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Strategy @ Risk

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Plans based on average assumptions ……
This entry is part 3 of 4 in the series The fallacies of scenario analysis

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 ((Most likely estimates are often made in-house based on experience and knowledge about their operations.)) or average values ((Forecasts for many types of variable can be bought from suppliers of ‘consensus forecasts’.)) (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:

Using the average ((The bin containing the average in the histogram.)) 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
01/03/2011
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
Working Capital and the Balance Sheet

This entry is part 2 of 3 in the series Working Capital

The conservation-of-value principle says that it doesn’t matter how you slice the financial pie with financial engineering, share repurchases, or acquisitions; only improving cash flows will create value. (Dobbs, Huyett & Koller, 2010).

The above, taken from “The CEO’s guide to corporate finance” will be our starting point and Occam’s razor the tool to simplify the balance sheet using the concept of working- and operating capital.

To get a better grasp of the firm’s real activities we will as well separate non-operating assets from operating assets – since it will be the last that defines the firm’s operations.

To find the amount of operating current assets we have to deduct the sum of minimum cash level, inventories and account receivables from total current assets. The difference between total- and operating current assets is assumed placed in excess marketable securities – and will not be included in the working capital.

Many firms have cash levels above and well beyond what is really needed as working capital, tying up capital that could have had better uses generating higher return than mere short-term placements.

The net working capital now found by deducting non-interest bearing current liabilities from operating current assets, will be the actual amount of working capital needed to safely run the firms operations – no more and no less.

By summing net property, plant and equipment and other operating fixed assets we find the total amount of fixed assets involved in the firm’s operations. This together with net working capital forms the firms operating assets, assets that will generate the cash flow and return on equity that the owners are expecting.

The non-operating part – excess marketable securities and non-operating investments – should be kept as small as possible, since this at best only will give an average market return. The rest of the above calculations give us the firm’s total liability and equity, which we will use to set up the firm’s ordinary balance sheet:

However, by introducing operating-, non-operating- and working capital we can get a clearer picture of the firm’s activities ((Used in yearly reports by Stora Enso, a large international Pulp & Paper company, noted on NASDAQ OMX in Stockholm and Helsinki.)):

The balance sheet’s bottom line has been reduced by the smallest value of operating current assets and non-interest bearing debt and the difference between them – the working capital – will be an asset or a liability depending on which of them that have the largest value:

The above calculations is an integral part of our balance simulation model and the report that can be produced for planning, strategy- and risk assessment from the simulation can be viewed her; report for the most likely outcome (Pdf, pp 32). However this report can be produced for every run in the simulation giving the opportunity to look at tail events that might arise, distorting expectations.

Simplicity is the ultimate sophistication. — Leonardo da Vinci

References

Dobbs, D, Huyett, H, & Koller, T. (2010). The ceo’s guide to corporate finance. McKinsey Quarterly, 4. Retrieved from http://www.mckinseyquarterly.com/home.aspx

Endnotes

01/12/2010
Uncertainty modeling
This entry is part 2 of 3 in the series What We Do

Prediction is very difficult, especially about the future.
Niels Bohr. Danish physicist (1885 – 1962)

Strategy @ Risks models provide the possibility to study risk and uncertainties related to operational activities; cost, prices, suppliers, markets, sales channels etc. financial issues like; interest rates risk, exchange rates risks, translation risk , taxes etc., strategic issues like investments in new or existing activities, valuation and M&As’ etc and for a wide range of budgeting purposes.

All economic activities have an inherent volatility that is an integrated part of its operations. This means that whatever you do some uncertainty will always remain.

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

The results from these analyzes can be presented in form of B/S and P&L looking at the coming one to five (short term) or five to fifteen years (long term); showing the impacts to e.g. equity value, company value, operating income etc. With the purpose of:
- Improve predictability in operating earnings and its’ expected volatility
- Improve budgeting processes, predicting budget deviations and its’ probabilities
- Evaluate alternative strategic investment options at risk
- Identify and benchmark investment portfolios and their uncertainty
- Identify and benchmark individual business units’ risk profiles
- Evaluate equity values and enterprise values and their uncertainty in M&A processes, etc.
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.

