Unfit for Purpose:
The Market's Evaluation of Financial Economics*
Shane Whelan
UCD School of Mathematical Sciences
*Based on
Actuaries' Evaluation of the Utility of Financial Economics.
Chapter 6 in Fabozzi, F. (Ed.) (2008) Handbook of Finance,
Volume II: Investment Management and Financial Management, John Wiley & Sons, New York, pp. 53-64.
I acknowledge, with thanks, a Government of Ireland Research Fellowship from
the Irish Research Council for the Humanities and Social Sciences for 2008/09.
Two Cultures



C. P. Snow (1959) drew attention to “two cultures”
– the sciences & the humanities
Two distinct cultures study the capital markets
– market practitioners & academics (financial economists)
Distinction
– mark-to-market –v- peer review
– financial rewards –v- prestige
– trial and error –v- scientific process

Value system
– NOT money –v- knowledge
– BUT utility –v- learning
Two Cultures

History largely written from the academic perspective
– Bernstein (1992), Dimson & Mussavian (1998, 1999, 2000)

Cast market practitioners as ‘natural luddites”
– persisting in stock-picking despite the dictates of the efficient
market hypothesis
– inefficiently employing capital to back guarantees on equity
investments rather than adopting dynamic hedging strategies
– deliberating over dividend policy when that is shown not to matter
– continuing the cult of the equity in pension fund investing when
bonds are shown to be preferable

Academics attribute the market’s method of discovering value
with ‘informational efficiency’

So what is the market’s valuation of financial
economics?
‘Natural luddites’: UK Actuaries

Pioneers of actuarial science:
– Halley, Maclaurin, Price, Young, Gompertz, …
– “Men of Science” FRSs etc.


Insurance as `cutting edge’ research in 17th & 18th
centuries
Basic science worked out by 1848
– So practical application of prime importance

1848 – Institute of Actuaries; 1856 Faculty of
Actuaries
–
–
–
–
–
Qualification examinations set by practitioners
Sessional meetings (= research seminars)
Own research journals (JIA, TFA, BAJ, AAS)
Syllabus based on journals
No link to any university – for 100 years
UK Actuaries: Faustian Deal



Actuaries are financial economists who did a
Faustian deal with Queen Victoria in the midnineteenth century
Monopoly privileges for maintaining the public’s
confidence in pension, life assurance and other
institutions
Price to pay:
– (1) Personal shame and disgrace on failure of company
– (2) Daily problems not so elegant:
“On returning to London he became an energetic
actuary for a life insurance company. Such work
for a creative mathematician is poisonous
drudgery, and Sylvester almost ceased to be a
mathematician.”
E T Bell, Men of Mathematics, 1937 on J J Sylvester
So what was actuaries evaluation of models in
financial economics?
So what was actuaries evaluation of models in
financial economics?
Unfit for Purpose
“warn students that such analysis must not be
taken seriously and applied in practice”
2008
1900
2008
1900
Louis Bachelier: Theory of Speculation.
2008
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.
2008
1973
1944
1900
Fischer Black & Myron Scholes: The Pricing of Option Contracts and
Corporate Liabilities.
Robert Merton: Theory of Rational Option Pricing.
John von Neumann & Oskar Morgenstern:
Theory of Games and Economic Behaviour.
Louis Bachelier: Theory of Speculation.
2008
1973
1944
Fischer Black & Myron Scholes: The Pricing of Option Contracts and
Corporate Liabilities.
Robert Merton: Theory of Rational Option Pricing.
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.
1900
Louis Bachelier: Theory of Speculation.
2008
1973
1944
1900
Fischer Black & Myron Scholes: The Pricing of Option Contracts and
Corporate Liabilities.
Robert Merton: Theory of Rational Option Pricing.
John von Neumann & Oskar Morgenstern:
Theory of Games and Economic Behaviour.
Louis Bachelier: Theory of Speculation.
2008
1973
1944
1900
Fischer Black & Myron Scholes: The Pricing of Option Contracts and
Corporate Liabilities.
Robert Merton: Theory of Rational Option Pricing.
John von Neumann & Oskar Morgenstern:
Theory of Games and Economic Behaviour.
Louis Bachelier: Theory of Speculation.
Work of
Probabilists:
Levy,
Cramér,
Wiener,
Kolmogorov,
Doblin,
Khinchine,
Feller,
Itô.
Financial Economics: Three Prongs

