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.