Warning: define(): Argument #3 ($case_insensitive) is ignored since declaration of case-insensitive constants is no longer supported in /home/u742613510/domains/strategy-at-risk.com/public_html/wp-content/plugins/wpmathpub/wpmathpub.php on line 65
Articles – Page 2 – Strategy @ Risk

Strategy @ Risk

Blog

Distinguish between events and estimates
This entry is part 1 of 2 in the series Handling Events

Large public sector investment projects in Norway have to go through an established methodology for quality assurance. There must be an external quality assurance process both of the selected concept (KS1) and the projects profitability and cost (KS2).

KS1 and KS2

Concept quality control (KS1) shall ensure the realization of socioeconomic advantages (the revenue side of a public project) by ensuring that the most appropriate concept for the project is selected. Quality assurance of cost and management support (KS2) shall ensure that the project can be completed in a satisfactory manner and with predictable costs.

I have worked with KS2 analysis, focusing on the uncertainty analysis. The analysis must be done in a quantitative manner and be probability based. There is special focus on probability level P50, the project’s expected value or the grant to the Project and P85, the Parliament grant. The civil service entity doing the project is granted the expected value (P50) and must go to a superior level (usually the ministerial level) to use the uncertainty reserve (the difference between the cost level P85 and).

Lessons learnt from risk management in large public projects

Many lessons may be learned from this quality assurance methodology by private companies. Not least is the thorough and methodical way the analysis is done, the way uncertainty is analysed and how the uncertainty reserve is managed.

The analogy to the decision-making levels in the private sector is that the CEO shall manage the project on P50, while he must go to the company’s board to use the uncertainty reserve (P85-P50).

In the uncertainty analyses in KS2 a distinction is made between estimate uncertainty and event uncertainty. This is a useful distinction, as the two types of risks are by nature different.

Estimate uncertainty

Uncertainty in the assumptions behind the calculation of a project’s cost and revenue, such as
- Prices and volumes of products and inputs
- Market mix
- Strategic positioning
- Construction cost
These uncertainties can be modelled in great detail ((But remember – you need to see the forest for the trees!)) and are direct estimates of the project’s or company’s costs and revenues.

Event Uncertainties

These events are not expected to occur and therefore should not be included in the calculation of direct cost or revenue. The variables will initially have an expected value of 0, but events may have serious consequences if they do occur. Events can be modeled by estimating the probability of the event occurring and the consequence if they do. Examples of event uncertainties are
- Political risks in emerging markets
- Paradigm Shifts in consumer habits
- Innovations
- Changes in competitor behavior
- Changes in laws and regulations
- Changes in tax regimes
Why distinguish between estimates and events?

The reason why there are advantages to separating estimates and events in risk modeling is that they are by nature different. An estimate of an expense or income is something we know will be part of a project’s results, with an expected value that is NOT equal to 0. It can be modeled as a probability curve with an expected outcome and a high and low value.

An event, on the other hand, can occur or not, and has an expected value of 0. If the event is expected to occur, the impact of the event should be modeled as an expense or income. Whether the event occurs or not has a probability, and there will be an impact if the event occurs (0 if it doesn’t occur).

Such an event can be modeled as a discrete distribution (0, it does not occur, 1if it occurs) and there is only an impact on the result of the project or business IF it occurs. The consequence may be deterministic – we know what it means if it happens – or it could be a distribution with a high, low and expected value.

An example

I have created an example using a private manufacturing company. They have an expected P&L which looks like this:

The company has a high export share to the EU and Norwegian cost (both variable and fixed). Net margin is expected to fall to a level of 17% in 2018. The situation looks somewhat better when the simulated – there is more upside than downside in the market.

