Value at Risk and Decision Trees Lecture 25

• Read Chapter 9• Lecture 25 VAR Analysis.xlsx• Lecture 25 Simple VAR.xlsx• Lecture 25 Decision Tree.XLSX

Value at Risk Analysis

• Value at Risk – VAR• Originally VAR used to quantify

market risk, but considered only 1 source of risk

• By year 2000 businesses were integrating their risk management systems across all of the enterprises– Focus on analyzing multiple sources of

risk including market risk• Now market based VAR analyses

measure integrated market and credit risk

VAR as Risk Capital

• VAR is the equity capital that should be set aside to cover most all potential losses with a probability of “c”

• Thus, the VAR is the amount of capital reserves that should be held to meet shortfalls

Value At Risk Model

• If “c” is the selected confidence level, VAR corresponds to the 1-c lower tail of the probability distribution (the quantile).

Value At Risk (VAR) Model

To estimate the VAR quantile for a risky business use these steps:

1. Develop a stochastic simulation model of the risky business decision

2. Validate stochastic variables and validate the model

3. Pick a ‘c’ value, say, 5%, so 1-c = 95%4. Simulate the model and analyze the KOV5. Calculate the quantile for the c value6. Calculate VAR = Mean – Quantile at 1-c7. Report the results

Value At Risk (VAR) Model

• On selecting the ‘c’ value – literature uses the 95% level

• This level of ‘c’ would assure the manager that ending cash will be positive with 95% confidence

• If simulating 1,000 iterations, the quantile will be the 50th value, so we can sort the stochastic results and read the 50th value

• Or simply use the PDF in Simetar

VAR in Simetar

• Simulate the KOV and draw a PDF• Change the Confidence level to 0.90 for “c” =

5%• Edit the title of the PDF chart• VAR value is the Lower Quantile

Valuation Models

• A variation on VAR is the traditional valuation model

• Valuation models focus on the mean and the variation below the mean

VAR for Comparing Risky Alternatives

• Simulate multiple scenarios and calculate VAR for each alternative

VAR for Calculation with Simetar

• Simulate multiple scenarios and use the SimData statistics and the QUANTILE function

• =QUANTILE(simulated values, 0.05)• Can graph the PDFs and change

confidence level

VAR Shortcomings• VAR analyses generally used in business

gives a false sense of security • The literature assumes Normality for the

random variables, why?– Normal is easy to simulate – Can easily calculate the Quantile if you know

mean and std deviation VAR = Mean – (2.035 * Std Dev)

• The chance of a Black Swan is ignored– This understates the Quantile and the equity

capital reserve needed to cover cash flow deficits– Contributed to the 2008 Recession

Overcoming VAR Shortcomings• Modify the probability distributions for the random

variables that affect the business• Incorporate low probability events that could cause

major harm to the business, i.e., Black Swans• Use and EMP distribution and adjust the Probabilities

and Sorted Deviates as a Fraction for Black Swan events– Change the F(X) values for the low probability– Change the minimum Xs

• Many textbooks are available to discuss decision trees and their application to decision making

• Decision trees are a simple way to organize decisions and outcomes

• Decision trees do not use simulation• Decision trees can be used to construct

simulation models• Outline for this section of the lecture

– Demonstrate a simplified decision tree – Demonstrate its use for decision making– Demonstrate how a decision tree can be used

to formulate a simulation model

Decision Trees

• Box represents a decision

• Circle denotes an outcome

• Decision tree organizes decisions and outcomes

Decision Tree Terminology

Hurricane coming to Galveston

Stay in Houston 45% chance Die

Stay in College Station 0% chance Die

Run

Stay in Galveston and Die with a 90% probability

• A startup business faces the decision to expand or exit

Decision Tree for Business

Business breaks even for years, no big profits earned

Franchise Business, rich beyond belief

Continue Development

Sell business

Business Fails, dog dies, spouse leaves with an employee, you become a street person

• A startup business facing the decision to expand considers more options, such as

Decision Tree for Business

Business breaks even for years, no big profits earned

Franchise BusinessContinue

Development

Sell business at a loss

Franchise Business Fails to get started

High Demand

Moderate DemandLow Demand

Fails to take off

• Assign probabilities to each outcome and PDFs of net returns for each choice

Decision Tree to Simulation

Business breaks even for years, no big profits earned P(breakeven) = 0.25

Franchise BusinessInvest $1 million P(Success) = 0.75

Continue Development

Sell business at a loss of 50% of the initial investment

Franchise Business Invest $1 Million Fails P(Fail) = .25

P(High) = .25

P(Mod) = .30

P(Low) = .40

P(Less Return) =0.05

Start

Decision Model with Risk

Decision Model with Risk

Decision Model with Risk

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Franchise Do Not Franchise Sell Business

Decision Model with Risk

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Stochastic Efficiency with Respect to A Function (SERF) Under a Neg. Exponential

Utility Function

Franchise Do Not Franchise Sell Business

• Useful concept• Maybe most useful for structuring our

thinking about the options and the probabilities for each possible outcome

• When combined with a risk model it can add value to the simulation model results

• Is applicable for branch type decisions

Decision Trees Summary

• What you need to start a business– Legal entity– A product or service– Website– Web sales capability

• Credit card acceptance – Use PayPal• Personal Horror Story

– Website developed by professional• Contract with reputable firm who has

reasonable rates• Contract with a server host

Setting Up an Internet Business

• Legal entity– Need a lawyer – Get a corporate name– Set up a corporation or LLC– File articles of incorporation with the

state• $2,000 plus

– Things to consider for corporation• Transfer of shares• President• General manager and Treasurer• Secretary• Surviror ship terms

Setting Up an Internet Business

• Product or Service to sell• Protect your product• Copyright or patent

– What is the difference• Copyright protects software for life

of author + 16 years– Cost to file copyright is low about $50– http://www.copyright.gov/– Easy to do– Patent has limited life

Setting Up an Internet Business

• Website– Know what you want – Have a good design– Check out the website host

• What are their annual fees to host website

• What are other sites they host• What are their provisions for 24/7 service

– redundancy in servers • Will they interface with PayPal?

– Get a firm date for delivery and going live• Build in a penalty for late delivery

Setting Up an Internet Business

• Website development– Use a local website developer– Examine websites they developed

that offer services you require– Can they program the website to

accept credit cards with high level of security

– Are they going to program it locally? Or sub it out to a programmer in a foreign country

– Will they develop it to your time schedule

– What is the cost and cost of changes• Can you get access to change it yourself/

Setting Up an Internet Business

• Website sales support is essential• Need support from website host to

set this up• What is the monthly access fee?

– PayPal charges $30/month to let you process credit cards manually

• What are the hidden costs – 5% or less credit transactions

Setting Up an Internet Business