Asset Pricing: A Structural Theory and Its Applications by Bing Cheng

By Bing Cheng

Sleek asset pricing types play a primary function in finance and monetary concept and functions. This ebook introduces a structural thought to judge those asset pricing types and throws gentle at the life of fairness top rate Puzzle. according to the structural concept, a few algebraic (valuation-preserving) operations are built in asset areas and pricing kernel areas. This has a vital implication resulting in functional counsel in portfolio administration and asset allocation within the international monetary undefined. The publication additionally covers themes, reminiscent of the function of over-confidence in asset pricing modeling, courting of the portfolio assurance with alternative and consumption-based asset pricing types, and so on.

Contents: advent to fashionable Asset Pricing; A Structural idea of Asset Pricing; Algebra of Stochastic components; funding and intake in a Multi-Period Framework.

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Ideally, ρ = 1]. n ˆ 2. Suppose that E[m| n] = i=1 ai ei and, without loss of generality, ˆ m| we assume that E[ ˆ n ] ∈ L , where L is the subspace of n with L ˆ m| L ≤ n, and a representation E[ ˆ n ] = i=1 bi ei . Then we have L n (ai − bi d= )2 a2i > 0. 26) i=L+1 ˆ ˆ ˆ n ] by E[m| ˆ 3. e. Sn = E[xn (xn )T ]. ˆ m| 4. 29) where the weight vectors w = (w1 , · · · , wn )T and v = (v1 , · · · , vn )T . Proof: The main ideas of the proof come from Hansen and Jagannathan ˆ (1997). Since ∀x ∈ n , π(x) = E[mx] = E[E[m| n ]x].

11) 2 p = 0 means that a free contract is allowed. Here we assume that no free contract i exists in the asset market. 18 Chapter 2. 1 Under the above setup, π is called a correctly pricing functional (CPF) for the asset space X, given the market prices. Let m be an SDF. , ∀x ∈ X, π(x) = E[mx]) induced by m is a CPF, then m is called a correctly pricing SDF. Obviously, a CPF to an asset space with feasible economic parameters will mean there is no equity premium puzzle for the asset space. According to the definition, a CPF and a correctly pricing SDF are equivalent notions.

1), we have pj0 = j−1 π(xj0 ) = j−1 i=1 ci π(xi ) = π( i=1 ci xi ). 11). We must therefore have π(ej0 ) = 0. This is a contradiction. Thus, F ≡ X ∗ . We turn to sufficiency next. 1, there is a unique correctly pricing SDF m in X. Let pricing functional π be induced by m. 20 Chapter 2. 1: The Uniqueness Theorem of the minimum correctly pricing functional space. That is ∀x ∈ X, π(x) = E[mx]. Then π is a CPF in F = X ∗ . Suppose there are two CPFs, say π1 and π2 , in F . When X = n , since π1 (xi ) = π2 (xi ) for i = 1, · · · , n and n = span{x1 , · · · , xn }, we have π1 = π2 in F .

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