1Topic 5Risk and returnObjectivesOn completion of this topic, you should be able to: define and measure investment risk and return describe the nature of the risk-return trade-off explain and demonstrate how risk is reduced by diversification describe and identify the two components of an asset’s risk within a portfolio context:unsystematic and systematic risk describe, apply … Continue reading “Capital Asset Pricing Model (CAPM) | My Assignment Tutor”
1Topic 5Risk and returnObjectivesOn completion of this topic, you should be able to: define and measure investment risk and return describe the nature of the risk-return trade-off explain and demonstrate how risk is reduced by diversification describe and identify the two components of an asset’s risk within a portfolio context:unsystematic and systematic risk describe, apply and appraise the Capital Asset Pricing Model (CAPM) use and interpret beta discuss the efficient markets hypothesis and its implications for investorsIntroductionIn earlier topics, we have focussed on time value of money, a cornerstone concept in finance asdemonstrated by its many applications. In this topic, we consider another powerful concept infinance, diversification, which then leads us to one of the enduring models of finance, the CapitalAsset Pricing Model (CAPM).In the last topic, we introduced a fundamental valuation model that applies to all assets. Recall that,a general level, to value an asset we need to estimate the amount and timing of the asset’s cashflows, as well as a required rate of return that incorporates the asset’s risk to use as a discount rate.We then applied this model in the context of bond valuation.Share valuation is much more subjective than bond valuation. One of the reasons for this is theinability to directly observe the required return on a share, and therefore to derive a discount ratefor our share valuation. The CAPM gives us an indirect method for estimating this required returnvia a theoretical model built on a number of assumptions. While not perfect, it has obvious practicalimplications for managers, investors and finance specialists who have little else to work off. Fromthe company’s perspective, a shareholder’s required return is a cost. Therefore, the CAPM helpscompany management determine the cost of equity capital.In this topic, we will also build on some other ideas covered in our previous study. We extend thedimensions of risk, such as default risk, liquidity risk etc., as they apply to fixed income securities(e.g. bonds) to look at more general concepts of risk that apply to all investments. We start withtotal, or stand-alone, risk and then break this down into two important components – systematicrisk and unsystematic risk. We assume that investors are ‘risk averse’, that is, if two assets offer2equal returns, the investor will select the asset with the lower level of risk.After careful study of this topic, you will have a solid understanding of the basics of risk and returnthat will allow you to analyse any investment more critically.What is return?In finance, a return is the gain or loss in wealth achieved on an investment over a given period oftime. Recall from Week 1 that a focus of finance is measuring value over time and with uncertainty.Returns represent a change (or expected change) in value. We will therefore cover a number ofreturn measurements this week. To consider the uncertainty factor in measuring value we will alsoconsider a number of risk measurements and then link return and risk together.When we are using the term ‘returns’ in finance, we are usually referring to the rate of return, whichis a more comparable measure of return. This rate is usually expressed on an annual percentagebasis.Let’s consider calculation of returns in the context of an investment in shares. (We will ignore theimpact of taxes and brokerage costs in order to keep the discussion simple.)The return on an investment in shares is the change in the price of the share (the capital gain orloss) plus any dividends received, all expressed as a percentage of the initial amount that wouldneed to be invested in the shares. From a finance perspective, capital gain (appreciation) should beincluded in calculating return regardless of whether the shares were actually bought at thebeginning of the period or sold at the end of the period, as long as they were held over that period.It is change in wealth that we are trying to measure.There are two main types of return that you will come across in the rest of this topic. Historical (or realised) return: Relates to past periods and is measured using historicaldata. May be presented in nominal or real terms. Expected return: Relates to expectations about future returns. The expected return, as youwill see, can be measured by several approaches including a probability-weighted average ofpossible returns or an application of the CAPM.Stand-alone riskThe risk of an investment is the likelihood that it will earn something different to that expected. (Ofcourse, we are often more concerned with an investment earning less than expected – that is,downside risk – but in finance we generally use the general term ‘risk’ in a value neutral manner.)So risk is reflected in the fluctuation, variability or volatility in returns. Volatility, measured by thestandard deviation of returns, is also called stand-alone or total risk. It is the extent to