Page 86 - DCOM504_SECURITY_ANALYSIS_AND_PORTFOLIO_MANAGEMENT

Unit 2: Risk and Return

Notes
Example: The possible outcomes of two alternatives A and B, depending on the state of
economy, are as follows:
State of economy Possible outcome (`)
A B
Normal 100 100
Boom 110 200

If we assume that the three states of the economy are equally likely, then expected value
for each alternative is 100.
1. A risk-seeker is one who, given a choice between more or less risky alternatives
with identical expected values, prefers the riskier alternative i.e. alternative B.

2. A risk averted would select the less risky alternative i.e. alternative A.
3. The person who is indifferent to risk (risk neutral) would be indifferent to both
alternative A and B, because they have same expected values.

The empirical evidence shows that majority of investors are risk-averse. Some
generalisations concerning the general shape of utility functions are possible. People
usually regard money as a desirable commodity, and the utility of a large sum is usually
greater than the utility of a smaller sum. Generally a utility function has a positive slope
over an appropriate range of money values, and the slope probably does not vary in
response to small changes in the stock of money. For small changes in the amount of
money going to an individual, the slope is constant and the utility function is linear. If the
utility function is linear, the decision-maker maximises expected utility by maximising
expected monetary value. However, for large variations in the amount of money, this is
likely to be the case. For large losses and large gains, the utility function often approaches
upper and lower limits. The slope of the curve will usually increase sharply as the amount
of loss increases, because the dis-utility of a large loss is proportionately more than the
disutility of a small loss, but the curve will flatten as the loss becomes very large. For a
risk-averse decision-maker, the expected utility of a function is less than the utility of the
expected monetary value. It is also possible for the decision-maker to be risk preferring,
at least over some range of the utility function. In this case, the expected utility of a
function is more than the utility of the expected monetary value (EMV).
Figure 2.4: Utility Function and Risk Taking

Risk averse
Utility
Risk neutral

Risk Preferring

O Money

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