management of risk module 1

8/13/2019 Management of Risk Module 1

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Introduction

Dr. Sankersan Sarkar


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Glimpses In To The Domain of Risk

Sickness of individuals and their dependants isanother cause of concern because of its

adverse economic consequences on theaffected individuals, that arise of out of themedical expenses they have to bear to treat

the sickness. . The Medical Insurance businessthrives because of this need of a large sectionof the society.


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Almost every form of sports involve the risk ofphysical injury which can be temporary orpermanent or may even be fatal. Yet sports of

all types are a popular pastime or recreationor profession.

Almost every profession involves certain typesof hazard or possibilities of injuries or sicknessor ailments. However there cannot be alivelihood without the pursuit of a profession.


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Natural calamities are unpredictable andthey have a devastating impact on the

society causing widespread economiclosses. Destruction / loss of business assets may

arise out of various causes and can beseriously damaging for the firms carryingout business and they require protection.


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Firms often make large scale capitalexpenditure either to expand their

existing business or to enter into newones. Adverse developments in thebusiness environment of the firms havean impact on the profit margins andalso on the survival for the firms.


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A widespread practice among firmsthroughout the world is to create new

products by carrying out R&D. R&D is anactivity that requires substantial amountsof commitment of funds and time. If the

product is acceptable to the market thefirms gain significantly; however they lose ifthe product turns out to be otherwise,

leading to huge losses to the affected firms.


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Firms often invest funds into projects thatmay not be viable in the near future but

may eventually become profitable at laterpoints in time in future. Yet firms make suchinvestments in the hope of earning high

returns if the project succeeds in the future,which may not turn out to be so.


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Investors of various types make financialinvestments in the hope of earning returns.

However investments may eventually turn outto be bad for multiple reasons. As a resultinvestors may have to incur high amounts of

capital losses which may wipe out their entireinvestment. Financial investments may offerhigh gains or high losses, but investors do

invest notwithstanding the possible losses.


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Across the world some types ofinvestments such as investment in

Govt. securities are considered to berisk-free. Investors seeking a securedreturn and protection for capital prefersuch types of investments.


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Lotteries offer huge gains in a smalltime for a small price. Throughout the

world people seeking quick gains arelured into lotteries and most of themactually lose the price they have paidto enter into the lottery.


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In those countries where gambling islegally allowed, people enter into

gambles for a variety of reasonsranging from making big money in notime to gambling just for fun. Gamblingis a thriving business.


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Speculation is an activity that iswidespread in the financial markets

worldwide. It leads to both gains andlosses and often of large magnitude.But speculators knowingly enter intosuch activities, many a time ending upin huge losses.


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What is common and what is not inthe above instances?

How many kinds of risk are there? Do we: hate risk or love it or seek it

or tolerate it or avoid it? Can we prevent risk altogether?


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THE BIG QUESTIONS Can we live without risk? Can we do business without risk? Is risk bad or good for

businesses? How can we make the most out

of business amidst risk?


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GOAL OF RISK MANAGEMENT

Goal is NOT to eliminate risk.Why?

Goal is to maintain risk at apredetermined level of

acceptability


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What is Risk? It is present in situation(s) that have many

possible outcomes and some or all of theoutcomes may be adverse

Such situations are referred to as experiments The various possible outcomes may be known

but cannot be predicted with certainty

e.g. Death or sickness of an individual, lossesdue to natural calamities, destruction / loss ofbusiness assets, investment losses, losses from

gambles and losses from speculation ...


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Some Essential Elements of Risk Multiple outcomes Some (or all) of the outcomes may be adverse Occurrence of any of the possible outcomes

cannot be predicted with certainty Or the order in which the outcomes will occur

cannot be predicted with certainty


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Why is Risk Important

Investment choices:3 aspects of investment decision making Asset allocation: Cash/Bonds/Stocks Asset selection

Performance evaluation: a. How do wemeasure risk? b. How much riskadjusted return do we expect?