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.

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 expected or average values of input data; sales, cost, interest and currency rates etc.

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.

S@R has set out to create models that can give answers to both deterministic and stochastic questions, 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 ‘short cut’ method.
The first approach implies setting up a dedicated Ebitda subroutine to the balance model. This will 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 second (‘the short cut’) uses coefficients of fabrications and their variations, and is a low effort (cost) alternative, usually using the internal accounting as basis. This will in many cases 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:

The ‘short cut’ approach is especially suited for quick appraisals of M&A cases where time and data is limited and where one wishes to limit efforts in an initial stage. Later the data and assumptions can be augmented to much more sophisticated analysis within the same ‘short cut’ framework. In this way analysis can be successively built in the direction the previous studies suggested.

This also makes it a good tool for short-term (3-5 years) analysis and even for budget assessment. Since it will use a limited number of variables – usually less than twenty – describing the operations, it is easy to maintain and operate. The variables describing financial strategy and the economic environment come in addition, but will be easy to obtain.

Used in budgeting it will give the opportunity to evaluate budget targets, their probable deviation from expected result and the probable upside or down side given the budget target (Upside/downside ratio).

Done this way analysis can be run for subsidiaries across countries translating the P&L and Balance to any currency for benchmarking, investment appraisals, risk and opportunity assessments etc. The final uncertainty distributions can then be “aggregated’ to show global risk for the mother company.

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.

Since all runs (500 to 1000) in the simulation produces a complete P&L and Balance the uncertainty curve (distribution) for any financial metric like ‘Yearly result’, ‘free cash flow’, economic profit’, ‘equity value’, ‘IRR’ or’ translation gain/loss’ etc. can be produced.

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.

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 will key people from the controller group be adequate for this work and if they don’t have the direct knowledge they usually know who 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.

For S&R the time frame 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 first alternative for more complex models. The total time will also depend on the number of analysis that needs to be run and the type of reports that has to be delivered.

Selecting strategy

Models like this are excellent for selection and assessment of strategies. Since we can find the probability distribution for equity value, changes in this brought by different strategies will form a basis for selection or adjustment of current strategy. Models including real option strategies are a natural extension of these simulation models:

If there is a strategy with a curve to the right and under all other feasible strategies this will be the stochastic dominant one. If the curves crosses further calculations needs to be done before a stochastic dominant or preferable strategy can be found:

Types of problems we aim to address:

The effects of uncertainties on the P&L and Balance and the effects of the Boards strategies (market, hedging etc.) on future P&L and Balance sheets evaluating:
- Market position and potential for growth
- Effects of tax and capital cost
- Strategies
- Business units, country units or product lines – capital allocation – compare risk, opportunity and expected profitability
- Valuations, capital cost and debt requirements, individually and effect on company
- The future cash-flow volatility of company and the individual BU’s
- Investments, M&A actions, their individual value, necessary commitments and impact on company
- Etc.
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 uncertain factors.

Used in budgeting, this will improve budget stability 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.

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.

A severe depression like that of 1920-1921 is outside the range of probability. –The Harvard Economic Society, 16 November 1929
24/11/2010
Working Capital Strategy

This entry is part 1 of 3 in the series Working Capital

Passion is inversely proportional to the amount of real information available. See Benford’s law of controversy.

The annual “REL ((REL Consultancy. (2010). Wikipedia. Retrieved October 10, 2010, from http://en.wikipedia.org/wiki/REL_Consultancy)) /CFO Working Capital Survey” made its debut in 1997 in the CFO Magazine. The magazine identifies working capital management as one of the key issues facing financial executives in the 21st century (Filbeck, Krueger, & Preece, 2007).

The 2010 Working Capital scorecard (Katz, 2010) and its accompanying data ((http://www.cfo.com/media/201006/1006WCcompletev2.xls)) gives us an opportunity to look at working capital management ((Data from 1,000 of the largest U.S. public companies)); that is the effect of working capital management on the return on capital employed (ROCE):

or,

From the last formula we can see that – all else kept constant – a reduction in net operating working capital should imply an increased return on capital employed.

