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- 1. Krupanidhi school of management Prof. V.N.V.SASTRY SAPM-4 ANALYSIS OF RISK AND RETURNInvestment decisions are influenced by various decisions. Some people invest in abusiness to acquire control and enjoy the prestige associated with it. Some peopleinvest in expensive yatches and famous villas to display their wealth. Mostinvestors are guided by the pecuniary motive of earning a return on theirinvestment.For earning returns investors have to almost invariably bear some risk. In generalrisk and return go hand in hand. Investment decisions involve a trade off betweenrisk and return.Return: Return is the primary motivating force that drives investment. Itrepresents the reward for undertaking investment. Since the game of investing isabout returns (after allowing for risk), measurement of realized (historical) returnsis necessary to asses how well the investment manager has done. In additionhistorical returns are often used as an important an input in estimating future(prospective returns)Components of return: it has two components:Current return: the first component that often comes to mind when one isthinking about return is periodic cash flow ( income), such as dividend or interest,generated by the investment. Current returns is measured as the periodic incomein relation to the beginning prices of the investment.Capital return: the second component of returns is reflected in the price changecalled the capital return- it is simply the price appreciation ( or depreciation)divided by the beginning price of the asset. For assets like equity stocks, thecapital return predominates.Thus the total return for any security ( or for that matter any asset) is defined as :Total return =current return + capital returnThe current return can be zero, or +ve , where as capital return can be –ve , zero or+ve.Risk: Risk refers to the actual outcome of an investment will differ from itsexpected outcome. Forces that contribute to variations in return price or dividend(interest)- constitute elements of risk. Some influences are external to the firmcannot be controlled, and affect large number of securities. Other influences areinternal to the firm and are controllable to a large degree. In investments, forcesthat are uncontrollable, external, and broad in their effect are called ‘sources ofsystematic risk”. Conversely, controllable, internal factors some what peculiar toindustries and/ or firms are referred t as ‘ sources of unsystematic risk’.Systematic risk refers to that portion of total variability in return caused by factorsaffecting the prices of all securities. Economic, political and sociological changesare sources of systematic risk. Their effect is to cause prices of nearly all
- 2. Krupanidhi school of management Prof. V.N.V.SASTRYindividual common stocks and or all individual bonds to move together in thesame manner.Unsystematic risk is the portion of total risk that ,is unique to a firm or industry.Factors such as management capability, consumer preferences, and labour strikescause systematic variability of returns in a firm. Unsystematic factors are largelyindependent of factors that are affecting securities markets. Because these factorsaffect one firm, they must be examined for each firm.Three major sources of risk= business risk , interest rate risk, and market riskUnsystematic risk: business risk, financial riskSystematic risk: market risk, interest rate risk , purchasing power riskInterest rate risk: the changes in interest rate have a bearing on the welfare ofinvestors. As the interest rates go up, the market price of existing fixed incomesecurities falls, and vice versa. This happens because the buyer of a fixed incomesecurity would not buy it at its par value or face value if its fixed interest rate islower than the prevailing interest rate on a similar security. For ex. A debenturethat has a face value of Rs.100 and a fixed rate of 12%will sell at a discount if theinterest rate moves up from , say 12% to 14%. While the changes in interest ratehave direct bearing on the prices of fixed income securities, they affect equityprices too, albeit some what indirectly. The changes in the relative yields ofdebenture and equity shares influence equity prices.Market rate risk: even if the earning power of the corporate sector and theinterest rate structure remain more or less unchanged, prices of securities, equityshares in particular, tend to fluctuate. While there can be several reasons for thisfluctuations, a major cause appears to be the changing psychology of theinvestors. There are periods when investors become bullish and their investmenthorizons lengthen. Investors optimism, which may border on euphoria, duringsuch periods drives share prices to great heights. The buoyancy created in thewake of this development is pervasive, affecting all most all the shares. On theother hand when a wave of pessimism ( which often is an exaggerated response tosome unfavorable political or economic development) sweeps the market,investors turn bearish and myopic. Prices of almost all equity shares registerdecline as fear and uncertainty pervade the market.The market tends to move in cycles. As John Train explains “the ebb and flow ofmass emotion is quite regular. panic is followed by relief, and relief by optimism,then comes enthusiasm ; then euphoria and rapture, then the bubble bursts, andpublic felling slides off again into concern, desperation, and finally a new panic”.One would expect large scale participation of institutions to dampen the pricefluctuations in the market. After all institutional investors have core professional
