Inter-Temporal Correlation of Cash Flows and the Risk of Multi-Period Investment Projects

Abstract

In capital budgeting when the net present value method (NPV) is used and future cash flows are uncertain, the measurement of the standard deviation of the project's net present value (0 ) is unusually difficult. Typically the investment life of the project is more than one year, and the cash flows of each period are correlated with each other. The difficulty in determining the exact inter-temporal correlation (p ) of cash flows creates special problems in estimating the overall variance of the investment project. For example, see [5, pp. 125-131]. This paper attempts to isolate the possible impact of the inter-temporal correlation of cash flows upon the total risk of the project under the assumption that the standard deviations of cash flows for each time period of the project are known. It also provides upper and lower bounds of 0 for a multi-period investment project where the degree of the inter-temporal correlation is not exactly known. Most texts on capital budgeting give the equations for 0 , assuming p = 0 and p = 1, and then with an example illustrate the range of U , Ut)(i t , L.TJG magnitude o can take on when P . 0 varies between 0 and 1. See, for example, [1, 4, 5, 6], However, it is possible that p may be negative, as well as positive. Therefore, this paper will examine the values cr can assume, allowing p . to vary between +1 and -1. t, t+? Section II presents the general case for o where p belongs to any value from the range [-1,1]. Section III presents the upper and lower bounds of o for the general case. Section IV summarizes by the use of a simple example. The Appendix provides a formal proof of the upper and lower bounds.