Gross and Net Operating Working Capital

A firm’s gross working capital comprises its total current assets. One part of it will consist of financial current assets held for various reasons other than operational, and the other part of receivables from operations and the inventory and cash necessary to run these operations. It is this last part that interests us.

The firm’s operations will have been long term financed by equity from owners and by loans from lenders. Firms usually also have short term financing from banks (short term credit + overdraft facilities/ credit lines) and most always from suppliers by trade credit. The rest of the current liabilities; current tax and dividends will not be considered as parts of operating current liabilities, since they comprises only non recurrent payments.

Net working capital is defined as the difference between current assets and current liabilities (see figure below). It can be both positive and negative depending on the firm’s strategic position in the market.

However usually a positive net working capital is required to ensure that the firm is able to continue its operations and that it has sufficient funds to satisfy both maturing short-term debt and upcoming operational expenses. In the following we assume that any positive net working capital is held as cash and that all excess cash is held as marketable securities.

By removing from both current assets and liabilities all items not directly related to and necessary for the operations, we arrive at net operating working capital as the difference between operating current assets and operating current liabilities:

Net operating working capital = Operating current assets – Operating current liabilities

Since the needed amount of working capital will differ between industries and be dependent on company size it will be easier to base comparisons on the cash conversion cycle.

Working Capital Management

Working capital management is the administration of current assets as well as current liabilities. It is the main part of a firm’s short-term financial planning since it involves the management of cash, inventory and accounts receivable. Therefore, working capital management will reflect the firm’s short-term financial performance.

Current assets often account for more than half of a company’s total assets and hence, represent a major investment for small firms as they can not be avoided in the same way as investments in fixed assets can – by renting or leasing. A large inventory will tie up capital but it prevents the company from lost sales or production stoppages due to stock-out. A high level of current assets hence means less risk to the company but also lower earnings due to higher capital tie-up – the risk-return trade-offs (Weston & Copeland, 1986).

Since the needed amount of working capital will differ between industries and also will be dependent on company size it will be easier to base comparisons of working capital management between companies and industries on their cash conversion cycle (CCC).

The Cash Conversion Cycle

The term “cash conversion cycle” (CCC) refers to the time span between a firm’s disbursing and collecting cash and will thus be ‘unrelated’ to the firm’s size, but be dependent on the firm’s type of business (see figure below).

Companies that have high inventory turnover and do business on a cash basis – usually have a low or negative CCC and hence needs very little working capital.

For companies that make investment products the situation is a completely different. As these types of businesses are selling expensive items on a long-term payment basis, they will tend to have a high CCC and must keep enough working capital on hand to get through any unforeseen difficulties.

The CCC cannot be directly observed in the cash flows, because these are also influenced by investment and financing activities and must be derived from the firm’s balance sheet:

+ Inventory conversion period (DSI)
+ Receivables conversion period (DSO)
– Payable conversion period (DPO)
= Cash Conversion Cycle (days)

Where:

DSI = Days sales of inventory, DSO = Days sales outstanding, DPO = Days payable outstanding, WIP = Work in progress, Period = Accounting period and COGS = Cost of goods sold ((COGS = Opening inventory + Purchase of goods – Closing inventory)) or:

+ Average inventory+WIP / [COGS/days in period]
+ Average Accounts Receivable / [Revenue / days in period]
+ Average Accounts Payable / [(Inventory increase + COGS)/ days in period]
= Cash Conversion Cycle (days)

The Observations

Even if not all of the working capital is determined by the cash conversion cycle, there should be a tendency for higher return on operating capital with lower CCC. However the data from the annual survey (Katz, 2010) does not support this ((Data used with permission from REL/CFO. Twenty of the one thousand observations have been removed as outliers, to give a better picture of the relation)):

The scatter graph shows no direct relation between return on operating capital and the cash conversion cycle. A closer inspection of the data for the surveys different industries confirms this.

