ASSET PRICING MODEL: LAPM


Let us now develop a more general framework. There are three periods, t = 0,1, 2. At date 1, a state of nature ш in fi is revealed to all economic agents. There is a further resolution of uncertainty at date 2, but in our risk neutral framework, only date-1 expectations matter so we need not specify the date-2 random events. The state of nature ш may include the date-1 profits of the various industries in the corporate sector (as in the example above), their date-1 reinvestment needs (as in our 1998 paper ), news about the prudential requirements or government policy, or signal/prospects about date-2 revenues.

• Investors. As in the example, and in order to highlight the departure from the canonical asset pricing model, we assume that investors are risk neutral and have an exogenously given discount rate, normalized at zero. That is, investors value consumption stream (c0,ci,c2) at cq + c\ + c^. One could assume more generally that investors have endogenously determined and possibly stochastic discount factors. Similarly, the implicit assumption that investors face no liquidity needs could be relaxed (see section 6.1).

• Noncorporate claims. At date 0, there are К noncorporate assets,K such as Treasury securities or real estate. The return on asset k at date 1, that is, the date-1 dividend plus the date-1 price, is equal to Ok = 0fc(u>) > 0. The mean return on each asset is normalized to be one: Eo[0k(oo)\ = 1, where [•] denotes the expectation of a variable conditional on the information available at date t. Let denote the supply of asset k. At date 0, asset k trades at price per unit, where <& > 1 from the nature of consumer preferences. The liquidity premium on asset k is equal to q^ — 1.

Note that the returns are exogenously given. In section 6 we will analyze two examples with endogenous returns. Note also that claims К do not include claims on the corporate sector (shares, bonds, deposits, CDs,…). We will later provide valuation formulae for these.

• Corporate sector. Our model treats the productive and financial sectors as a single, aggregated entity, called the “corporate sector.” The Appendix provides sufficient conditions validating this approach. The corporate sector invests at dates 0 and 1 and receives proceeds at dates 1 and 2. Let I denote the corporate sector’s date-0 gross investment (or vector of gross investments) in productive (illiquid) assets. Its date-0 net investment, N(I), is equal to the difference between the gross investment and the productive sector’s capital contribution at date 0 (in the example above, N(I) = I since the entrepreneurs had no initial wealth).

Tags: , ,