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Balance simulation – Strategy @ Risk

Strategy @ Risk

Series: Balance simulation

Stochastic Balance Simulation
This entry is part 1 of 6 in the series Balance simulation

Introduction

Most companies have some sort of model describing the company’s operations. They are mostly used for budgeting, but in some cases also for forecasting cash flow and other important performance measures. Almost all are deterministic models based on a single values forecasts; the expected or average value of the input data; sales, cost, interest and currency rates etc. We know however that forecasts based on average values are on average wrong (Savage, 2002). In addition deterministic models will miss the important dimension of uncertainty – that gives both the different risks facing the company and the opportunities they produce.

In contrast, a stochastic model will be calculated a large number of times with different values for the input variable drawn from all possible values of the individual variables. Each run will then give a probable realization of future cash flow or of the company’s equity value etc. With thousands of runs we can plot the relative frequencies of the calculated values:

and thus, we have succeeded in generating the probability distribution for the company’s equity value. In insurance this type of technique is often called Dynamic Financial Analysis (DFA) which actually is a fitting name.

The Balance Simulation Model

The main tool in the S&R toolbox is the balance model. The starting point is the company’s balance, which is treated as the simulations opening balance. In the case of a greenfield project – new factories, power plants, airports, etc. built from scratch – the opening balance is empty.

The successive balances are then built from the Profit & Loss, by simulation of the company’s operation thru an EBITDA model mimicking the real life operations. Investments can be driven by demand (capacity calculations) or by investment programs giving the necessary or planned production capacity. The model will throughout the simulation raise debt (short and/or long term) or equity (domestic or foreign) according to the financial strategy set out by the company and the difference between cash outflow and inflow adjusted for the minimum cash level.

Since this is a dynamic model, it will raise equity when losses occur and/or the maximum Debt/equity ratio has been exceeded. On the other hand it will repay loans, pay dividend, repurchase shares or purchase excess marketable securities (cash above the need for the operations) – all in line with the board’s shareholder strategy.

The ledger and Double-entry Bookkeeping

The activity described in the EBITDA model; investments, purchase of raw materials, production, payment of wages, income from sales, payment of special taxes on investments etc. is registered as transactions in the ledger, following a standard chart of accounts with double-entry bookkeeping. In a similar fashion are all financial transactions; loans repayments, cash, taxes paid and deferred, Agio and Disagio, etc. posted in the ledger. Currently, approximately 400 accounts are in use.

The Trial Balance and the Financial Statements

The trial balance (Post-Closing) is compiled and checked for balance between total debts and total credits. The income statement is then prepared using revenue and expense accounts from the trial balance and the balance sheet is prepared from the asset and liability accounts by including net income with the other equity accounts – using the International Financial Reporting Standards (IFRS).

The general purpose of producing the trial balance is to ensure that the entries in the ledger are mathematically correct. Have in mind that every run in a simulation will produce a number of entries in the ledger and that they might differ not only in size but also in type depending on the realized states of the company’s operations (see above). We therefore need to be sure that the final financial statements – for every run – are correctly produced, since they will be the basis for all further financial analysis of the company.

There are of course other sources of errors in book keeping; compensating errors, errors of omission, errors of principle etc. but after many years of use – with millions of runs – we feel confident that the ledger and financial statements are produced correctly. The point is that serious problems need serious models.

However there are more benefits to be had from simulating the ledger and trial balance:
1. It increases the models transparency; the trial balance can be printed out and audited. Together with the models extensive reporting and error/consistency control, it is no longer a ‘black box’ to the user.
2. It makes it easy to plug inn new EBITDA models for other types of industry giving an automated check for consistency with the main balance simulation model.
3. It is used to ensure correct solving of all implicit equations in the model, the most obvious is of course the interest and bank balance equation (interest depends on the bank balance and the bank balance depends on the interest) but others like translation hedging and limits set by the company’s financial strategy, create large and complicated systems of simultaneous equations.
4. The trial balance changes from year to year are also used to ensure correct year to year balance transition.
Financial Analysis, Financial Measures and Valuation

Given the framework described above financial analysis can be performed and the expected value, variability and probability distributions for the different types of ratios; profitability, liquidity, activity, debt and equity etc. can be calculated and given as graphs. All important measures are calculated at least twice from different starting points to ensure consistency and correct solving of implicit equations.