But potential events that may affect the result are not yet modeled, and what impact can they have? Let’s look at two examples of potential events:
1. The introduction of a duty of 25% on the company’s products in the EU. The company will not be able to lift the cost onto the customers, and therefore this will be a cost for the company.
2. There are only two suppliers of the raw materials the company uses to produce its products and the demand for it is high. This means that the company has a risk of not getting enough raw materials (25% less) in order to produce as much as the market demands.
As the table shows the risk that the events occur increase with time. Looking at the consequences of the probability weighted events in 2018, the impact on the expected result is:

The consequence of these events is a larger downside risk (lower expected result) and higher variability (larger standard deviation). The probability of a 0 result is
- 14% in the base scenario
- 27% with the event “Duty in the EU”
- 36% with the event “Raw material Shortage” in addition
The events have no upside, so this is a pure increase in company risk. A 36% probability of a result of 0 or lower may be dramatic. The knowledge of what potential events may mean to the company’s profitability will contribute to the company’s ability to take appropriate measures in time, for instance
- Be less dependent on EU customers
- Securing a long-term raw materials contract
and so on.

Normally, this kind of analysis is done as a scenario. But a scenario analysis will not provide the answer to how likely the event is nor to what the likely consequence is. Neither will it be able to give the answer to the question: How likely it is that the business will make a loss?

One of the main reasons for risk analysis is that it increases the ability to take action in time. Good risk management is all about being one step ahead – all the time. As a rule, the consequences of events that no one has thought of (and thus no plan B is in place) are greater than that of events which have been thought through. It is far better to have calculated the consequences, reflected on the probabilities and if possible put in place risk mitigation.

Knowing the likelihood that something can go horribly wrong is also an important tool in order to properly prioritize and put mitigation measures in at the right place.
07/10/2013
The risk of planes crashing due to volcanic ash
This entry is part 4 of 4 in the series Airports

When the Icelandic volcano Eyafjallajøkul had a large eruption in 2010 it lead to closed airspace all over Europe, with corresponding big losses for airlines. In addition it led to significant problems for passengers who were stuck at various airports without getting home. In Norway we got a new word: “Ash stuck” ((Askefast)) became a part of Norwegian vocabulary.

The reason the planes were put on ground is that mineral particles in the volcanic ash may lead to damage to the plane’s engines, which in turn may lead to them crashing. This happened in 1982, when a flight from British Airways almost crashed due to volcanic particles in the engines. The risk of the same happening in 2010 was probably not large, but the consequences would have been great should a plane crash.

Using simulation software and a simple model I will show how this risk can be calculated, and hence why the airspace was closed over Europe in 2010 even if the risk was not high. I have not calculated any effects following the closure, since this isn’t a big model nor an in depth analysis. It is merely meant as an example of how different issues can be modeled using Monte Carlo simulation. The variable values are not factual but my own simple estimates. The goal in this article is to show an example of modeling, not to get a precise estimate of actual risk.

To model the risk of dangerous ash in the air there are a few key questions that have to be asked and answered to describe the issue in a quantitative way.

Variable 1. Is the ash dangerous?

We first have to model the risk of the ash being dangerous to plane engines. I do that by using a so called discrete probability. It has a value 0 if the ash is not dangerous and a value 1 if it is. Then the probabilities for each of the alternatives are set. I set them to:
- 99% probability that the as IS NOT dangerous
- 1% probability that the ash IS dangerous
Variable 2. How many planes are in the air?

Secondly we have to estimate how many planes are in the air when the ash becomes a problem. Daily around 30 000 planes are in the air over Europe. We can assume that if planes start crashing or get in big trouble the rest will immediately be grounded. Therefore I only use 2/24 of these planes in the calculation.
- 2 500 planes are in the air when the problem occurs
I use a normal distribution and set the standard deviation for planes in the air in a 2 hour period to 250 planes. I have no views on whether the curve is skewed one way or the other. I assume it may well be, since there probably are different numbers of planes in the air depending on weekday, whether it’s a holiday season and so on, but I’ll leave that estimate to the air authority staff.

Variable 3. How many people are there in each plane?

Thirdly I need an estimate on how many passengers and crew there are in each plane. I assume the following; I disregard the fact that there are a lot of intercontinental flights over the Eyafjallajøkul volcano, likely with more passengers than the average plane over Europe. The curve might be more skewed that what I assume:
- Average number of passengers/crew: 70
- Lowest number of passengers/crew: 60
- Highest number of passengers/crew: 95
The reason I’m using a skewed curve here is that the airline business is constantly under pressure to fill up their planes. In addition the number of passengers will vary by weekday and so on. I think it is reasonable to assume that there are likely more passengers per plane rather than fewer.

