Shane Whelan

1
Actuarial Investments (FIN 3044)

• Shane Whelan

2
Overview of Two Important Topics
3
Two Important Topics

• One must be aware of the key ideas/results in
  financial economics
• Yet this course does not build, in any material
  way, on financial economics. It is assumed
  background knowledge.
• One must have a sound knowledge of the history of
  markets, how they delivered returns, what drives
  them, etc.
• I start by treating both these topics in a survey
  talk on each.

4
103 Years of Financial Economics (bringing out
the involvement of actuaries)
5
2003
1900
6
2003
Louis Bachelier Theory of Speculation.
1900
7
2003
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
8
2003
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
9
2003
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
10
2003
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
11
2003
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, Kolmog
orov, Doblin, Khinchine, Feller, Itô.
John von Neumann Oskar Morgenstern Theory of
Games and Economic Behaviour.
1944
Louis Bachelier Theory of Speculation.
1900
12
2003
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
todays 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, Kolmog
orov, Doblin, Khinchine, Feller, Itô.
Louis Bachelier Theory of Speculation.
1900
13
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

14
Orthodox History
2003
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
15
Orthodox History
2003
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
16
1900 Bacheliers 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.

17
1900 Bacheliers Theory of Speculation
Price
Future Period
18
Actuaries Role

• Main practical import of Bacheliers 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?

19
Actuaries Role

• Text-book for French actuaries in 1908
  disseminated the Bachelier model.
• Alfred Barriol, Théorie et pratique des
  opérations financières. Paris 1908.

20
Wilderness Years to 1950s

• Data Collection
• 1932 Cowles Commission for Research in Economics
  (Econometrica, SP 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.

21
Wilderness Years to 1950s

• The Dividend Discount Model
• VD/(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.

22
Portfolio Selection, CAPM, Equilibrium Models
1973
1952
Harry Markowitz Portfolio Selection.
1950
23
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.)
24
Portfolio Selection, CAPM, Equilibrium Models
1973
1953
Maurice Kendall The Analysis of Time Series,
Part I Prices.
1952
Harry Markowitz Portfolio Selection.
1950
25
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
26
Portfolio Selection, CAPM, Equilibrium Models
1973
1953
Maurice Kendall The Analysis of Time Series,
Part I Prices.
1952
Harry Markowitz Portfolio Selection.
1950
27
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
28
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
29
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
30
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.)
31
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
32
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
33
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.)
34
Treynor-Sharpe-Lintner-Mossin CAPM

• CAPM in form presented in modern textbooks
• ERi-r ??i(ERm-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.

35
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
36
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
37
Option Pricing - Actuaries Role

• Colm Fagan (to Society of Actuaries in Ireland,
  1977), Maturity Guarantees under Unit-Linked
  Contracts.
• Gets very close to the Black-Merton-Scholes
  breakthrough.
• Tom Collins (JIA, 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.

38
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

39
The Contribution of Actuaries

• Superficially, Bühlmann not altogether correct.
• Bühlmann right in a deeper more disturbing way
• Actuaries did not build on knowledge or
  disseminate it

40
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 useThe 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.

41
Key References

• Whelan, S. (2002)
• Actuaries' Contributions to Financial Economics
• The Actuary, December 2002.
• Whelan, Bowie, Hibbert (2002)
• A Primer in Financial Economics
• British Actuarial Journal, Vol. 8, I, 27-74
• 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.
• Dimson, E. Mussavian, M. (1999)
• Three centuries of asset pricing.
• Journal of Banking Finance, Vol. 23.

42
Concludes Review of 103 Years of Financial
Economics

• Shane Whelan