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Corporate Finance:3 major decisions in corporate

finance Investment (capital expenditures) Financing (debt vs. equity) Profit allocation

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Valuation of assets Risk affects Asset Pricing

As it is in the real world, it may be / notbe done rationally Rational valuation is likely to lead to

gains Irrational valuation is likely to lead to

losses 26


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Risk Aversion

Natural reaction to presence of risk in thedecision making scenario

Affects valuation The higher the risk the higher is the risk-

aversion and the higher is the impact on

assessment of asset value


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Evidences on risk aversion fromExperiments

a) Extent of risk aversionb)Differences across different

settingsc) Risk aversion differences across

subgroups


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a. Extent of Risk Aversion: Human beings are risk averse Risk aversion increases with

increase in stake Differences in risk aversion exist

across individuals: Risk averse / Risk

neutral / Risk seeker 29 f


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b. Differences across settings: Differences across the settings in which the

choices are presented: circumstances &conditions

Choice of risky situations: lotteries vsgambling games vs auctions

Differences in institutional mechanisms thatmonitor the risky situations

Extent of information given to the decision

maker for choice of risk

d k f


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c. Differences across subgroups: Gender: Males vs. females

Age: Young vs. old Experience: Experienced vs.inexperienced Racial & cultural differences


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Pricing of Risky Assets

Assets with various degrees of risk aretraded widely in financial markets Financial markets represent live experiments

of a very large scale on the collective risk-return preferences of the investors at large

Market prices of risky assets provide morerealistic measures of risk aversion thanexperiments and surveys carried out undercontrolled conditions


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Pricing of risky assets

Value of an equity share can be arrived by thefollowing formula:

This relationship can also be used to estimate

the required rate of return on the market indexgiven the cumulative dividends expected onthe stocks in the index and the growth rate in

index.

DPSinrateGrowth-equityonreturnof rate Required periodoneafterexpectedshare perDividend Value


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Example 1

As on a specific date the level of S&P 500Index was 857.14 and the dividend yield forthe next period was 2.5%. The long term

growth rate of cumulative dividends on theindex was 5%. Estimate the required rate ofreturn on the market index using the abovedata. Also calculate the risk premiumembedded in the required rate if the return onthe 10 year govt. bonds was 5.5%.


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Replace the terms in the expression bycumulative dividends expected on the

stocks comprising the index, market valueof the index now, growth rate in the index &required rate of return on market index

Solving this equation for required rate ofreturn on market & subtracting the riskfree rate of return will give us the impliedequity risk premium or market riskpremium


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Investors collectively are risk averse indicated bythe fact that observed market risk premiums are

positive The risk aversion of investors changes over time

indicated by the fact that market risk premiums

change significantly over time Moreover investors become more risk averse some

times & less risk averse in others because risk

premiums are more in some periods & less in others Equity risk premiums and Stock prices are inversely

related. Why ?

f


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Other financial markets

The behavior shown in equitymarkets by the investors canalso be seen in other financialmarkets e.g. bonds, derivatives,forex etc

l b


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General Observations

Individuals are risk averse and theytend more to be so when stakesare large

Differences in risk aversion existacross the population and

significant differences have beenobserved across subgroups

l b


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General Observations Individuals are affected more by losses

than by equivalent gains (loss aversion) Decision making in risky situations depends

on the situations presented to individuals(Framing) Individuals appear to be more willing to

take risks with money that has beenearned without efforts than with moneyearned with efforts (House Money effect)


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Measuring risk aversion

Degree of risk aversion should be a functionof the impact of risk on the financial wellbeing of the individual and hence on theutility of the individual

Out of several approaches for measuringrisk aversion, two important ones are:

Certainty Equivalents Risk Aversion Coefficients


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Certainty Equivalents

It is the guaranteed or certain amount thatwill deliver the same utility (satisfaction) toan individual as the expected utility of the

uncertain outcomes of a gamble or a riskysituation If A and B are two outcomes in a risky

situation with probabilities p and (1 -p)respectively then expected value of theoutcomes is = p A+(1-p) B

f


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Let the utilities of the outcomes A & B bedenoted by U(A) and U(B) respectively. Let