Mathematical Finance/Market Modelling



Asset Pricing



modelling how prices evolve in (near) efficient markets
e.g., so evaluating any function of those prices; quantifying
mismatch risk; probability of market crashes
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
2008
1973
1900
Academics’ History
Fischer Black & Myron Scholes: The Pricing of Option Contracts and
Corporate Liabilities.
Robert Merton: Theory of Rational Option Pricing.
Louis Bachelier: Theory of Speculation.
2008
Academics’ History
1973
Fischer Black & Myron Scholes: The Pricing of Option Contracts and
Corporate Liabilities.
Robert Merton: Theory of Rational Option Pricing.
1958
Franco Modigliani & Merton Miller: The Cost of Capital,
Corporation Finance and the Theory of Investments
1900
Louis Bachelier: Theory of Speculation.
2008
1973
1964
1958
1900
Academics’ History
Fischer Black & Myron Scholes: The Pricing of Option Contracts and
Corporate Liabilities.
Robert Merton: Theory of Rational Option Pricing.
William Sharpe: Capital Asset Prices: A Theory of Market Equilibrium
under Conditions of Risk.
Franco Modigliani & Merton Miller: The Cost of Capital,
Corporation Finance and the Theory of Investments
Louis Bachelier: 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
Price
Future Period
1900: Bachelier’s Theory of Speculation

Main practical import of Bachelier’s model
– s.d. of return distribution is proportional to the square root
of elapsed time

But not really new…
– “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’ Evaluation

Text-book for French actuaries in 1908 disseminated
the Bachelier model.
– Alfred Barriol, Théorie et pratique des opérations financières. Paris 1908

Model not considered reliable
– “In connection with speculative Stock Exchange transactions, M.
Barriol includes an investigation – based on the assumption that
the distribution of prices would be in accordance with the normal
law of error – ...but apart from doubts …whether variations in
prices could be regarded as following even approximately the law
of error, it would seem to be difficult, in applying the formula
practically, to determine the modulus of the particular curve to be
employed for a specified security. At times of active speculation –
when options are most in demand – the average deviation in the
price of the security for the period covered by the option might be
a very unreliable measure of the range of fluctuation.”
» Anonymous Book Review in Journal of the Institute of Actuaries,
XLVIII (1914), 311-312.
2008
1900
Louis Bachelier: Theory of Speculation.
2008
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.
2008
1973
Fischer Black & Myron Scholes: The Pricing of Option
Contracts and Corporate Liabilities.
Robert Merton: Theory of Rational Option Pricing.
Vinzenz Bronzin: Theorie der Prämiengeschäfte
anticipated every modern idea in option pricing: the put-call
parity, no-arbitrage arguments, perfect-hedging pricing
conditions, risk neutral pricing, and “his equation is closer to the
Black-Scholes formula than anything published before Black,
Scholes, and Merton. He moreover develops a simplified
procedure to find analytical solutions for [European] option
prices…” Zimmermann & Hafner (2006)
1908
1900
Louis Bachelier: Theory of Speculation.
The Two Cultures in Practice

1997 Press release announcing that Merton and Scholes
were awarded the Bank of Sweden Prize in Economic
Sciences :
– “The method adopted by this year’s laureates can therefore be
used to value guarantees and insurance contracts. One can thus
view insurance companies and the option market as
competitors.”

Option writing, dynamic hedging, thin-tailed risk
models, etc. generally not in insurance/pensions.
– Actuarial models assume price process is Levy process rather
than a diffusion
– Return distributions are thick-tailed rather than thin-tailed
Option Pricing - Actuaries’ Evaluation

Colm Fagan (1977), Maturity Guarantees under UnitLinked Contracts.
– Independently arrives at the Black-Merton-Scholes
breakthrough.

