Asset pricing theory

Asset pricing theory describes the methodologies involved in the evaluation and pricing of an asset. Asset pricing theory originates from the simple concept that the expected price is calculated as the expected discounted payoff. Other calculations of asset prices are special cases and applications of the central equation.

There are two approaches to asset pricing in the financial literature (Cochrane, 2005).

The first, commonly used by academics, is absolute pricing, where the price of each asset is measured at a given level of risk and its future profit. The capital asset pricing model (CAPM) embodies this absolute pricing approach.

The second approach is relative pricing, which relies on pricing related assets and their associated risk factors to define asset price. This approach is limited because it overlooks many market characteristics. However, it provides a precision of calculation in many applications. The Black-Scholes option pricing model is a good example of this relative pricing approach.

This dissertation examines the risks of investing in Emerging Eastern Europe by applying the absolute approach of asset pricing theory. In particularly, the price for an asset is assumed to be:

(1) P_t E_t



_t1d_t1



,_,

where Pt is an asset price at time t, µt+1 is a function of stochastic discount and risk factors and dt+1 is an expected asset payoff in t+1 period.

The interdependence of stock markets in Emerging Eastern Europe can be characterized as full integration or partial segmentation. Under full integration, the expected returns on assets should be the same after adjusting for their risk characteristics. A stock market is considered integrated when the state and the exchange impose no restrictions on the securities transactions of local or foreign investors seeking to diversify their investment portfolios in international capital

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markets. With financial market integration, it is assumed that assets in all national markets have the same set of risk factors and therefore the same risk premium for each factor (although not the same risk sensitivity).

Adler and Dumas (1983) note that the global value-weighted market portfolio is the relevant risk factor. If investors do not hedge against exchange-rate risks and a risk-free asset exists, the conditional version of the world CAPM implies the following restriction for nominal excess returns:

(2) _{, , ,} ,

(3) _, ^{, , ,}

, ,

where Et[ri,t+1] and Et[rm,t+1] are the conditional expected excess returns on asset i and the global market portfolio, also known as market risk premium at time t+1. All returns are measured in excess of the risk-free rate of return rft for the period t to t+1 in the numeraire currency.

The empirical tests for this model are focused on implications of the zero intercept, the perfect beta capture of the cross-sectional variation of expected excess returns, and the positive-signed market risk premium. Currency risk is not priced; investors diversify out of it as they do with idiosyncratic company risk. This model also holds for the local market portfolio because the local market portfolio is tradable.

However, where the risk-free rate is unobservable, Black (1972) suggests a more general version of an absolute pricing model (Black-version CAPM), where the expected excess return of asset i and the global market portfolio can be used in excess of the zero-beta portfolio associated with m. This portfolio is assumed to have a minimum variance of all portfolios not correlated with m.

While the basic world CAPM may be used to obtain the expected excess returns of a fully integrated stock market, real-world markets are typically not fully integrated into the world equity market. Therefore, Errunza and Losq (1985) show that one has to include a local risk factor for partially (mildly) segmented markets. Thus, for any asset i, the excess return can be given as:

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(4) E_t

 

r_i,_t1 _i^g,_t1E_t



r_gm,_t1



_i^l,_t1E_t

 

r_lm,_t1 ,

where g and l refer to the global and local market portfolios and betas, respectively.

However, investment in a foreign country must be considered as a combination of investment in the asset itself and development of the foreign currency relative to the currency in which the investor holds capital. In the absence of purchasing power parity, real returns are treated differently because investors seek to hedge an exchange rate risk (Adler and Dumas, 1983). Thus, the conditional asset pricing model for partially segmented markets implies the following restriction for the expected return of asset i in the numeraire currency (e.g., De Santis and Gérard, 1998):

(5)

      _  

where βc,t+1 is the conditional currency beta for currency c.

Note that this model becomes intractable when many currencies are examined simultaneously (i.e., when C is large). This model is therefore practical only in studying a subset of currencies. Following Ferson and Harvey (1998) and Harvey (1995b) regarding the use of a single aggregate exchange risk factor, Equation (5) may be reduced to the following three-factor model:

(6)

E

_t

  r

_i,t₁

 

_i,^g_t₁

E

_t

 r

_gm,t₁

  

_i^l_,t₁

E

_t

  r

_lm,t₁

 

_i^c_,t₁

E

_t

  r

_c,t₁ , where βc,t+1 is the conditional currency beta for a particular currency that is the official currency of trade for country c.

Discrete and continuous stochastic and multi-dimensional processes are frequently used in testing asset pricing models. Random walk, autoregressive and ARCH processes, for example, are commonly applied discrete stochastic processes in the finance field. In continuous stochastic processes such as Brownian motion, diffusion, Itô and jump processes, stochastic integrals and Itô Lemma are not avoided as methodological methods for studying the prices of assets. If market shocks in the

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model are continuous, then the model settings are considered to be framed by multi-dimensional Brownian motion and diffusion processes.

2.2 Methodological approaches

In document Interdependence of Emerging Eastern European stock markets (sivua 30-33)