Option Valuation

In my last blog entry I introduced the notion that optimal decision making wasn’t ‘on the radar’ for many clients in Australasia, and laid out a couple of ideas why. I too once focussed on Monte Carlo simulation rather than decision evaluation, but last year the most obscure event changed that.

Call me a nerd of you will, but I like modelling problems in Excel. There is skill involved in setting up a problem such that the model assumptions aren’t too gross, and an art to making the model elegant. This elegance can be very important to optimisation problems, but more on that later. My first homemade optimisation problem was generated by motorcycle racing! MotoGP, to be precise. A friendly tipping competition with friends was formed at the start of the 2009 season with the following structure:

• Entrants played the role of Team Manager.
• Team Managers had a fixed budget to spend on riders.
• Either a few good riders could be purchased, or many lesser riders, or something in between.
• The team that had accumulated the most points at the end of the season was the winner and received kudos!

Although the future results could not be known of course so I set up and ran the optimisation with Evolver after the event to see what the optimal team selection would have been. Historical data could have been used to discover the type of rider mix that tended to be optimal and thus make an informed decision for this competition. The risk in having only a few riders was that any misfortune would have a big negative impact on the points won, whereas a team consisting of many (cheaper) riders was less likely to suffer such a fate. This downside scenario will be modelled into the 2010 MotoGP Team Manager predictive, optimised model (currently in production)!

What has this to do with the corporate world? Replace “team” with portfolio and “riders” with “assets”, “shares” or “projects” and you have a classic portfolio optimisation model. I hadn’t created this model with business applications in mind but I realised that was precisely what I was doing. An instant later I realised just how useful Evolver would be in many decision scenarios even though it doesn’t incorporate uncertainty (RISKOptimizer does).

In the next instalment I will further explore some practical applications for Evolver and you’ll see just how universally appropriate it can be.

» Making Optimal Choices, Part 1

Rishi Prabhakar
Trainer/Consultant

Something has troubled me for some time regarding the choices being made in risk land. I train and work with many clients whom have adopted Monte Carlo simulation techniques (via @RISK for Excel) into the day-to-day running of their businesses. By doing so they (hopefully) now have a good understanding of the exposure they are facing be it in project cost estimation, discounted cash flow analysis or, well, anything really. But this is only one facet of risk and decision assessment, specifically dealing with the descriptive statistical output from a simulation. What of the decision evaluation component? Why aren’t more of my customers analysing the decisions they make, or better yet actually optimising them? I have a few ideas why.

If you’re in business you have to make decisions. Big ones, little ones, yes/no, multiple state and continuous value decisions. Decisions that impact other decisions in simple or complex dependency structures. But are you making the best decisions possible? I’m sure important decisions aren’t being made completely randomly (I hope!) but I see many companies who rely completely upon qualitative techniques for their decision making (experience, gut feel, etc.) which of course means optimality is no more than a hoped for outcome rather than something that is actually being worked towards.
Firstly the decision model must be identified and then quantified, and this can be a difficult task. There is a level of modelling aptitude necessary for effective modelling that goes beyond merely knowing Excel and its functions, and into the construction of logical mathematical descriptions of possibly complicated processes. Relevant decisions need to be identified and the impact of those decisions combined into a formula that can be mathematically optimised. A critical component to all this is the knowledge that spreadsheet models can actually be optimised, and that in cases where Excel’s Solver fails there are Palisade products (Evolver and RISKOptimzer) that can perform optimisations under virtually any circumstance.

I too used to focus on Monte Carlo simulation rather than decision evaluation, and this was mainly a product of the clients I was dealing with almost exclusively when I first worked for Palisade. In my next blog I’ll tell you why that changed and also get a little more into the nuts and bolts of optimisation.

Rishi Prabhakar
Trainer/Consultant

Where I left off last time was lamenting the use of Monte Carlo simulation to create a single value (statistic etc.) from a model. It might still not be clear why this is anathema to me, so here goes.