- 3. Krupanidhi school of management Prof. V.N.V.SASTRYexpertise to do fundamental analysis and greater financial resources to act onfundamental analysis. However , nothing of this kind has happened. On thecontrary, price fluctuations seem to have become wider after the arrival ofinstitutional investors in large numbers. Why? , perhaps the institutions and theiranalysts have not displayed more prudence and rationality than the generalinvesting public and have succumbed in equal measure to the temptation tospeculate. As John Marynard Keynes had argued, factor that contribute to thevolatility f the market are not likely to diminish when expert professionalspossessing better judgement and knowledge compete in the market place. Why?According to Keynes, even these people are concerned with “speculation” (theactivity of forecasting the psychology of the market) and not “enterprise” ( theactivity of forecasting the prospective yield of assets over their whole life).(Fischer and Jordan)Purchasing power risk: market risk and interest risk can be defined in terms ofuncerainities as to the amount of current dollars to received by an investor.Purchasing power risk is the uncertainit;y of the purchasing power of the amountsto be received. In more everyday terms, purchasing power risk refers to the impactof inflation or deflation on an investment.If we think investment is the postponement of consumption, we can see that whena person purchases a stock, he has foregone the opportunity to buy some good orservice for as long as he owns the stock. If during the holding period prices ondesired goods and services rise, the investor actually losses purchasing power.Rising prices on goods and services are associated with what is referred to asinflation. Falling prices on good and services are termed as deflation. Bothinflation and deflation are covered in the all-encompassing term purchasing powerrisk. Generally purchasing power risk has come to be identified withinflation(rising prices); the incidence of declining prices in most countries hasbeen slight.Financial risk: risk is associated with the way in which a company finances itactivities. We usually gauge financial risk by looking at the capital structure of afirm. The presence of borrowed money or debt in the capital structure creates fixedpayments in the form of interest hat must be sustained by the firm. The presenceof these interest commitments – fixed interest payments due to debt or fixeddividend payments on preferred stock – causes the amount of residual earningsavailable for common stock dividends to be more variable than if no interestpayments were required. Financial risk is avoidable risk t the extent thatmanagements have the freedom to decide to borrow or not to borrow funds. Afirm with no debt financing has no financial risk.By engaging in debt financing , the firm changes the characteristic of the earningstreams available to the common stock holders. Specifically, the reliance on debt
- 4. Krupanidhi school of management Prof. V.N.V.SASTRYfinancing called ‘financial leverage” has at least three important effects oncommon stock holder. 1. increases the variability of their returns 2. affects theirexpectations concerning their returns. 3. increases their risk of being ruined.Business risk: as a holder of corporate securities (equity shares or debentures),you are exposed to the risk of poor business performance. This many be caused bya variety of factors like heightened competition , emergence of new technologies,development of substitute products, shifts in consumer preference , in adequatesupply of essential inputs , changes in governmental polices an so on. Often ofcourse, the principal factor maybe inept and incompetent management. The poorbusiness performance definitely affects the interest of equity share holders, whohave a residual claim on the income and wealth of the firm. It can also affect theinterest of a debenture holders if he ability of the firm to meet its interest andprincipal payments obligation is impaired. In such a case, debenture holders facethe prospect of default risk.Types of risk: modern portfolio theory looks at risk from a different perspective.It divides total risk as follows: total risk = unique risk + market riskThe ‘unique risk’ of security represents that portion of its total risk which stemsfrom firm specific factors like the development of a new product, labour strike , orthe emergence of a new competitor. Evens of this nature primarily affects thespecific firm and not all firms in general. Hence the unique risk of a stock can bewashed away by combining it with other stocks. In a diversifies portfolio , uniquerisks of different stocks tend to cancel each other- a favourable development inone firm may offset an adverse happening in another and vice versa. Hence uniquerisk is also referred to as a diversifiable risk or unsystematic risk.The ‘market risk’ of a stock represents that portion of its risk which is attributableto economy-wide factors like the growth rate of GDP, the level of governmentspending, money supply, interest rate structure, and inflation rate. Since thesefactors affect all firms to a greater of lesser degree, investors cannot avoid the riskarising from them, however diversified their portfolio maybe. Hence it is alsoreferred to as ‘systematic risk’ (as it affects all securities) or non-diversiable risk.Bodie et.al.Risk and risk aversion:The presence of risk means that more than one outcome is possible. A simpleprospect is an investment opportunity in which a certain wealth is placed at risk,and there are only two possible outcomes. For the sake of simplicity, it is useful toelucidate some basic concepts using simple prospect.
