unit-3 risk and financial assets.doc

8/14/2019 UNIT-3 RISK AND FINANCIAL ASSETS.doc

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INTRODUCTION

Risk is one of the basic factors that affect the prices of securities. Inasset markets, there are market risks. Risk is associated with apossibility of loss.It is associated with uncertainty. Earlier, some economists

like Frank Knight used to distinguish between situations of uncertainty andthat of risk. The latter were situations where individuals can list the possibleoutcomes and can assign probabilities to these outcomes. We now turn tomethods that attempt to uantify risk and return to an asset.The risk!return tradeoff could easily be called the "ability#to#sleep#at#nighttest." While some people can handle the euivalent of financial skydivingwithout batting an eye, others are terrified to climb the financial ladder withouta secure harness. $eciding what amount of risk you can take while remainingcomfortable with your investments is very important.

In the investing world, the dictionary definition of riskis the chance that an

investment%s actual return will be different than e&pected. Technically, this ismeasured in statistics by standard deviation. 'isk means you have thepossibility of losing some, or even all, of our original investment

(ow levels of uncertainty )low risk* are associated with low potential returns.+igh levels of uncertainty )high risk* are associated with high potential returns.The risk!return tradeoff is the balance between the desire for the lowestpossible risk and the highest possible return. This is demonstrated graphicallyin the chart below. higher standard deviation means a higher risk and higherpossible return.

common misconception is that higher risk euals greater return. Therisk!return tradeoff tells us that the higher risk gives us thepossibilityof higher
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returns. There are no guarantees. -ust as risk means higher potential returns, italso means higher potential losses.

n the lower end of the scale, the risk#free rate of returnis represented by thereturn on /.0. 1overnment 0ecurities because their chance of defaultis ne&t

to nothing. If the risk#free rate is currently 23, this means, with virtually norisk, we can earn 23 per year on our money.The common uestion arises4 who wants to earn 23 when inde& fundsaverage563 per year over the long run7 The answer to this is that even the entiremarket )represented by the inde& fund* carries risk. The return on inde& fundsis not 563 every year, but rather #83 one year, 683 the ne&t year, and so on.n investor still faces substantially greater risk and volatility to get an overallreturn that is higher than a predictable government security. We call thisadditional return the risk premium, which in this case is 23 )563 # 23*.

1. Explain the concept of Risk. How is different with certainty and

uncertainty?

Ans Risk is a concept that denotes the precise probability of specificeventualities. Technically, the notion of risk is independent from the notion ofvalue and, as such, eventualities may have both beneficial and adverseconseuences. +owever, in general usage the convention is to focus only onpotential negative impact to some characteristic of value that may arise froma future event.

'isk can be defined as 9the threat or probability that an action or event willadversely or beneficially affect an organisation%s ability to achieve its

ob:ectives;. In simple terms risk is


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deviation. (ike the sun rising in the east and inevitability of death. 0imilarly,there may be some business situations involving near certainty. E&pecting tosell a certain number of bags of rice in a locality, when you are a monopolitistand rice is the staple food of the people of the locality./ncertainty is a situation that makes prediction difficult. ne may not be sure

of the occurrence of a particular event with any degree of precision. Aeoplefind it often difficult to make predictions pertaining to weather. 0o also, themeteorological department, sometimes. To attempt to define uncertainty withany rigor presents e&tremely comple& and ha@ardous conceptual andmathematical problems. In practice also, it is difficult to deal with thesituations of uncertainty, since nothing stands to prediction.The third state of possibility, i.e., risk, is said to be a situation lying in betweenthe above two states, vi@., certainty and uncertainty. This can be bestunderstood in the form of a continuum with certainty and uncertainty on thetwo ends and risk covering the middle ground.

"ontinuum reflectin$ the possibility of occurrence of an E%ent

'isk>ertainty /ncertainty)5BB3* )B3*

In statistical terminolo$y, Risk is referred to be a situation in whichfuture outcomes, to$ether with their associated probabilities are

known. In other words, it is said to be as dispersion in a sub&ecti%eprobability distribution.'ncertainty4 The lack of complete certainty, that is, the e&istence of morethan one possibility. The "true" outcome!state!result!value is not known.(easurement of uncertainty4 set of probabilities assigned to a set ofpossibilities. E&ample4 "There is a 2B3 chance this market will double in fiveyears"Risk4 state of uncertainty where some of the possibilities involve a loss,catastrophe, or other undesirable outcome.(easurement of risk4 set of possibilities each with uantified probabilitiesand uantified losses. E&ample4 "There is a CB3 chance the proposed oil well

will be dry with a loss of D56 million in e&ploratory drilling costs".ne may have uncertainty without risk but not risk without uncertainty. Wecan be uncertain about the winner of a contest, but unless we have somepersonal stake in it, we have no risk. If we bet money on the outcome of thecontest, then we have a risk. In both cases there are more than one outcome.