Variable 4. How many of the planes which are in the air will crash?

The last variable that needs to be modeled is how many planes will crash should the ash be dangerous. I assume that maybe no planes actually crash, even though the ash gets into their engines. This is the low end of the curve. I have in addition assumed the following:
- Expected number of planes that crash: 0, 01%
- Maximum number of planes that crash: 1, 0%
Now we have what we need to start calculating!

The formula I use to calculate is as follows:

If(“Dangerous ash”=0;0)

If(“Dangerous ash”=1;”Number of planes in the air”x”Number of planes crashing”x”Number of passengers/crew per plane”)

If the ash is not dangerous, variable 1 is equal to 0, no planes crash and nobody dies. If the ash is dangerous the number of dead is a product of the number of planes, number of passengers/crew and the number of planes crashing.

Running this model with a simulation tool gives the following result:

As the graph shows the expected value is low; 3 people, meaning that the probability for a major loss of planes is very low. But the consequences may be devastatingly high. In this model run there is a 1% probability that the ash is dangerous, and a 0, 01% probability that planes actually crash. However the distribution has a long tail, and a bit out in the tail there is a probability that 1 000 people crash into their death. This is a so called shortfall risk or the risk of a black swan if you wish. The probability is low, but the consequences are very big.

This is the reason for the cautionary steps taken by air authorities. Another reason is that the probabilities both for the ash being dangerous and that planes will crash because of it are unknown probabilities. Thirdly, changes in variable values will have a big impact.

If the probability of the ash being dangerous is 10% rather than 1% and the probability of planes crashing is 1% rather than 0,01%, as much as 200 dead (or 3 planes) is expected while the extreme outcome is close to 6 400 dead.

This is a simplified example of the modeling that is likely to be behind the airspace being closed. I don’t know what probabilities are used, but I’m sure this is how they think.

How we assess risk depends on who we are. Some of us have a high risk appetite, some have low. I’m glad I’m not the one to make the decision on whether to close the airspace or not. It is not an easy decision.

My model is of course very simple. There are many factors to take into account, like wind direction and – strength, intensity of eruption and a number of other factors I don’t know about. But as an illustration both of the factors that need to be estimated in this case and as a generic modeling case this is a good example.

Originally published in Norwegian.
23/09/2013
Simulation of balance sheet risk
This entry is part 6 of 6 in the series Balance simulation

As I wrote in the article about balance sheet risk, a company with covenants in its loan agreements may have to hedge balance sheet risk even though it is not optimal from a market risk perspective.

But how can the company know which covenant to hedge? Often a company will have more than one covenant, and hedging one of them may adversely impact the other. To answer the question it is necessary to calculate the effect of a hedge strategy, and the best way to do that is by using a simulation model. Such a model can give the answer by estimating the probability of breech of a covenant.

Which hedging strategy the company is to choose demands knowledge about what covenant is the most at risk. How likely is it that the company will face a breech? Like I described in the previous article:

Which hedging strategy the company chooses depends on which covenant is most at risk. There are inherent conflicts between the different hedging strategies, and therefore it is necessary to make a thorough assessment before implementing any such hedging strategy.

In addition:

If the company hedges gearing, the size of the equity will be more at risk [..], And in addition, drawing a larger proportion of debt in the home (or functional) currency may imply an increase in economic risk. [..] Hence, if the company does not have to hedge gearing it should hedge its equity.

To analyse the impact of different strategies and to answer the questions above I have included simulation of currency rates in the example from the previous article:

The result of strategy choice given a +/- 10% change in currency rates was shown in the previous article. But that model cannot give the answer to how likely it is that the company will face a breech situation. How large changes in currency rates can the company take?