The following table shows the reconciliation of Economic Profit, initially calculated from (ROIC-WACC) multiplied with Invested capital:

The motivation for doing all these consistency controls – in all nearly one hundred – lies in previously experience from Cash Flow/ Valuation models written in Excel. The level of detail is more often than not so low that there is no way to establish if they are right or wrong.

More interesting than ratios, are the yearly distributions for EBITDA, EBIT, NOPLAT, Profit (loss) for the period, Free cash Flow, Economic profit, ROIC, Wacc, Debt and Equity and Equity value etc. giving a visual picture of the uncertainties and risks the company faces:

Financial analysis is the conversion of financial data into useful information for decision making. Therefore, virtually any use of financial statements or other financial data for some purpose is financial analysis and is the primary focus of accounting and finance. Financial analysis can be internal (e.g., decision analysis by a company using internal data to understand or improve management and operating results) or external (e.g., comprehensive analysis for the purposes of commercial lending, mergers and acquisition or investment activities). The key is how to analysis available data to make correct decisions.

Input

As input the model needs parameter values and operational data. The parameter values fall in seven groups:
1. Parameters describing investors preferences; Market risk premium etc.
2. Parameters describing the company’s financial strategy; Leverage, Long/Short-term Debt ratio, Expected Foreign/ Domestic Debt Ratio, Economic Depreciation, Maximum Dividend Pay-out Ratio, Translation Hedging Strategy etc.
3. Parameters describing the economic regime under which it operates: Taxes, Depreciation Scheme etc.
4. Opening Balance etc.
Since the model have to produces stochastic forecasts of interest(s) and exchange rates it will need for every currency involved (included lower and upper 5% probability limit):
1. The Yield curves,
2. Expected yearly inflation
3. Depending on the forecast method(s) chosen for the exchange rates; the different currencies expected risk premiums or real exchange rates etc.
Since there is a large number of parameters they are usually read from an excel template but the program will if necessary ask for missing or report inconsistent values of the parameters.

The company’s operations are best described through an EBITDA model even if prices, costs and production coefficients and their variability can be read from an excel template. A dedicated EBITDA model will always give the opportunity to give a more detailed and in some cases complex description of the operations, include forecast and demand models, ‘exotic’ taxes, real options strategies etc., etc.

Output

S@R has set out to create models that can give answers to both deterministic and stochastic questions the tables will answer most deterministic issues while graphs must be used to answer the risk and uncertainty related questions:

[TABLE=6]

1.   In all 27 different reports with more than 70 pages describing operations and the economics of operations.
2.   In addition the probability distributions for all input and output variables are produced.

Use

By linking dedicated EBITDA models to holistic balance simulation, taking into account all important factors describing the company. The basis is a real balance simulation model – not a simple cash flow forecast model.

Both the deterministic and stochastic balance simulation can be set about in two different alternatives:
1.   by a using a EBITDA model to describe the companies operations or
2.   by using coefficients of fabrications (e.g. kg flour pr 1000 bread etc.) as direct input to the balance model.

The first approach implies setting up a dedicated EBITDA performance and uncertainty, but entails a higher degree of effort from both the company and S@R.

The use of coefficients of fabrications and their variations is a low effort (cost) alternative, using the internal accounting as basis. This will in many cases give a ‘good enough’ description of the company – its risks and opportunities: The data needed for the company’s economic environment (taxes, interest rates etc.) will be the same in both alternatives.

In some cases we have used both approaches for the same client, using the last approach for smaller daughter companies with production structures differing from the main companies.
The second approach can also be considered as an introduction and stepping stone to a more holistic EBITDA model.
What problems do we solve?
- The aim regardless of approach is to quantify not only the company’s single and aggregated risks, but also the potential, thus making the company capable to perform detailed planning and of executing earlier and more apt actions against risk factors.
- This will improve stability to budgets through higher insight in cost side risks and income-side potentials. This is achieved by an active budget-forecast process; the control-adjustment cycle will teach the company to better target realistic budgets – with better stability and increased company value as a result.
- Experience shows that the mere act of quantifying uncertainty throughout the company – and thru modeling – describe the interactions and their effects on profit, in itself over time reduces total risk and increases profitability.
- This is most clearly seen when effort is put into correctly evaluating strategies-projects and investments effects on the enterprise. The best way to do this is by comparing and choosing strategies by analyzing the individual strategies risks and potential – and select the alternative that is dominant (stochastic) given the company’s chosen risk-profile.
- Our aim is therefore to transform enterprise risk management from only safeguarding enterprise value to contribute to the increase and maximization of the firm’s value within the firm’s feasible set of possibilities.
Strategy@Risk takes advantage of a program language developed and used for financial risk simulation. We have used the program language for over 25years, and developed a series of simulation models for industry, banks and financial institutions.

