Risk Analysis

Instructor: Maharouf Oyolola

Introduction

• Until now we have examined managerial decision making under conditions of certainty. In such cases, the manager knows exactly the outcome of each possible course of action.

• In many managerial decisions, however, the manager often does not know the exact outcome of each possible course of action.

• For example, the return on a long-run investment depends on economic conditions in the future, the degree of future competition, consumer tastes, technological advances, the political climate, and many other such factors about which the firm has only imperfect knowledge. In such cases, we say that the firm faces “risk” or “uncertainty”. Most strategic decisions of the firm are of this type.

Risk and Uncertainty in Managerial Decision Making

• Managerial decisions are made under conditions of certainty, risk, or uncertainty

Certainty

• Certainty refers to the situation where there is only one possible outcome to a decision and this outcome is known precisely.

Example

• Investing in Treasury bills or T-bills leads to only one outcome (the amount of the yield), and this is known with certainty.

• However, when there is more than one outcome to a decision, risk or uncertainty is present.

Risk

• Risk refers to a situation in which there is more than one possible outcome to a decision and the probability of each specific outcome is known or can be estimated.

• Risk requires that the decision maker know all the possible outcomes of the decision and have some idea of the probability of each outcome’s occurrence.

Example

• In tossing a coin, we can get either a head or a tail, and each has an equal (i.e., a 50-50) chance of occurring (if the coin is balanced).

Uncertainty

• Uncertainty is the case when there is more than one possible outcome to a decision and where the probability of each specific outcome occurring is not known or even meaningful.

• This may be due to insufficient past information or instability in the structure of the variables.

States of nature

• Refers to conditions in the future that will have a significant effect on the degree of success or failure of any strategy, but over which the decision maker has little or no control.

• For example, the economy may be booming, normal, or in recession in the future. The decision maker has no control over any of these three states of nature.

Measuring risk with probability distributions

• In this section, we examine the meaning and characteristics of probability distributions, and then use these concepts to develop a precise measure of risk.

Probability Distributions

• The probability of an event is the chance or odds that the event will occur. For example, if we say that the probability of booming conditions in the economy next year is 0.25, or 25 percent, this means that there is 1 chance in 4 for this condition to occur.

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

Probability Distribution of states of the economy

State of the economy Probability of occurrence

Boom 0.25

Normal 0.50

Recession 0.25

Total 1.00

• The concept of probability distributions is essential in evaluating and comparing investment projects.

• In general, the outcome or profit of an investment project is highest when the economy is booming and smallest when the economy is in a recession.

Expected Profit

• It is the weighted average of all possible profit levels that can result from the investment under the various states of the economy, with the probability of those outcomes or profits used as weights.

• The expected profit is a very important consideration in deciding whether to undertake the project or which of two or more projects is preferable.

• Expected profit= i

n

ii pE .)(

1

Calculation of the expected profits of two projects

Project State of the economy Probability of occurrence Outcome of investment Expected value

Boom 0.25 $600 $150

A Normal 0.5 500 250

Recession 0.25 400 100

Expected profit from project A $500

Boom 0.25 $800 $200

B Normal 0.5 500 250

Recession 0.25 200 50

expected profit from project B $500

An Absolute measure of risk: the standard deviation

• The standard deviation (σ) measures the dispersion of possible outcomes from the expected value.

• The smaller the value of σ, the lower the risk.

An Absolute measure of risk: the standard deviation

• To find the value of the standard deviation (σ) of a particular probability distribution, we follow three steps:

n

iii

i

n

ii

ii

PXXdards

PXXiance

XXd

1

2

2

1

2

.)(tan

.)(var

Calculation of the standard deviation of profits for project A and project B

• See Microsoft Excel file

A relative measure of risk: the coefficient of variation

• The standard deviation is not a good measure to compare the dispersion (relative risk) associated with two or more probability distributions with different expected values or means.

• Thus, we use the coefficient of variation (V) to calculate the relative measure of risk.

A relative measure of risk: the coefficient of variation

• Coefficient of variation=v=

X

Example

• If the expected value or mean and standard deviation of project A were, respectively, XA (bar)= $5,000 and σA=$707.11 while XB (bar)= $500 and σB=$212.13

• Project is less risky than project B

42.0500$

13.212$

14.05000$

11.707$

B

BB

A

AA

XV

XV

Risk-Adjusted Discount Rate Approach

• When making long-term capital budgeting (investment) decisions, the risk-adjusted discount rate approach is a commonly used method for dealing with the uncertainty associated with future cash-flow estimates.

Risk-Adjusted Discount Rate Approach

• Net present value is defined as

NINVk

NCFNPV

n

ttt

1 )1(

Risk-Adjusted Discount Rate Approach

• NCFt=net cash flow in period t (for each of n periods)

• NINV= the net investment

• K=the firm’s cost of capital

Risk-Adjusted Discount Rate Approach

• An investment is accepted if its NPV is greater or equal to zero.

• In the risk-adjusted rate, k*, rather than the firm’s cost of capital (k).

• The magnitude of k* depends on the risk of the project- the higher the risk, the higher the risk-adjusted discount rate.

Example

• The Hamilton-Beach company has been offered a contract to supply private-label food processors to a regional discount store chain. The investment required for this project is $1,000,000. It is expected to produce annual net cash flows of $290,000 for a period of five years. Hamilton-Beach uses the risk-adjusted discount rates shown in table 19.1 when evaluating capital investment decisions.

Risk-adjusted discount rates: Hamilton-Beach Company

Project Risk Risk premium

(θ)

Risk-adjusted discount rate

K*= k + θ

Average risk 0% 12%

Above-average risk

3 15

High risk 8 20

Information and Risk

• Risk often results from lack of or inadequate information.

• The relationship between information and risk can be analyzed by examining asymmetric information, adverse selection, and moral hazard.

Asymmetric information

One party to a transaction (i.e., the buyer or seller of a product or service) often has less information than the other party with regard to the quality of the product or service.

Example

• The market for “lemons” (i.e., a defective product, such as a used car, that will require a great deal of costly repairs and is not worth its price).

• Specifically, sellers of used cars know exactly the quality of the cars that they are selling but prospective buyers do not. As a result, the market price for used cars will depend on the quality of the average used car available for sale.

• The owners of lemons would tend to receive a higher price than their cars are worth, while the owners of high-quality used cars would tend to get a lower price than their cars are worth.

Adverse selection

• The owners of high-quality used cars would therefore withdraw their cars from the market., thus lowering the average quality and price of the remaining used cars offered for sale.

• Sellers of the now above-average-quality cars withdraw their cars from the market, further reducing the quality and price of the remaining used cars offered for sale.

• Thus, the end result is that low-quality cars drive high-quality cars out of the market. This is known as adverse selection.

Adverse selection

• The problem of adverse selection that arises from asymmetric information can be overcome or reduced by the acquisition of more information by the party lacking it.

• For example, in the used-car market, a prospective buyer can have the car evaluated at an independent automobile service center, or the used car dealer can signal above-average-quality cars providing guarantees.