the assumption of market rationality | My Assignment Tutor

1Risky asset pricing models(the CAPM)2 Capital market line (CML)◦ Equation of CML:E(Ri) = Rf + i(E(Rm)-Rf)/m◦ Assumptions: Investors are risk averse, maximise utility, and face oneperiod horizon. Investors are only interested in risk and return, and haveaccess to unlimited borrowing and lending at Rf That there are no transaction costs or taxes. Investments are infinitely sum up: We live in a perfect market, but considerationis only limited between: Risk free assets Risky assets3 Capital market line (CML) (cont.)◦ Example: Assume E(Rm) = 14%, m= 16%, Rf = 6%. If a portfolio has a standard deviation of 10%what is: Case 1) the expected return on the portfolio? Case 2) the expected return if the investor chooses toinvest 40% in the risk-free asset? Case 3) the std. dev. if the investor wants an expectedreturn of 12%?4 Example (cont.):◦ Case 1) E(Ri) = Rf + i/m(E(Rm)-Rf)= 0.06 + 0.10/0.16(0.14-0.06)= 11%◦ Case 2) E(Ri) = WrfRf + (1-Wrf).E(Rm)= 0.40 x 0.06 + (1-0.40) x0.14= 10.8%◦ Case 3) E(Ri) = Rf + i/m(E(Rm)-Rf)0.12 = 0.06 + i x 0.5i = 12%5 Determine:◦ how the aggregate of investors will behave◦ how market clearing prices and returns are set◦ the relevant measure of risk◦ the relationship between risk and return for anyasset when markets are in equilibrium.i.e. the assumption of market rationality6 The capital assessing price model (CAPM) wasdeveloped by William Sharpe, John Lintner and Jan Mossinbetween 1964-1965. Security market line (SML)◦ E(Ri) = Rf + i(E(Rm)-Rf)where i = Covi,m/2m7a) Risk-free rate◦ Risk-free rate should have a duration equal to the assetlife.◦ CAPM is a one-period model.◦ To take a long-term security is typical.◦ To remove risk, government bonds are used (but notethese still have some risk).◦ Using a long-term government bond (e.g. 10-yearCommonwealth bond) is common.◦ Risk-free rate varies over time.◦ To smooth volatility, an average is often employed. E.g. the average over the last 40 trading days.8 b) Market risk premium◦ This requires an estimate of E(Rm)-Rf.◦ Ex-ante estimates are often made using ex-post returns.◦ Using a historical average is typical. However, history provides varying estimates: Ibbotson in USA: 8.4% pa. Other estimates: 5-9% pa. Australia: Officer: 7.9% pa. Dimson et al: 7.6% pa. Recent study: 1882–2005 Brailsford et al: 6% pa.10What does that imply? (your assignment 1) c) Beta◦ Beta estimates can be supplied through commercial vendors◦ Beta estimates can be calculated directly require returns on the asset (such as a share) require returns on a market index e.g. S&P/ASX 200 index use accumulation index (includes dividends).◦ From the CAPM, i = covi,m/2msince: covi,m = ri,m . si . Smtherefore: bi = ri,m . si /s2mhence, Beta can be estimated using the following regression: E(Ri) = ai +bi(E(Rm,t) + ei,t.◦ Beta estimates are imprecise: They vary according to data used for estimation. Thin trading creates bias. They vary over time for same firm.◦ Using five years of monthly returns is typical.12 Early tests of CAPM◦ Regress current returns against estimates of beta frompast return series:R*i = 0 + 1i + i (i.e. Y = C + MX + Error)where R*i = Ri – Rf.◦ Tests focused on: 0 = 0 (CAPM should completely explain return) i explaining return variation in total, and a linearrelationship in beta 1 = risk premium positive market risk premium, i.e. E(Rm)>Rf.13 Early tests of CAPM (cont.)◦ Evidence generally found: 1 was statistically significant i.e. positive relationship between risk and return 0 also statistically significant (should be 0)- other factors in pricing assets.◦ Tests of CAPM require an estimate of market return.◦ Roll (1977) argued that the market cannot be observedin total.◦ Even if possible, tests of CAPM are a test of theefficiency of the market.14 Early tests of CAPM (cont.)◦ Problems with testing the CAPM1. CAPM is an ex-ante model tests can only be done on ex-post data2. Return estimation– arithmetic/geometric/continuous– choice of Rf3. Beta estimation – stability, thin trading4. Survivorship bias.◦ Average stock returns are positively related tomarket.◦ Fama and French (1992) 50 year analysis in the USA after controlling for size, there is actually a negative relationshipbetween beta and realised return.15 Is Beta dead??◦ Subsequent studies have provided evidence that conflictswith Fama and French (1992).◦ Concerns include: CAPM provides for expected returns not actual returns criticism of data mining Roll’s problem of an inaccurate market proxy a poor proxy will create low correlation and hence low beta;high betas are relatively less affected an hence SML is flat.16 Researchers have investigated the impact of relaxingthe CAPM assumptions:◦ investors make decisions on mean and variance, (normaldistribution)◦ all assets are marketable◦ existence of risk-free asset◦ perfect capital markets◦ unequal borrowing and lending rates◦ zero taxes and transactions costs◦ homogenous expectations◦ one-period horizon.17 Non-normal distribution◦ Kraus and Litzenberger (1976)◦ Adjust CAPM If returns are positive skewed, reduce expected return. If returns are negative skewed, increase expected return. Non-marketable assets◦ Mayers (1972) provides an adjustment to CAPM for thintrading.18 No risk-free asset◦ Return on govt. bonds is usually used as proxy.