseminated the Bachelier model. • Alfred Barriol, Théorie et pratique des opérations financières. Paris 1908.**Wilderness Years to 1950s**• Data Collection • 1932 Cowles Commission for Research in Economics (Econometrica, S&P 500) • Actuaries Investment Index (Douglas, TFA XII; Murray, TFA XIII) • Little Processing/inference capability • no computer; statistical testing primative, prices have nasty statistical properties (Working (1934)). • Markets seen as a ‘compleat System of Knavery’ • 1929 Crash • Richard Whitney, President of NYSE, jailed.**Wilderness Years to 1950s**• The Dividend Discount Model • V=D/(i-g) • Generally attributed to Williams (1938) but... • Standard formula for actuaries • Todhunter, The Institute of Actuaries’ Textbook on Compound Interest and Annuities Certain. 1901. • Makeham, On the Theory of Actuaries Certain, JIA Vol. XIV 1869.**Portfolio Selection, CAPM, & Equilibrium Models**• 1973 1952 Harry Markowitz: Portfolio Selection. 1950**Portfolio Selection (MPT or Mean-Variance Analysis)**• Define risk as standard deviation (s.d.) • If, for each security, we can estimate its expected return, its s.d., and its correlation with every other security, then we can solve for the efficient frontier. Expected Return Efficient Frontier All Possible Portfolios Risk (s.d.)**Portfolio Selection, CAPM, & Equilibrium Models**• 1973 1953 Maurice Kendall: The Analysis of Time Series, Part I: Prices. 1952 Harry Markowitz: Portfolio Selection. 1950**Portfolio Selection, CAPM, & Equilibrium Models**• 1973 “Investors can, perhaps, make money on the Stock Exchange, but not, apparently by watching price-movements and coming in on what looks like a good thing.” 1953 Maurice Kendall: The Analysis of Time Series, Part I: Prices. 1952 Harry Markowitz: Portfolio Selection. 1950**Portfolio Selection, CAPM, & Equilibrium Models**• 1973 1953 Maurice Kendall: The Analysis of Time Series, Part I: Prices. 1952 Harry Markowitz: Portfolio Selection. 1950**Portfolio Selection, CAPM, & Equilibrium Models**• 1973 1958 Franco Modigliani & Merton Miller: The Cost of Capital, Corporation Finance and the Theory of Investments 1953 Maurice Kendall: The Analysis of Time Series, Part I: Prices. 1952 Harry Markowitz: Portfolio Selection. 1950**Portfolio Selection, CAPM, & Equilibrium Models**• 1973 1958 Franco Modigliani & Merton Miller: The Cost of Capital, Corporation Finance and the Theory of Investments 1953 Maurice Kendall: The Analysis of Time Series, Part I: Prices. 1952 Harry Markowitz: Portfolio Selection. 1950**Portfolio Selection, CAPM, & Equilibrium Models**• 1973 James Tobin: Liquidity Preference as Behavior Toward Risk. 1958 Franco Modigliani & Merton Miller: The Cost of Capital, Corporation Finance and the Theory of Investments 1953 Maurice Kendall: The Analysis of Time Series, Part I: Prices. 1952 Harry Markowitz: Portfolio Selection. 1950**Tobin: Unique Role of Risk-Free Asset**• Separation Theorem: The proportion of a portfolio held in the risk-free asset depends on risk aversion. The composition of the risky part of the portfolio is independent of the attitude to risk. Expected Return Efficient Frontier All Possible Portfolios Risk (s.d.)**Portfolio Selection, CAPM, & Equilibrium Models**• 1973 Franco Modigliani & Merton Miller: Dividend Policy, Growth, and the Valuation of Shares. 1961 1958 Franco Modigliani & Merton Miller: The Cost of Capital, Corporation Finance and the Theory of Investments 1953 Maurice Kendall: The Analysis of Time Series, Part I: Prices. 1952 Harry Markowitz: Portfolio Selection. 1950**Portfolio Selection, CAPM, & Equilibrium Models**• 1973 1964 William Sharpe: Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. Franco Modigliani & Merton Miller: Dividend Policy, Growth, and the Valuation of Shares. 1961 1958 Franco Modigliani & Merton Miller: The Cost of Capital, Corporation Finance and the Theory of Investments 1953 Maurice Kendall: The Analysis of Time Series, Part I: Prices. 1952 Harry Markowitz: Portfolio Selection. 1950**Sharpe: Equilibrium Model**• Everyone has the same optimum portfolio: it is the market portfolio. Efficient Frontier Expected Return Market Portfolio All Possible Portfolios Risk (s.d.)**Treynor-Sharpe-Lintner-Mossin CAPM**• CAPM in form presented in modern textbooks E[Ri]-r = i(E[Rm]-r) where, i = Cov(Ri, Rm)/Var(Rm) • Predictions empirically testable. • Does not stand up to testing – is have less explanatory power in counting for excess returns than relative market capitalisation or price-to-book ratios. [See Hawawini & Keim (2000) for a recent review of finding.]**Portfolio Selection, CAPM, & Equilibrium Models**• 1973 Paul Samuelson: Proof that Properly Anticipated Prices Fluctuate Randomly. 1965 1964 William Sharpe: Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. Franco Modigliani & Merton Miller: Dividend Policy, Growth, and the Valuation of Shares. 1961 1958 Franco Modigliani & Merton Miller: The Cost of Capital, Corporation Finance and the Theory of Investments 1953 Maurice Kendall: The Analysis of Time Series, Part I: Prices. 