A simulation is not a number. It’s not one possible (future) outcome – that’s a scenario. Monte Carlo simulation is a methodology for understanding one’s exposure to outcomes not situated close to the central tendency of the process/project in question. Note the plural “outcomes”. Risk analysis, when done properly, should let you know essentially all possible outcomes and how likely they are for your model. Output from a simulation can include a plot of means (over time), or P5s, or P95s, or the mean ± one standard deviation or any number of statistics. But that’s not plotting a simulation! Let’s not give a minimalist graph too much credit.

Such statements also perpetuate the idea that simulation is only used for creating means (or other centrally tending statistics) and ignores the wealth of information available. Risk simulation software exists to help you do risk analysis which must include not only several statistics but also sensitivity information. It is all too easy to turn a risk assessment into a hunt for a regularly asked for percentile (such as the P90) and there ends the task. I see this a lot, especially in project cost estimation where the pressure both from management and regulatory bodies is to accurately estimate some large percentile. Once found there is usually scant further risk analysis.

Nothing good ensues. When risk analyses are run “to get ‘the’ number” they become simply another box to tick in a process and ultimately any benefits (perceived or actual) will be forgotten and lost to the ages. The notion of context is also lost. No single number by itself really means anything, or at least shouldn’t mean anything to a decision maker. I have often heard phrases like “the model returned/gave $1.2m” followed by an audience nodding in agreement. Huh? Which statistic are you talking about there, and how about reporting a few other numbers around it to place that $1.2m somewhere meaningful?

In the next installment I will look further into this issue of context and hopefully prove the necessity of an holistic approach to understanding and reporting simulation results.

» Part 1

Rishi Prabhakar
Trainer/Consultant

I read an interesting article on the causes of the Global Financial Crisis by John B. Taylor. Although the topic is interesting enough already, especially for a member of a risk analysis-specialising company, something else caught my eye. I have observed in training workshops, onsite consulting and now academic papers a phenomenon regarding probabilistic modelling. Many of those using the methods don’t understand what they should actually be getting from the methodology. There is an intellectual leap from the deterministic to the probabilistic that sometimes does not get made. This limits the usefulness of Monte Carlo simulation, and the value of performing such statistical analyses.

Back to the article which spurred me to write this blog in the first place. Or rather, the graph. Yes a single graph of housing starts vs. time (and its brief description) leapt out at me. One of the lines on the graph was claimed to show model simulations of housing starts using the actual interest rate, compared to the interest rate ‘predicted’ by the Taylor Rule and a third line showing actual data.

So what’s the problem?

The problem is that simulation techniques should not be used to create a single value. The single ‘simulation’ line implies a single modelled/returned value for each time period. This is deterministic modelling. There may be a particular scenario that has been modelled, but it certainly isn’t a simulation that is being represented by that single line. Simulations produce thousands of data, observed values and their associated percentiles as well central moments (mean, variance etc.). Not just one value (sorry Value at Risk – that includes you too) that can be plotted as a single line. I would guess that if a simulation were run as I understand the term then the line in the chart was probably constructed using the simulated means. But I shouldn’t be guessing.

This is far from the only time I’ve seen simulation results reduced to a single entity. I have heard from clients in the past “the simulation gave $X” with little to no context around it, and this is supposed to both mean something to me and to their customers and help to make better decisions under uncertainty…

In the next blog I will explore this idea further and discuss the sorts of results that should be gleaned from a simulation. In particular, why narrowing simulation results down to a single number is counterproductive to healthy business practices.


Rishi Prabhakar
Trainer/Consultant

On Thursday, February 18, 2010, Prakash Shrivastava will present a free live webcast entitled. "Cost-Effectiveness Analysis of Patient Care using The DecisionTools Suite"

Cost-effectiveness analysis is often used to evaluate effectiveness of medical interventions and is one of the main topics in healthcare research. This analysis requires data evaluation, including building and testing decision analysis models. This free live webcast will illustrate how such models are easily built using the DecisionTools Suite. The first part of the webcast will introduce process, cost drivers and measures in healthcare. In the second part, cost-analysis examples will be presented. The webcast will conclude with a sensitivity analysis example.