Tom Collins (JIA (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.”
Financial Economics: Three Prongs

Mathematical Finance/Market Modelling



Asset Pricing



modelling how prices evolve in (near) efficient markets
e.g., so evaluating any function of those prices; quantifying
mismatch risk; probability of market crashes
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
Portfolio Selection, CAPM, & Equilibrium Models
1973
1952
1950
Harry Markowitz: Portfolio Selection.
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
James Tobin: Liquidity Preference as Behavior Toward Risk.
1958
1952
1950
Franco Modigliani & Merton Miller: The Cost of Capital,
Corporation Finance and the Theory of Investments
Harry Markowitz: Portfolio Selection.
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
1964
1958
1952
1950
William Sharpe: Capital Asset Prices: A Theory of Market Equilibrium
under Conditions of Risk.
Franco Modigliani & Merton Miller: The Cost of Capital,
Corporation Finance and the Theory of Investments
Harry Markowitz: Portfolio Selection.
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.]
Actuaries’ Evaluation of
MPT/CAPM

Markowitz’s modelling very simplistic
– Actuaries had all those insights
– actuarial modelling of risk was altogether more
sophisticated (Borch (1967)).

And it did not work
– In theory, using just the first two moments to define a
preference ordering on distributions can lead to
inconsistencies (see Borch (1974)).
– the problem of parameter estimation means impractical (see,
for instance, Windcliff and Boyle (2004), for a recent
development of this argument).

Conclude:
– “...I shall continue to use mean-variance analysis in teaching,
but I shall warn students that such analysis must not be
taken seriously and applied in practice” (Borch (1974), p.
430).
Other Issues: Efficient Market Hypothesis

EMH is really just Bachelier’s martingale assumption
– Symmetry from information processing of buyer & seller

But misinterpreted by economists who presumed to assess the
information processing itself…
– “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.” Kendall (1953), p. 18
But a respect for evidence compels me to be inclined toward the
hypothesis that most portfolio decision makers should go out of
business – take up plumbing, teach Greek,... Even if this advice to
drop dead is good advice, it obviously is not counsel that will be
eagerly followed. Few people will commit suicide without a push.”
Samuelson (1974)

The finding of such statistical investigations says more about the
sophistication of the statistical investigations than about the markets or
market practitioners.
Modelling Problems: Orders of
Complexity
 Level 1 - Two body problem
 e.g., gravity, light through prism, etc.
 Level 2 - N-identical body with local interaction
 e.g., Maxwell-Boltzmann’s thermodynamics
 e.g., Ising model of ferromagnetism
 Level 3 - N-identical body with long-range interaction
 Level 4 - N-non-identical body with multi-interactions
 Modelling Markets
 Modelling economics systems generally
 General actuarial modelling
 The History of Science gives us no example of a complex problem of Level 3 or 4
being adequately modelled
From Roehner, B.M., Patterns of Speculation: A Study in Observational Econophysics.
CUP 2002
Challenges of Modelling Markets
 Returns are non-stationary – almost all models are
stationary.
 Data mining compromises statistical investigations
 Asset price models currently only model the demand
side for securities, not the supply side, which clearly
is significant to their equilibrium price.
 But real issue
 Markets evolve
 In an unbounded world, can the scientific method with its
need to demonstrate its propositions beyond reasonable
doubt ever catch up with, as Keynes put it, the market’s
“spontaneous optimism” and “animal spirits” ?
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 practitioner 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.
Unfit for Purpose:
The Market's Evaluation of Financial Economics*
Shane Whelan
UCD School of Mathematical Sciences
*Based on
Actuaries' Evaluation of the Utility of Financial Economics.
Chapter 6 in Fabozzi, F. (Ed.) (2008) Handbook of Finance,
Volume II: Investment Management and Financial Management, John Wiley & Sons, New York, pp. 53-64.
I acknowledge, with thanks, a Government of Ireland Research Fellowship from
the Irish Research Council for the Humanities and Social Sciences for 2008/09.