The Mathematics of Financial Modelingand Investment Management

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344 The Mathematics of Financial Modeling and Investment Management

evidence has not been confirmed by later studies.^19 Kim, Nelson and

Startz have argued that mean-reversion is a pre-World War II phenome-

non.^20 However, more recent papers give new support to the hypothesis

of mean reversion.^21

Common trends in exchange rates have documented by Baillie and

Bollerslev^22 and by Kasa^23 in equity prices. Cross-correlations at differ-

ent lags between equities have been reported in the literature. For

instance, Campbell, Lo, and MacKinley^24 report significant autocorrela-

tions of portfolio returns for selected portfolios, a fact that is attributed

to the existence of autocross-correlations. An interpretation of the same

phenomena on the same data set based on cointegration has been pro-

posed by Kanas and Kouretas.^25

Evidence on asset price cointegration and the use of cointegration in

asset allocation and portfolio management is discussed in a number of

papers. See, for instance, Lucas,^26 Alexander,^27 and Alexander and Dim-

itriu.^28 In most cases cointegrating relationships are found in small port-

folios. How to select the cointegrated portfolios in large sets of price

(^19) See: Eugene F. Fama and Kenneth.R. French, “Permanent and Temporary Com-
ponents of Stock Prices,” Journal of Political Economy 96, no. 2 (1988), pp. 246–
273 and Campbell, Lo, and MacKinley, The Econometrics of Financial Markets.
(^20) M.J. Kim, C.R. Nelson and R. Startz, “Mean Reversion in Stock Prices? A Reapprais-
al of the Empirical Evidence,” Review of Economic Studies 58 (1991), pp. 515–528.
(^21) See: Kent Daniel (2001) “Power and Size of Mean Reversion Tests,” Journal of
Empirical Finance 8, no. 5 (December 2001), pp. 493–535; Steen Nielsen and Jan
Overgaard Olesen, “Regime-Switching Stock Returns and Mean Reversion,” Work-
ing paper 11–2000, Department of Economics and EPRU, Copenhagen Business
School; and Ole Risager, “Random Walk or Mean Reversion: the Danish Stock Mar-
ket since World War I,” Working paper 7–98, Department of Economics and EPRU,
Copenhagen Business School.
(^22) R. Baillie and T. Bollerslev, “Common Stochastic Trends in a System of Exchange
Rates,” Journal of Finance 44 (1989), pp. 167–182.
(^23) K. Kasa, “Common Stochastic Trends in International Stock Markets,” Journal of
Monetary Economics 29 (1992), pp. 95–124.
(^24) See Campbell, Lo, and MacKinley, The Econometrics of Financial Markets.
(^25) A. Kanas and G.P. Kouretas, “A Cointegration Approach to the Lead-Lag Effect
Among Size-Sorted Equity Portfolios,” 2001.
(^26) A. Lucas, “Strategic and Tactical Asset Allocation and the Effect of Long-Run
Equilibrium Relations,” Research Memorandum, Vrije Universiteit Amsterdam,
1997-42 (1997).
(^27) C.O. Alexander, “Optimal Hedging Using Cointegration,” Philosophical Trans-
actions of the Royal Society A 357 (1999), pp. 2039–2058.
(^28) C.O. Alexander and A. Dimitriu, “The Cointegration Alpha: Enhanced Index
Tracking and Long-Short Equity Market Neutral Strategies,” Discussion Paper
2002-08, ISMA Centre Discussion Papers in Finance Series, 2002.