# Formulating Optimal R&D Portfolios: Here's a Simpler Version of a Rigorous Method for Generating Portfolios That Minimize Risk for a Given Level of Return

## Article excerpt

In a May-June 2000 RTM article, written with Randolph Case, we illustrated a new technique for formulating optimal R&D portfolios (1). That paper showed that a relatively simple model in an EXCEL spreadsheet could be used to develop R&D portfolios, which would be preferred by all risk-averse decision makers regardless of the particular shape of their utility functions. After applying the methodology to an artificial group of just five projects, we applied the same methods to a group of 30 real R&D projects taken from an anonymous pharmaceutical company.

One of the strengths of the model was that it required very little data about the individual projects making up the portfolio. The analysts need only estimate for each project the high return, the low return, and their probabilities. The high return is the return associated with a successful project, the low return is the return associated with an unsuccessful project.

The methodology required, first, the setup of a linear program, which minimized risk subject to a given level of return. Then the linear program was run repeatedly, with slight increases in the required level of return between each run. The results of these runs were then plotted on a set of risk--reward axes forming an efficient frontier. Then, using the risk--reward axes, the portfolios were screened to find only those that were preferred by all risk-averse decision makers.

The measure of risk used was a novel one for R&D portfolio selection models, namely, the Gini coefficient. The Gini coefficient bears some resemblance to the more conventional standard deviation or variance in that it is a measure of the variability of the returns from a given portfolio. Specifically, the Gini coefficient is measured as E|R-r|/2, where R and r are two random returns from the same project. Thus, the Gini coefficient measures the expected value of half the distance between two random returns.

The formula above gives an intuitive picture of the Gini coefficient as a measure of variability, but it is not a form that is practical for actually estimating the Gini coefficient from real-world data. In order to do that, the Gini is estimated as twice the covariance between the project return and the cumulative distribution of the portfolio.

In our 2000 paper, the Gini was estimated from the portfolio containing all available projects. This estimate of the Gini is conservative and overestimates the risk for all portfolios containing less than the full set of projects. In the new approach, discussed here, we use a more precise estimate of Gini.

A New Approach

The model presented here is a simplified form of the one in references (1) and (2). As with that model, we use the Gini coefficient as a measure of risk; however, no linear programming is required. Here, a technique called branch and bound replaces the linear programming, resulting in a conceptually simpler model.

Our method may also be compared to multiple-objective mathematical programming models (3). These models do produce non-dominated portfolios but have a limited capacity to evaluate risk. Mean-variance models can also be used in this context but they place significant restrictions on the decision maker's utility function and on the probability distribution of returns. Stochastic dominance may also be applied but it requires pairwise comparison of all projects (4).

Branch and bound analysis, as described in detail below, is a sort of decision tree methodology that allows us to easily uncover portfolios that are not dominated by any others. A portfolio is non-dominated if there are no others that have the same level of risk and a higher return or that have the same level of return at a lower risk. Here, we will measure risk as the Gini coefficient of the portfolio. First, though, we outline the methodology, which will be described in more detail below:

1. Compute the mean return and Gini coefficient for the portfolio including all n projects. …

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