2002 1973 1900 Fischer Black & Myron Scholes: The Pricing of Option Contracts and Corporate Liabilities.
Robert Merton: Theory of Rational Option Pricing. Louis Bachelier: Theory of Speculation.

Slide5:

2002 1973 1900 Fischer Black & Myron Scholes: The Pricing of Option Contracts and Corporate Liabilities.
Robert Merton: Theory of Rational Option Pricing. Louis Bachelier: Theory of Speculation. 1944 John von Neumann & Oskar Morgenstern:
Theory of Games and Economic Behaviour.

Slide6:

2002 1973 1900 Fischer Black & Myron Scholes: The Pricing of Option Contracts and Corporate Liabilities.
Robert Merton: Theory of Rational Option Pricing. Louis Bachelier: Theory of Speculation. 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.

Slide7:

2002 1973 1900 Fischer Black & Myron Scholes: The Pricing of Option Contracts and Corporate Liabilities.
Robert Merton: Theory of Rational Option Pricing. Louis Bachelier: Theory of Speculation. 1944 John von Neumann & Oskar Morgenstern:
Theory of Games and Economic Behaviour.

Slide8:

2002 1973 1900 Fischer Black & Myron Scholes: The Pricing of Option Contracts and Corporate Liabilities.
Robert Merton: Theory of Rational Option Pricing. Louis Bachelier: Theory of Speculation. 1944 John von Neumann & Oskar Morgenstern:
Theory of Games and Economic Behaviour. Work of Probabilists:
Levy,
Cramér,
Wiener,
Kolmogorov,
Doblin,
Khinchine,
Feller,
Itô.

Slide9:

2002 1973 1900 Fischer Black & Myron Scholes: The Pricing of Option Contracts and Corporate Liabilities.
Robert Merton: Theory of Rational Option Pricing. Louis Bachelier: Theory of Speculation. Work of Probabilists:
Levy,
Cramér,
Wiener,
Kolmogorov,
Doblin,
Khinchine,
Feller,
Itô. “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

Financial Economics: Three Prongs:

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

Slide11:

2002 1973 1900 Fischer Black & Myron Scholes: The Pricing of Option Contracts and Corporate Liabilities.
Robert Merton: Theory of Rational Option Pricing. Louis Bachelier: Theory of Speculation. Orthodox History

Slide12:

2002 1973 1900 Fischer Black & Myron Scholes: The Pricing of Option Contracts and Corporate Liabilities.
Robert Merton: Theory of Rational Option Pricing. Louis Bachelier: Theory of Speculation. 1958 Franco Modigliani & Merton Miller: The Cost of Capital,
Corporation Finance and the Theory of Investments Orthodox History

1900: Bachelier’s Theory of Speculation:

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:

1900: Bachelier’s Theory of Speculation Future Period Price

Actuaries’ Role:

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:

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:

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:

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 (MPT or Mean-Variance Analysis):

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 Risk (s.d.) Efficient Frontier All Possible Portfolios

Slide21:

1973 1950 1952 1953 Harry Markowitz: Portfolio Selection. Maurice Kendall: The Analysis of Time Series, Part I: Prices. Portfolio Selection, CAPM, & Equilibrium Models

Slide22:

1973 1950 1952 1953 Harry Markowitz: Portfolio Selection. Maurice Kendall: The Analysis of Time Series, Part I: Prices. Portfolio Selection, CAPM, & Equilibrium Models “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.”

Slide23:

1973 1950 1952 1953 Harry Markowitz: Portfolio Selection. Maurice Kendall: The Analysis of Time Series, Part I: Prices. Portfolio Selection, CAPM, & Equilibrium Models

Slide24:

1973 1950 1952 1958 1953 Harry Markowitz: Portfolio Selection. Maurice Kendall: The Analysis of Time Series, Part I: Prices. Portfolio Selection, CAPM, & Equilibrium Models Franco Modigliani & Merton Miller: The Cost of Capital,
Corporation Finance and the Theory of Investments

Slide25:

1973 1950 1952 1958 1953 Harry Markowitz: Portfolio Selection. Maurice Kendall: The Analysis of Time Series, Part I: Prices. Portfolio Selection, CAPM, & Equilibrium Models Franco Modigliani & Merton Miller: The Cost of Capital,
Corporation Finance and the Theory of Investments

Slide26:

1973 1950 1952 1958 1953 Harry Markowitz: Portfolio Selection. Maurice Kendall: The Analysis of Time Series, Part I: Prices. Portfolio Selection, CAPM, & Equilibrium Models Franco Modigliani & Merton Miller: The Cost of Capital,
Corporation Finance and the Theory of Investments James Tobin: Liquidity Preference as Behavior Toward Risk.