which thereturns of a single asset held in isolation vary from period to period. For example, if you investedonly in Telstra shares, the standard deviation would give you a measure of the risk of thatinvestment.3Diversification and risk-return trade-offAn important assumption in traditional finance theory is that market participants on average arerisk-averse and this assumption leads to the important conclusion that there is a trade-off betweenrisk and return. Risk-averse investors will only take on risk if they are compensated for doing so inthe form of additional returns.History provides evidence of this trade-off between risk and return for large portfolios. A portfoliois a collection or holding of more than one individual asset. Portfolios with higher average returns,such as the share market, have higher risk (as measured by standard deviation) than portfolioswith lower average returns.Average realised returns and standard deviations of several classes of investments in Australia forthe period 1959 to 2013 are shown in Table 5.1. The portfolio labelled ‘large listed shares’ is the300 largest companies on the ASX. The other asset classes are unlisted property investments and10-year Australian government bonds. The returns in the table for each class of investments arenominal returns so inflation in Australia (as measured by the Consumer Price Index or CPI) duringthe period is also included in the table so that real returns (i.e. adjusted to remove the effect ofinflation) can be approximated. For example, the average nominal return on 10-year governmentbonds was 8.8% p.a. while the inflation rate was 5.7%. Therefore the average real return on 10-year government bonds was approximately 3%.Table 5.1 Large listedsharesUnlistedPropertyTen-yeargovernmentbondsInflation(CPI)Average return13.7%10.2%8.8%5.7%Standard deviation22.4%8.5%3.5%4.1%Risk premium over10-year gov’t bonds4.9%1.4%– (Source: Grenfell 2013 and author’s calculations for excess return)When we graph the average return against the standard deviation, we can see a very clear relationbetween risk and return. This is shown by the trend line in Figure 1. The equation of the trend linetells us that taking an additional 10 percentage points of risk (e.g. going from 5% to 15%) adds anaverage of 2.58% to nominal return. (Use decimals for risk in using the equation; e.g. 5% = 0.05.)4Figure 5.1(Source: Author’s modelling based on data from Grenfell 2013)Interestingly, the historical evidence of a risk-return trade off as depicted in Figure 5.1 usingstandard deviation as the measure of risk only applies to large portfolios. It does not apply whenconsidering the standard deviations of individual assets. In the latter case, the average returns andstandard deviations for individual shares, for example, would plot all over the graph with noparticular pattern except that they would tend towards higher risk than the large listed portfolio.The reason for this relates to the important concept of diversification (investing in a variety ofassets). Diversification can reduce risk. This is because losses on some assets in a diversifiedportfolio should be offset by gains on other assets in the portfolio, thus reducing the volatility (totalrisk) of the portfolio return.How diversification works: A simple exampleLet’s take an extreme and hypothetical example to see how diversification works to reduce risk.Table 5.2 show the returns over five years for two hypothetical shares, A and B. Notice that thereturns of each share are quite variable but note also their returns tend to move in oppositedirections. For example, when Share A’s return is high in Year 1, Share B’s return is negative. Theopposite occurs in Year 2. Despite this, each share has the same average return and same standarddeviation.Table 5.2Large listedsharesUnlistedproperty10 yr gov’tbondsy = 0.08 + 0.258xR² = 0.99980%2%4%6%8%10%12%14%16%18%20%0% 5% 10% 15% 20% 25% 30%Return (arithmetic mean)Risk (standard deviation)5The final column shows a portfolio with equal investment in each share. The returns of the portfolioare a weighted average of the returns on the shares in the portfolio, where the weights are portfolioweights, in this case equal proportions (0.5 each). Notice that the portfolio return in each year is15% and therefore so is the portfolio average return.Although each share and the portfolio in this case have the same average return, the standarddeviation (total risk measure) is much lower (zero!) for the portfolio. This means the portfolio hasno volatility (risk). This can be clearly seen in Figure 5.2 where the portfolio returns even out thevolatility in the individual share returns.Figure 5.2The reason this portfolio has no risk is that Shares A and B are perfectly negatively correlated; i.e.over time their returns move in opposite directions, changing by the same proportion. However, asnoted, this is an extreme and hypothetical example. In practice it is virtually impossible to findperfectly negatively related shares to make a riskless portfolio. Despite this, the example showshow diversification works to reduce risk.In practice we need a wider range of shares and other assets in our portfolio and we would still be6left with some risk, called systematic (or non-diversifiable or market) risk. The risk that has beendiversified away by holding a large portfolio is called unsystematic (or diversifiable or firmspecified) risk. Thus