Since the total amount of capital invested in the CCC is:

and is thus a function of sales. The company size will then certainly play a role when we only look at the yearly data. The survey however also gives the change from 2008 to 2009 for all the companies so we are able to remove the size effect by looking at the changes (%) in ROCE by a change in CCC:

The graph still shows no obvious relation between change (%) in CCC and change (%) in ROCE. Now, we know that the shorter this cycle, the fewer resources the company needs to lock-up; reduced debtor levels (DSO), decreased inventory levels (DSI) and/or increased creditor levels (DPO) must have an effect on the ROCE – but will it be lost in the clutter of all the other company operations effects on the ROCE?

Cash Management

Net operating working capital is the cash plus cash equivalents needed to pay for the day-to-day operation of the business. This will include; demand deposits, money market accounts, currency holdings and highly liquid short-term investments such as marketable securities ((Marketable securities with a maturity of less than three months are referred to as ‘cash equivalents’ on the balance sheet, those with a longer maturity as ‘short-term investments’)); portfolios of highly liquid, near-cash assets which serves as a backup to the cash account.

There are many reasons why holding cash is important; to act as a buffer when daily cash flows do not match cash out flows (Transaction motive), as a safety stock to face forecast errors and unforeseen expenses (Precautionary motive) or to be able to react immediately when opportunities can be taken (Speculative motive). If the cash level is too low and unexpected outflows occurs, the firm will have to either borrow funds or in the case of an investment – forgo the opportunity.

Such short-term borrowing of funds can be costly as can a lost opportunity by the lost returns of rejected investments. Holding cash however also induces opportunity costs due to loss of interest.

Cash management therefore aim at optimizing cash availability and interest income on any idle funds. Cash budgeting – as a part of the firm’s of short-term planning – constitutes the starting-point for all cash management activities as it represents the forecast of cash in- and outflows and therefore reflects the firm’s expected availability and need for cash.

Working Capital Strategy

We will in the following look closer at working capital management using balance simulation ((In the Monte Carlo simulation we have used 200 runs, as that was sufficient to give a good enough approximation of the distributions)). The data is from a company with large fixed assets in infrastructure. The demand for its services is highly seasonal as schematic depicted in the figure below:

A company like this will need a flexible working capital strategy with a low level of working capital in the off-seasons and high levels in the high seasons. As the company wants to maximize its equity value it is looking for working capital strategies that can do just that.

The company has been working on its cash conversion cycle, and succeeded in that with on average of only 11,1 days 1M (standard deviation 0,2 days) (across seasons) for turning supplied goods and services into cash:

All the same, even then a substantial amount, on average €4,1M (standard deviation €1,8M) of the company’s resources, is invested in the cash conversion cycle:

In addition the company needs a fair amount of cash to meet its other obligations. Its first strategy was to keep cash instead of using short term financing in the high seasons. In the off-seasons this strategy gives a large portfolio of marketable securities – giving a low return and thereby a low contribution to the ROCE. This strategy can be described as being close to the red line in the seasonal graph above.

When we now plot the two hundred observed (simulated) values of working capital and the corresponding ROE (from now we use return on equity (ROE) since this of more interest to the owners), we get a picture as below:

This lax strategy shows little relation between the amount of working capital and the ROE and – from just looking at the graph it would be easy to conclude that working capital management is a waste of time and effort.

Now we turn to a stricter strategy: keeping a low level of cash through all seasons, using short term financing in the high seasons and always have cash closely connected to expected sales. Again plotting the two hundred observed values we get the graph below:

From this graph we can clearly see that if we can reduce the working capital we will increase the ROE – even if we live in a stochastic environment. By removing some of the randomness in the amount of working capital by keeping it close to what is absolutely needed – we get a much clearer picture of the effect. This strategy is best described as being close to the green line in the seasonal graph.

Since we use pseudo-random ((Pseudo random number generator (PRNG), also known as a deterministic random bit generator, is an algorithm for generating a sequence of numbers that approximates the properties of random numbers. The sequence is not truly random in that it is completely determined by a set of initial values, called the seed number)) simulation we have replicated the first simulation (blue line), for the stricter strategy (green line).

