ASSET PRICING MODEL: Concluding remarks 2

Our model is quite special in that asset prices are entirely driven by a corporate demand for liquidity; consumers hold no bonds or other assets that sell at a premium. It has been suggested to us that once the model is changed so that consumers also have a liquidity demand, MRSs of consumers and firms will be equalized, and we are back to the old problem with excess asset price volatility. However, if consumers participate selectively in asset markets, then the MRSs of the relevant sub-population may have high volatility and yet be hard to detect. In this case, the equality between consumer and producer MRSs can be exploited in the reverse: by evaluating corporate MRSs, we can infer what the MRS of the representative consumer in the sub-population is. This may be a useful empirical strategy if firm data are more readily available and easier to analyze than consumer data.

Finally, we note that violations of the martingale condition, as illustrated by the end-of-period drop in the liquidity premium, may help to explain the well-known paradox that prices of long-term bonds tend to move up rather than down, following a period in which the yield spread (long/short) is exceptionally high. This finding is very difficult to reconcile with the standard expectations theory (Campbell, 1995), but could perhaps be accounted for in a theory where liquidity demand shifts between short and long instruments in response to changes in liquidity needs.

Appendix: Treatment of the productive sector as an aggregate

Suppose that there are n firms, i = 1,…, n, each run by an entrepreneur, say. Firm i starts with initial wealth Ajt and invests so that the net outlay for investors is ) = I{ — A{. At date 1, in state ш, firm i takes a decision di(oo) in a subset A(w, Щ{ш)) of the technologically feasible set Д, where Щ{ш) ^ 0 is the net liquidity available to firm i in state ш. Щ{ш) > 0 means that firm i uses liquidity, and Щ{ш) < 0 means that firm i supplies liquidity in state ш. The decision di(oo) generates an expected pledgeable income from productive assets rj(/j, ш, di(uj)) and a total expected income from productive assets di(uo)).
Let
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denote the nonpledgeable income of firm i that must go to entrepreneur i. Entrepreneur i may, however, be paid more than B{. Let и(ш) > 0 denote the expected transfer on top of the nonpledgeable income B{. (t{(-) could without loss of generality be chosen equal to 0 in the example.) So entrepreneur i obtains, in state ш, Bi(Ii,u),di(u))) + ti(uo). If firm i withdraws gross liquidity ti(uo) from noncorporate assets, then the net liquidity available to the firm is Щ{ш) = Li{uj)—ti{uj). payday loans reviews

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