Prakash Shrivastava is a Principal at Strategic Management International, Inc. He specializes in Research, Analysis and Simulation of Control Systems, Business Models and Processes. He worked in Automotive Industry for over 22 years and Aerospace Industry for 7 years. He holds a Masters Degree from Indian Institute of Technology, Bombay, a Doctoral degree from Princeton University, NJ and a Masters degree in Management of Technology from RPI.

» Register now (FREE)
» View archived webcasts

Two weeks ago, I attended IQPC’s (International Quality & Productivity Center) Lean Six Sigma and Process Improvement Summit in Orlando, Florida. During the past 4 years, I have watched the conference, the attendees, and their projects evolve. The IQPC did an excellent job keeping the quality of the conference at an A+ level despite wrangling with the effects of a down market and near zero travel budgets for many companies. This conference has earned it place as one of the premier Six Sigma events of the year.

With attendance numbers on par with last year (which are only slightly down from a few years ago), the major difference that I noticed was the attendees' passion. As the economy has worsened and media’s perception of Six Sigma waned, practitioners and champions are more passionate and committed now than ever. Perhaps it’s because they still have jobs and their companies understand the value of cost reduction in both their processes and product/ process development programs. They - and the companies who employ them - have every right to be excited and passionate because they are making positive changes to their organizations that will hopefully lead them to recovery and stability faster than others.
 

Many companies, large and small, represented practically every industry. Farmers Insurance and Capital One were two representatives from the insurance and banking industries. Technology and pharmaceuticals were well represented by Seagate, Motorola, Merck and Johnson & Johnson. In addition, the energy sector was well represented, as were the military, aerospace and services sectors. (If you want a complet list of companies attending, it may be available at www.sixsigmaiq.com)

The overriding message heard over and over again, was, “We need to make your Six Sigma deployments stick.” Initially, I found this to be an interesting message since it came from a group of many highly intelligent and motivated individuals who were obviously very successful in doing just that: “Making it Stick”. This message serves as a clarion call for all of us. We need to look for new tools, philosophies and approaches to make our improvement initiative better and “stickier” so that they can pass the test of time.

The highlight of every year is the awards ceremony. There were many great projects honored this year, and congratulations to the winners and everyone who submitted their projects! At the awards ceremony I had the pleasure to meet a great group from the Bahamas Telecommunications Company. They are the pioneers for Lean Six Sigma for their company. (I tried to get them to need an onsite training session in some of the Palisade tools, but have been thus far unsuccessful!) Good luck on your Six Sigma Journey, I hope to see you accepting an award next year!

In my last blog I mentioned a ‘fact’ about data that came up during a recent public training course (Decision-Making and Quantitative Risk Analysis). This fact stuns me every time I think about it, and certainly floored me the first time I encountered it. So many companies just don’t have it.

Data, that is. Historical data from completed projects, sometimes billion-dollar projects, is simply not collected especially in resources and infrastructure cost estimation. Instead every risk is re-estimated from scratch in every new project based entirely upon an estimator’s recollections or guesses. This is not a suggestion that estimators don’t know what they’re talking about, rather that the benefits of adding historical data to the analysis far outweigh the cost of gathering the information in the first place.

I first worked in the banking sector, hence my surprise to learn of this lack of data storage in certain areas of risk analysis. Project cost estimation, especially in resources and infrastructure – I’m talking to you. In financial circles there are literally millions of data points collected daily across the entire organisation. Gathering data (and then analysing it for some benefit) is simply ‘what we do’, and this process isn’t challenged. Some of the data is quite ‘small’, such as the number of seconds a particular caller was kept on hold before being answered, and others are quite ‘big’, such as multi-million dollar losses due to fraudulent activities. Regardless, it’s all kept in the knowledge that information is power – in this case the power to make intelligent decisions in the future.

