Good decision makers tend to worry more about the losers than the winners.
Avoiding big losses keeps you in the game and allows the successful investments to accumulate wealth and create value over time. How much risk analysis performed in the corporate environment gets close to answering these questions:
- Do we fully understand the risks involved with this transaction?
- What are the probabilities of these risks arising?
- Can we quantify their financial impact, particularly on the downside?
- What is the best way of monitoring and taking early action to mitigate this risk?
When I interviewed the late Richard Cousins, former CEO of Compass, on the topic of corporate investment decision making he was cynical about the way modern corporate finance had left things. He was concerned that theories rarely mirrored reality, and a lack of understanding around the representation of risk was present in organisations. It was almost as though there was only half a job done with theory not quite addressing the practice. He felt many participants had a poor understanding of what they were really presenting and that there was little transparency around imbedded risks in what is often a static set of numbers. Cousins was an exceptional leader, and his views sum up a general suspicion in the corporate world about where modern financial thinking has left us. Part of the problem is presenting risk in a transparent and simple manner. The quality of risk analysis in financial evaluation is variable and often inconsistent and confusing. Many companies and in particularly their treasury departments wrestle with the best way to present risk in a transparent and simple manner.
The truth of the matter is that executives making decisions are concerned about the risks they are taking on and yet frustrated by the tools available to them to measure risk.
The current corporate toolkit
Taking stock, the mainstream tools to analyse and present risk look like this:
- Qualitative analysis describing the risks often supported with some very rudimentary calculations
- A net present value (NPV) financial model showing output in value terms
- Scenario analysis flexing the model for a small number of deviations from the expected result
- Sensitivity analysis flexing the model to the point where it destroys value or break even
- Statistical analyse such as value at risk (VaR) and its offshoots
While the techniques listed above can certainly enhance the understanding of risk, for such a critical and all-pervasive area, Cousins was right to feel a little short-changed by the contribution these tools make. In fact, there is a danger these tools can mislead and misrepresent risks if the analysis and presentation is not carefully thought through.
Value at Risk (VaR)
VaR’s big advantage is that it can summarise risk into a single number at a known confidence level. This is also potentially its biggest weakness. Add to the mix the inherent danger within correlations, especially where real world explanations for statistical correlations are not obvious. In the corporate environment there are some specific dangers in using VaR. It can create a false sense of security, for instance losses can turn out to be greater than expected and confidence levels of 95 or 99 percent sound impregnable but are often not. It requires volatility input, which flows easily from financial markets where data points proliferate. But in the corporate environment, where commercial issues interact with markets, it can be much harder to determine volatility. It can be static, meaning it can be difficult to show VaR on a scale or display an average downside or upside to the mean. Finally, it is not intuitive. Consider the definition of standard deviation: it is the square root of the average quadratic deviation around the arithmetic mean of outcomes.
Companies face an interaction of market and commercial risks and it can be both extremely difficult to gauge volatility of the commercial risks and estimate any correlation between these risk types. Add into the equation the fact that the financial mindset is usually one of a fixed forecast, budget or cash flow profile, sometimes going out several years. Several key assumptions will always lie behind these fixed numbers, yet it is surprisingly difficult to tease out what these can be and then apply a sensible level of probability to them. There are inherent dangers in using VaR in many corporate risk management situations.
A statistical approach such as VaR can provide some level of risk analysis in vanilla decisions such as where an interest rate might get to in a year’s time. However, where commercial and market risks interact a technique like Monte Carlo simulation is much more useful.
Introducing the gain-loss spread
The concept of the “gain-loss” spread was introduced by Javier Estrada (first published in the Journal of Applied Corporate Finance, Vol 21, no. 4, Fall 2009) in the context of portfolio investment. It is a simple and powerful technique that fits neatly into the corporate toolkit when analysing and explaining risk. The table below takes us through the four simple steps involved in calculating the gain-loss spread.