- 5. Krupanidhi school of management Prof. V.N.V.SASTRYTake as an example initial wealth , W of $100,000 and assume two possibleresults, with a probability p=0.6, the favourable outcome will occur leading tofinal wealth W1= $150,000, other wise, with probability 1-p = 0.4, a lessfavourable outcome, W2 = $80,000, will occur. We can represent the simpleprospect using an event tree.Fig -1Suppose an investor is offered an investment portfolio with a payoff of 1 yeardescribed by such a simple prospect. How can you evaluate this portfolio? First try to summarise it using descriptive statistics. For instance, the mean orexpected end-of-year wealth denoted by E(W), isE(W) =pW1 +(1-p)W2 = (0.6 x 150,000) + (0.4 x 80,000) = $122,000The expected profit on the $100,000 investment portfolio is $22,000 (122000-100000).The variance , σ2 , of the portfolio’s pay off is calculated as the expected value ofthe squared deviation of each possible outcome from the mean:σ2 = p[W1-E(W)]2 + (1-p) [W2 – E(W)]2=0.6 [150,000-122000]2 + 0.4[80,00-122000]2 = 1,176,000,000 The standard deviation σ = $34292.86Clearly this is a risky business. The standard deviation of the pay off is large muchlarger than the expected profit of $22,000. whether the expected profit is largeenough to justify such risk depends on alternatives to this portfolio.Let us suppose, treasury bills are one alternative to the risky portfolio. Supposethat at the time of the decision, a 1 year T-bill offers a rate of return of 5% ;$100,000 can be invested to yield a sure profit of $5000. we can now drawdecision tree.Fig -2Earlier we showed that the expected profit on the prospect to be $22000. thereforethe expected marginal, or incremental, profit of the risky portfolio over investingin safe T-bill is 22000-5000=$17000, meaning that one can earn a ”risk premium”of $17000 as a compensation of the investment. The question of whether a givenrisk premium provides adequate compensation for an investment ‘s risk isage old.
- 6. Krupanidhi school of management Prof. V.N.V.SASTRYIndeed one of the central concerns of finance theory ( and much of this text) is themeasurement of risk and the determination of the premium that investor canexpect of risky assets in well functioning capital markets.Risk, speculation and gambling:One definition of ‘ speculation’ is the “assumption of considerable business riskin obtaining commensurate gain”. Although this definition is fine linguistically, itis useless with out first specifying what is meant by “commensurate gain” and“commensurate risk”.By commensurate gain” we mean a positive premium, that is an expected profitgreater than the risk free alternative. In our example, the dollar risk premium is$17000, the incremental expected gain from taking on the risk. By “considerablerisk” we mean that the risk is sufficient to affect the decision. An individual mightreject a prospect that has a positive risk premium because the added gain isinsufficient to make up for risk involved.To gamble is “to bet or wager on an uncertain outcome”. If your compare thisdefinition to that of speculation, you will see that the central difference is the lackof “commensurate gain”. Economically speaking, a gamble is the assumption ofrisk for no purpose, but enjoyment of the risk itself, here as speculation isundertaken ‘inspite’ of the risk involved because one perceives a favourablerisk-return tradeoff. To turn a gamble into a speculative prospect requires anadequate risk premium to compensate risk –averse investors for the risk they bear.Hence “ risk aversion and speculation are not inconsistent”In some cases a gamble may appear to the participants as speculation. Supposetwo investors disagree sharply about the future exchange rate of US dollar againstBritish pound. They may choose to bet on the outcome. Suppose that Paul will payMary $100 if the value of a pound exceeds $1.70 one year from now, where asMary will pay Paul if the pound worth is less than $ 1.70 . There are only tworelevant outcomes: 1. the pound will exceed $1.70 or 2. it will fall below $1.70. ifboth Paul and Mary agree on the probabilities of two possible outcomes. And ifneither party anticipates a loss, it must be that they assign p=0.5 to each outcome.In that case the expected profit to both is zero and each has entered one side of agambling prospect.What is more likely, however is the bet results from differences in the probabilitiesthat Paul and Mary assign to the outcome. Mary assigns it p> 0.5 where as Paulassessment is p<0.5. they perceive subjectively, two different prospects.Economists call this case of differing beliefs “heterogeneous expectations”. Insuch cases investors on each side of a financial position see themselves asspeculating rather than gambling.Both Paul and Mary should be asking, why is the other willing to invest in theside of a risky prospect that I believe offers a negative expected profit?. The ideal
