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Financial Economics, Time Variation in the Market Return

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Encyclopedia of Complexity and Systems Science

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Definition of the Subject

The realized return to any given asset varies over time, occasionally in a dramatic fashion. The value of an asset, its expected return, and its volatility, are of great interest to investors and to policy makers. An asset's expected return in excess of the return to a riskless asset (such as a short‐term US Treasury bill) is termed the equity premium. The value of the equity premium is central to the valuation of risky assets, and hence a much effort has been devoted to determining the value of the equity premium, whether it varies, and if it varies, how predictable it is. Any evidence of predictable returns is either evidence of a predictably varying equity premium (say, because risk varies predictably) or a challenge to the rationality of markets and the efficient allocation of our society's scarce resources.

In this article, we start by considering the topic of valuation, with emphasis on simulation‐based techniques. We consider the valuation of...

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Abbreviations

AR (k):

An autoregressive process of order k; a time series model allowing for first order dependence; for instance, an AR(1) model is written as \( y_t= \alpha + \rho_1 y_{t-1} + \epsilon_t \) where α and ρ are parameters, ρ is typically assumed to be less than 1 in absolute value, and ϵ t is an innovation term, often assumed to be Gaussian, independent, and identically distributed over t.

ARCH (q):

A special case of the GARCH(p, q) model (see below) where \( { p=0 } \).

Basis point:

A hundredth of one percent.

Bootstrap :

A computer intensive resampling procedure, where random draws with replacement from an original sample are used, for instance to perform inference.

Discount rate:

The rate of return used to discount future cashflows, typically calculated as a risk‐free rate (e. g. the 90-day US T‑bill rate) plus an equity risk premium.

Equity premium puzzle :

The empirical observation that the ex post equity premium (see entry below) is higher than is indicated by financial theory.

Ex ante equity premium:

The extra return investors expect they will receive for holding risky assets, over and above the return they would receive for holding a risk‐free asset like a Treasury bill. “Ex ante” refers to the fact that the expectation is formed in advance.

Ex post equity premium:

The extra return investors received after having held a risky asset for some period of time. The ex post equity premium often differs from the ex ante equity premium due to random events that impact a risky asset's return.

Free cash flows:

Cash flows that could be withdrawn from a firm without lowering the firm's current rate of growth. Free cash flows are substantially different from accounting earnings and even accounting measures of the cash flow of a firm.

Fundamental valuation :

The practice of determining a stock's intrinsic value by discounting cash flows to their present value using the required rate of return.

GARCH (p, q):

Generalized autoregressive conditional heteroskedasticity of order (p, q), where p is the order of the lagged variance terms and q is the order of the lagged squared error terms; a time series model allowing for dependence in the conditional variance of a random variable, y. A GARCH(1,1) model is specified as:

$$ \begin{aligned} y_t&= \alpha + \epsilon_t;\quad \epsilon_t \sim \big(0, h^2_t\big)\\ h^2_t&= \theta + \beta h^2_{t-1} + \gamma \epsilon^2_{t-1}\:, \end{aligned} $$

where α, θ, β, and γ are parameters and ϵ t is an innovation term.

Market anomalies :

Empirical regularities in financial market prices or returns that are difficult to reconcile with conventional theories and/or valuation methods.

Markov model :

A model of a probabilistic process where the random variable can only take on a finite number of different values, typically called states.

Method of moments :

A technique for estimating parameters (like parameters of the conditional mean and conditional variance) by matching sample moments, then solving the equations for the parameters to be estimated.

SAD :

Seasonal Affective Disorder, a medical condition by which reduced daylight in the fall and winter leads to seasonal depression for roughly ten percent of the world's population.

Sensation seeking :

A measure used by psychologists to capture an individual's degree of risk tolerance. High sensation‐seeking tendency correlates with low risk tolerance, including tolerance for risk of a financial nature.

Simulated method of moments :

A modified version of the method of moments (see entry above) that is based on Monte Carlo simulation , used in situations when the computation of analytic solutions is infeasible.

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Author information

Authors and Affiliations

  1. Schulich School of Business, York University, Toronto, Canada

    Mark J. Kamstra

  2. Rotman School of Management, University of Toronto, Toronto, Canada

    Lisa A. Kramer

Authors
  1. Mark J. Kamstra
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  2. Lisa A. Kramer
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Editors and Affiliations

  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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Kamstra, M.J., Kramer, L.A. (2009). Financial Economics, Time Variation in the Market Return. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_207

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