To look at this issue I have used the following modeling of currency rates:
- Rates at the last day of every quarter from 31/12/02 to 30/06/2013. The reason for choosing these dates is of course that they are the dates when the balance sheet is measured. It doesn’t matter if the currency rates are unproblematic March 1^st if they are problematic March 31^st. Because that is the date when books are closed for Q1 and the date when the balance sheet is measured.
- I have analysed the rated using Excel @Risk, which can fit a probability curve on historical rates. There are, of course, many methods for estimating currency rates and I will get back to that later. But this method has advantages; the basis is actual rates which have actually occurred.
The closest fit to the data was a LapLace-curve ((RiskLaplace (μ,σ) specifies a laplace distribution with the entered μ location and σ scale parameters. The laplace distribution is sometimes called a “double exponential distribution” because it resembles two exponential distributions placed back to back, positioned with the entered location parameter.)) for EUR and a Uniform-curve ((RiskUniform(minimum,maximum) specifies a uniform probability distribution with the entered minimum and maximum values. Every value across the range of the uniform distribution has an equal likelihood of occurrence)) for USD against NOK.

It is always a good idea to ask yourself if the fitted result has a good story behind it. Is it logical? What we want is to find a good estimate for future currency rates. If the logic is hard to see, we should go back and analyze more. But there seems to be a good logic/story behind these estimates in my opinion:
- EUR against NOK is so called mean reverting, meaning that it normally will revert back to a level of around 8 NOK +/- for 1 EUR. Hence, the curve is pointed and has long tails. We most likely will have to pay 8 NOK for 1 EUR, but it can move quite a bit away from the expected mean, both up and down.
- USD is more unpredictable against NOK and a uniform curve, with any level of USD/NOK being as likely, sound like a good estimate.
In addition to the probability curves for USD and EUR an estimate for the correlation between them is needed. I used the same historical data to calculate historical correlation. On the end quarter rates it has been 0,39. A positive correlation means that the rates move the same way – if one goes up, so does the other. The reason is that it was the NOK that moved against both currencies. That’s also a good assessment, I believe. History has shown it to be the case.

Now we have all the information needed to simulate how much at risk our (simple) balance sheet is to adverse currency movements. And based on the simulation, the answer is: Quite a bit.

I have modeled the following covenants:
- Gearing < 1,5
- Equity > 3 000
This is the result of the simulation (click on the image to zoom):

Gearing is the covenant most at risk, as the tables/graphs show. Both in the original mix (all debt in NOK) and if the company is hedging equity there is a high likelihood of breaching the gearing covenant.

There is a probability of 22% in the first case (all debt in NOK) and a probability of 23% in the second (equity-hedge). This is a rather high probability, considering that the NOK may move quite a bit, quit quickly.

The equity is less at risk and the covenant has more headroom. There is a 13% probability for breech with all debt in NOK, but 0% should the company choose either of the two hedging strategies. This is due to the fact that currency loans will reduce risk, regardless of whether debt fully hedges assets, or only partially.

Hence, based on this example it is easy to give advice to the company. The company should hedge gearing by drawing debt in a mix of currencies reflecting its assets. Reality is of course more complex than this example, but the mechanism will be the same. And the need for accurate decision criteria – likelihood of breech – is more important the more complex the business is.

One thing that complicates the picture is the impact different strategies have on the company’s debt. Debt levels may vary substantially, depending on choice of strategy.

If the company has to refinance some of its debt, and at the same time there is a negative impact on the value of the debt (weaker home currency), the refinancing need will be substantially higher than what would have been the case with local debt. This is also answers you can get from the simulation modeling.

The answer to the questions: “How likely is it that the company to breech its covenants and what are the consequences of strategic choices on key figures, debt and equity?” is something really only a good simulation model can give.

Originally published in Norwegian.
20/09/2013
Hedging the balance sheet
This entry is part 5 of 6 in the series Balance simulation

A hedging strategy should be oriented towards hedging the company’s market value to build shareholder value. Normally hedging of balance sheet items is not a good argument for hedging from the shareholders point of view, since a company’s balance sheet not necessarily reflect its market value.