- 7. Krupanidhi school of management Prof. V.N.V.SASTRYway to resolve heterogeneous belief is for Paul and Mary to “merge heirinformation”, that is for each party to verify that he or she posses all relevantinformation and processes that information properly. Of course , the acquisition ofinformation and the extensive communication that is required to eliminate allhetrogeneity in expectations is costly, and thus up to a point of heterogeneousexpectation cannot be taken as irrational. If however , Paul and Mary enter suchcontracts frequently, they would recognize the information problem in one of twoways: either they will realize that they are creating gambles when each wins halfof the bets, or the consistent losses will admit that he or she has been betting onthe basis of inferior forecasts.Risk aversion and utility values: we have discussed risk withsimple prospect and how risk premium bear on speculation. A prospect that haszero risk premium is called a ‘ fair game’. Investors who are “ risk averse” rejectinvestment portfolios that are fir games or worse. Risk-averse investors are willingto consider only risk- free speculative prospects with positive risk premia.Loosely speaking, a risk-averse investor “penalizes” the expected rate of return ofa risky portfolio by a certain percentage (or penalizes the expected profit by adollar amount) to account for the risk involved. The greater the risk, the larger thepenalty. One might wonder why we assume risk aversion as fundamental. Webelieve that most investors would accept this view from simple introspection.We can formalize the notion of a risk penalty system. To do so we will assumethat each investor can assign a welfare or ‘utility ‘ score to competing investmentportfolios based on the expected return and risk of those portfolios. The utilityscore may be viewed as a means of ranking portfolios. Higher utility values areassigned to portfolios with more attractive risk-return profiles. Portfolios receivehigher utility scores for higher expected returns and lower scores for highervolatility. Many particular ‘scoring’ system are legitimate. One reasonablefunction that is commonly employed by financial theorists and the AIMR(Association of Investment Management and Research) assign a portfolios withexpected return E(r) and variance of return σ2 the following utility score.U = E® - 0.005 A σ 2 where U is the utility value and A is an index of theinvestors risk aversion. The factor of 0.005 a scaling conversion that allows us toexpress the expected return and standard deviations in the above equation aspercentage rather than decimal.The equation is consistent with the notion that utility is enhanced by high expectedreturns and diminished by high risk. The extent to which variance lowers utilitydepends on A, the investors degree of risk aversion. More risk-aversion investors(who have larger As) penalize risky investments more severely. Investorschoosing among competing investment portfolios will select the one providing the
- 8. Krupanidhi school of management Prof. V.N.V.SASTRYhigh utility. Risk aversion obviously will have a major impact on the investor’sappropriate risk-return trade-off.Notice in the above equation that the utility provided by risk-free portfolio issimply the rate of return on the portfolio, because there is no penalization for risk.This provides us with a convenient bench mark for evaluating portfolios.Evaluating investments by using utility scores: in the earlierexample of choosing between portfolio with an expected return of 22% andstandard deviation σ =34% and T bills providing risk-free return of 5%. Althoughthe risk premium on the risky portfolio was large ,17% the risk of project is sogreat that an investment would not need to be very risk averse to choose the safeall bills strategy . Even A=3, a moderate risk aversion parameter as per theequation show that the risky portfolio utility value as, 22 – (0.005 x 3 x 34 2) =4.66% , which is slightly lower than the risk free rate. In this case one would rejectthe portfolio in faovour of T bills.The