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Operations – Page 2 – Strategy @ Risk

Strategy @ Risk

Category: Operations

The Uncertainty in Forecasting Airport Pax

This entry is part 3 of 4 in the series Airports

When planning airport operations, investments both air- and land side or only making next years budget you need to make some forecasts of what traffic you can expect. Now, there are many ways of doing that most of them ending up with a single figure for the monthly or weekly traffic. However we do know that the probability for that figure to be correct is near zero, thus we end up with plans based on assumptions that most likely newer will happen.

This is why we use Monte Carlo simulation to get a grasp of the uncertainty in our forecast and how this uncertainty develops as we go into the future. The following graph (from real life) shows how the passenger distribution changes as we go from year 2010 (blue) to 2017 (red). The distribution moves outwards showing an expected increase in Pax at the same time it spreads out on the x-axis (Pax) giving a good picture of the increased uncertainty we face.

This can also be seen from the yearly cumulative probability distributions given below. As we move out into the future the distributions are leaning more and more to the right while still being “anchored” on the left to approximately the same place – showing increased uncertainty in the future Pax forecasts. However our confidence in that the airport will reach at least 40M Pax during the next 5 years is bolstered.

If we look at the fan-chart for the Pax forecasts below, the limits of the dark blue region give the lower (25%) and upper (75%) quartiles for the yearly Pax distributions i.e. the region where we expect with 50% probability the actual Pax figures to fall.

The lower und upper limits give the 5% and 95% percentiles for the yearly Pax distributions i.e. we can expect with 90% probability that the actual Pax figures will fall somewhere inside these three regions.

As shown the uncertainty about the future yearly Pax figures is quite high. With this as the backcloth for airport planning it is evident that the stochastic nature of the Pax forecasts has to be taken into account when investment decisions (under uncertainty) are to be made. (ref) Since the airport value will relay heavily on these forecasts it is also evident that this value will be stochastic and that methods from decision making under uncertainty have to be used for possible M&R.

Major Airport Operation Disruptions

Delays – the time lapse which occurs when a planned event does not happen at the planned time – are pretty common at most airports Eurocontrol estimates it on average to approx 13 min on departure for 45% of the flights and approx 12 min for arrivals in 42% of the flights (Guest, 2007). Nevertheless the airport costs of such delays are small; it can even give an increase in revenue (Cook, Tanner, & Anderson, 2004).

We have lately in Europe experienced major disruptions in airport operations thru closing of airspace due to volcanic ash. Closed airspace give a direct effect on airport revenue and a higher effect the closer it is to an airport. Volcanic eruptions in some regions might be considered as Black Swan events to an airport, but there are a large number of volcanoes that might cause closing of airspace for shorter or longer time. The Smithsonian Global Volcanism Program lists more than 540 volcanoes with previous documented eruption.

As there is little data for events like this it is difficult to include the probable effects of closed airspace due to volcanic eruptions in the simulation. However, the data includes effects of the 9/11 terrorist attack and the left tails of the yearly Pax distributions will be influenced by this.

References

Guest, Tim. (2007, September). A Matter of time: air traffic delay in Europe. , EUROCONTROL Trends in Air Traffic I, 2.

Cook, A., Tanner, G., & Anderson, S. (2004). Evaluating the true cost to airlines of one minute of airborne or ground delay: final report. [University of Westminster]. Retrieved from, www.eurocontrol.int/prc/gallery/content/public/Docs/cost_of_delay.pdf

22/04/2010
The Value of Information
This entry is part 4 of 4 in the series A short presentation of S@R

Enterprise risk management (ERM) only has value to those who know that the future is uncertain

Businesses have three key needs:

First, they need to have a product or service that people will buy. They need revenues.

Second, they need to have the ability to provide that product or service at a cost less than what their customers will pay. They need profits. Once they have revenues and profits, their business is a valuable asset.

So third, they need to have a system to avoid losing that asset because of unforeseen adverse experience. They need risk management.

