management of risk module 1
TRANSCRIPT
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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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Glimpses In To The Domain of Risk
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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Glimpses In To The Domain of Risk
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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Glimpses In To The Domain of Risk
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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Glimpses In To The Domain of Risk
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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Glimpses In To The Domain of Risk
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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Glimpses In To The Domain of Risk
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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Glimpses In To The Domain of Risk
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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Glimpses In To The Domain of Risk
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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Glimpses In To The Domain of Risk
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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Glimpses In To The Domain of Risk
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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Glimpses In To The Domain of Risk
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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Why is Risk Important
Corporate Finance:3 major decisions in corporate
finance Investment (capital expenditures) Financing (debt vs. equity) Profit allocation
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Why is Risk Important
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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Evidences on risk aversion fromExperiments
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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Evidences on risk aversion fromExperiments
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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Evidences on risk aversion fromExperiments
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
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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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