◦ CAPM can be derived using a zero beta portfolio. Transaction costs◦ Difficult to gauge impact but if a marginal trader is a largeinstitution with low trans. costs, then impact is likely to besmall. Heterogeneous (non-homogeneous) expectations◦ can be dealt with under CAPM. Multi-period investment horizon◦ CAPM can be extended to multi-period.◦ a complex model and not generally used in practice.19Alternative risky asset pricing models20 The consumption capital asset pricing model(CCAPM) was developed by Rubinstein (1978). CCAPM defines the expected return of a portfolio asa linear function of the growth rate in consumption.◦ E(Ri) = E(RZ) + ic E(RZ) = the return on a portfolio with zero consumptionbeta. i = covic/2c and is a measure of the relationship betweenportfolio i and the growth rate in aggregate consumption(c). c = the premium for consumption risk.21 Example: An asset has a consumption beta of 0.6. The expected return on an asset with a consumptionbeta of zero is 5% and the market price ofconsumption risk is 10%. Given this information, the expected return for thisasset can be calculated as:◦ E(Ri) = 0.05 + (0.6 x 0.10)= 0.11 or 11.0%.22 APT motivation:◦ overcome shortcomings of CAPM◦ less restrictive assumptions of CAPM◦ APT is empirically testable. APT is based on the law of one price. APT has no special role for the market portfolio. There are two forms of the APT:◦ Ross (1976)◦ equilibrium model.23 The Ross model◦ Ri = E(Ri) + bi11+ bi22 + …+ bikk+ i bik is the sensitivity of asset i’s returns to risk factor k k is the common explanatory factor k.◦ This model does not require: quadratic preference functions normally distributed returns identification of market model.24 The Ross model◦ Given an economy where pricing is driven by arbitrageit is possible to show that the expected return on anyasset is:E(Ri) = 0 + bi11 + bi22 +… + bikk where 0 = expected return on asset with 0 systematicrisk.◦  (factors) can be anything such as GDP, inflation,commodity prices, etc.25  Problems with the APT◦ Reasons for lack of acceptance: complexity application difficulty doubts about performance of model theoretical limitations.◦ APT does not identify what the factors are.◦ APT is an average pricing model. It may have limited application where the number ofsecurities in a market is small.27 Problems with the APT◦ Example: Say an arbitrage portfolio exists that includesone asset A with total market value of $1.00 and tenother assets with a combined market value of $9999,giving a total portfolio value of $10 000.◦ Assume that asset A is mispriced, with pricing error of$0.40 (or 40%), while the remainder of the assets arepriced correctly according to the factor structure.28◦ The average pricing error for this portfolio is essentiallyzero:arbitrage portfolio pricing error= (1/10 000)*0.40 + (9999/10 000)*0.00= 0.00004 Empirical evidence on APT◦ Empirical tests have followed two forms:1. Statistical techniques to identify unobservable factors• Roll and Ross (1980)• Dhrymes, Friend and Gultekin (1984)• Faff (1988–1992) identifies 5 factors but inconsistency in thenumber of factors over different time periods and differentportfolio sizes• factor structure generally in the range of 3–5 factors.2. Arbitrary selection of economic variables Use macro-economic variables but selection is arbitrary andincludes: firm size book-to-market values term premium.29 Recall that the beta is dead argument. 3-factor model:◦ E(Ri) = Rf + bi [E(RM) – Rf] + si E(SMB) + hi E(HML) Rf is the risk-free rate. MRP is the market risk-premium. SMB is the size premium. HML is the book-to-market premium. Estimation of factors/premiums◦ Past returns are typically used for estimations.◦ Generally, these factors have a positive averageconsistent with the notion of a positive risk andreturn relationship.30  Example◦ The market premium is 8.06% per annum, the SMBpremium is 3.81% per annum and the HMLpremium is 4.36% per annum.◦ The long-term bond rate is 4.2% per annum toapproximate the risk-free rate.◦ The sensitivity of the stock to the market, SMB andHML factors are 0.8, 0.5 and 0.2 respectively.33 Example (cont.)◦ Using these values, the expected return can be estimatedas:E(Ri) = Rf + bi [E(Rm) – Rf] + si E(SMB) + hi E(HML)= 0.042 + 0.8*0.0806) + 0.5*0.0381 + 0.2*0.0436E(R) = 0.134 or 13.4% p.a.34 The international CAPM prices stocks as if thereare no national or political boundaries. The model assumes a completely integratedglobal financial market. It assumes that there are no investmentrestrictions or barriers to capital flows.35  An Australian investor would have no barrier tobuying shares in New York, Moscow or Singapore. Under these conditions, an investor will hold stocksfrom many countries National influences on stocks will becomediversifiable and hence the only relevant factors inpricing an asset are global factors that arepervasive across every market.37Market efficiency38 Why should we expect efficiency to occur?