This means that the same events happened for both strategies; changes in sale, prices, costs, interest and exchange rates etc. The effects for the amount of working capital are shown in the graph below:

The lax strategy (blue line) will have an average working capital of €4,8M with a standard deviation of €3.0M, while the strict strategy (green line) will have an average working capital of €1,4M with a standard deviation of €3.3M.

Even if the stricter strategy seems to associate lower amounts of working capital with higher return to equity (se figure) and that the amount of working capital always is lower than under the laxer strategy, we have not yet established that it is a better strategy.

To do this we need to simulate the strategies over a number of years and compare the differences in equity value under the two strategies. Doing this we get the probability distribution for difference in equity value as shown below:

The expected value of the strict strategy over the lax strategy is €3,4 M width a standard deviation of €6,1 M. The distribution is skewed to the right, so there is also a possible additional upside. From this we can conclude that the stricter strategy is stochastic dominant to the laxer strategy. However there might be other strategies that can prove to be better.

This brings us to the question: does an optimal working capital strategy exist? What we do know that there will be strategies that are stochastic dominant, but proving one to be optimal might be difficult. Given the uncertainty in any firm’s future operations, you will probably first have to establish a set of strategies that can be applied depending on the set of events that can be experienced by the firm.

References

Filbeck, G, Krueger, T, & Preece, D. (2007). Cfo magazine’s “working capital survey”: do selected firms work for shareholders?. Quarterly Journal of Business and Economics , (March), Retrieved from http://www.allbusiness.com/company-activities-management/financial/5846250-1.html

Katz, D.M.K. (2010). Working it out: The 2010 Working Capital Scorecard. CFO Magazine, June, Retrieved from http://www.cfo.com/article.cfm/14499542

Weston, J. & Copeland, T. (1986). Managerial finance, Eighth Edition, Hinsdale, The Dryden Press

Footnotes

18/10/2010
Solving Uncertainty in Simulation Models
I shall be telling this with a sigh
Somewhere ages and ages hence:
Two roads diverged in a wood, and I–
I took the one less travelled by,
And that has made all the difference

…Robert Frost, 1916

Uncertainty in your operations is most likely complex and will need systematic treatment through simulation modeling. S@R carries out thorough analysis of companies risk and uncertainties with aim of producing good decision support tools. Making sure the client takes a huge step forward from scenario analysis.

The Four Levels of Uncertainty

The uncertainty that remains after the best possible analysis has been done is what we call residual uncertainty (Courtney, Kirkland & Viguerie, 1997).

In our world ‘the best possible analysis’ means that we have a model ‘good enough’ to describe the business under study. The question then is – do we need to take into account the uncertainties that always will be inherent in its operations and markets? And if we have to, is it possible?

A useful distinction between the different situations that can arise is given by Courtney et al. as four levels of residual uncertainty (see figure below, McKinsey Quarterly, Dec. 2008):
1. A Clear-Enough Future; managers can develop a single forecast of the future that is precise enough for strategy development.
2. Alternate Futures; the future can be described as one of a few discrete scenarios. Analysis cannot identify which outcome will occur, although it may help establish probabilities.
3. A Range of Futures; a range of potential futures can be identified. That range is defined by a limited number of key variables, but the actual outcome may lie anywhere along a continuum bounded by that range.
4. True Ambiguity; multiple dimensions of uncertainty interact to create an environment that is virtually impossible to predict.
In real life there is however a problem with identifying the level we are facing. The definition of 1^thlevel uncertainty indicates that the residual uncertainty is irrelevant to the strategic decisions under study. But how is it possible to know this before an uncertainty analysis has been performed?

The answer has to be that the best possible analysis performed has been a risk/uncertainty analysis taking into account all known uncertainties in the business’s environment and that of all the business’s feasible strategies one is always best (1^th order stochastic dominance).

The best strategy will then be the one giving a probability distribution for the business’s equity value that is located to the right and under the distributions for all other strategies. In this case the resulting equity value is of less importance since it anyway will be larger than under any other strategy. With this established, the actual analysis can be performed as a deterministic calculation.