The language has as one of its strengths, to be able to solve implicit equations in multiple dimensions. For the specific problems we seek to solve, this is a necessity that provides the necessary degrees of freedom to formulate the approach to problems.

The Strategy@Risk tools have highly advance properties:
- Using models written in dedicated financial simulation language (with code and data separated; see The risk of spreadsheet errors).
- Solving implicit systems of equations giving unique WACC calculated for every period ensuring that “Free Cash Flow” always equals “Economic Profit” value.
- Programs and models in “windows end-user” style.
- Extended test for consistency in input, calculations and results.
- Transparent reporting of assumptions and results.
References

Savage, Sam L. “The Flaw of Averages”, Harvard Business Review, November 2002, pp. 20-21

Mukherjee, Mukherjee (2003). Financial Accounting. New York: Harper Perennial, ISBN 9780070581555.
24/05/2010
Corporate Risk Analysis

This entry is part 2 of 6 in the series Balance simulation

Strategy @Risk has developed a radical and new approach to the way risk is assessed and measured when considering current and future investment. A key part of our activity in this sensitive arena has been the development of a series of financial models that facilitate understanding and measurement of risk set against a variety of operating scenarios.

We have written a paper which outlines our approach to Corporate Risk Analysis to outline our approach. Read it here.

Our purpose in this paper is to show that every item written into a firm’s profit and loss account and its balance sheet is a stochastic variable with a probability distribution derived from probability distributions for each factor of production. Using this approach we are able to derive a probability distribution for any measure used in valuing companies and in evaluating strategic investment decisions. Indeed, using this evaluation approach we are able to calculate expected gain, loss and probability when investing in a company where the capitalized value (price) is known.

03/02/2009
Planning under Uncertainty

This entry is part 3 of 6 in the series Balance simulation

‘Would you tell me, please, which way I ought to go from here?’ (asked Alice)
‘That depends a good deal on where you want to get to,’ said the Cat.
‘I don’t much care where—‘said Alice.
‘Then it doesn’t matter which way you go,’ said the Cat.
– Lewis Carroll, Alice’s Adventures in Wonderland

Let’s say that the board have sketched a future desired state (value of equity) of the company and that you are left to find if it is possible to get there and if so – the road to take. The first part implies to find out if the desired state belongs to a set of feasible future states to your company. If it does you will need a road map to get there, if it does not you will have to find out what additional means you will need to get there and if it is possible to acquire those.

The current state (equity value of) your company is in itself uncertain since it depends on future sales, costs and profit – variable that usually are highly uncertain. The desired future state is even more so since you need to find strategies (roads) that can take you there and of those the one best suited to the situation. The ‘best strategies’ will be those that with highest probability and lowest costs will give you the desired state that is, that has the desired state or a better one as a very probable outcome:

Each of the ‘best strategies’ will have many different combinations of values for the variables –that describe the company – that can give the desired state(s). Using Monte Carlo simulations this means that a few, some or many of the thousands of runs – or realizations of future states-will give equity value outcomes that fulfill the required state. What we need then is to find how each of these has come about – the transition – and select the most promising ones.

The S@R balance simulation model has the ability to make intermediate stops when the desired state(s) has been reached giving the opportunity to take out complete reports describing the state(s) and how it was reached and by what path of transitional states.

The flip side of this is that we can use the same model and the same assumptions to take out similar reports on how undesirable states were reached – and their path of transitional states. This set of reports will clearly describe the risks underlying the strategy and how and when they might occur.

The dominant strategy will then be the one that has the desired state or a better one as a very probable outcome and that have at the same time the least probability of highly undesirable outcomes (the stochastic dominant strategy):

Mulling over possible target- or scenario analysis; calculating backwards the value of each variable required to meet the target is a waste of time since both the environment is stochastic and a number of different paths (time-lines) can lead to the desired state:

And even if you could do the calculations, what would the probabilities be?

Carroll, L., (2010). Alice‘s Adventures in Wonderland -Original Version. City: Cosimo Classics.

07/12/2010
Introduction to Simulation Models
This entry is part 4 of 6 in the series Balance simulation

Simulation models sets out to mimic real life company operations, that is describing the transformation of raw materials and labor to finished products in such a way that it can be used as support for strategic decision making.