Tobin: Unique Role of Risk-Free Asset:

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 Risk (s.d.) All Possible Portfolios Efficient Frontier

Slide28:

1973 1950 1952 1958 1953 Harry Markowitz: Portfolio Selection. Maurice Kendall: The Analysis of Time Series, Part I: Prices. Portfolio Selection, CAPM, & Equilibrium Models Franco Modigliani & Merton Miller: The Cost of Capital,
Corporation Finance and the Theory of Investments 1961 Franco Modigliani & Merton Miller: Dividend Policy, Growth, and the Valuation of Shares.

Slide29:

1973 1950 1952 1964 1958 William Sharpe: Capital Asset Prices: A Theory of Market Equilibrium
under Conditions of Risk. 1953 Harry Markowitz: Portfolio Selection. Maurice Kendall: The Analysis of Time Series, Part I: Prices. Portfolio Selection, CAPM, & Equilibrium Models Franco Modigliani & Merton Miller: The Cost of Capital,
Corporation Finance and the Theory of Investments 1961 Franco Modigliani & Merton Miller: Dividend Policy, Growth, and the Valuation of Shares.

Sharpe: Equilibrium Model:

Sharpe: Equilibrium Model Everyone has the same optimum portfolio: it is the market portfolio. Expected Return Risk (s.d.) All Possible Portfolios Efficient Frontier Market Portfolio

Treynor-Sharpe-Lintner-Mossin CAPM:

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.]

Slide32:

1973 1950 1952 1964 1958 1965 Paul Samuelson: Proof that Properly Anticipated Prices Fluctuate Randomly. William Sharpe: Capital Asset Prices: A Theory of Market Equilibrium
under Conditions of Risk. 1953 Harry Markowitz: Portfolio Selection. Maurice Kendall: The Analysis of Time Series, Part I: Prices. Portfolio Selection, CAPM, & Equilibrium Models Franco Modigliani & Merton Miller: The Cost of Capital,
Corporation Finance and the Theory of Investments 1961 Franco Modigliani & Merton Miller: Dividend Policy, Growth, and the Valuation of Shares.

Slide33:

1973 1950 1952 1964 1958 1965 Paul Samuelson: Proof that Properly Anticipated Prices Fluctuate Randomly. William Sharpe: Capital Asset Prices: A Theory of Market Equilibrium
under Conditions of Risk. 1953 Harry Markowitz: Portfolio Selection. Maurice Kendall: The Analysis of Time Series, Part I: Prices. Portfolio Selection, CAPM, & Equilibrium Models Franco Modigliani & Merton Miller: The Cost of Capital,
Corporation Finance and the Theory of Investments Fischer Black & Myron Scholes: The Pricing of Option Contracts and Corporate Liabilities.
Robert Merton: Theory of Rational Option Pricing. 1961 Franco Modigliani & Merton Miller: Dividend Policy, Growth, and the Valuation of Shares.

Option Pricing - Actuaries’ Role:

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:

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:

Can this 102 Year Old Science Still Surprise?

102nd Year:

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:

Returns on 19 Major Stock Markets, 1970-1998 -4% -2% 0% 2% 4% 6% 8% 10% 12% 14% 16% Australia Austria Belgium Canada Denmark France Germany Hong Kong Italy Japan Netherlands Norway Singapore South Africa* Spain Sweden Switzerland UK US Average November-April Average May-October Source: MSCI Total Return Indices, data kindly supplied by Bouman & Jacobsen

102nd Year:

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:

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:

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.

Slide42:

Shane Whelan
102 Years of Financial Economics

Key References :

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:

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.

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By: bigsumo (48 month(s) ago)

May I have a copy of your powerpoint? Thank you for an interesting presentation. Especially the refereences to the early work of the french actuaries.