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The measure of uncertainty refers only to the probabilities assigned tooutcomes, while the measure of risk reuires both probabilities for outcomesand losses uantified for outcomes.

). Explain the difference between *ystematic Risk and 'nsystematic

Risk.

Ans 0ystematic risk is due to risk factors that affect the entire market such asinvestment policy changes, foreign investment policy, change in ta&ationclauses, shift in socio#economic parameters, global security threats andmeasures etc.

/nsystematic risk is due to factors specific to an industry or a company likelabor unions, product category, research and development, pricing, marketingstrategy etc.

0ystematic risk is beyond the control of investors and cannot be mitigated to alarge e&tent. In contrast to this, the unsystematic risk can be mitigatedthrough portfolio diversification. It is a risk that can be avoided and the marketdoes not compensate for taking such risks.

+owever the systematic risks are unavoidable and the market doescompensate for taking e&posure to such risks.

+he indi%idual components of systematic risk are the followin$)i* arket risk)ii* Interest rate risk

)iii* Aurchasing power risk

+otal Risk *ystematic risk - 'nsystematic Risk

The various types of unsystematic risks can be subdivided into severalcategories depending on the root causes. ?usiness 'isk is where the revenuesof the company are insufficient to cover the fi&ed cost of the operations.Financial 'isk occurs when the revenues are insufficient to cover fi&ed chargessuch as interest rate payments on debt.+igh# geared companies )companies that are more reliance on borrowed fundsthan euity* are more e&posed to this type of risk. anagement 'isk is where

the managers of the company are unable to manage the business at a profitmay be due to ine&perience or incompetence=s or where there is evidence oforgani@ed fraud by the management. Finally, there is >ollateral 'isk, whichrefers to the inadeuacy of the claims )security* that a lender may have on a


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borrower. In the case of a company going into liuidation, an ordinaryshareholder faces a much higher >ollateral 'isk than a secured creditor.We can see from the above points that unsystematic risk does not depend oneconomic activities and therefore it can be reduced and essentially eliminatedby applying a diversification strategy. This means, if you have a number of

assets in your portfolio, and as long as the unsystematic risk associated withthese assets are not correlated )not moving in the same direction*, the positiveand negative events should largely cancel out each other.

. /hat is the Relationship between the Return and Risk?0R

What Does RiskReturn +radeoffMean?Ans There is a positive relationship between return and risk in termspossibility only. +igher the risk on a security, higher the possibility to gethigher returns.The concept that the higher the return or yield, the larger the riskor vice versa. ll financial decisions involve some sort of risk#return trade#off.

The greater the risk associated with any financial decision, the greater thereturn e&pected from it. Aroper assessment and balance of the various risk#return trade#offs available is part of creating a sound financial and investmentplan. For e&ample, the less inventory a firm keeps, the higher the e&pectedreturn )since less of the firm%s current assets is tied up*. ?ut there is also agreater risk of running out of stock and thus losing potential revenue. In aninvestment arena, you must compare the e&pected return from a giveninvestment with the risk associated with it. 1enerally speaking, the higher therisk undertaken, the more ample the return conversely, the lower the risk, themore modest the return. In the case of investing in stock, you would demandhigher returnfrom a speculative stock to compensate for the higher level of risk.

n the other hand, /.0. T#bills have minimal risk so a low return is appropriate.The proper assessment and balance of the various risk#return trade#offs is partof creating a sound investment plan.The financial manager tries to achieve the proper balance between theconsiderations of


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T'$E FF

'isk#return trade off is the kingpin of entire financial decision making.Investors compare return to the amount of risk they undertake. systematiccomparison of this risk and return could be possible only when we are able tomeasure the risk in precise terms.

2. Explain the difference Expost Return and Exante Return.Ans In the financial world, the ex-ante return is the e&pected return of aninvestment portfolio.Epost translated from (atin means "after the fact". The use of historicalreturns has traditionally been the most common way to predict the probabilityof incurring a loss on any given day. Epost is the opposite of eante, whichmeans "before the event".