For the 2^ndlevel uncertainties with alternate futures, a scenario analysis is often advocated. However the same applies to each alternative future as for the 1^thlevel uncertainties (also see scenario analysis). In addition some assumptions have to be made on the probabilities of each of the alternative futures.

As an example we can take a company analyzing investment in production facilities in two alternative countries. In one country there is a sovereign risk of a future new tax scenario and if it is imposed two different scenarios is possible. In the other country there is a fixed tax scenario – not expected to change. In this case you will need at least three (maximum five) models all taking into account the inherent risk in the business, giving the probability distribution for equity value for;
1. current operations,
2. current operations + Investment in the country with no sovereign risk, and
3. current operations + Investment in the country with sovereign risk;
  1. no new tax scenario and
  2. with each of the two different new tax scenarios.
The reason for different models even if the operations in the new facility will be the same regardless of country, lies in the fact that the business strategy might differ between countries and the investment strategy might differ for different tax scenarios. The model with sovereign risk will switch between the different tax scenarios models, according to the probability of their occurrence – generating the distribution for equity value given the sovereign risk.

To invest, at least one of the equity distributions for ‘Current operations + Investment’ should be located to the right and under the distributions for ‘Current operations’ (or be stochastic dominant). Likewise, the best investment alternative will have an equity distribution located to the right and under the distributions for the other alternative (or be stochastic dominant).

Having the equity distribution for the dominant strategy, opens for measurement of the strategy’s inherent risk beyond the use of simple value at risk calculations, putting emphasis on the possibility of large losses and further unwanted capital infusions.

As we now can see, directly applying a standard scenario analysis can quickly lead decision makers astray.

The above classification for the two first levels can in general only be performed after a full the risk/uncertainty analysis and can never be used ex ante to select the appropriate method.

The 3^rd level uncertainties describes the normal situation where all exogenous variables have a range of possible values. Assuming that we can find (estimate or guesstimate) the probability distribution over that range, we can attack the problem by Monte Carlo simulation and calculate the probability distributions for our endogenous variables.

The 4^thlevel uncertainties comprises at least two different situations; where there are unknown but knowable probabilities and where there are unknown and unknowable probabilities:

Ambiguity is uncertainty about probability, created by missing information that is relevant and could be known (Camerer & Weber, 1992).

This leads us to a more comprehensive discussion of the situations that will arise in decision making processes:

More generally, we propose that in most decision problems, “choice” is nothing but the terminal act of a problem-solving activity, preceded by the formulation of the problem itself, the identification of the relevant information, the application of pre-existing competences or the development of new ones to the problem solution and, finally, the identification of alternative courses of action. (Dosi & Egidi, 1991)

The origin of uncertainty

Uncertainty may have two origins:
1. the lack of all the information which would be necessary to make decisions with certain outcomes (substantive uncertainty), and
2. limitations on the computational and knowledge based capabilities, given the available information (procedural uncertainty).
The first source of uncertainty comes from information incompleteness, and the second from the inability to recognize, interpret and act on the relevant information, even when it is available – knowledge incompleteness.

To distinguish between the two different situations giving Courtney‘s 4^th level uncertainty we will follow Dosi & Egidi:
1. Weak substantive uncertainty (analogous to Knight’s “risk”) is all circumstances where uncertainty simply derives from lack of information about the occurrence of a particular event – with a certain known (or at least knowable) probability distribution, and
2. Strong substantive uncertainty (analogous to Knight and Keynes “uncertainty”) is all cases involving unknown events or the impossibility, even in principle, of defining the probability distributions of the events themselves.
Types of Uncertainty

Uncertainty estimation usually includes the estimation of the uncertainty of the output parameters by estimating the uncertainty of the input parameters. This is done by estimating a probability distribution of the error. Hence, it is pretty much “straight forward” as long as the input parameters have values. However, the uncertainty of a model may not only be estimated via the parameters, there may also be uncertainty in the structure of a model, e.g. which variable and parameters are important in the model.