The top CFO concern is the firm’s ability to forecast results and the first stepping-stone in the process of forecasting results is to forecast demand – and this is where ERM starts.

The main risk any firm faces is the variability (uncertainty) of demand. Since all production activities like procurement of raw materials, sizing of work force, investment in machinery etc. is based on expected demand the task of forecasting future demand is crucial. It is of course difficult and in most cases not possible to perfectly forecast demand, but it is always possible to make forecasts that give better results than mere educated guesses.

We will attempt in the following to show the value of making good forecasts by estimating the daily probability distribution for demand. We will do this using a very simple model, assuming that:
1. Daily demand is normal distributed with expected sales of 100 units and a standard deviation of 12 units,
2. the product can not be stocked,
3. it sells at $4 pr unit, has a variable production cost of $2 and a fixed production cost of $50.
Now we need to forecast the daily sales. If we had perfect information about the demand, we would have a probability distribution for daily profit as given by the red histogram and line in the graphs below.
- One form of forecast (average) is the educated guess using the average daily sales (blue histogram). As we can see from the graphs, this forecast method gives a large downside (too high production) and no upside (too low production).
- A better method (limited information) would have been to forecast demand by its relation to some other observable variable. Let us assume that we have a forecast method that gives us a near perfect forecast in 50% of the cases and a probability distribution for the rest that is normal distributed with expected sales as for demand, but with a standard deviation of six units (green histogram).
With the knowledge we have from (selecting strategy) we clearly se that the last forecast strategy is stochastic dominant to the use of average demand as forecast.

So, what is the value to the company of more informed forecasts than the mere use of expected sales? The graph below gives the distribution for the differences in profit (percentage) using the two methods. Over time, the second method will give on average an 8% higher profit than just using the average demand as forecast.

However, there is still another seven to eight percent room for further improvement in the forecasting procedure.

If the company could be reasonable sure of the existence of a better forecast model than using the average, it would be a good strategy to put money into a betterment. In fact it could use up to 8% of all future profit if it knew that a method as good as or better than our second method existed.
15/03/2010
Concession Revenue Modelling and Forecasting
This entry is part 2 of 4 in the series Airports

Concessions are an important source of revenue for all airports. An airport simulation model should therefore be able to give a good forecast of revenue from different types of concessions -given a small set of assumptions about local future price levels and income development for its international Pax. Since we already have a good forecast model for the expected number of international Pax (and its variation) we will attempt to forecast the airports revenue pr Pax from one type of concession and use both forecasts to estimate the airports revenue from that concession.

The theory behind is simple; the concessionaires sales is a function of product price and the customers (Pax) income level. Some other airport specific variables also enter the equation however they will not be discussed here. As a proxy for change in Pax income we will use the individual countries change in GDP. The price movement is represented by the corresponding movements of a price index.

We assume that changes in the trend for the airports revenue is a function of the changes in the general income level and that the seasonal variance is caused by the seasonal changes in the passenger mix (business/leisure travel).

It is of course impossible to forecast the exact level of revenue, but that is as we shall see where Monte Carlo simulation proves its worth.

The fist step is a time series analysis of the observed revenue pr Pax, decomposing the series in trend and seasonal factors:

The time series fit turns out to be very good explaining more than 90 % of the series variation. At this point however our only interest is the trend movements and its relation to change in prices, income and a few other airport specific variables. We will however here only look at income – the most important of the variable.

Step two, is a time series analysis of income (weighted average of GDP development in countries with majority of Pax) separating trend and seasonal factors. This trend is what we are looking for; we want to use it to explain the trend movements in the revenue.