Investment Decisions

Financing Decisions

RETURN

Dividend Decisions

RISK

arket !alue of firm
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1 1 2 2 1 1 2 2 12

>alculating investment returns on a stock or a portfolio of stocks is usuallydone in one of two ways. n e& post analysis looks at past returns. It is areliable indicator because all of the inputs to the calculations are alreadyknown. These calculations look at what you invested at the start, what youearned in income during a given time period, and what your investment could

sell for at the end of the period. This analysis is done periodically to check howan investment has performed. The second type of approach is an e& anteanalysis, which forecasts what an investment might return in the future.

3. Explain the Risk and Return on portfolio"NS#The return on a portfolio of assets is calculated as4

N

rp = $ wiri i=1

where ri is the e&pected return on asset i, andwi is the weight of asset i in the portfolio.

Aortfolio risk is calculated using the risk of the individual assets )measuredby the standard deviation*, the weights of the assets in the portfolio, andeither the correlation between or among the assets or the covariance of theassets= returns.

For a two#asset portfolio, the risk of theAortfolio, Gp, is4

p = w2

2+w

22

+2w w

or


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12

1 1 2 2 1 2 12p = w

2

2+w

22

+2w w

cov since =cov12

12

where Gi is the standard deviation of asset i=s returns,

H56 is the correlation between the returns of asset 5 and 6, andcov56 is the covariance between the returns of asset 5 and 6.

Aroblem What is the portfolio standard deviation for a two#assetportfolio comprised of the following two assets if thecorrelation of their returns is B.87

Asset A AssetE&pected return 5B3 6B30tandard deviation ofe&pected

83 6B3

mount invested DCB,BBB D2B,BB

0olution Gp 5J.5583

>alculation

Gp B.C6B.B86 B.26 B.66 6)B.C*)B.B8*)B.2*)B.6*)B.8*

Gp I

G

p

I

Gp I

))B.52*)B.BB68** ))B.J2*)B.BC** ))6*)B.BB56**

B.BBBC B.B5CC B.BB6C

B.B5L6 B.5J55CM or 5J.55CM3


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9. Explain the "A:("A:I+A8 A**E+ :RI"I5; (06E8"NS#

"apital sset Aricing odelThe >A developed by William F 0harpe, -ohn (inter and -an ossinestablishes a linear relationship between the reuired rate of return of

a security and its beta. ?eta, as we know is the non#diversifiable risk ina portfolio. portfolio=s standard deviation is a good indicator of itsrisk. Thus if adding a stock to a portfolio increases its standarddeviation, the stock adds to the risk of the portfolio. This risk is the un#diversified risk that can not be eliminated. ?eta measures the relativerisk associated with any individual portfolio as measured in relation tothe risk of the market portfolio.4eta nondi%ersifiable risk of Asset or portfolio < Risk ofmarket portfolio

Thus ?eta is a measure of the non#diversifiable or systematic risk of an

asset relative to that of the market portfolio. beta of 5 indicates anasset of average risk. If beta is more than 5, then the stock is riskierthan the market. n the other hand, if beta is less than one, market isriskier.(athematically, the e=uation of "A:( is $i%en as under

E>Ri Rf - b >RmRf

Where E%Ri& E&pected return on the security'f 'isk Free return

'm 'eturn from the market portfolio? ?eta

+he "A:( is based on a list of critical assumptions

Investors are risk averse and use the e&pected rate of return and

standard deviation of return as appropriate measures of risk andreturn for their portfolio.

Investors make their investments decisions based on a single period

hori@on which is the immediate ne&t time period.

Transaction costs are either absent or so low that these can be

ignored.

ssets can be bought and sold in any desired unit. The investor is limited by his wealth and the price of the asset only.

Ta&es do not affect the choice of buying assets.

ll individuals assume that they can buy the assets at the goingmarket price and they all agree on the nature of the return and riskassociated with each investment.


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In the >A, the e&pected rate of return is eual to the reuired rateof return because the market is in euilibrium. The risk#less rate can beearned by investing in instruments like treasury bills. In addition to therisk free rate, investors also e&pect a premium over and above the risk

free rate to compensate them for investing in risky assets since theyare risk averse. Thus the reuired rate of return for the investorsbecomes eual to the sum of 'isk#free rate and the risk premium.The risk premium can 'e calculated as the product of (eta and market risk premium) i.e.difference 'et*een e+pected rate of return and risk,free rate of return.

