Sunday, 11 March 2012

On Eggs and Baskets

Reading the papers the last couple of weeks, the reported rise of investments in both the chemical and the oil & gas industry caught my attention. The top 20 European chemical companies had doubled their investments from 1.5% of total revenue in 2008 to more than 3.1% in 2011, which is about €5 billon. The oil & gas industry also displays an increase of investments driven by the race for new production wells. Petrobras is investing a stunning $225 billion in exploration of new oil fields over the period 2011-2015, making it one of the world’s biggest corporate investment programmes. Not only Petrobras, other major oil companies report a significant rise in investments as well. Royal Dutch Shell for example reported a€12 billion investment to explore the Prelude-gas field in Australia. Chemical and oil & gas companies have to make numerous investment decisions, each of them concerning large initial investments and uncertain returns. Business executives in both industries therefore require rigor in decision making when deciding on their capital investments. One lesson they all know too well is to make sure that they diversify their investments and not place all of their eggs in one basket.  But how do they decide which baskets to invest in and how many eggs to put in each of them?

Diversification of investments is not an idea that came out of the modern portfolio theory as Harry Markowitz developed it. The knowledge was already available 3000 year ago as the book of Ecclesiastes (about 935 B.C) advices you to "divide your investments among many places, for you do not know what risks might lie ahead". It’s even part of classical English literature. Antonio in Shakespeare’s Merchant of Venice tells Salarino that his ventures are not in one bottom trusted, nor to one place. The work of Harry Markowitz however gave us a formal method for deciding on the best possible portfolio of investments, minimizing risk given a required return. He was rewarded the Nobel Prize for Economics in 1990 for this work.  Key in the work of Markowitz work is the concept of diversification which reduces the risk of an investment portfolio, but can appear counterintuitive.

To illustrate imagine two projects, a safe and a risky one, with independent probabilities of success. Each project requires an initial investment of €10 million. The table above summarizes the probabilities and pay offs for each of the projects. Note that the expected pay off for each of the projects is €30 million. Investing in the higher risk project will not increase the expected return, so the safe project is the obvious better choice.  Now suppose that it would be possible to split the €10 million investment in two and invest €5 million in the safe project and €5 million in the risky project. Would that be a better choice? Intuitively it would seem like a bad idea to take money invested in the save project and invest in the risky project and I expect that many business executives also follow that instinct. However, diversification of the investment, spreading the eggs over the two baskets, will reduce overall risk. Let me show you how. Instead of just two outcomes, we now have 4 possible outcomes as summarized in the table below. The expected value of the 50/50 split remains €30 million but compared to investing solely in the safe project the probability of losing €10 million is reduced from 33% to 22%, a significant reduction of risk. Although moving money from a safe investment to a more risky one seems counterintuitive, doing so will reduce risk showing the effect of diversification.

Note that when the projects would have been positively correlated (for example when drilling for oil in the same area) this risk reduction would have been less significant. If the safe project fails, because of the positive correlation, the risky project has a greater probability of failure resulting in a higher than 22% probability of losing €10 million. On the other hand if they would have been negatively correlated the risk reduction would have been even more significant. In deciding on which projects to invest in, the executives in the chemical and oil & gas industry therefore need to spread their investments seeking the negatively correlated projects, and avoiding the positively correlated ones. A challenge that can be solved well with the optimisation techniques of Operations Research.