◦ That is, what makes investors want to trade until pricesreflect information? This requires zero cost for information and trading Obviously these requirements are not met. Can efficiency be achieved in imperfect markets?◦ Ball (1995) views market efficiency as an exercise in cost–benefit analysis. In an efficient market, the marginal cost of obtaining andacting on information should not exceed the marginal benefitderived from such actions.◦ Jensen (1978) argues that for a market to be trulyinefficient, any inefficiencies must give rise to profitmaking opportunities. Thus, inefficiencies that are not economically exploitablecan still be consistent with an efficient market.39 Recall definition of efficiency – prices fully reflectavailable information.◦ Therefore, two components to efficiency:1. unformational efficiency i.e. speed of incorporation of ‘new information’2. market rationality i.e. new information correctly incorporated into stock prices.40 ‘An efficient market is one where prices reflect thevalue of information.’ A share’s value is defined by the present value ofexpected future cash flows:41 tValue of share (PV)=iE(C )t t=1i[1+E(r )]i=1      PV model requires information on:◦ future cash flows (i.e. dividends)◦ ‘risk’ via the cost of capital. Market bases expectations on this information. Prices respond to changes in expectations. Changes in expectations arise from new information. Therefore, prices change as new information arrives.42 Classes of information◦ No discussion of efficiency can be held in theabsence of defining available information.◦ Fama (1991) has proposed a three-way classificationof market efficiency in which each group is based ontest methods used to assess market efficiency.43 Classes of information (cont.)◦ First, tests of return predictability generally focus onwhether current market prices fully reflect informationcontained in past price sequences. That is, do prices reflect the value of information about pasttrends, historical trading volumes, moving averages and so on? In essence, many of these tests focus on the profitability oftechnical analysis.◦ Second, event study tests generally focus on the pricereaction to publicly released information. This information includes financial reports, press releases,stock exchange announcements, capital structure changes andtakeover announcements. These tests are concerned with speed of reaction andunderreaction or overreaction.44 Classes of information (cont.)◦ Third, tests of private information seek to examinewhether the possession of private information leads toexcess returns. Examples include: the analysis of share transactions by corporate executivesin their own company the information content of brokers’ reports the investment performance of large institutional fundmanagers.45 Problem of the joint test◦ Any test of market efficiency necessarily compares returnsagainst some benchmark.◦ But how do we define excess returns?◦ A benchmark for the expected return is required before wecan measure excess returns.◦ One possible benchmark is a formal asset pricing model,such as the capital asset pricing model (CAPM). However, to use the CAPM as the benchmark implies that themodel is appropriate. Hence, to define excess returns in order to test marketefficiency, a model for expected return is first required. Thus, any test of market efficiency is inherently a joint test ofmarket efficiency and the model of expected return.46 Types of traders (cont.)◦ When two investors agree upon a price, a transactionoccurs.◦ At the point in time that this transaction occurs, the twoinvestors are setting the market price and they representthe marginal investor.◦ For most of the market, the actual identity of themarginal investor at a point in time is hidden.47 Types of traders (cont.)◦ Investors can be classified into informed and uninformedtraders.◦ Informed traders then execute trades when they believethat market prices diverge from their fundamentalvalues. That is, informed traders transact when they believe asecurity to be mispriced.◦ As uninformed traders do not trade on specific pieces ofinformation, they can drive prices away fromfundamental values. Black (1986) terms such price movements as noise.48 Misconceptions about efficiency◦ Efficiency implies predictability. It is actually inefficiency that implies predictability.◦ Prices are randomly set versus random information arrival.◦ Large movements in prices are inconsistent withefficiency. If the rate of new information arrival is high and thisinformation implies variations in prices, then it is expectedthat price changes would be frequent and of varyingmagnitude49 Misconceptions about efficiency (cont.)◦ Expected return equals observed return. There is nothing in the model or in the efficient marketshypothesis that requires actual return to equate to expectedreturn given by the CAPM.◦ Investors will all perform equally. Some investors will win and some investors will lose.