Plans based on average assumptions .. Strategic Risk and Performance management by Strategy@Risk Ltd.

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http://www.strategy-at-risk.com/2011/03/01/plans-based-on-average-assumptions/ March 3, 2011
The Flaw of Averages states that: Plans based on the assumption that average
conditions will occur are usually wrong. (Savage, 2002)
Many economists use what they believe to be most likely or average values (Timmermann, 2006)
(Gavin & Pande, 2008) as input for the exogenous variables in their spreadsheet calculations.
We know however that:
1. the probability for any variable to have outcomes equal to any of these values is close to
zero,
1. and that the probability of having outcomes for all the (exogenous) variables in the
spreadsheet model equal to their average is virtually zero.
So why do they do it? They obviously lack the necessary tools to calculate with uncertainty!
But if a small deviation from the most likely value is admissible, how often will the use of a single
estimate like the most probable value be ‘correct’?
We can try to answer that by looking at some probability distributions that may represent the
‘mechanism’ generating some of these variables.
Let’s assume that we are entering into a market with a new product, we know of course the
maximum upper and lower limit of our future possible market share, but not the actual number so
we guess it to be the average value = 0,5. Since we have no prior knowledge we have to assume
that the market share is uniformly distributed between zero and one:
If we then plan sales and production for a market
share between 0, 4 and 0, 5 – we would out of a
hundred trials only have guessed the market share
correctly 13 times. In fact we would have
overestimated the market share 31 times and
underestimated it 56 times.
Let’s assume a production process where the
acceptable deviation from some fixed measurement
is 0,5 mm and where the actual deviation have a
normal distribution with expected deviation equal to
zero, but with a standard deviation of one:
Using the average deviation to calculate the expected
error rate will falsely lead to us to believe it to be
zero, while it in fact in the long run will be 64 %.
Let’s assume that we have a contract for drilling a
tunnel, and that the cost will depend on the
hardness of the rock to be drilled. The contract
states that we will have to pay a minimum of $ 0.5M
and a maximum of $ 2M, with the most likely cost
being $ 1M. The contract and our imperfect
knowledge of the geology make us assume the cost
distribution to be triangular:
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Using the average as an estimate for expected cost
will give a correct answer in only 14 out of a 100
trials, with cost being lower in 45 and higher in 41.
Now, let’s assume that we are performing deep sea
drilling for oil and that we have a single estimate for
the cost to be $ 500M. However we expect the cost
deviation to be distributed as in the figure below, with
a typical small negative cost deviation and on
average a small positive deviation:
So, for all practical purposes this is considered as a
low economic risk operation. What they have failed to
do is to look at the tails of the cost deviation
distribution that turns out to be Cauchy distributed
with long tails, including the possibility of
catastrophic events:
The event far out on the right tail might be
considered a Black Swan (Taleb, 2007), but as we
now know they happen from time to time.
So even more important than the fact that using a
single estimate will prove you wrong most of the
times it will also obscure what you do not know – the
risk of being wrong.
Don’t worry about the average, worry about how large
the variations are, how frequent they occur and why
they exists. (Fung, 2010)
Rather than “Give me a number for my report,”
what every executive should be saying is “Give
me a distribution for my simulation.”(Savage,
2002)
References
Gavin,W.,T. & Pande,G.(2008), FOMC Consensus Forecasts, Federal Reserve Bank of St. Louis
Review, May/June 2008, 90(3, Part 1), pp. 149-63.
Fung, K., (2010). Numbers Rule Your World. New York: McGraw-Hill.
Savage, L., S.,(2002). The Flaw of Averages. Harvard Business Review, (November), 20-21.
Savage, L., S., & Danziger, J. (2009). The Flaw of Averages. New York: Wiley.
Taleb, N., (2007). The Black Swan. New York: Random House.
Timmermann, A.,(2006). An Evaluation of the World Economic Outlook Forecasts, IMF Working
Paper WP/06/59, www.imf.org/external/pubs/ft/wp/2006/wp0659.pdf
Endnotes
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Category: Balance sheet and P&L simulation, Corporate risk analysis, Modelling, Other topics,
Uncertainty
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