How can you judge the efficacy of an estimation process (workshops etc.) if you don’t track the final observed outcomes specifically to make such a judgment? Well, you can’t. And that leaves your company’s risk and decision assessment process in limbo. Without measurement there can be no process improvement or corporate learning. Are you ‘passing’ or ‘failing’ with your use of Monte Carlo simulation via risk analysis software?

Generally the observed outcomes for risks in models will be near the estimated value, and this is to be expected. However the main role of risk analysis is to adjudge exposure to the unexpected. Far too many cost estimation models have very little volatility in their line items. I am very curious to know just how often the realised value of a given line item is outside the range of “possible values” as defined in the model. And what about the total project costs overall? This hints at and leads to the big question which is what could/should be done with such data if it were to be recorded?

I shall address these questions in the next blog. I know you’re excited to find out!

Rishi Prabhakar
Trainer/Consultant

An anonymous comment in the Vail (Colorado) Daily News about the dangers of overanalyzing a decision reminded me that, while the benefits of risk analysis have been much vaunted, the costs of decision evaluation have not been clearly defined.  Sure, it's pretty easy to come up with a figure for a DFSS training effort or a budget for an entire risk management department. But what about the statistical analysis process itself?  

Well, there's staff time or your own time (which is worth something), Monte Carlo software, some portion of your computing costs,data acquisition, and on and on. Many variables. But the kind of costs I'm thinking of are the kind you rack up while you're analyzing, say, option valuation, and not doing something else.  These are opportunity costs.  They are what really limit how thoroughgoing your risk analysis becomes, which layer you drill down to--and they are very difficult to quantify.

How do you calculate whether the time you're spending in risk assessment is cost-effective? It's a problem of operations risk.  So I suppose you could enumerate all the other activities that would consume the same amount of time and model their paybacks.  But that would cost you more time in statistical analysis. . . . and you would be left in a positive feedback loop.

In the days ahead I'll be talking to risk management and operations research folks to find out how they decide how much analysis is just the right amount--not too much, and not too little.   I'll be surprised if I turn up any computational approaches--but who knows?  

In a recent public training workshop (for @RISK for Excel) I was reminded of an unusual fact regarding data.

Commonly @RISK for Excel is used to fit distributions to historical data for use in risk modelling, and it sure beats wildly guessing obscure parameters. However there are (naturally) a litany of woe-inducing problems with all historical data sets: non-stationary data series, extreme values/outliers, data recording errors, seasonality and heteroskedasticity to name a few. Excessive ‘cleansing’ of the data set is commonly prescribed, but the statistician in me cringes to even type those words! Quality control and transforming the data will help to eliminate most of those problems, but what about outliers?

In the early Naughties I was working for a large Australian bank, forecasting their daily call centre volumes for the purpose of planning staff levels and predicting service levels. A particular call centre averaged 30,000 calls per weekday. Yet on September 12th, 2001, calls dropped to less than 10,000. Along with the rest of the world, Australians were watching the terrorist attacks on television and the internet rather than calling to fix spelling mistakes in their contact details or transfer small sums of money between accounts. But what to do with that data point? Presuming the forecasting model is not intended to include such extreme events as terrorist attacks then the point could simply be filtered out of the data set and not thought of again.

But now consider a process that should include rarer events, such as flood damage or operational risk, as one of the risks in a model. If you have 10 years of good data (say), but the set includes an event that should only occur every 100 years. This level of impact is thus drastically overrepresented in the data and any fitted distribution will be biased toward such extremes. Yet the data point can not be completely ignored as such values can occur and the simulation models must have the capacity to sample such values (though with a reasonable likelihood). In this case the artistry that is fitting distributions to data comes to the fore. The data point could be removed from the set but not from our decision making process.

From the range of distributions that can be selected, the optimal choice should not only represent the remaining data well but also have a tail that samples events in the vicinity of those that have been excluded from the analysis with reasonable probability. No, that’s not always easy to do. But as with many elements of probabilistic modelling it simply must be done in order to provide useful information to decision makers.

