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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. - PowerPoint PPT PresentationTRANSCRIPT

bellShane Whelan

Financial Economics Seminar Staple Inn Hall, 16th Sept.

2002

1900

2002

1900

Financial Economics Seminar Staple Inn Hall, 16th Sept.

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.

Financial Economics Seminar Staple Inn Hall, 16th Sept.

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

Theory of Games and Economic Behaviour.

Financial Economics Seminar Staple Inn Hall, 16th Sept.

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

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.

Financial Economics Seminar Staple Inn Hall, 16th Sept.

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

Theory of Games and Economic Behaviour.

Financial Economics Seminar Staple Inn Hall, 16th Sept.

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

Theory of Games and Economic Behaviour.

Work of Probabilists:

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

Asset Pricing

e.g., comparative assessment of growth versus value indicators; pricing anomalies

Corporate Finance

e.g., capital structure; dividend policy; pension fund investment

Financial Economics Seminar Staple Inn Hall, 16th Sept.

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

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

Corporation Finance and the Theory of Investments

Orthodox History

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.

Financial Economics Seminar Staple Inn Hall, 16th Sept.

1900: Bachelier’s Theory of Speculation

Future Period

Actuaries’ Role

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?

Financial Economics Seminar Staple Inn Hall, 16th Sept.

Actuaries’ Role

Text-book for French actuaries in 1908 disseminated the Bachelier model.

Alfred Barriol, Théorie et pratique des opérations financières. Paris 1908.

Financial Economics Seminar Staple Inn Hall, 16th Sept.

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

Markets seen as a ‘compleat System of Knavery’

1929 Crash

Financial Economics Seminar Staple Inn Hall, 16th Sept.

Wilderness Years to 1950s

The Dividend Discount Model

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.

Financial Economics Seminar Staple Inn Hall, 16th Sept.

1973

1950

1952

Financial Economics Seminar Staple Inn Hall, 16th Sept.

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

1973

1950

1952

1953

Maurice Kendall: The Analysis of Time Series, Part I: Prices.

Portfolio Selection, CAPM, & Equilibrium Models

Financial Economics Seminar Staple Inn Hall, 16th Sept.

1973

1950

1952

1953

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.”

Financial Economics Seminar Staple Inn Hall, 16th Sept.

1973

1950

1952

1953

Maurice Kendall: The Analysis of Time Series, Part I: Prices.

Portfolio Selection, CAPM, & Equilibrium Models

Financial Economics Seminar Staple Inn Hall, 16th Sept.

1973

1950

1952

1958

1953

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

Financial Economics Seminar Staple Inn Hall, 16th Sept.

1973

1950

1952

1958

1953

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

Financial Economics Seminar Staple Inn Hall, 16th Sept.

1973

1950

1952

1958

1953

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.

Financial Economics Seminar Staple Inn Hall, 16th Sept.

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.)

1973

1950

1952

1958

1953

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.

Financial Economics Seminar Staple Inn Hall, 16th Sept.

1973

1950

1952

1964

1958

William Sharpe: Capital Asset Prices: A Theory of Market Equilibrium

under Conditions of Risk.

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.

Financial Economics Seminar Staple Inn Hall, 16th Sept.

Sharpe: Equilibrium Model

Everyone has the same optimum portfolio: it is the market portfolio.

Expected Return

Risk (s.d.)

Treynor-Sharpe-Lintner-Mossin CAPM

E[Ri]-r = i(E[Rm]-r)

where,

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.]

Financial Economics Seminar Staple Inn Hall, 16th Sept.

1973

1950

1952

1964

1958

1965

William Sharpe: Capital Asset Prices: A Theory of Market Equilibrium

under Conditions of Risk.

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.

Financial Economics Seminar Staple Inn Hall, 16th Sept.

1973

1950

1952

1964

1958

1965

William Sharpe: Capital Asset Prices: A Theory of Market Equilibrium

under Conditions of Risk.

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.

Financial Economics Seminar Staple Inn Hall, 16th Sept.

Option Pricing - Actuaries’ Role

Independently arrives at the Black-Merton-Scholes breakthrough.

Tom Collins (BAJ, Vol. 109, 1982)

The replicating 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.”

Financial Economics Seminar Staple Inn Hall, 16th Sept.

1973: Only a beginning

Empirical studies

Financial Economics Seminar Staple Inn Hall, 16th Sept.

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

Financial Economics Seminar Staple Inn Hall, 16th Sept.

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

Average November-April

Average May-October

Source: MSCI Total Return Indices, data kindly supplied by Bouman & Jacobsen

97% of market capitalisation of world market. (99)

Total Returb indices

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).

Financial Economics Seminar Staple Inn Hall, 16th Sept.

The Contribution of Actuaries

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?

Financial Economics Seminar Staple Inn Hall, 16th Sept.

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.

Financial Economics Seminar Staple Inn Hall, 16th Sept.

Shane Whelan

Financial Economics Seminar Staple Inn Hall, 16th Sept.

Key References

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:

Journal of Banking & Finance, Vol. 23.

Financial Economics Seminar Staple Inn Hall, 16th Sept.