PROBLEM:A COMPANY pays a dividend of Rs 2 per share with a growth rate of 7 perent!

The ris"#free rate is $ per ent and the %ar"et rate of ret&rn' () per ent! The

o%pany has a *eta fator of (!+,! -owever' d&e to a deision of the .inane

Manager' *eta is /i"e/y to inrease to (!7+! .ind o&t the present as we// as the /i"e/y

va/&e of the share after the deision.

Ans>A Formula4 E>Ri Rf - b >RmRf

= 9 per cent + 1.50 (13 per cent - 9 per cent)

= 9 per cent + 6 per cent = 15 per cent

E>Ri is taken as Ke.

6i%idend $rowth model #e 61< :o - $

15 per cent = 2.14/Po + 7 per cent

15 per cent - 7 per cent = 2.14/Po

Po = 2.14/8 per cent = Rs 26.75 present value o s!are.

b) eta increases to 1.75 !

E>Ri = 9 per cent + 1.75 (13 per cent - 9 per cent)

9 per cent + 7 per cent = 16 per cent

E>Ri is taken as Ke.

16 per cent = 2.14/Po + 7 per cent


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16 per cent - 7 per cent = 2.14/Po

:o ).12


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+he A:+ model

'isky asset returns are said to follow a factor structureif they can bee&pressed as4

where

E)rj*is thejth asset%s e&pected return, Fkis a systematic factor )assumed to have mean @ero*, bjkis the sensitivity of thejth asset to factor k, also called

factor loading,

and Njis the risky asset%s idiosyncratic random shock withmean @ero.

.

The AT states that if asset returns follow a factor structure then thefollowing relation e&ists between e&pected returns and the factorsensitivities4

where

RPkis the risk premium of the factor, rfis the risk#free rate,

That is, the e&pected return of an assetjis a linear function of theassets sensitivities to the nfactors.

4uildin$ portfoliosThe AT is a useful tool for building portfoliosadapted to particular needs. For e&ample, suppose a ma:or oilcompany wanted to create a pension fund portfolio that was insulatedagainst shock to oil prices. The AT allows the manager select adiversified portfolio of stocks that has low e&posure to inflation shocks)oil prices are correlated to inflation*. If the >A is a "one si@e fits all"model of investing, the AT is a "tailor#made suit." In the AT world,people can and do have different tastes and care more or less aboutspecific factors.

Con/&sion0 APT as a Mode/ of 1peted Ret&rns


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The AT has a number of benefits. First, it is not as a restrictive as the>A in its reuirement about individual portfolios. It is also lessrestrictive with respect to the information structure it allows. The ATis a world of arbitrageurs and vendors of information. It also allowsmultiple sources of risk, indeed these provide an e&planation of what

moves stock returns. The benefits also come with drawbacks. The ATdemands that investors perceive the risk sources, and that they canreasonably estimate factor sensitivities. In fact, even professionals andacademics can%t agree on the identity of the risk factors, and the morebetas you have to estimate, the more statistical noise you must livewith.

B. /hat are the ad%anta$e and disad%anta$e of A:+

A5* +HE A6CA5+A;E A56 6I*A6CA5+A;E 07 A:+

The advantage of AT, compared with >A, can be its ability toprovide better description of the e&pected returns on assets. >onnorand Kora:c@yk )5MOO* estimate and test the pervasive factorsinfluencing asset returns and restrictions implied by the AT. lthoughtheir evidences show that neither of the >A nor AT can be theperfect model of asset pricing, the AT is consistent with the si@e#related seasonal effects in asset pricing. They therefore argue that ATcan be the reasonable alternative to the >A. 0uch empirical findingsthat indicate the better performance of AT to >A can also be foundin $hrymes=s article )5MOC*. The recent work of Ferson and Kora:cyk)5MM8* also show that the AT capture the great fraction of

predictability for all of the investment hori@on, even for the long#hori@on returns )6 years*. Therefore, AT provides a feasiblealternative to >A as a practical method of risk estimation for theinvestors.

