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Advance Topics in Financial Modeling

Lecture 2Kaushank Khandwala

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Plan for this lecture

• Applications of Financial Modeling• Revisit Trend and Overlay Chart Applications• Crystal Ball’s basic probability distributions• Defining decision variables

Financial Modeling – Applications

In Corporate finance, investment banking and PE profession ,financial modeling is concerned with cash-flow projection and forecasting

• Business valuation, (discounted cash flow, price multiples)• Scenario planning and management decision making • Capital budgeting, Cost of capital (i.e. WACC) calculations• Project Finance, Financial statement analysis

Financial Modeling – Applications

In quantitative finance, financial modeling entails development of a sophisticated math model dealing with asset prices, market movements, portfolio returns.

Applications include:• Option pricing and calculation of  "Greeks"• Structuring Other derivatives, especially Interest rate derivatives and Exotic derivatives• Corporate financing activity prediction problems• Real options• Risk modeling and Value at risk. 

Charts Revisited

• Charts help us visualize, understand, and communicate the simulation results.

• Overlay and Trend charts can help comparison of results from multiple forecast charts simultaneously.

• A trend chart summarizes and displays information from multiple forecasts, making it easy to • discover and analyze trends that might exist between related forecasts. You can customize

your trend chart to display the probability that given forecasts will fall in a particular range.

• Overlay chart feature to view the relative characteristics of forecasts on one chart. The overlay chart superimposes the frequency data from selected forecasts so you can compare differences or similarities that otherwise might not be apparent. There is no limit to the number of forecasts you can overlay

Trend Chart

Trend chart comparing accumulated values after 30 years of retirement savings for nine different allocations into stocks and bonds each year.

Overlay Chart

• Overlay chart comparing accumulated value after 30 years of retirement savings for two different allocations into stocks and bonds each year.

• The 90–10 portfolio almost completely dominates the 50–50 portfolio in the sense that the line representing the 90–10 portfolio is above and to the right of the 50–50 line almost everywhere.

Overlay Chart

• For Year 30 Wealth values below about $1 million, the lines are virtually indistinguishable.

• While very risk-averse investors might prefer the 50–50 portfolio because it dominates the 90–10 portfolio slightly in the worst 10 percent of the cases, most investors would prefer the 90–10 portfolio’s wealth distribution because of its near equivalence in the lowest 10 percent and dominance in the upper 90 percent of the potential returns.

Type of Distributions

Basic distributions listed in Crystal Ball’s distribution gallery.

Bernoulli Yes-No Distribution

• The random variable Y has the Bernoulli distribution if it can take only one of two possible values, y = 0 or y = 1. The value y = 1 is called a ‘‘success,’’ and y = 0 is called a ‘‘failure’’ in probability parlance.

• In Crystal Ball, the Bernoulli distribution is known as the yes-no distribution.

Binomial Distribution

• Binomial(p,n) is the distribution of the sum of a fixed number, n, of Bernoulli trials that all have the same probability of success, p.

• The problem of determining the distribution of the number of heads in five tosses of a fair coin can be solved by using one Crystal Ball assumption—the binomial(0.5,5)

Discrete Uniform Distribution

• Discrete uniform(L,H) distribution assigns equal probability to the set of integers between L and H, inclusive.

• For L = 1 and H = 6, it is the probability distribution representing the number of spots showing on the top face of a fair die rolled randomly

Uniform Distribution

• Uniform distribution has only two parameters, the minimum and maximum values.

• It produces any continuous value between the minimum and maximum with equal likelihood

Triangular Distribution

• Triangular distribution is appropriate for use when you have little or no data available, but you know the minimum, maximum, and most likely values of a random variable.

• The triangular distribution is completely specified by its three parameters, Minimum, Likeliest, and Maximum. These three values are sufficient to determine the triangular shape shown in the icon.

Normal Distribution

• Normal distribution is describes many natural phenomena. The normal distribution is specified by its two parameters, the Mean and Std Dev (standard deviation).

• Because it is symmetrical, the mean is equal to the median (50th percentile). • The mode (point on the horizontal axis at which the PDF is highest) is also equal to

the mean and median. • Values simulated from the normal distribution are more likely to be close to the mean

than far away.

Lognormal Distribution

Lognormal distribution takes its name from the fact that it represents a random variable whose natural logarithm follows the normal distribution.

The lognormal distribution is bounded on the left by zero; however, it is unbounded on the right just as the normal distribution.

This makes it useful for situations where values are positively skewed and cannot benegative, such as the total return on stock when the stockholder’s potential loss islimited to the amount he or she has invested, or for sales of a product, which cannotbe negative.

HISTORICAL DATA TO CHOOSE DISTRIBUTIONS

• If you have historical data on an input variable, there are two different methods for using them in a Crystal Ball model:

(1) direct sampling, and (2) sampling from a fitted distribution.

HISTORICAL DATA TO CHOOSE DISTRIBUTIONS

• Direct simulation can only reproduce what has already happened, and the number of trials usually exceeds the number of data values available, so that you will be using the same values many times over.

• Using direct sampling can lead to a false sense of precision and is not generally recommended.

• Sampling from a Fitted Distribution involves standard techniques of statistical inference to fit a theoretical distribution to your data using one of the distribution gallery’s continuous distributions.

• The fitting and selection is nearly automatic, although it does require some judgment and subject matter knowledge to use most effectively.

What If No Historical Data Are Available?

• Financial models are often built to analyse situations that do not yet exist; for example, new products or projects in which the company has little or no historical data to help choose assumptions.

• In this case, you will have to make your own subjective estimates of which assumptions to use in the model, or solicit the help of a SME.

• Building a model without historical data can provide many valuable insights.• However, as soon as possible, you should collect data on the stochastic variables

driving your forecasts and parameterize the assumptions.

• Among other reasons, this will also allow you to estimate any correlations between the assumptions, which can make a huge difference in the forecast results.

• Common techniques used are : Specifying the Spearman/Pearson estimators,• Batch Fitting .