Thus the context of the modelling can go a long way to determine the most appropriate steps to take with your data set. If that sounds like a subjective guideline then you read it correctly. Not enough people realise just how important experience and intuition can be in the seemingly prescriptive fields of mathematics and statistics. Fitting distributions to data is no different.

And yet that isn’t the unusual fact I was reminded of in the workshop! But I’ll leave that for Part 2 of my Data Issues blog.

Rishi Prabhakar
Trainer/Consultant

New measures were published by the UK Government in November 2009 to protect communities at risk from ‘flash’ flooding when drains get overwhelmed by sudden downpours.  The Flood & Water Management Bill going before Parliament will give new powers to local authorities to manage surface water.  Environment Secretary Hilary Benn said, “We’ll see more severe weather as climate change takes hold, with heavier rainfall and potential flooding. The weather in the last couple of weeks has shown that this risk is very real.” 

Recent events in Cumbria in the UK suggest climate change really should be at the top of the agenda, and this new bill will certainly go some way to managing the risk associated with it.

Risk analysis has its place in determining the risk associated with climate change, and Palisade's risk modeling software has helped numerous organizations develop reports on likely outcomes. Cambridge University’s Judge Business School recently used @RISK to provide key input to the Stern Review on the Economics of Climate Change. Released in 2006, this report undertaken by the British government by Lord Stern discusses the effect of climate change and global warming on the world economy and is the largest and most widely referenced report of its kind.

They researched issues such as the impacts of the sea level rising and increases in temperature making land infertile or unfarmable, and balanced these against the costs of various options available to tackle global warming.  

At one end of the scale, doing nothing costs nothing, but the environmental consequences will be high. However, activity that reduces the severity of the impacts may itself be very expensive. The aim of the @RISK model was to enable people to make informed decisions on the optimum way to deal with climate change (ie how much to cut back on damaging activity and what methods to use).

@RISK risk simulation software also helped researchers tackle a key problem associated with investigating climate change, namely that the different effects of the various factors which influence it are themselves, undetermined. For example, the historical evidence does not pin down exactly how much global temperatures will increase if CO2 emissions double. @RISK enabled researchers to quantify this uncertainty in order that they have a measurement of the accuracy of their findings.

Risk analysis models should go some way to determining outcomes, and potentially help us prepare for the tragic events that have unfolded in recent days in the UK.

Craig Ferri
EMEA Managing Director of Risk & Decision Analysis

Resolved for 2010:

Having talked in previous posts as to why it’s important, and today how accessible it is for any size of organisation to adopt a healthy approach to risk, I’ll now take you through my top ten tips on how you can maximize your risk management programme:

1. Get buy-in
Risk management is not an optional extra. It is a business critical tool that is an asset and an integral part of the project. The company culture must be developed to embrace QRM (quantitative risk management) and DMU (decision making under uncertainty) in order that everyone understands their benefits and therefore accepts the need for them.

2. Get budget
Business tools cost money, but managing risk is an investment - not an overhead – and must be regarded as such. Allocating resource and making it a formal business process should be seen as an insurance policy.  Not only will it help organisations make better decisions that will save them money in the long term but, by identifying potential risks and adverse events, it can protect them against unexpected costs in the future.

3. Get words
As with any organisational change, it is essential that everyone is clear on the new processes. Therefore a common risk language – or 'glossary' – needs to be developed to avoid misunderstanding and to ensure a consistent approach to QRM and DMU.

4. Get numbers
Qualitative assessment is essential, but numbers are more powerful – for example the percentage chance of meeting a deadline or budget. Monte Carlo simulation random sampling provides the margin of error for a venture and is a good way to illustrate the consequences of different courses of action. Risk management experts must ensure everyone understands these figures, and accepts them.

5. Get structure
Managing risk in order to make better-informed decisions requires an appropriate organisational structure. Individuals and groups need clearly defined roles, and must then each take responsibility for their own area of expertise.

