6.found.risk ana

8/12/2019 6.Found.risk Ana.

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Chapter 6(8): Foundations

of Risk AnalysisThe essence of risk:A firmsexpectation about

future profit may not be according to desire. There

may be variation of actual profit (return) from

expected profit (return). In fact, the best that a firm

can reasonably be expected to do is to make some

estimate of the range of possible future costs and

benefits and the relative chances of earning a high or

low profit on the investment. The essence of risk

deals with two states of expectations:


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The essence of risk:Certainty: Certainty refers to expectations which are

single valued i.e. prospective profits are

represented in terms of a single outcome and not interms of a range of alternative possible outcomes.

For example, a firm decides to invest in three-

month treasury bills. By investing in these short-

term treasury bills, the firm can calculate the exactreturn that will be received at the end of three

months.


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The essence of risk:Uncertainty/Risk: The future unknown,

unexpected or undesired event/situation is

termed as uncertainty and themathematical/statistical/numericalexpression of chance of occurring thatunknown event is called risk. Sometimes

uncertainty and risk are used as synonym. Itdescribes an investment whose profit is notknown in advance with absolute certainty.


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6-5

Alternative investment criteria

1. The maximum return criterion (MRC): To

choose the investment out of all alternatives

that provides the rate of return with perfectcertainty is known as maximum return

criterion. For example, if returns from

investment X is 10% and from investment Y is12%, then clearly maximum return criterion

prefers investment Y.


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2. Maximum expected return criterion

(MERC): Expected return is sum ofmultiplicative results of possible rate of

return and associated probability of earning

that and the investment offers the highest

expected return choosing that investment is

known as maximum expected return

criterion.


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Alternative investment criteriaThe MERC can be applied to uncertain investments

since each investment can be characterized bysingle measure of probability and therefore all

investment proposals can be ranked according tothis criterion. For example:

E(Rx) = 0.80X0.30 + 0.20X0.10 = 0.26= 26%

E(Ry) = 0.25X(-0.08) +0.50X0.16+0.25X0.24=12%

E(Rz) = 0.20X0.12+0.30X0.06+0.10X0.09+0.40X(-0.05)=3.10%

Investment X is chosen according to MERC.


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6-8

Alternative investment criteria3. Maximum expected utility criterion (MEUC):

Utility is the level of satisfaction can be

enjoyed by converting money in term ofgoods or services. Generally level of utilityfor increasing the conversion of money interms of level of goods or services is

decreasing that is called diminishingmarginal utility. This utility theory/conceptrecognizes that it is the pleasure or

satisfaction


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6-9

Alternative investment criteriathat can be obtained from money, not money

itself, which is more important. The sum of

multiplicative results of utility againstmoney and respective probability is called

expected utility. According to maximum

expected utility criterion theinvestment/asset involves the highest

MEUC is to be chosen.


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6-10


Investment A Investment B

Prob. Profit Utility Prob. Profit Utility

0.50 1000 1.00 0.50 0 0.00

0.50 3000 2.50 0.50 4000 3.00

E(P) 2000 Same 2000

E(U) 1.75 Prefers A 1.50


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Alternative attitudes toward risk

It is convenient for the purpose of the analysis to

distinguish among major categories of investors

such as:i. Risk avertersindividuals with concave utility

function/curve (dislike risk). The utility function

is concave if U'(X) 0 and U'' (X) 0.

ii. Risk loversindividuals with convex utilityfunction/curve (prefer risk). The utility function

is convex if U'(X) 0 and U'' (X) 0.


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Alternative attitudes toward risk

iii. Risk neutralindividuals with linear utility

function/curve (indifferent to risk). Linear

utility function U(X), where U(X) = a+bx(where b >0) hence U'(X) = b> 0 and U'' (X)

= 0.

Problems: 8.2, 8.3, 8.6, 8.10 (a, b & c).

6.found.risk ana

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