Optimal Cash Management for Investment Funds

We consider the question of how much cash should be held by an investment fund for transactions purposes. Cash is needed to meet redemptions and rights offerings; it is generated by dividends and contributions. It is assumed the cumulative cash flow follows a random walk, perhaps with a drift. If transactions costs were zero, it would be optimal to keep zero cash balances, since cash reduces expected return and adds to tracking error. But keeping cash balances at zero would be very expensive in the presence of transactions costs, since random walks have infinite variation. The optimal cash policy requires a no trade interval [*]. If cash balances are within this interval, no transfers between cash and portfolio securities takes place. If cash falls beneath zero, securities should be sold to return the cash balance to zero. If cash exceeds L*, cash should be invested in the portfolio to reduce the cash balance to L*. We derive closed form solutions for L*, and show how this responds to changes in transactions costs and other parameters of cash flows and portfolio returns. Finally, a closed form estimate of expected turnover associated with optimal strategies is derived.