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# Economic Risk in Hydrocarbon Exploration

by Ian Lerche and James A. MacKay, 1999, Academic Press, 404 p., hardcover.

In the 1970's, John Cozzolino presented a formula for calculating risk adjusted value (RAV) for exploration prospects.  RAV is synonymous with what most of us call certain(ty) equivalent.   It uses a two-outcome case: success or failure.  Further, Cozzolino's formula assumes the exponential utility function to characterize risk attitude.  The advantage of Cozzolino's approach is a simple formula provides the calculation:

RAV = -RT ln{ps exp(-WV/RT) + (1-ps) exp(WC/RT)}

where RT is the risk tolerance coefficient, ps is the probability of success, W is the working interest, V is the value of discovery, and C is the cost of failure.

Authors Lerche and MacKay extend Cozzolino's approach.  The aim of this book is to provide formulas for rapid analysis of prospects.

The authors provide an alternative utility function shape, a hyperbolic tangent formula.  This is a new shape for me:

U(x) = 1 - tanh(x/RT)

This book is heavily algebraic and not for the mathematically faint of heart.

Among the topics are:

• Optimizing working interest
• Portfolio balancing under a budget constraint
• Value of added information
• Bidding
• Options in exploration

This book treats utility in ways that differ from my beliefs.  For example, I question the suitability of using distributions for probability of success and risk tolerance. Further, in my opinion, risk aversion should be a non-issue for widely-held companies.

 Author Jim MacKay and I at one time agreed on the utility methodology and approach.  However, my opinion is that Texaco's risk tolerance coefficient should be 3 or 4 orders of magnitude larger than implied by the company's past decisions.

The authors are mathematically proficient and surely know some things that I don't.  If your are interested in utility theory to optimize working interest, then you may be interested in obtaining this book and deciding for yourself.

—John Schuyler, February 1999

Copyright © 1999 by John R. Schuyler. All rights reserved. Permission to copy with reproduction of this notice.