Selected Other References

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.

Financial Economics Seminar Staple Inn Hall, 16th Sept.

2002

1900

2002

1900

Financial Economics Seminar Staple Inn Hall, 16th Sept.

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.

Financial Economics Seminar Staple Inn Hall, 16th Sept.

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

Theory of Games and Economic Behaviour.

Financial Economics Seminar Staple Inn Hall, 16th Sept.

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

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.

Financial Economics Seminar Staple Inn Hall, 16th Sept.

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

Theory of Games and Economic Behaviour.

Financial Economics Seminar Staple Inn Hall, 16th Sept.

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

Theory of Games and Economic Behaviour.

Work of Probabilists:

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

Asset Pricing

e.g., comparative assessment of growth versus value indicators; pricing anomalies

Corporate Finance

e.g., capital structure; dividend policy; pension fund investment

Financial Economics Seminar Staple Inn Hall, 16th Sept.

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

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

Corporation Finance and the Theory of Investments

Orthodox History

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.

Financial Economics Seminar Staple Inn Hall, 16th Sept.

1900: Bachelier’s Theory of Speculation

Future Period

Actuaries’ Role

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?

Financial Economics Seminar Staple Inn Hall, 16th Sept.

Actuaries’ Role

Text-book for French actuaries in 1908 disseminated the Bachelier model.

Alfred Barriol, Théorie et pratique des opérations financières. Paris 1908.

Financial Economics Seminar Staple Inn Hall, 16th Sept.

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

Markets seen as a ‘compleat System of Knavery’

1929 Crash

Financial Economics Seminar Staple Inn Hall, 16th Sept.

Wilderness Years to 1950s

The Dividend Discount Model

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.

Financial Economics Seminar Staple Inn Hall, 16th Sept.

1973

1950

1952

Financial Economics Seminar Staple Inn Hall, 16th Sept.

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

1973

1950

1952

1953

Maurice Kendall: The Analysis of Time Series, Part I: Prices.

Portfolio Selection, CAPM, & Equilibrium Models

Financial Economics Seminar Staple Inn Hall, 16th Sept.

1973

1950

1952

1953

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.”

Financial Economics Seminar Staple Inn Hall, 16th Sept.

1973

1950

1952

1953

Maurice Kendall: The Analysis of Time Series, Part I: Prices.

Portfolio Selection, CAPM, & Equilibrium Models

Financial Economics Seminar Staple Inn Hall, 16th Sept.

1973

1950

1952

1958

1953

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

Financial Economics Seminar Staple Inn Hall, 16th Sept.

1973

1950

1952

1958

1953

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

Financial Economics Seminar Staple Inn Hall, 16th Sept.

1973

1950

1952

1958

1953

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.

Financial Economics Seminar Staple Inn Hall, 16th Sept.

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.)

1973

1950

1952

1958

1953

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.

Financial Economics Seminar Staple Inn Hall, 16th Sept.

1973

1950

1952

1964

1958

William Sharpe: Capital Asset Prices: A Theory of Market Equilibrium

under Conditions of Risk.

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.

Financial Economics Seminar Staple Inn Hall, 16th Sept.

Sharpe: Equilibrium Model

Everyone has the same optimum portfolio: it is the market portfolio.

Expected Return

Risk (s.d.)

Treynor-Sharpe-Lintner-Mossin CAPM

E[Ri]-r = i(E[Rm]-r)

where,

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.]

Financial Economics Seminar Staple Inn Hall, 16th Sept.

1973

1950

1952

1964

1958

1965

William Sharpe: Capital Asset Prices: A Theory of Market Equilibrium

under Conditions of Risk.

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.

Financial Economics Seminar Staple Inn Hall, 16th Sept.

1973

1950

1952

1964

1958

1965

William Sharpe: Capital Asset Prices: A Theory of Market Equilibrium

under Conditions of Risk.

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.

Financial Economics Seminar Staple Inn Hall, 16th Sept.

Option Pricing - Actuaries’ Role

Independently arrives at the Black-Merton-Scholes breakthrough.

Tom Collins (BAJ, Vol. 109, 1982)

The replicating 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.”

Financial Economics Seminar Staple Inn Hall, 16th Sept.

1973: Only a beginning

Empirical studies

Financial Economics Seminar Staple Inn Hall, 16th Sept.

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

Financial Economics Seminar Staple Inn Hall, 16th Sept.

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

Average November-April

Average May-October

Source: MSCI Total Return Indices, data kindly supplied by Bouman & Jacobsen

97% of market capitalisation of world market. (99)

Total Returb indices

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).

Financial Economics Seminar Staple Inn Hall, 16th Sept.

The Contribution of Actuaries

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?

Financial Economics Seminar Staple Inn Hall, 16th Sept.

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.

Financial Economics Seminar Staple Inn Hall, 16th Sept.

Shane Whelan

Financial Economics Seminar Staple Inn Hall, 16th Sept.

Key References

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:

Journal of Banking & Finance, Vol. 23.

Financial Economics Seminar Staple Inn Hall, 16th Sept.

Selected Other References

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.