RISK ANALYSIS

Prepared By: Hammad Latif

Difference Between Risk and Uncertainty

Measuring Risk with Probability Distribution

Probability Distribution

An Absolute Measure of Risk: The Standard Deviation

Measuring Probabilities with Normal Distribution

A Relative Measure of Risk: The Coefficient of Variation

1. Probability Distribution

By listing all the possible outcomes of an event and the probability attached to each, we get a probability distribution

For Example: 3 states of economy

Boom

Normal

Recession

2. Standard Deviation

Standard Deviation measures the dispersion of possible outcomes from the expected value. The smaller the value of σ, the tighter or less dispersed is the distribution.

3. Normal Distribution

To find the probability of a particular outcome falling within a specific range, we simply subtract the expected value or mean of the distribution from the outcome.

z = 𝜋𝑖 − 𝜋

σ

4. The Coefficient of Variation

The standard deviation is not a good measure to compare the dispersion associated with two or more probability distributions with different expected values. The distribution with very largest expected value or mean may very well have a larger standard deviation but not necessarily a larger relative dispersion.

V = σ𝑿

Utility Theory and Risk AversionThere are three types of managers

Risk Seekers

Risk Neutral

Risk Averters

Utility of Money

Money or Wealth

Increasing

Marginal

Diminishing Marginal Utility

A

Techniques for Incorporating Risk into Decision Making

Decision Trees

Simulation

1. Decision Trees

2. Simulation

Simulation is also knows as “Virtual Reality”

Foreign Exchange Risks and Hedging

Foreign Exchange Risks

While investing in foreign securities, there is always a risk that the foreign currency can depreciate or decrease in value during the time of the investment

Hedging

Hedging refers to the covering of a foreign-exchange risk. Hedging is usually accomplished with a forward contract. This is an agreement to purchase or sell a specific amount of a foreign currency at a rate specified today for delivery at a specific future date.

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