In some cases, however, it may be argued that hedging the balance sheet creates shareholder value, since a lack of hedging may lead to the company breeching covenants in loan agreements. The cost for the shareholders in that case is, as a minimum, increased cost in the form of higher margins on debt. Ultimately, it may mean that the company is technically bankrupt and that the share capital is lost, in which case the shareholders values are lost. Therefore, implicitly this is a hedging strategy which is necessary from the shareholders point of view.

Theoretically it may also be claimed that companies should not hedge at all, as the shareholders may achieve the wanted level of risk by diversifying their portfolios. But in the case of balance sheet risk this is not possible. Since the risk is in the books of the company, it is only in the company the risk may be hedged and have the desired impact on the bankruptcy risk of the company. This is therefore a special case compared to many other risks.

Covenants in loan agreements may warrant hedging to avoid breech solely because of changes in currency rates. Such covenants may for instance be on gearing (debt/equity) or on tangible net worth. If the company has such covenants and not a clear margin on breeching them, it may be necessary to limit or indeed immunize the negative impact from currency movements.

To look at this issue I will look at a company which has assets in currency and all its debt in NOK, its home or functional currency. The initial balance sheet looks like this:

Initial balance sheet

Which hedging strategy the company chooses depends on which covenant is most at risk. There are inherent conflicts between the different hedging strategies, and therefore it is necessary to make a thorough assessment before implementing any such hedging strategy.
- To immunize gearing from any impact of changes in currency rates the company needs to draw debt in currency in the same mix as the currency mix of assets, including assets in the home currency, NOK, like this:
Hedge gearing
- To protect equity against changes in currency rates the company should draw all debt in foreign currency, corresponding to the mix of currency assets ((If the sum of assets is bigger than the sum of debt, the company may in addition use off balance sheet hedging to reach full hedge. If debt is bigger than the sum of foreign currency denominated assets, the company only draws currency debt until it matches the assets. The rest is drawn in NOK)), like so:
Hedge equity

If the company hedges gearing, the size of the equity will be more at risk, since the company hedges a smaller proportion of its assets in foreign currency. And in addition, drawing a larger proportion of debt in the home (or functional) currency may imply an increase in economic risk. Normally a company with foreign assets also has revenue streams in foreign currency, while it by drawing debt in the home currency takes on local cost, thus increasing economic exposure. Hence, if the company does not have to hedge gearing it should hedge its equity.

Choice of hedging strategy will have different results:

Impact on gearing of different hedging strategies

Impact on equity of different strategies

As the graphs show, gearing or equity hedge will have different impact on key figures. However, no hedge at all (all debt in the home currency) will have the biggest impact both on gearing and equity, or tangible net worth:

Overview of impact on key ratios

If the impact on balance sheet values due to movements in currency rates may result in breach of covenants in loan agreements, the risk should therefore be hedged in a way which limits the impact on the most vulnerable figure, be it gearing or equity.

Originally written in Norwegian.
19/09/2013
Risk tolerance

One of the most important concepts within risk management is risk tolerance. Without clearly defining risk tolerance it is virtually impossible to implement good risk management, since we do not know what to measure risk against.

Defining risk tolerance means to define how much risk the business can live with. Risk tolerance is vitally important in choice of strategy and in implementation of the chosen strategy. It may well be that the business is unable to take strategic opportunities because it does not have the ability to carry the risk inherit in the wanted strategy.

The risk carrying ability must therefore be mapped and preferably quantified in the beginning of the strategy process, and throughout the process possible strategic choices must be measured against the risk carrying ability of the business. For example, if the financing ability puts a stop to further expansion, it limits the strategic choices the business may make.

Risk tolerance must be measured against the key figures for which the business is the most vulnerable. To assess risk tolerance as a more or less random number (say, for instance, 1 million) makes it close to impossible to understand risk tolerance in an appropriate way. Hence, the business needs to have a good understanding of what drives its value creation, and also what sets limits on strategic choices. If the most vulnerable key figure for a business is its equity ratio, then risk tolerance needs to be measured against this ratio.