◦ Market realignments have to occur. Price levels will be maintained until new information arrives.50 Judgments about efficiency◦ The issue of efficiency is ultimately a matter of degree, ratherthan extremes.◦ Believers of market efficiency argue that the existence ofbelievers in market inefficiency keeps the market efficient. Investors who seek to exploit market inefficiencies by their ownactions ensure that any inefficiencies are eliminated. Competition among investors trading on perceived inefficiencieshelps to maintain efficient prices.◦ Bowman and Buchanan (1995) argue that two sets offorces are at work that operate as impediments to theacceptance of efficient markets: market structure forces behavioural forces.51 Judgments about efficiency (cont.)1. Market structure forces Uncertainty means that extreme observations are found indistributions. It is difficult to distinguish skill from luck. There are rarely any observations that can be tested under thesame conditions. There is a vested interests in maintaining inefficiency.2. Behavioural forces (week 6) aversion to loss realisation individuals appear to have an aversion to loss realisation paper losses are somehow better than real losses illusion of knowledge winners disclose and losers hide attribution theory skill versus luck.52 Random walk model◦ Price changes are assumed to be independent andidentically distributed. Filter rules◦ A filter rule involves buying a share after it hasmoved up by x% and holding the share until the pricemoves down by x%. Trends (e.g. charting, week 6) Technical analysis (week 6)◦ Elliot waves◦ moving averages.53 Momentum◦ There is an observed relationship between performanceover the previous 3–12 months and future share priceperformance.◦ Jegadeesh and Titman (1993) find that the buy winnersand sell losers trading strategy earned statisticallysignificant positive returns averaging 12.01% p.a. This is based on a six-month past performance period and asix-month holding period.54 Response to earnings announcements◦ Test response using event studies methodology. Define the event. Group the event into news. Convert to event time. Form expected returns. Use the CAPM or other pricing model. Analyse the excess returns. Excess return is the observed return less the expected return. Accounting information◦ earnings announcements◦ components of earnings◦ dividend information◦ speed of reaction, liquidity, volume and volatility◦ post-earnings drift.55 Raises questions about market efficiency and thecorrect asset pricing model Banz (1981)◦ In USA, shares in small companies were found tooutperform shares in larger companies on a riskadjusted basis.◦ Evidence that a trading strategy of taking long positionsin a portfolio of small firms and short positions in aportfolio of large firms can earn risk-adjusted profits ofaround 20% p.a.56 Banz (1981) (cont.)◦ The relationship between firm size and abnormal returns isnot linear and is concentrated in the smallest decile offirms. Brown, Keim, Kleidon and Marsh (1983); Beedles, Dodd andOfficer (1988); Anderson, Lynch and Mathiou (1990); Gaunt,Gray and McIvor (2000) confirm the result in Australia.◦ Keim (1983) finds that about half of the annual sizepremium to small firms occurs in January and that abouthalf of this effect occurs over the first five trading days ofthe new calendar year.57 Initial public offering (IPO)◦ short-run high profits◦ long-run under-performance◦ rights issues (i.e. bad news)◦ bonus issues◦ share buy-backs◦ debt swaps.58 Volatility can loosely be described as the variabilityof price movements.◦ If no volatility, there is no incentive to trade.◦ Excess volatility debate (Shiller 1981): Are share prices are too volatile? How much is too much volatility? Crashes Wall Street 1929–30 October 1987 Global Financial Crisis (GFC) of 2007–08. Are circuit-breakers or bailouts necessary?59 General conclusions regarding market efficiency◦ Shares prices appear to do a reasonable job in providingan unbiased consensus judgment of the firm’s relativevalue. Hence, changes in the share price may be used asan assessment of value and management performance.◦ There is some evidence of predictability.◦ There is evidence of seasonality.◦ Shares in small sized companies outperform shares inlarge sized companies on a risk-adjusted basis (butliquidity and information risk).◦ Shares in firms with high book-to-market ratios (valueshares) appear to outperform shares in firms with lowbook-to-market ratios (growth shares).60 General conclusions regarding market efficiency (cont.)◦ The market appears to be reasonably efficient with respectto its short-term reaction to financial information and isable to differentiate between different signals.◦ The market is generally not fooled by the manipulation ofaccounting numbers.◦ There is some evidence of post-announcement driftfollowing the release of information, especially earnings◦ On average, IPOs give rise to quick profits, but they do notappear to represent a profitable long-run investment.◦ There appears to be long-run abnormal performancefollowing various capital restructuring activities.61


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