Abstract
Oil and Gas investments are inherently risky, especially in upstream exploration where technical risk is predominant. Because of the large upfront expenditure required for these projects, it is imperative that investors in the business are well informed of the risk to which their capital is exposed. However, most commonly used performance measures focus on one aspect of what is a multidimensional problem. While expected value gives an indication of the amount of value created by the investment, the standard deviation gives an insight into the distribution of expected returns. The Performance Index combines these two insights into a single measure, value created per unit of variability (the standard deviation), which is a significant improvement over the one dimensional measures.
However, the Performance Index, PI is based on total variance and does not reflect the uncertainty structure of the risky investment. PI does not distinguish between upside and downside variances and can sometimes give a lower ranking to a prospect with large upside variance (High gain situation) leading to the Paradox of aversion to incremental reward (PAIR). We show this flaw in PI in an expected value maximization context as well as in an expected utility maximization context.
Semi-variance analysis gives an insight into the uncertainty structure of a risky investment. We use semi-variance analysis to propose a modification to PI to eliminate the problem of PAIR. Total variance is decomposed into upside and downside variances and the modified PI estimated based on downside variance alone. In decomposing the variance, we recommend using a threshold value to avoid the problem of a "shifting mean". We demonstrate through two examples (1) that though conventional PI may correctly rank risky prospects, non-recognition of the uncertainty structure does not accurately reflect the risk characteristics of an investment, and through a second example, a well drilling situation in which conventional and the modified PI lead to different ranking and investment decision recommendations.