A full simulation model will usually consist of two separate models:
1. an EBITDA model that describes the particular firm’s operations and
2. an generic P&L and Balance simulation model (PL&B).
The EBITDA model ladder

Both the deterministic and stochastic balance simulation can be approached as a ladder with two steps, where the first is especially well suited as an introduction to risk simulation and the second gives a full blown risk analysis. In these successive steps the EBITDA calculations will be based on:
1. financial information only, by using coefficients of fabrications and unit prices (e.g. kg flour per 1000 bread and cost of flour per kg, etc.) as direct input to the balance model – the direct method and
2. EBITDA models to give a detailed technical description of the company’s operations.
The first step uses coefficients of fabrications and their variations give a low effort (cost) alternative, usually using the internal accounting as basis. In many cases, this will often give a ‘good enough’ description of the company – its risks and opportunities. It can be based on existing investment and market plans. The data needed for the company’s economic environment (taxes, interest rates etc.) will be the same in both alternatives.

This step is especially well suited for introduction to risk simulation and the art of communicating risk and uncertainty throughout the firm. It can also profitably be used in cases where time and data is limited and where one wishes to limit efforts in an initial stage. Data and assumptions can later be augmented to much more sophisticated analyses within the same framework. This way the analysis can be successively built in the direction the previous studies suggested.

The second step implies setting up a dedicated EBITDA subroutine to the balance model. This can then give detailed answers to a broad range of questions about markets, capacity driven investments, operational performance and uncertainty, but entails a higher degree of effort from both the company and S@R. This is a tool for long-term planning and strategy development.

The EBITDA model can both be a stand-alone model and a subroutine to the PL&B model. The stand-alone EBITDA model can be used to in detail study the firm’s operations and how different operational strategies will or can affect EBITDA outcomes and distribution.

When connected to the PL&B model it will act as a subroutine giving the necessary information to produce the P&L and ultimately the Balance and the – outcomes distributions.

This gives great flexibility in model formulations and the opportunity to fit models to different industries and accommodate for the data available.

P&L and Balance simulation

The generic PL&B model – based on the IFRS standard – can be used for a wide range of business activities both:
1. describes the firm’s financial environment (taxes, interest rates, currency etc.) and
2. acts as a testing bed for financial strategies (hedging, translation risk, etc.)
Since S@R has set out to create models that can give answers to both deterministic and stochastic questions thus the PL&B model is a real balance simulation model – not a simple cash flow forecast model.

All runs in the simulation produces a complete P&L and Balance it enables uncertainty curves (distributions) for any financial metric like ‘Yearly result’, ‘free cash flow’, economic profit’, ‘equity value’, ‘IRR’ or’ translation gain/loss’ etc. to be produced.
People say they want models that are simple, but what they really want is models with the necessary features – that are easy to use. If something is complex but well designed, it will be easy to use – and this holds for our models.

The results from these analyses can be presented in different forms from detailed traditional financial reports to graphs describing the range of possible outcomes for all items in the P&L and Balance (+ much more) looking at the coming one to five (short term) or five to fifteen years (long term) and showing the impacts to e.g. equity value, company value, operating income etc.

The goal is to find the distribution for the firm’s equity value which will incorporate all uncertainty facing the firm.

This uncertainty gives both shape and location of the equity value distribution, and this is what we – if possible – are aiming to change:
1. reducing downside risk by reducing the left tail (blue curve)
2. increasing expected company value by moving the curve to the right (green curve)
3. increasing the upside potential by increasing the right tail (red curve) etc.
The Data

To be able to simulate the operations we need to put into the model all variables that will affect the firm’s net yearly result. Most of these will be collected by S@R from outside sources like central banks, local authorities and others, but some will have to be collected from the firm.

The production and firm specific variables are related to every day’s activities in the firm. Their historic values can be collected from internal accounts or from production reports. Someone in the procurement-, production- or sales department will have their records and most always the controllers. The rest will be variables inside the domain of the CEO and the company treasurer.

The variables fall in five groups:

i.      general variables describing the firm’s financial environment ,
ii.      variables describing the firms strategy,
iii.      general variables used for forecasting purposes,
iv.      direct problem related variables and
v.      the firm specific:

a. production coefficients and

b. cost of raw materials and labor related variables.

The first group will contain – for all countries either delivering raw materials or buying the finished product (s) – variables like: taxes, spot exchange rates etc. For the firm’s domestic country it will in addition contain variables like: Vat rates, taxes on investments and dividend income, depreciation rates and method, initial tax allowances, overdraft interest rates etc.

