The Bank of Canada has released Working Paper 2010-1 by B. Ravikumar and Enchuan Shao titled Search Frictions and Asset Price Volatility:
We examine the quantitative effect of search frictions in product markets on asset price volatility. We combine several features from Shi (1997) and Lagos and Wright (2002) in a model without money. Households prefer special goods and general goods. Special goods can be obtained only via a search in decentralized markets. General goods can be obtained via trade in centralized competitive markets and via ownership of an asset. There is only one asset in our model that yields general goods. The asset is also used as a medium of exchange in the decentralized market to obtain the special goods. The value of the asset in facilitating transactions in the decentralized market is determined endogenously. This transaction role makes the asset pricing implications of our model different from those in the standard asset pricing model. Our model not only delivers the observed average rate of return on equity and the volatility of the equity price, but also accounts for most of the spectral characteristics of the equity price.
This is a good paper; unfortunately the prosaic explanations of the model are rather heavily larded with the math; and I am not sufficiently comfortable with the math to provide my own textual explanation. But I’ll do what I can.
The authors were most interested in attacking the excess volatility puzzle:
LeRoy and Porter (1981) and Shiller (1981) calculated the time series for asset prices using the simple present value formula – the current price of an asset is equal to the expected discounted present value of its future dividends. Using a constant interest rate to discount the future, they showed that the variance of the observed prices for U.S. equity exceeds the variance implied by the present value formula (see figure 1). This is the excess volatility puzzle.
After the rather precious definition of the General Good as a “tree” and the Special Goods as “fruits”, they explain:
Random matching during the day will typically result in non-degenerate distributions of asset holdings. In order to maintain tractability, we use the device of large households along the lines of Shi (1997). Each household consists of a continuum of worker-shopper (or, seller-buyer) pairs. Buyers cannot produce the special good, only sellers are capable of production. We assume the fraction of buyers = fraction of sellers = 1 / 2 . Then, the probability of single coincidence meetings during the day is 1/4 α. Each household sends its buyers to the decentralized day market with take-it-or-leave-it instructions (q; s) – accept q units of special goods in exchange for s trees. Each household also sends its sellers with “accept” or “reject” instructions. There is no communication between buyers and sellers of the same household during the day. After the buyers and sellers finish trading in the day, the household pools the trees and shares the special goods across its members each period. By the law of large numbers, the distributions of trees and special goods are degenerate across house-holds. This allows us to focus on the representative household. The representative household’s consumption of the special good is [q α/4].
…. and the interesting part is …
To compute the “liquidity value” of the asset, we set β and δ set at their benchmark values (Table 1) and calculate the price sequence for a standard asset pricing model such as Lucas (1978). This is easily done by setting u'(qt α / 4) = 1 for all t in equation (10). Since the standard asset pricing model does not assign any medium of exchange role to the asset, the difference between the prices implied by the standard model and ours would be the liquidity value of the asset. We compute the liquidity value as a fractionof the price implied by the standard model i.e., liquidity value = (Pmodel – PLucas) / PLucas. The mean liquidity value implied by our model is 17.5%.
This is a fascinating result, illustrating the value of liquidity in a segmented market. It is the function of dealers – and their capital – to reduce friction for all players, but to keep a piece for themselves . I will be fascinated to follow the progress of this model as, perhaps, it gets extended to include “households” that function in such a manner.
It is also apparent that when friction increases, the “flight to quality” into government bonds may be characterized to a great extent as a “flight to liquidity”.