| Step 1: run a Monte Carlo simulation to generate 1,000s of data points | Example
1,000 data points are generated through a Monte Carlo simulation. 250 data points are a loss (25 percent) 750 data points are gain (75 percent) The population mean is +15 The mean of the gains is 10 The mean of the losses is -5 Calculate the gain-loss spread: Gain-loss spread is 10 – -5 = 15 |
| Step 2: sort data into gains and losses | |
| Step 3: calculate total population mean, and mean of gains and losses | |
| Step 4: the gain-loss spread is the difference between the mean gain & loss |
The gain-loss spread in 4 simple steps
The simplicity of the calculation helps to engender trust and transparency and therefore a willingness to accept the output. Being able to express the outcome in terms of the “difference between the average gain and the average loss” is an intuitively easier message to communicate. The average gain or loss alongside the probability of these arising are useful anchor points for decision makers. The table below shows a comparison of gain-loss output and VaR output on a simple asset valuation model which has been run through a Monte Carlo simulation. The gain-loss spread output significantly aids presentation and understanding of the underlying level of risk, while VaR projects a “black box” aura with the attendant difficulties in generating faith in the output.
| Baseline: an asset with an initial cost of £12m and expected value of £15m, ie NPV positive by £3m, is tested through Monte Carlo simulation. Three levels of volatility have been modelled (high, medium and low) | |||
| High volatility model | Medium volatility model | Low volatility model | |
| Gain-loss spread | |||
| Spread | 15 | 7 | 4 |
| Average gain | 9 | 5 | 3 |
| Average loss | (6) | (2) | (1) |
| Probability of gain (%) | 60 | 69 | 90 |
| Probability of loss (%) | 40 | 31 | 10 |
| Maximum gain | 18 | 11 | 7 |
| Maximum loss | (12) | (5) | (1) |
| Gain-loss index (ranking) | 0.2 | 0.4 | 0.8 |
| Value at Risk | |||
| Volatility (standard dev) (%) | 57 | 29 | 15 |
| Loss @ 95% confidence | (11) | (4) | (1) |
| Probability of loss (%) | 36 | 24 | 8 |
The standard output from gain-loss spread analysis and VaR analysis
For example, taking the medium volatility output in the table (middle column), the gain-loss representation of the risk is that two-thirds of the time the asset could be worth more than its expected value and that the average of this upside is five. A third of the time it will be worth less and the average of this downside is two. The riskiness of the asset is a spread of seven around the expected value of fifteen. Compare this to the VaR answer which is a volatility of 29 percent and it is obvious that gain-loss presentation is more informative.
There is another potentially very valuable contribution gain-loss spread analysis makes to the decision-making process. The analysis itself lends itself to a measure of choosing between two or more competing projects when resources are restricted. Financial theory in this regard points us towards a “profitability index” which looks at present value of inflows over initial capital outlay. Project resources are allocated in descending order of indexed value until the available resources are consumed. A similar index score approach is easily available through gain-loss analysis. The gain-loss index is shown in table three and is simply the expected NPV of three divided by the spread. For instance, the high volatility model shows that an NPV of 0.2 is produced for every unit of spread (risk) compared to 0.8 for the low volatility model. Unless the objective is to actively seek risk, the low volatility route is the better choice.
The richer presentation of risk of the gain-loss spread approach is clear.
The measurement and presentation of risk is a perennial problem for the corporate treasurer. While there are several tools available, often they leave decision makers frustrated by the lack of clarity. VaR, the most common statistical based approach, suffers in the corporate environment when market risks interact with commercial risks. Often volatility and correlation are difficult to determine.
There is no escaping the fact that the corporate must take the plunge and determine a range of possible outcomes and their probabilities for it to move forwards and begin to visualise its risks. A key message from the first article in this series is that the act of doing this is just as important as the actual output.
The simplicity of a gain-loss spread analysis is one of its core strengths and the audience can intuitively understand the concept of an average gain and an average loss, with the level of risk as being the gap between these. VaR suffers in comparison with the mathematics behind its determination poorly understood and the traditional output abstract in nature. The gain-loss approach tells the audience a level of risk, a probability of loss or gain and an average and maximum loss or gain. These directly address the question decision makers want to know when assessing risk. Lastly the gain-loss approach gives a further ability to determine between mutually exclusive projects on a “risk per unit of value basis”.
As we move on in future articles to discuss risk approaches in more specific treasury related settings, Monte Carlo simulation and the gain-loss spread approach covered in these first two articles will be referenced as appropriate. However, I hope that these techniques act as an introduction to a useful and flexible toolkit for addressing the risk issues specific to your own situations.