1952 Harry Markowitz: Portfolio Selection. 1950**Portfolio Selection, CAPM, & Equilibrium Models**• 1973 Fischer Black & Myron Scholes: The Pricing of Option Contracts and Corporate Liabilities. Robert Merton: Theory of Rational Option Pricing. Paul Samuelson: Proof that Properly Anticipated Prices Fluctuate Randomly. 1965 1964 William Sharpe: Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. Franco Modigliani & Merton Miller: Dividend Policy, Growth, and the Valuation of Shares. 1961 1958 Franco Modigliani & Merton Miller: The Cost of Capital, Corporation Finance and the Theory of Investments 1953 Maurice Kendall: The Analysis of Time Series, Part I: Prices. 1952 Harry Markowitz: Portfolio Selection. 1950**Option Pricing - Actuaries’ Role**• Colm Fagan (1977), Maturity Guarantees under Unit-Linked Contracts. • Independently arrives at the Black-Merton-Scholes breakthrough. • Tom Collins (BAJ, Vol. 109, 1982) • The replicating strategy “…compares unfavourably with the conventional strategy” and that a “…disturbing reason for the poor performance of the immunization strategy was that from time to time (e.g. early in 1975) the unit price was subject to sudden large fluctuations which were inconsistent with the continuous model assumed in deriving it.”**1973: Only a beginning**• Option pricing • interest rate, e.g., Ho & Lee model • capital project appraisals, e.g., Brennan & Schartz • Empirical studies • Empirical models of asset pricing • Statistical regularities in asset returns • Form of unconditional distribution known**Can this 102 Year Old Science**Still Surprise?**102nd Year**• Bouman & Jacobsen (2002) investigate • “Sell in May and go away but buy back by St. Leger Day” • It works – • halves the risk of equity markets but leaving return largely unchanged • In 36 out of 37 markets investigated over last decade and three decades**Returns on 19 Major Stock Markets, 1970-1998**16% 14% 12% 10% 8% 6% 4% 2% 0% UK US Italy Japan Spain Austria France Canada Belgium Norway Sweden Australia Denmark Germany Singapore Switzerland -2% Hong Kong Netherlands South Africa* -4% Average November-April Average May-October Source: MSCI Total Return Indices, data kindly supplied by Bouman & Jacobsen**102nd Year**• Bouman & Jacobsen (2002) investigate • “Sell in May and go away but buy back by St. Leger Day” • It works – • halves the risk of equity markets but leaving return largely unchanged • In 36 out of 37 markets investigated over last decade and three decades • It works almost everytime • In small markets and large markets. • In 10 out of 11 markets as far back as records allow • In particular, UK market as far back as 1694 • Results statistically significant • Not a result of data mining – • it holds when further tested on an independent and near virgin data set (Lucey & Whelan).**The Contribution of Actuaries**• Superficially, Bühlmann not altogether correct. • Bühlmann right in a deeper more disturbing way • Did not build on knowledge or disseminate it • Are we a learning profession? • Will we recognise and seize on the next major development in our underlying science to further our profession?**Concluding Words by Merton**“Any virtue can become a vice if taken to an extreme, and just so with the application of mathematical models in finance practice. I therefore close with an added word of caution about their use…The practitoner should therefore apply the models only tentatively, assessing their limitations carefully in each application.” R.C. Merton, Influence of mathematical models in finance on practice: past, present and future in Mathematical Models in Finance, Chapman & Hall for The Royal Society (London), 1995.**102 Years of Financial Economics**Shane Whelan**Key References**• Whelan, Bowie, & Hibbert (2002) A Primer in Financial Economics. British Actuarial Journal, Vol. 8, I. • Bernstein, P.L. (1992) Capital Ideas: The Improbable Origins of Modern Wall Street. The Free Press, New York, 340 pp. • Dimson, E. & Mussavian, M. (1998) A brief history of market efficiency. European Financial Management, Vol. 4, No. 1, 91-103. • Nobel Prize Website: www.nobel.se/ • Cootner, P. (Ed) (1964) The Random Character of Stock Market Prices. MIT Press. Journal of Banking & Finance, Vol. 23.**Selected Other References**• Dimson, E. & Mussavian, M. (1999) Three centuries of asset pricing. Journal of Banking & Finance, Vol. 23. • Hawawini, G. & Keim, D.B (2000) The cross section of common stock returns: a review of the evidence and some new findings. In Security Market Imperfections in World Equity Markets, Keim & Ziemba (Ed.), CUP. • Bouman, S. & Jacobsen, B. (2002) The Halloween indicator, ‘sell in May and go away’: another puzzle. Forthcoming in American Economic Review. • Lucey, B. & Whelan, S. (2001) A promising timing strategy in equity markets. Forthcoming in Journal of the Statistical & Social Inquiry Society of Ireland.