Step three, is then a regression of the revenue trend on the income trend as shown in the graph below. The revenue trend was estimated assuming a quadratic relation over time and we can see that the fit is good. In fact 98 % of the variance in the revenue trend can be explained by the change in income (+) trend:

Now the model will be as follows – step four:
1. We will collect the central banks GDP forecasts (base line scenario) and use this to forecast the most likely change in income trend
2. More and more central banks are now producing fan charts giving the possible event space (with probabilities) for their forecasts. We will use this to establish a probability distribution for our income proxy
Below is given an example of a fan chart taken from the Bank of England’s inflation report November 2009. (Bank of England, 2009) ((The fan chart depicts the probability of various outcomes for GDP growth. It has been conditioned on the assumption that the stock of purchased assets financed by the issuance of central bank reserves reaches £200 billion and remains there throughout the forecast period. To the left of the first vertical dashed line, the distribution reflects the likelihood of revisions to the data over the past; to the right, it reflects uncertainty over the evolution of GDP growth in the future. If economic circumstances identical to today’s were to prevail on 100 occasions, the MPC’s best collective judgement is that the mature estimate of GDP growth would lie within the darkest central band on only 10 of those occasions. The fan chart is constructed so that outturns are also expected to lie within each pair of the lighter green areas on 10 occasions. In any particular quarter of the forecast period, GDP is therefore expected to lie somewhere within the fan on 90 out of 100 occasions. The bands widen as the time horizon is extended, indicating the increasing uncertainty about outcomes. See the box on page 39 of the November 2007 Inflation Report for a fuller description of the fan chart and what it represents. The second dashed line is drawn at the two-year point of the projection.))

3. We will then use the relation between historic revenue and income trend to forecast the revenue trend
4. Adding the seasonal variation using the estimated seasonal factors – give us a forecast of the periodic revenue.

For our historic data the result is shown in the graph below:

The calculated revenue series have a very high correlation with the observed revenue series (R=0.95) explaining approximately 90% of the series variation.

Step five, now we can forecast the revenue from concession pr Pax figures for the next periods (month, quarters or years), using Monte Carlo simulation:
1. From the income proxy distribution we draw a possible change in yearly income and calculates the new trend
2. Using the estimated relation between historic revenue and income trend we forecast the most likely revenue trend and calculate the 95% confidence interval. We then use this to establish a probability distribution for the period’s trend level and draws a value. This value is adjusted with the period’s seasonal factor and becomes our forecasted value for the airports revenue from the concession – for this period.
Running thru this a thousand times we get a distribution as given below:

In the airport EBITDA model this only a small but important part for forecasting future airport revenue. As the models data are updated (monthly) all the time series analysis and regressions are redone dynamically to capture changes in trends and seasonal factors.

The level of monthly revenue from the concession is obviously more complex than can be described with a small set of variable and assumptions. Our model has with high probability specification errors and we may or may not have violated some of the statistical methods assumptions (the model produces output to monitor this). But we feel that we are far better of than having put all our money on a single figure as a forecast. At least we know something about the forecasts uncertainty.

References

Bank of England. (2009, November). Inflation Report November 2009 . Retrieved from http://www.bankofengland.co.uk/publications/inflationreport/ir09nov5.ppt
11/11/2009
Airport Simulation

This entry is part 1 of 4 in the series Airports

The basic building block in airport simulation is the passenger (Pax) forecast. This is the basis for subsequent estimation of aircraft movements (ATM), investment in terminal buildings and airside installations, all traffic charges, tax free sales etc. In short it is the basic determinant of the airport’s economics.

The forecast model is usually based on a logarithmic relation between Pax, GDP and airfare price movement. ((Manual on Air Traffic Forecasting. ICAO, 2006)), ((Howard, George P. et al. Airport Economic Planning. Cambridge: MIT Press, 1974.))

There has been a large number of studies over time and across the world on Air Travel Demand Elasticities, a good survey is given in a Canadian study ((Gillen, David W.,William G. Morrison, Christopher Stewart . “Air Travel Demand Elasticities: Concepts, Issues and Measurement.” 24 Feb 2009 http://www.fin.gc.ca/consultresp/Airtravel/airtravStdy_-eng.asp)).

In a recent project for an European airport – aimed at establishing an EBITDA model capable of simulating risk in its economic operations – we embedded the Pax forecast models in the EBITDA model. Since the seasonal variations in traffic are very pronounced and since the cycles are reverse for domestic and international traffic a good forecast model should attempt to forecast the seasonal variations for the different groups of travellers.