+owever, AT does have some disadvantages. The arbitrage pricingtheory does not indicate what the underlying factors are and howmany factors are needed to form the formula. The pervasive andsystematic influences on the asset price are vague in theory P unlike>A, which reduces all the macroeconomic variables into one well#defined factor, the return on the market portfolio. The gap between the

theory and application can be possibly reduced in searching theempirical factors which can e&plain the relation between return andrisk. ?ased on their empirical finding, >hen, 'oll and 'oss )5MO2*assert the stock returns are priced in accordance with the theire&posures to the systematic economic news. The news can beidentified and measured as the innovation in stated variables. In otherwords, they believe that different securities have different sensitivitiesto the systematic factors and the ma:or sources of security portfolio


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risk are captured in them. They further claim that there are four factorsfound to be significant in e&plaining the e&pected stock returns. Thefour factors are the spread between long and short interest rates,e&pected and une&pected inflation, industrial production, and thespread between high and low grade bonds )5MO2*. oreover, according

to a recent work on the effect of economic forces on /K stock market)>heng, 5MM8*, the appropriate variables in e&plaining /K stock marketcan be categorised into three economic factors. The first economicfactor is comprised mainly of market indices. The second economicfactor represents mainly the longer leading indicator, lagging indicator,money supply, interest rate, and unemployment rate. The thirdeconomic factor consists of the variables of output measures, such as1$A, consumer e&penditures on durable goods, industrial production,and short leading indicator.

*'((ARD

The benefit of arbitrage pricing theory can be characterised asproviding a better e&planation of the relation between risk and return.AT=s better performance stems from its using several macroeconomicvariables to e&plain variation in stock return, instead of using singlefactor as derived from >A. lthough it is still in need of moreempirical evidence to e&amine its application, AT has beenrecognised as the most possible alternative for >A. +owever, ATalso has its defects. The theory does not indicate what theseunderlying factors are and how many should be reuired for thesufficient e&planation. AT however needs more research to identify

the determinant economic forces behind those statically constructedfactors.

@. /hat do you mean by Efficient (arket Hypothesis?

Q04 Efficient arket +ypothesis

market theory that evolved from a 5M2B%s Ah.$. dissertation byEugene Farma, the efficient market hypothesis states that at any given

time and in a liuid market, security prices fully reflect all availableinformation. The E+ e&ists in various degrees4 weak, semi#strong andstrong, which addresses the inclusion of non#public information inmarket prices. This theory contends that since markets are efficientand current prices reflect all information, attempts to outperform themarket are essentially a game of chance rather than one of skill.


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The weak form of E+ assumes that current stock prices fully reflectall currently available security market information. It contends thatpast price and volume data have no relationship with the futuredirection of security prices. It concludes that e&cess returns cannot beachieved using technical analysis.

The semi#strong form of E+ assumes that current stock prices ad:ustrapidly to the release of all new public information. It contends thatsecurity prices have factored in available market and non#marketpublic information. It concludes that e&cess returns cannot be achievedusing fundamental analysis.

The strong form of E+ assumes that current stock prices fully reflectall public and private information. It contends that market, non#marketand inside information is all factored into security prices and that noone has monopolistic access to relevant information. It assumes a

perfect market and concludes that e&cess returns are impossible toachieve consistently.

(,! /rite short note on (arkowit (odel of :ortfolio+heory?

A5*Mar"owit3 Mode/

+arry arkowit@ put forward this model in 5M86. It assists in theselection of the most efficient by analy@ing various possible portfolios

of the given securities. ?y choosing securities that do not %move%e&actly together, the + model shows investors how to reduce theirrisk. The + model is also called ean#Rarianceodel due to the factthat it is based on e&pected returns )mean* and the standard deviation)variance* of the various portfolios. +arry arkowit@ made thefollowing assumptions while developing the + model4

5. 'isk of a portfoliois based on the variability of returns from the saidportfolio.

6. n investor is risk averse.

J. n investor prefers to increase consumption.

C. The investor%s utility functionis concave and increasing, due to hisrisk aversion and consumption preference.

8. nalysis is based on single period model of investment.S
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2. n investor either ma&imi@es his portfolio return for a givenlevel ofrisk or ma&imi@es his return for the minimumrisk.

L. n investor is rational in nature.

To choose the best portfolio from a number of possible portfolios, eachwith different return and risk, two separate decisions are to be made4

5. $etermination of a set of efficient portfolios.

6. 0election of the best portfolio out of the efficient set.

