Portfolio Models With Stochastic Cash Demand, Borrowing and Fixed Transfer Costs

Abstract

Portfolio models of the Markowitz-Tobin type implicitly assume that the investor does not have to liquidate any part of his portfolio to meet some exogenous cash demand. Since liquidity needs can be an important factor in portfolio management, Chen, Jen, and Zionts [3] in a recent paper developed a model assuming stochastic demand for cash and the possibility of meeting the cash demand by liquidating one or more assets. However, borrowing is an important alternative t o liquidating assets. This paper considers that possibility. Unlike Chen, Jen, and Zionts, this paper also considers the more difficult question of liquidation costs being partly fixed and partly variable. In order to make the consideration of borrowing and fixed transfer costs mathematically tractable, the problem is first cast in a framework different from that of [3].Whalen [lo] extended the Baurnol-Tobin [ I ] [7] model for the transaction demand for money by allowing firms or individuals to borrow in order t o meet their scheduled disbursements. However, like Baumol and Tobin, Whalen assumed that the expenditure stream planned by the individual concerned is certain. On the other hand, Chen, Jen and Zionts [3] (hereafter CJZ) developed a model assuming stochastic demand for cash and, unlike Baumol-Tobin-Whalen, they considered the possibility of liquidating one or more assets (depending on the quantum of cash demand) to meet the cash demand. However, CJZ did not consider the possibility of borrowing as an alternative to liquidating the assets to meet the cash demand. CJZ assumed the liquidation cost to be completely variable and indicated that fixed transfer costs cannot be considered in their framework. Tsiang [9], who developed a model very similar to that of CJZ, recognized borrowing as an alternative to liquidating the assets,' but did not explicitly introduce borrowing in his model.