In the following graph we have done just that, by adding seasonal factors to the forecast model based on the relation between Pax and change in GDP and air fare cost. We have however accepted the fact that neither is the model specification complete, nor is the seasonal factors fixed and constant. We therefore apply Monte Carlo simulation using estimation and forecast errors as the stochastic parts. In the figure the green lines indicate the 95% limit, the blue the mean value and the red the 5% limit. Thus with 90% probability will the number of monthly Pax fall within these limits.

From the graph we can clearly se the effects of estimation and forecast “errors” and the fact that it is international travel that increases most as GDP increases (summer effect).

As an increase in GDP at this point of time is not exactly imminent we supply the following graph, displaying effects of different scenarios in growth in GDP and air fare cost.

References

24/02/2009
Real options

In real life both for investment decisions and in valuation of companies there are managerial flexibility in the sense that at future points of time there is flexibility in choosing among alternatives.

When investing, the simplest example is the choice between to invest after a feasibility study or walk away. In valuation the choice can be at a future point of time to continue operation or disinvest.

These alternatives are real options available for the decision maker. Recognizing these real options will usually increase (reduce loss) the value of the investment or the company under valuation.

It is well known that most standard valuation techniques of risk-adjusted discounted cash flow (DCF) analysis fails to capture all sources of value associated with this type of investment, in that it assumes that the decision to invest is irreversible and inflexible, i.e., the investment cash flows are committed and fixed for the life of the project.

A main contribution of real options analysis is to incorporate managerial flexibility inherent in the project in its valuation. Added flexibility value, overlooked in DCF analysis, comes from managerial decisions that can take advantage of price movements: operating flexibility and investment timing flexibility.

Strategy @ Risk has the ability to incorporate a client’s specific decision alternative in the simulation model. Thus combining Monte Carlo simulation with decision tree analysis. The four-step process of the real option decision analysis is shown below.

Production Plant Case

The board faces the following situation: The company has a choice between building a plant with production capacity of 150 000 metric tons at a most likely cost of $450 mill. or a smaller plant with a capacity of 85 000 metric tons at a most likely cost of $300 mill..

The demand for the product is over 100 000 metric tons and rising. The decision between a small and large plant will be taken in year 1 and full production starts in year 2.

If the decision has been to build the smaller plant (at a higher cost per unit produced) the capacity can be increased by 65 000 metric tons at most likely cost of $275 mill. (Normal distributed with variance of ±25%). The decision to increase capacity will be taken in year 2 if the demand exceeds 110 000 metric tons. It is assumed that the demand is normally distributed with a most likely demand of 100 000 metric tons, and demand varies ±20% (upper and lower 5% limit). The demand later periods is assumed to have an increasing variance and a 30% autocorrelation

In year 3 and 4 it is considered that there is a 40% chance that if sales has been good (over 110 000 metric tons) a competitor will have entered the market reducing sales by 30 000 metric tons. If the demand falls below 70 000 metric tons the company will disinvest.

The decisions will be made on the value of the discounted cash flows (20% discount rate).
The above problem can be presented as a decision tree.

The boxes represent the “decision point”. The circles represent chance events. The chance events may be continuous, as is the case with demand forecasts, or discrete, as is the case of a competitor entering the market or not.

Net Present Value of the Alternatives

The analysis using both the decision tree and Monte Carlo simulation gives us the net present value of the different alternatives. As shown in the figures to the right, the best alternative is to build a large plant immediately giving a net present value of $679 mill.
A small plant will give a lower net present value (NPV $626 mill.) even if we increase the capacity at a later stage (NPV $637 mill.).

In this case it will never be profitable to disinvest at any point of time. This will always give a lower value.In some cases it is difficult to distinguish the best strategy from its alternatives. We will in a later post come back to selection strategies using stochastic dominance.

16/02/2008