Determining the Efficient Set

portfolio that gives ma&imum return for a given risk, or minimum riskfor given return is an efficient portfolio. Thus, portfolios are selected as

follows4

)a* From the portfolios that have the same return, the investor willprefer the portfolio with lower risk, and

)b* From the portfolios that have the same risk level, an investor willprefer the portfolio with higher rate of return.

Figure 54 'isk#'eturn of Aossible Aortfolios

s the investor is rational, they would like to have higher return. ndas he is risk averse, he wants to have lower risk. S2 In Figure 5, theshaded area ARWA includes all the possible securities an investor can
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invest in. The efficient portfolios are the ones that lie on the boundaryof AURW. For e&ample, at risk level &6, there are three portfolios 0, T,/. ?ut portfolio 0 is called the efficient portfolio as it has the highestreturn, y6, compared to T and /. ll the portfolios that lie on theboundary of AURW are efficient portfolios for a given risk level.

The boundary AURW is called the Efficient 7rontier. ll portfolios thatlie below the Efficient Frontier are not good enough because the returnwould be lower for the given risk. Aortfolios that lie to the right of theEfficient Frontier would not be good enough, as there is higher risk fora given rate of return. ll portfolios lying on the boundary of AURW arecalled Efficient Aortfolios. The Efficient Frontier is the same for allinvestors, as all investors want ma&imum return with the lowestpossible risk and they are risk averse.

Choosing the best Portfolio

For selection of the optimal portfolio or the best portfolio, the risk#return preferences are analy@ed. n investor who is highly risk aversewill hold a portfolio on the lower left hand of the frontier, and aninvestor who isn=t too risk averse will choose a portfolio on the upperportion of the frontier.

Figure 64 'isk#'eturn Indifference >urves

Figure 6 shows the risk#return indifference curve for the investors.Indifference curves >5, >6 and >J are shown. Each of the differentpoints on a particular indifference curve shows a different combinationof risk and return, which provide the same satisfaction to the investors.
http://en.wikipedia.org/wiki/Indifference_curvehttp://en.wikipedia.org/wiki/File:Risk-Return_Indifference_Curves.jpghttp://en.wikipedia.org/wiki/File:Risk-Return_Indifference_Curves.jpghttp://en.wikipedia.org/wiki/Indifference_curve


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risk and the uantity of risk, and the risk is the standard deviation ofthe portfolio.

The >( euation is 4

R: IR7- >R( IR7F:(. )' # I'F* is a measure of the riskpremium, or the reward for holding risky portfolio instead of risk#freeportfolio. G is the risk of the market portfolio. Therefore, the slopemeasures the reward per unit of market risk.

The characteristic features of >( are4

5. t the tangent point, i.e. Aortfolio A, is the optimum combination of

risky investments and the marketportfolio.

6. nly efficient portfolios that consist of risk free investments and themarket portfolio A lie on the >(.

J. >( is always upward sloping as the price of risk has to be positive. rational investor will not invest unless he knows he will becompensated for that risk.
http://en.wikipedia.org/wiki/Interesthttp://en.wikipedia.org/wiki/Standard_Deviationhttp://en.wikipedia.org/wiki/Markethttp://en.wikipedia.org/wiki/Interesthttp://en.wikipedia.org/wiki/Standard_Deviationhttp://en.wikipedia.org/wiki/Market


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Figure 84 >( and 'isk#Free (ending and ?orrowing

Figure 8 shows that an investor will choose a portfolio on the efficientfrontier, in the absence of risk#free investments. ?ut when risk#freeinvestments are introduced, the investor can choose the portfolio onthe >( )which represents the combination of risky and risk#freeinvestments*. This can be done with borrowing or lending at the risk#free rate of interest )I'F* and the purchase of efficient portfolio A. Theportfolio an investor will choose depends on his preference of risk. Theportion from I'F to A, is investment in risk#free assets and is called

8endin$ :ortfolio. In this portion, the investor will lend a portion atrisk#free rate. The portion beyond A is called 4orrowin$ :ortfolio,where the investor borrows some funds at risk#free rate to buy more ofportfolio A.

6emerits of the H( (odel

5. It reuires lots of data to be included. n investor must obtainvariances of return, covariance of returns and estimates of return forall the securities in a portfolio.

6. There are numerous calculations involved that are complicatedbecause from a given set of securities, a very large number of portfoliocombinations can be made.

J. The e&pected return and variance will also have to be computed foreach of the securities in the portfolio.
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unit-3 risk and financial assets.doc

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