Adopting the distinction between parametric- and structural uncertainty (Kyläheiko et al., 2002) we can further specify model uncertainty:
1. Parametric; uncertainty or imperfect knowledge about the parameters in the decision model, and
2. Structural (epistemic); uncertainty or imperfect knowledge about the structure of the model.
Combining the above we can describe the types of risk and uncertainty facing both the decision maker and the decision support model as in the following picture:

The purpose is then to solve weak substantive parametric and structural uncertainty using good methods and models. The model will constitute a mix of facts ((In a simulation the opening balance is usually considered as certain, but the balance sheet often contains highly uncertain items. In fact auditors should give interval estimates for the most critical items in the yearly balance report)) (certain values), risks with known (objective) probability distributions, uncertainties given by subjective probability distributions and a script of the firm’s operations.

Modeling

However, models will always have some structural uncertainty – even if it would be possible to remove all by introducing more and more variable and relations. Occam’s Razor can usually be applied with good results; select the model that introduces the fewest assumptions and postulates the fewest entities while still sufficiently answering the question. Borrowing from multidimensional scaling the term ‘stress’ – as the violation done to the actual decision structure by removing parameters or variable from the model – we can visualize this by the following figure:

Reducing the dimensionality of the model will not necessarily reduce or move (distort) the endogenous variables event space since correlation exists between variable omitted and variable kept in the model and – depending on estimation methods – the standard errors of estimated relationships will increase, maintaining the original model variability.

Strategy

Maybe the world and the uncertainties we face haven’t changed all that much as a result of the financial crisis, but our perception of risks has. That means there is a real opportunity to rethink the way we make strategic decisions, the way we plan under uncertainty. (Courtney, McKinsey Quarterly, Dec. 2008)

The development of strategy requires the courage to accept uncertainty. Strategists must accept that they will not have all of the information and not see the full spectrum of possible events, yet be committed to create and implement strategy. The uncertainty that exists is not only a product of not having complete information and being able to predict future events, it also is a product of the events generated by dynamic and thinking competitors.

By its nature, uncertainty invariably involves the estimation and acceptance of risk. Risk is equally common to action and inaction. Risk may be related to gain; greater potential gain often requires greater risk. However, we should clearly understand that the acceptance of risk does not equate to the imprudent willingness to gamble the entire likelihood of success on improbable events.

One important step in the direction of better and more informed decision making is the removal of procedural uncertainty by having good models capable of framing the environment of the circumstances under which the decisions are made – giving the best possible analysis.

It is tempting, if the only tool you have is a hammer, to treat everything as if it were a nail. (Maslow, 1966)

S@R carries out thorough analysis of companies risk and uncertainties with aim of producing good decision support tools. Making sure the client takes a huge step forward from scenario analysis.

References

A fresh look at strategy under uncertainty: An interview, McKinsey Quarterly, December 2008.

http://www.mckinseyquarterly.com/fresh_look_at_strategy_under_uncertainty_2256.

Camerer, C. & Weber, M., (1992). Recent Developments in Modelling Preferences: Uncertainty and Ambiguity, Journal of Risk and Uncertainty, Springer, vol. 5(4), 325-70.

Courtney, H., (2001). 20/20 Foresight. Boston: Harvard Business School Press.

Courtney, H. G., Kirkland, J., & Viguerie, P. S., (1997). Strategy Under Uncertainty. Harvard Business Review, 75(6), 67-79.

Dequech, D., (2000), Fundamental Uncertainty and Ambiguity, Eastern Economic Journal, 26(1), 41-60.

Dosi, G & Egidi, M, (1991). Substantive and Procedural Uncertainty: An Exploration of Economic Behaviours in Changing Environments, Journal of Evolutionary Economics, Springer, 1(2), 145-68.

Frost, R., (1916). Mountain interval. Henry Holt And Company.

Keynes, J., (2004). A Treatise on Probability. New York: Dover Publications.

Knight, F. (1921). Risk, Uncertainty and Profit. Boston: Houghton Mifflin.

Kylaheiko K., Sandstrom J. & Virkkunen V., (2002). Dynamic capability view in terms of real options. International Journal of Production Economics, Volume 80 (1), 65-83(19).

Maslow, A., (1966). The Psychology of Science. South Bend: Gateway Editions, Ltd.

Endnotes
02/08/2010