Applications of state space models in finance

Appendix A
Brief review of asset pricing theory
The concept of mean-variance efficient portfolios introduced in the seminal work of
Markowitz (1959) represents a cornerstone of modern finance theory. The risk-return
relationship of a portfolio is usually characterized by an asset pricing model, i.e. a linear
factor model that decomposes the return on an asset into a possibly multidimensional
set of common risk factors and an asset-specific component. Linear pricing models are
commonly employed to predict returns, to identify risk sensitivities and to estimate
abnormal returns. Following Cochrane (2005, ¢ 1–2) this section briefly summarizes the
basic ideas of asset pricing theory.
A.1 The discount factor view of asset pricing
The cornerstone of asset pricing theory is that the value of an asset is equal to the
expected discounted payoff. The risk related to the asset’s payment is explicitly taken
into account. One distinguishes between relative and absolute asset pricing. The former
refers to the pricing of an asset given the prices of other assets. In absolute pricing,
which is at the heart of finance and of this thesis, each asset is valued according to its
exposure to fundamental macroeconomic risks.
By employing the discount factor view of asset pricing as proposed, among others, by
Rubinstein (1976) or Hansen and Jagannathan (1991), asset pricing can be summarized
by the following two equations:
pt = Et(mt+1xt+1), (A.1)
mt+1 = f(data, parameters), (A.2)
where pt is the asset’s price at date t, xt+1 is the asset payoff at time t + 1 and mt+1
denotes the stochastic discount factor. This simple and universal approach allows for a
separation of (i) determining the empirical representation in (A.1), and (ii) specifying the
model assumptions in (A.2). By making different choices for the function f(·), different
asset pricing models can be derived.