In calculating investment decisions, and also many life decisions, the upside and downside of outcomes is often skewed one way or the other.
If you purchase a lottery ticket, for example, there is a very small probability that you will have a big win. This is called positive skewness.
A car breakdown or losing your job, on the other hand, are examples of negatively skewed risks. There is a small probability that something will happen, and if it does it will be a major loss. If things go well, then nothing will happen.
In the financial markets, the returns of the aggregated US stock market are negatively skewed, which means that crashes are more likely to occur than booms.
This concept of skewness and how it may apply to understanding investment decisions has been the subject of a recent study co-authored by Paul Karehnke, a lecturer in the school of banking and finance at UNSW Business School.
"If people study the behaviour around risk and decision-making, then you can see that skewness is driving many decisions," says Karehnke.
"Avoiding or judging the downside risk is really a first order driver to so much of our decision-making, and that is why it presents as an interesting area of study."
‘‘What we have done is start with something normal,
which is symmetrical, and then through introducing varying degrees of
asymmetries, we get an understanding of the relation between skewness and the
probability and magnitude of potential losses’ – paul karehnke
The most important characteristic of risk is its downside, or its potential to create losses.
But the return distributions from investments are rarely the same for losses or gains. They are most often skewed either positively or negatively, but the most widely used risk measures, such as the standard deviation, ignore asymmetries.
In A Simple Skewed Distribution with Asset Pricing Applications, Karehnke, along with co-author Frans de Roon from Tilburg University in The Netherlands, seeks to find a simpler and easier understanding of skewness, with the goal of creating a practical model that can be used by asset managers as they assess the downside risk of investment allocations.
Skewness, says Karehnke, is of particular interest for asset managers, who factor in the probability of losses and need to understand the value at risk (VaR) or the expected shortfall (ES) that can flow from their investment decisions.
"Many market risks have significant negative skewness, and it is important to take this into account in the estimation of VaR and ES," he says.
'Quite good odds'
In the asset management industry, Julian Morrison – the national key account manager at fund management house Allan Gray Australia – has worked with the concept of VaR, and says that while it is "accurate for a high percentage of the time", the times when it is most useful is "when you haven't contemplated how bad it can really get".
"The range of outcomes is very wide indeed and the question you need to ask yourself is what does very very bad look like, and what will that do to me financially," says Morrison.
As an investment house, Allan Gray generally takes a different approach to downside risk and the market than investors who "buy the whole market" through index funds, and are more focused on understanding historical returns.
Allan Gray is a "contrarian investor" and Morrison and his colleagues work to find good companies to invest in, where the share price has been discounted and depressed by the market.
"We never buy something which is fair value or above, we always want a really big discount," he says.
"This gives us a better return and a margin of safety on the downside, and the upside takes care of itself.
"If you have a stock which is so depressed it could go up 10 times, and there is a 50% chance of it going up and a 50% chance of it going to zero, these are actually quite good odds for us."
A measure of asymmetry
Karehnke acknowledges that complex and effective risk models exist, and that there are sophisticated models in use that deliver an accurate understanding of downside risk and the probability of losses.
His work with de Roon, he says, aims to make a contribution to this area through creating a model that enables skewness to be more easily included and better understood.
While investors are often driven by skewness when they make their allocations, risk management is more often calculated using mathematical concepts of mean and variance, which have more straightforward interpretations.
In modelling based on mean and variance, the upside and downside risks are represented symmetrically, in what is called a normal distribution.
In Karehnke's modelling, a mathematical formula is used which creates a skewed distribution which, in graphic terms, produces an asymmetrical result where the upside or downside risks are shown as two differently shaped tails.
"Skewness is basically a measure of asymmetry," says Karehnke.
"A skewness of zero means the distribution is symmetric, but when you start to introduce skewness, that is when asymmetry starts to come in.
"What we have done is start with something normal, which is symmetrical, and then through introducing varying degrees of asymmetries, we get an understanding of the relation between skewness and the probability and magnitude of potential losses."
The modelling shows that even modest levels of skewness can have a significant impact on VaR and ES.
Modelling for a skewness of negative 0.40 compared with the normal symmetric distribution of risk will produce an 11% increase in VaR and a 12% increase in the ES.
you realise that the distribution is not normal is probably in real time when
things start to go wrong’– julian morrison
Karehnke says the research so far suggests that factoring skewness into decisions can deliver particular value in situations where anticipated returns can be high, volatility is low, and investors are more risk tolerant and are not under short-sale constraints.
An understanding of skewness, he says, is particularly relevant in the present investment climate, where volatility is a global phenomenon.
An example of this is the market for government bonds. Bond returns have long been considered to be positively skewed, but the current low interest rate environment has turned that around, to the point that the bonds are now a negatively skewed investment.
Further research will be to model the downside risk of mixed portfolios, which comprise diverse assets including derivatives, where the skewness can be complicated and greater than for other assets such as bonds and equities.
The modelling could also be used to evaluate the performance of a hedge fund manager. As these managers regularly use derivatives, which deliver highly asymmetric returns, an understanding of the skewness behind their decision-making could be useful to investors.
Asset manager Morrison says that, historically, investors have analysed data sets which are normally distributed.
"When you realise that the distribution is not normal is probably in real time when things start to go wrong," he says.
"If someone can do a better job than the normal distribution, which is what the Karehnke research appears to do, then yes this is probably relevant to some investors on a practical level.
"And it is relevant, because all investors should have an idea of the overall market and the distribution of returns."
VBA Excel functions associated to Karehnke's work to calculate the probability of losses, VaR and ES with skewness are available for download at: http://tiny.cc/tf1kcy