The second group will contain variables like: minimum cash levels, debt distribution on short and long term loans and currencies, hedge ratios, targeted leverage, economic depreciation etc.

The third group will contain variables needed for forecasting purposes: yield curves, inflation forecasts, GDP forecasts etc. The expected values and their 5 % and 95 % probability limits will be used to forecast exchange rates, interest rates, demand etc. They will be collected by S@R.

The fourth group will contain variables related to sales forecasts: yearly air temperature profiles (and variation) for forecasting beer sales and yearly water temperature profiles (and variation) for forecasting increase in biomass in fish farming.

The fifth group will contain variables that specify the production and costs of production. They will vary according to the type of operations e.g.: operating rate (%), max days of production, tools maintenance (h per 10.000 units) , error rate (errors per 1000 units), waste (% of weight of prod unit), cycle time (units per min), number of machines per shift (#), concession density (kg per m³), feed rates (%), mortality rates (%) etc., etc.. This variable specifies the production and will they be stochastic in the sense that they are not constant but will vary inside a given – theoretical or historic – range.

To simulate costs of production we use the coefficients of fabrication and their unit costs. Both the coefficients and their unit costs will always be of stochastic nature and they can vary with capacity utilization: energy per unit produced (kwh/unit) and energy price (cost per Kwh), malt use (kg per hectoliter), malt price (per kg), maximum takeoff weight (ton), takeoff charge (per ton), specific consumption of wood, (m³/Adt), cost of round wood (per m³), etc., etc.

The uncertainty (and risk) stemming from all groups of variables will be propagated through the P&L and down to the Balance, ending up as volatility in the equity distribution.

The aim is to estimate the economic impact that such uncertainty may have on corporate earnings at risk. This will add a third dimension – probability – to all forecasts, give new insight, and the ability to deal with uncertainties in an informed way – and thus benefits above ordinary spread-sheet exercises.

Methods

To be able to add uncertainty to financial models, we also have to add more complexity. This complexity is inevitable, but in our case, it is desirable and it will be well managed inside our models.

Most companies have some sort of model describing the company’s operations. They are used mostly for budgeting, but in some cases also for forecasting cash flow and other important performance measures.

If the client already has spread sheet models describing the operations, we can build on this. There is no reason to reinvent what has already been done – thus saving time and resources that can be better utilized in other phases of the project.

We know however that forecasts based on average values are on average wrong. In addition will deterministic models miss the important uncertainty dimension that gives both the different risks facing the company and the opportunities they bring forth.

An interesting feature is the models ability to start simulations with an empty opening balance. This can be used to assess divisions that do not have an independent balance since the model will call for equity/debt etc. based on a target ratio, according to the simulated production and sales and the necessary investments. Questions about further investment in divisions or product lines can be studied this way.

In some cases, we have used both approaches for the same client, using the last approach for smaller daughter companies with production structures differing from the main companies.

The first approach can also be considered as an introduction and stepping-stone to a more complete EBITDA model and detailed simulations.

Time and effort

The work load for the client is usually limited to a small team of people ( 1 to 3 persons) acting as project leaders and principal contacts, assuring that all necessary information, describing value and risks for the clients’ operations can be collected as basis for modeling and calculations. However, the type of data will have to be agreed upon depending on the scope of analysis.

Very often, key people from the controller group will be adequate for this work and if they do not have the direct knowledge, they usually know whom to ask. The work for this team, depending on the scope and choice of method (see above) can vary in effective time from a few days to a couple of weeks, but this can be stretched from three to four weeks to the same number of months – depending on the scope of the project.

For S&R, the period will depend on the availability of key personnel from the client and the availability of data. For the second alternative, it can take from one to three weeks of normal work to three to six months for the second alternative for more complex models. The total time will also depend on the number of analyses that needs to be run and the type of reports that has to be delivered.

The team’s participation in the project also makes communication of the results up or down in the system simpler. Since the input data is collected by templates this gives the responsible departments and persons, ownership to assumptions, data and results. These templates thus visualize the flow of data thru the organization and the interdependence between the departments – facilitating the communication of risk and the different strategies both reviewed and selected.

No knowledge or expertize on uncertainty calculations or statistical methods is required from the clients side. The team will thru ‘osmosis’ acquires the necessary knowledge. Usually the team finds this as an exciting experience.
09/12/2011
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
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