Deals with describing risk, preferences towards risk, how to reduce risk, and the demand for risky assts

1. UNCERTAINTY AND CONSUMER
BEHAVIOUR
1.Describing risk
2.Preferences towards risk
3.Reducing risk
4.The demand for risky assets

2. Probability - Likelihood that a given outcome will occur.
Expected value - Probability-weighted average of the payoffs
associated with all possible outcomes.
Payoff - Value associated with a possible outcome.

3. PROBABILITY
Let us take an example of an oil exploration company.
The present share of the company is $30. If the
company succeeds in its new venture than the share
will rise to $40 or else it will reduce to $20. The
probability of success and failure of oil exploration
are ¼ and ¾ respectively, which is derived from the
previous experience.

4. The expected value measures the central tendency - the payoff or value
that we would expect on average.
Expected value =Pr(success)($40/share)+Pr(failure) ($20/share)
= (1/4)($40/share) + (3/4)($20/share) = $25/share
With two possible outcomes, the expected value is
E(X) = Pr1X1 + Pr2X2
When there are ‘n’ possible outcomes, the expected value becomes
E(X) = Pr1X1 + Pr2X2 + . . . + PrnXn

5. • Variability - Extent to which possible outcomes of an
uncertain event differ.
• Deviation – Difference between the expected payoff
and actual payoff.
• Standard deviation- Square root of the weighted
average of the squares of the deviations of the payoffs
associated with each outcome from their expected
values.

6. VARIABLITY
For Job 1 Expected income is 0.5x$2000 + 0.5 x $1000 = $1500
For Job 2 Expected income is 0.99x$1510 + 0.01x $510 = $1500
Particulars OUTCOME 1 OUTCOME 2 EXPECTED
INCOME
PROBABILITY INCOME ($) PROBABILITY INCOME ($)
Job 1: Commission 0.5 2000 0.5 1000 1500
Job 2: Fixed Salary 0.99 1510 0.01 510 1500
DEVIATIONS FROM EXPECTED INCOME
Particulars Outcome 1 Deviation Outcome 2 Deviation
Job 1 2000 500 1000 -500
Job 2 1510 10 510 -990

7. Deviations do not provide a measure of variability. Values may be positive or negative. To get rid of
this, we square the variations and then measure the variability by calculating the standard deviation.
Weighted average deviation squared for job 1 is given by = 0.5 x $250000 + 0.5 x $250000 = $250000
Standard deviation = 500
Weighted average deviation squared for job 2 is given by = 0.99 x $100 + 0.01 x $980100 = $9900
Standard deviation = 99.50
The second job is less risky than the first job.
Deviation Squared deviation Deviation Squared
deviation
Weighted average
deviation squared
Standard deviation
500 250000 - 500 250000 250000 500
10 100 - 990 980100 9900 99.50

8. Decision Making
Suppose we add $100 to each of the payoffs in the first job, so that the expected
payoff increases from $1500 to $1600.
The two jobs can now be described as follows:
Job 1: Expected Income = $1600, Standard Deviation = $500
Job 2: Expected Income = $1500, Standard Deviation = $99.50
Job 1 offers a higher expected income but is much riskier than Job 2.
Which job is preferred depends on the individual. While an aggressive entrepreneur
who doesn’t mind taking risks might choose Job 1, with the higher expected income
and higher standard deviation. Whereas a more conservative person might choose the
second job.

9. Expected utility - Sum of the utilities associated with all
possible outcomes, weighted by the probability that each
outcome will occur.
Risk averse - Condition of preferring a certain income to a
risky income with the same expected value.
Risk loving- Condition of preferring a risky income to a certain
income with the same expected value.
Risk neutral- Condition of being different between a
certain income and an uncertain income with the same
expected value.
Risk premium - Maximum amount of money that a risk-
averse person will pay to avoid taking a risk.

10. PREFERENCES TOWARDS RISK
In the example a person has a certain income of $20,000 or a job with
income $30,000 with probability 0.5 and an income of $10,000 with
probability 0.5. The expected utility of the uncertain income is 14 point F
(Average of point A and point E). The expected utility for income earned
without risk is 16, which is higher that the uncertain income.
For risk averse person losses are more important than gains. Increase
in income from $20,000 to $30,000 generates an gain of two utility and a
decrease in income from $20,000 to $10,000 generates a loss of six units.

12. RISK NEUTRAL
Person with risk neutral is indifferent
between a certain income and an uncertain
income with the same expected value. The
utility associated with a job generating an
income of either $10,000 or $30,000 with
equal probability is 12, as is the utility of
receiving a certain income of $20,000.
The marginal utility of income is constant
for a risk neutral person.

13. RISK LOVING
Person loving risk prefers an uncertain
income to a certain one, even if the expected value
of the uncertain income is less than that of the
certain income. The expected utility of an uncertain
income, which is either $10,000 with probability 0.5
or $30,000 with probability 0.5, is higher than the
utility associated with a certain income of $20,000.
Numerically it is:
E(u) = 0.5u($10,000)+0.5u($30,000) = 0.5 (3) + 0.5 (18)
= 10.5 > u($20,000) i.e., 8

14. REDUCING RISK
1. DIVERSIFICATION - Practice of reducing risk by allocating
resources to a variety of activities whose outcomes are not closely
related. Eg. Selling AC and Heaters
• Negatively correlated variables - Variables having a tendency to
move in opposite directions. Sales of one is strong and the other is
weak at a time.
• Mutual funds - Organization that pools funds of individual investors
to buy a large number of different stocks or other financial assets.
• Positively correlated variables - Variables having a tendency to
move in the same direction. Stock prices tend to move in the
same direction in response to changes in economic conditions.

15. 2. INSURANCE
The risk averse people are willing to pay to avoid risk. If the
cost of insurance is equal to the expected loss, risk averse people
will buy enough insurance to recover fully from any financial
losses they might suffer.
LAW OF LARGE NUMBERS:
Insurance companies by selling large number of policies, they
face relatively little risk. This tells us that although single events
may be random and largely unpredictable, the average outcome
of may similar events can be predicted.

16. 3. THE VALUE OF INFORMATION
The difference between the expected value of a choice when there
is complete information and the expected value when information is
incomplete.
The value of information is computed as
Expected value with complete information: $ 8500
Less: Expected value with uncertainty –$ 6750
Equals:Value of complete information $ 1750
Thus it is worth paying up to $1750 to obtain an accurate
prediction of sales.

17. THE TRADE OFF BETWEEN RISK AND RETURN
An individual wants to invest the savings in two assets – short term
government bonds which are risk free and a group of stocks. The individual
should decide how much to invest in each asset. The individual can invest in
bonds or stocks or a combination of both.
At the time of investment decision, we know the set of possible outcomes
and the likelihood of each, but we do not know what particular outcome will
occur. The risky asset will have a higher expected return than the risk free
asset. Otherwise, risk averse investors would buy only short term
government bonds and no stocks will be sold.