6. Get lateral
Every organisation has risks that it deals with on a daily basis and which must therefore be factored in to the decision-making model. However, no enterprise operates in isolation, so other external variables must be included. For example, even a small rise in fuel costs could have a major effect on revenues if raw materials need transporting long distances.

7. Get perspective
Political, cultural and social risk factors can be explored by involving all stakeholders.  Investing time and money in consultation and research ensures that businesses have a clear idea of the complete environment in which they operate, and therefore minimise the chances of products and services failing.

8. Get reporting
Risks, and the management of them, must be reviewed regularly – and the programme amended if necessary. This requires a regular reporting process, in which risks are clearly identified and prioritised.

9. Get with it
Being risk aware does not mean being risk averse. Businesses should guard against rigidly adhering to 'the way we've always done it' approach, instead keeping up-to-date, learning new tricks and not being afraid to be bold.  Although risky on the surface, these tactics prevent being left behind – much of the potentially uncertainty can also be removed with QRM and DMU.

And finally…

10. Get it documented
Back up the commitment to a thorough QRM and DMU programme with documentation. This validates the budget and buy-in requested at the start. And it’s good for business – organisations this thorough are guaranteed a competitive edge.

Craig Ferri
EMEA Managing Director of Risk & Decision Analysis

At November's supercomputing conference in Portland, Oregon, IBM announced that its researchers working with a team from Stanford University had succeeded in developing an accurate simulation of human brain function. The simulation will be capable of emulating sensation, perception, action, interaction and cognition.

As anyone who does risk analysis is aware, the flip side of opportunity is risk, or maybe opportunity is the upside of risk.  They are always there together, the two sides of chance, but it's great to occasionally see the brighter side of the coin. 

In a report issued last month, KPMG emphasizes the need for comprehensive, strategic risk management across an organization. Entitled “The Business Case for a Risk Executive: Leading Efforts to Avoid Surprises, Maneuver through Challenges, and Add Value,” the report notes that most current risk management efforts are specific to particular departments, projects, or regulations, and do not approach risk from an enterprise level. This had led to critical oversights and missed opportunities.

To address this gap, KMPG recommends the appointment of a risk executive. This person’s dedicated purpose is “to help prepare the organization to respond to change and the risks that emerge in changing times, and to turn those efforts into opportunities that benefit the organization.” More specifically, such an executive would unify risk approaches across business units and departments, standardize reporting, and establish a common risk “language.” (Note: Risk modeling software and Monte Carlo techniques play central roles in this effort.)

Expounding on the importance of risk management experts, the report concludes, "Without a risk executive, risk management efforts will likely continue to lag and hamper the organization’s effort to recover. But with a risk executive owning the process, risk management can move beyond a support role and help enable the organization to realize its strategic goals and rebuild business value."

» Read the full report (PDF)

Wayne Winston is the newest blogging personality at the Huffington Post! His first post, “The Importance of Schedule Strength in Sports,” appeared yesterday. Wayne will focus on the interface between math and sports, with detailed explanations of statistical analysis and spreadsheet modeling, including @RISK risk analysis models. You can find a link to the Wayne Winston blog from the newly-launched HuffPost Sports.

Wayne is the John and Esther Reese Professor of Decision Sciences at Indiana University’s nationally ranked Kelly School of Business. He has won over 30 teaching awards, and written over 20 journal articles and 15 books.  Wayne has consulted for many organizations including the Dallas Mavericks, USA Diving, Cisco, Microsoft, US Army, Eli Lilly, Diamond Consulting, Tellabs and Medtronics. He has also developed online spreadsheet modeling and mathematics courses for Harvard Business School Publishing. And, Wayne is a two time Jeopardy! champion!

Wayne’s latest book, Mathletics, provides an introduction to the use of math by baseball, football, and basketball teams. He has also authored several books published by Palisade, including Financial Models Using Simulation and Optimization I, Financial Models Using Simulation and Optimization II: Investment Valuation, Options Pricing, Real Options & Product Pricing Models, and Decision Making Under Uncertainty with RISKOptimizer.


DMUU Training Team