Dynamic Programming Models and Algorithms for the Mutual Fund Cash Balance Problem

Abstract

Fund managers have to decide the amount of a fund's assets that should be kept in cash, considering the trade-off between being able to meet shareholder redemptions and minimizing the opportunity cost from lost investment opportunities. In addition, they have to consider redemptions by individuals as well as institutional investors, the current performance of the stock market and interest rates, and the pattern of investments and redemptions that are correlated with market performance. We formulate the problem as a dynamic program, but this encounters the classic curse of dimensionality. To overcome this problem, we propose a provably convergent approximate dynamic programming algorithm. We also adapt the algorithm to an online environment, requiring no knowledge of the probability distributions for rates of return and interest rates. We use actual data for market performance and interest rates, and demonstrate the quality of the solution (compared to the optimal) for the top 10 mutual funds in each of nine fund categories. We show that our results closely match the optimal solution (in considerably less time), and outperform two static (newsvendor) models. The result is a simple policy that describes when money should be moved into and out of cash based on market performance.mutual fund cash balance, approximate dynamic programming

Fully Polynomial Time Approximation Schemes for Stochastic Dynamic Programs

“…Pseudopolynomial time algorithm [16]; heuristic that converges to the optimum [60] FPTAS; #P-hardness proof; approximated limit policy C Third, we illustrate the generality and applicability of our framework by providing FPTASs to 10 different optimization problems as summarized in Table 2. (No FPTAS has been reported in the literature for any of these problems except for problem 5.)…”

“…Other classical models closely related to this problem include [21,78]. Recently, Nascimento and Powell [60] have studied a similar cash balance problem with a fairly general setting, which includes a Markovian demand process and time-dependent costs on positive and negative cash levels. Their model assumes that the per-unit stock selling cost s and the per-unit stock buying cost b are equal.…”

A comparison of approximate dynamic programming techniques on benchmark energy storage problems: Does anything work?

“…[16] takes a similar approach of exploiting concavity for a generic problem with a scalar resource, but within an approximate value iteration framework. Moreover, [20] considers a simple storage problem motivated by mutual fund management and solves it using a lookup table approach exploiting concavity. Also taking advantage of structure, [21] exploits the monotonicity in the value functions in a lookup table approach to solving an optimal bidding and storage problem.…”

“…Also taking advantage of structure, [21] exploits the monotonicity in the value functions in a lookup table approach to solving an optimal bidding and storage problem. In both the cases of [20] and [21], pure lookup table without structure does not work in practice within reasonable time constraints. [7] solves the natural gas storage control problem through the discretization of a continuous time model and applying a basis function approximation of the value function.…”

A Computationally Efficient FPTAS for Convex Stochastic Dynamic Programs

“…This approach builds a piecewise linear approximation of the value function that maintains concavity, and it is provably convergent for certain classes of finite-horizon problems with special structure [32,33]. The concavity property exploited by SPAR is strictly related to the convexity properties required in the framework presented in this paper, and in fact the resource management problems of [31] to which SPAR is applied also fit in our framework.…”