downward adjustment of the expected return as a penalty for risk is 0.005 x 3x342= 17.34%. if the investors were less risk averse (more risk tolerant), for ex.With A=2, she would adjust the expected rate of return downward by only11.56%. in that case the utility level of the portfolio would be 10.44%, higher thanthe risk free rate, leading her to accept the profit.Ex. A portfolio has an expected rate of return of 20% and std. deviation 20%. Billsoffer a sure rate of 7%. Which investment alternative will be choosen by aninvestor whose A=4? What if A=8?U= 20 – (0.005x 4 x 202) = 12% and U= 20 – (0.005 x 8 x 202) = 4%Choose the investment where A = 4.Because we can compare utility values to the rate offered on risk free investmentswhen choosing between a risky portfolio and a safe one, we may interpret aportfolio’s utility value as its ‘certainty equivalent’ rate of return to an investor.That is the ‘certainty equivalent rate’ of a portfolio is the rate that risk freeinvestments would need to offer with certainty to be considered equally attractiveas the risky portfolio.Now we can say that a portfolio is desirable only if its certainty equivalent returnexceeds that of the risk free alternative. A sufficiently risk averse investor mayassign any risky portfolio, even one with a positive risk premium, a certaintyequivalent rate of return that is below the risk free rate, which will cause theinvestor to reject the portfolio. At the same time a less risk averse (more risktolerant) investor may assign the same portfolio a certainty equivalent rate thatexceeds the risk free rate and thus will prefer the portfolio to the risk freealternative. If the risk premium is zero or negative to begin with , any downward
- 9. Krupanidhi school of management Prof. V.N.V.SASTRYadjustment to utility makes the portfolio look worse. Its certainty equivalent ratewill be below that of risk free alternative for all risk averse investors. In contrast to risk averse investors, “risk –neutral” investors judge risky prospectssolely by their expected rates of return. The level of risk is irrevalent to the risk –neutral investor, meaning that there is no penalization for risk. For this investor aportfolio’s certainty equivalent rate is simply its expected rate of return.A “risk lover” is willing to engage in fair games and gamble ; this investor adjuststhe expected return upward to take into account the ’fun’ of confronting theprospects is. Risk lovers will always take a fair game because their upwardadjustment of utility for risk gives the fair game a certainty equivalent thatexceeds the alternative of the risk free investment.We can depict the individual’s trade off between risk and return by plotting thecharacteristics of potential investment portfolios that the individual would view asequally attractive on a graph ( pl. see graph below).Fig -3With axes measuring expected values and standard deviation of portfolio returns.Portfolio ‘p’, which has expected return E(rp) and standard deviation σp ispreferred by risk averse investors to any portfolio in quadrant IV. Because it hasan expected return equal to or greater than any portfolio in that quadrant and astandard deviation equal to smaller than any portfolio in that quadrant.Conversely any portfolio in quadrant I is preferable to portfolio ‘p’ because itsexpected return is equal to greater than ‘p’s and its standard deviation is equal toor smaller than ‘p’s.This is the mean-standard deviation , or equivalently, mean variance (M-V)criterion. It can be stated as : A dominates B ifE(rA) ≥ E(rb) and σA ≤ σB . and at least one inequality is strict (rules out theequality)In the expected return-standard deviation plane in the above graph the preferreddirection is north west, because in this direction we can simultaneously increaseexpected return and decrease he variance of the rate of return. This means thatany portfolio that lies north west of ‘p’ is superior to ‘p’.What can be said about portfolios in quadrant II and III? their desirability,compared with ‘p’ depends on the exact nature of the investor’s risk aversion.Suppose an investor identifies all portfolios that are equally attractive as portfolio‘p’, starting at ‘p’, an increase in standard deviation lower utility ; it must becompensated for by an increase in expected return. Thus point Q in the graphbelow is equally desirable to this investor as ‘p’. investors will be equallyattracted to portfolios with high risk and high expected returns compared withother portfolios with lower risk but lower expected return. These equally
