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AFM476: Real Options

y DCF ignores options that are embedded into many corporate projectsy Real option approach is the extension of option pricing theory to options in real assetsy Helps managers to plan and manage strategic investments

Types of Real Options1. Timing option (when to take certain actions)2. Option to expand3. Option to abandon

Problems with Valuation of Real Optionsy Underlying asset not traded and hard to valuey Pricing of the asset may not follow a continuous processy Variance may not be known or may change over the life of the optiony Exercising may not be instantaneous

Options Valuation Calls

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Options Valuation Puts

Timing ofProjects

1. When a firm has exclusive rights to a project or product for a specific period, it can delaytaking this project or product until a later date.

2. Having the exclusive rights to a product or project is valuable, even if the product or project isnot viable today. The value of these rights increases with the volatility of the underlying

business.

3. The cost of acquiring these rights (by buying them or spending money on development, forinstance) has to be weighed off against these benefits.

Option to Expand1. Taking a project today may allow a firm to consider and take other valuable projects in the

future.

2. A firm may accept a negative NPV on the initial project because of the possibility of highpositive NPVs on future projects

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Example for Expansion

Assume that Home Depot is considering opening a small store in France. The store will cost 100

million FF to build, and the present value of the expected cash flows from the store is 80 million FF.

Stand-alone investment NPV = -$20m

By opening this store, Home Depot acquires the option to expand into a much larger store any time

over the next five years. The cost of expansion will be 200 million FF, and it will be undertaken only if

the present value of expected cash flows exceeds 200 million FF. At the moment, the present value of

the expected cash flow is believed to be only 150 million FF. The standard deviation in the underlying

assets value is 28.3%. The risk-free rate is 6.00%. Should Home Depot open the store in France?

AFM476: Risk Management

Regression Methody Estimate risk based on factor betas derived from historical returnsy Fama French, is an example of an APT regression method to quantify risk

Simulationsy Forecast returns or cash flows for a variety of factor realizationsy Ex. a wide range of exchange rates, profit estimates or FCFs

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VAR

Given a distribution of daily returns, VAR is the highest value within the bottom 5% of returns. For

example, if the high end of the 5% left tail is -10% and we have a portfolio of $1M, then the value-at-

risk is $100,000. Can be calculated for whatever interval.On a portfolio, the VAR assumes that no

additional trading was done during the day.

y A single number used to encapsulate a firms market risky Used commonly to measure the risk to value of a portfolio of securitiesy Easy to find, and intuitive for non-finance people to understand.The preferred method under

Basel accords for banking regulation

y % change of at least a specific lossy Says nothing about the size of the loss within the % limit

o Just an amount above a specific sizey Historical simulation uses past data to generate rolls of the dicey Delta-method: uses distributions and covariances to derive a distribution for the portfolioy Monte Carlo method: uses simulation about historical distributions

VARs for different positions

y WFCy WFC+AAPLy WFC+AAPL+XOMy WFC+AAPL-XOM

Which one of the above has higher VAR?

W

FC by itself probably has the highestVAR.

Diversification reduces value-at-risk.