The fact that risk tolerance needs to be measured against something means that it is a great advantage for a business to have models that can estimate risk in a quantitative manner, showing clearly what variables and relationships that have the biggest impact on the key figures most at risk.

Originally published in Norwegian.

08/09/2013
The Most Costly Excel Error Ever?
This entry is part 2 of 2 in the series Spreadsheet Errors

Efficient computing tools are essential for statistical research, consulting, and teaching. Generic packages such as Excel are not sufficient even for the teaching of statistics, let alone for research and consulting (ASA, 2000).

Introduction

Back early in 2009 we published a post on the risk of spreadsheet errors. The reference above is taken from that post, but it seems even more relevant today as show in the following.

Growth in a Time of Debt

In 2010, economists Reinhart and Rogoff released a paper, “Growth in a Time of Debt.” Their “main result was:
1. Average growth rates for countries with public debt over 90% of GDP are roughly 4% lower than when debt is low (under 30% of GDP).
2. Median growth rates for countries with public debt over 90% of GDP are roughly 2.6% lower than the when debt is low (under 30% of GDP).
3. Countries with debt-to-GDP ratios above 90 percent have a slightly negative average growth rate (-0.1%).
The paper has been widely cited by political figures around the world, arguing the case for reduced government spending and increased taxes and ultimately against government efforts to boost the economy and create jobs. All based on the papers conclusion that any short-term benefit in job creation and increased growth would come with a high long-term cost.

Then in 2013, Herndon, Ash and Pollin (Herndon et. al., 2013) replicated the Reinhart and Rogoff study and found that it had:
1. Coding errors in the spreadsheet programming,
2. Selective exclusion of available data, and
3. Unconventional weighting of summary statistics.
All this led to serious errors that inaccurately estimated the relationship between public debt and GDP growth among 20 advanced economies in the post-war period. Instead they found that when properly calculated:

That the average real GDP growth rate for countries carrying a public-debt-to-GDP ratio of over 90 percent is actually 2.2 percent, not -0:1 percent as published in Reinhart and Rogoff.

That is, contrary to the Reinhart and Rogoff study – average GDP growth at public debt/GDP ratios over 90 percent is not dramatically different than when debt/GDP ratios are lower.

Statistics and the use of Excel

Even if the coding error only accounted for a small part of the total error, “everyone” knows that excel is error-prone in a way that any programming language or statistical package is not; it mixes data and code and makes you do things by hand that would be automatically done in the other settings.

Excel is good for ad-hoc calculations where you’re not really sure what you’re looking for, or for a first quick look at the data, but once you really start analyzing a dataset, you’re better off using almost anything else.

Basing important decisions on excel models or excel analysis only is very risky – unless it has been thoroughly audited and great effort has been taken to ensure that the calculations are coherent and consistent.

One thing is certain, serious problems demands serious tools. Maybe it is time to reread the American Statistical Association (ASA) endorsement of “Guidelines for Programs and Departments in Undergraduate Mathematical Sciences”

References

Herndon, T., Ash, M. and Pollin, R. (April 15, 2013). Does High Public Debt Consistently Stifle Economic Growth? A Critique of Reinhart and Rogoff, PERI, University of Massachusetts, Amherst. http://www.peri.umass.edu/fileadmin/pdf/working_papers/working_papers_301-350/WP322.pdf

American Statistical Association (ASA) (2000). Endorsement of the Mathematical Association of America (MAA): “Guidelines for Programs and Departments in Undergraduate Mathematical Sciences” http://www07.homepage.villanova.edu/michael.posner/sigmaastated/ASAendorsement2.html

Baker, D. (16 April 2013) How much unemployment did Reinhart and Rogoff’s arithmetic mistake cause? The Guardian. http://www.guardian.co.uk/commentisfree/2013/apr/16/unemployment-reinhart-rogoff-arithmetic-cause

Reinhart, C.M. & Rogoff, K.S., (2010). Growth in a time of Debt, Working Paper 15639 National Bureau of Economic Research, Cambridge. http://www.nber.org/papers/w15639.pdf
22/04/2013