V be a certain amount that can be receivedwithout risk having an utility U(V). Also letV be equal to the expected value of the risky

outcomes. Thus V= p A+(1-p) B For a risk neutral individual the utility of

receiving a certain amount V, equal to theexpected value of the risky outcomes, isequal to the expected utility of the riskyoutcomes. U(V)= p U(A) + (1-p) U(B)

B i k i di id l ld d i h


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But a risk averse individual would derive muchgreater utility from a guaranteed outcome thanfrom the uncertain outcomes of the riskysituation.

Hence for a risk averse person the utility derivedfrom a guaranteed amount that is equal to theexpected value of the risky outcomes, is greaterthan the expected utility of the risky outcomes.U(V)> p U(A) + (1-p) U(B)

This means there will be a value (less than V),which if guaranteed, would offer the sameexpected utility as the risky outcomes.

V


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Thus The difference between V and is called the

risk premium Risk premium = With increase in risk aversion of an individual,

risk premium will also increase So the higher the risk aversion the lower will be

the amount of certainty equivalent OR highershould be the amount of risky outcomes See example: Damodaran/ch.2/p.19-20

U(B) p)-(1U(A) p)VU(

V

V-V


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Example 2

An individual is assumed to have a log utilityfunction. A gamble is offered to him in which hecan win $10 or $100 with equal probability. If the

individual is risk averse then calculate:1. The certainty equivalent of the individual2. The risk premium for the individual


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Significance of Certainty Equivalents

Generally the risk hedging products (insurance /derivatives) are priced in such a manner that theyoffer the hedgers a definite (certain) cost in

exchange for an indefinite (uncertain) cost Known cost is the price of the hedge product

(insurance premium, option price)

Unknown cost is the loss to be borne from the riskyevent if the hedge is not used So the cost of the hedge is the certainty equivalent

of the uncertain outcomes of the risky event


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Significance of Certainty Equivalents

The fact that risk hedging products exist widelyand many users pay a price to use such productsto hedge various types of risk indicate that they

are willing to accept a known or definite orcertain cost (or loss) instead of an unknown one


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Risk Aversion Coefficients It is a measure of the amount of the utility gained

(or lost) as an individuals wealth increases (ordecreases)

According to the above concept the risk aversioncoefficient should be the first derivative of theutility function of the individual denoted by U(W)

But this measure is not comparable acrossindividuals with different utility functions

Hence an improved measure of risk aversion hasbeen proposed by Arrow & Pratt

A P tt Ri k A i C ffi i t


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Arrow-Pratt Risk Aversion Coefficients Arrow-Pratt Absolute Risk Aversion

= -U(W) / U(W) This would result a positive number

for a risk averse individual and willincrease with the degree of risk

aversion.

Arro Pratt Risk A ersion Coefficients


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Arrow-Pratt Risk Aversion Coefficients Decreasing absolute risk aversion indicates:

amount of wealth one is willing to put at riskincreases as wealth increases

Increasing absolute risk aversion indicates:amount of wealth one is willing to put at riskdecreases as wealth increases

Constant absolute risk aversion indicates:amount of wealth one is willing to put at riskremains unchanged or fixed as wealthincreases

A P i k i ffi i


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Arrow-Pratt risk aversion coefficients But the absolute risk aversion coefficients can

not be compared across individuals withoutreference to their level of wealth

Hence an improved measure proposed isArrow-Pratt Relative Risk Aversion Coefficient= -W*U(W) / U(W)+ Where W is the level of wealth


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Decreasing relative risk aversion indicates:

proportion of wealth one is willing to put atrisk increases as wealth increases Increasing relative risk aversion indicates:

proportion of wealth one is willing to put atrisk decreases as wealth increases

Constant relative risk aversion indicates:proportion of wealth one is willing to put atrisk remains unchanged or fixed as wealthincreases

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management of risk module 1

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