- 10. Krupanidhi school of management Prof. V.N.V.SASTRYpreferred portfolios will lie in mean-standard deviation plane on a curve thatconnects all portfolio points with the same utility value called the ‘indifferencecurve’.To determine some of the points that appear on the indifference curve , examinethe utility values of several possible portfolios for an investor with A=4, presentedin the table below . note that each portfolio offers identical utility , because thehigh-return portfolios also have high risk.Utility value of possible portfolios for investor with risk aversion, A=4Expected return E(r) Standard deviation σ Utility= E(r )- 0.005A σ210% 20% 10-(.005x4x400)=215% 25.5% 15-(.005x4x650)=220% 30% 20-(.005x4x900)=225% 33.9% 25-(.005x4x1150)=2Prasanna chandraRisk aversion and required return:You are lucky to be invited by the host of a television show. After the usualintroduction , the host shows two boxes to you. He tells you that one box containsRs. 10,000 and the other box is empty. He does not tell you which one is which.The host asks you t open any one of the boxes and keep what ever you find in it.You are not sure which box you should open. Sensing your vacillation, he says hewill offer you a certain sum of Rs. 3000 if you forfeit the option to open a box.You do not accept his offer. He raises his offer to Rs.3500. now you feelindifferent between a certain return of Rs. 3500 and a risky(uncertain) expectedreturn of Rs.5000. This means that a certain return of Rs. 3500 provides you withthe same satisfaction as a risky return of Rs.5000. Thus your certainty equivalent(Rs.3500) is less than the risky expected value (Rs 5000).Empirical evidence suggests that most individuals, if placed in a similar situation,would have a certainty equivalent which is less than the risky expected value.The relationship of a person’s certainty equivalent to the expected monetary valueof a risky investment defines his attitude towards risk. If the certainty equivalentis equal to the expected value, the person is “risk-averse”; if the certaintyequivalent is equal to the expected value, the person is “risk-neutral”; finally if thecertainty equivalent is equal to more than the expected value, the person is “riskloving”.
- 11. Krupanidhi school of management Prof. V.N.V.SASTRYIn general, investors are risk averse. This means that risky investments must offerhigher expected returns than less risky investments to induce people to invest inthem. Remember, however that we are talking about “expected” return and“actual” return on a risky investment may well turn out to be less than “actual”return on a less risky investment.Put differently risk and return go hand in hand. This indeed is a well establishedempirical fact, particularly over long periods of time. For example, the averageannual rates and annual standard deviation for Treasury bills, bonds, and commonstocks in the U.S. over 75 years period (1926-2000) as calculated by IbbotsonAssociates have been shown below:Port folio Average annual rate of Standard deviation % return%Treasury bills 3.9 3.2Govt bonds 5.7 9.4Corporate bonds 6 8.7Common stocks (S & P 13.0 20.2500)Small firm common 17.3 33.4stocksFrom the above it is clear that a. treasury bills, the least risky of financial assetsearned the lowest average annual rate of return b. common stocks, the most riskyof financial assets, earned the highest average annual rate of return c. bonds whichoccupy a middling position on the risk dimension, earned a middling averageannual return.Risk premium:Investors assume risk so that they are rewarded in the form of higher return. Hencerisk premium may be defined as the additional return investors expect to get, orinvestors earned in the past, for assuming additional risk. Risk premium may becalculated between two classes of securities that differ in their risk level. There arethree well known risk premiums:Equity risk premium: this is the difference between the return on equity stocksas a class and the risk free represented commonly by the return on treasury bill.Bond horizon premium: this is the difference between the long term governmentbonds and return on treasury bills.Bond default premium: this is the difference between the return on long – termcorporate bonds (which have probability of default) and return on long-termgovernment bonds (which are free from default risk).

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