total risk (measured by the standard deviation of returns) is made up of twotypes of risk: systematic and unsystematic. Diversification reduces the unsystematic component oftotal risk.Since unsystematic risk can be virtually eliminated by an investor at virtually no cost by simplyhaving a well-diversified portfolio, the market does not reward investors (through a risk premiumor extra return) for bearing unsystematic risk. Therefore, only systematic risk matters to adiversified investor. This is the primary conclusion of CAPM, which specifies the relationshipbetween risk and expected rates of return on assets when they are held in well-diversifiedportfolios. Asset prices and returns reflect the amount of systematic risk an individual asset bringsto a portfolio, not the stand-alone risk of the individual asset. We will have more to say about thisand CAPM in a later section.Components of riskThe definitions of stand-alone risk and its two components are as follows.Total riskAlso called stand-alone risk or volatility.This is the risk of an asset if held in isolation and it is measured by the standard deviation of returns.Investments with bigger standard deviations have more volitility in their returns and thereforegreater total risk.Systematic riskAlso called market risk or non-diversifiable risk.This is the volatility in returns caused by broad economic and social conditions that tend to affectall firms and assets. However, some firms and assets are more sensitive to changes in theseconditions than others. Examples of sources of systematic risk include interest rate changes(interest rate risk), political risk, changes in inflation and changes in exchange rates.Unsystematic riskAlso called firm/asset-specific risk or diversifiable risk.This is the volatility in returns caused by factors unique to a particular firm or asset or at most asmall number of firms or assets. In the context of a firm’s shares, this risk stems from the way aparticular firm conducts its business. This includes the type of industries the firm operates in, theway the firm is financed, where the firm is located, the quality of the firm’s management, the lossof a key client and other firm-specific events.7Expected returns, beta and the CAPMSo far, we have focussed on historical returns but investors and managers will want to estimateexpected future returns. We could base this estimate on historical returns but that would requirerelying on the assumption that the future will be the same as the past. This is unlikely to be arealistic assumption in a constantly changing world.Another approach for making such estimates is called the probabilistic approach. At its core, thisapproach uses probability distributions and estimates of returns in various scenarios to determinean overall expected return. Often the scenarios are based on various states of the economy or acertain market/industry. The approach calls for analysts to think carefully about the links betweenan asset’s returns and various scenarios. It also requires the analyst to estimate the probability ofeach scenario occurring.A further approach is to estimate returns using the Security Market Line (SML), which describesthe relationship between risk and return predicted by the Capital Asset Pricing Model (CAPM).Before explaining this approach, you need to know about a risk measure called beta.When deciding whether to buy a particular asset, the diversified investor is only concerned withhow much risk the asset will add to their well-diversified portfolio. CAPM implies systematic riskis the only factor that explains share returns. Beta measures relative systematic risk and describeshow an asset’s returns tends to move with a changes in the market return.Beta is calculated as the slope of a regression line fitted to historical share and market return data.The greater this slope, the more volatile are the returns on the share compared to returns on themarket portfolio and the greater the market risk of the share, i.e. the higher is the beta value for theshare. You are not required to calculate beta using regression in this unit but you do need to learnwhat it measures, be able to interpret it and be able to use it in calculating expected returns andportfolio beta. A share portfolio’s beta is simply the weighted average of the betas of individualshares that make up that portfolio.Interpreting betaIn interpreting beta, you need to consider both its sign (+ or –) and its magnitude. The sign of betatells us the average direction of movements in an asset relative to the market. Most shares havepositive betas, meaning that, on average, the share’s returns move in the same direction as themarket. A negative beta is possible but rare in practice and means that the asset’s returns move inthe opposite direction to the market. For example, if an asset has a positive beta, its returns tend toincrease when market returns increase. If an asset has a negative beta, its returns tend to decreasewhen market returns increase.In considering the magnitude of beta, note that the greater its absolute value (that is, ignoring itssign), the greater the movement in the asset’s returns relative to the market and the higher theasset’s systematic risk. For example, an asset with a beta of 2.0 has twice as much systematic riskas an average asset. An asset with a beta of 1.0 has the same systematic risk as an average asset(which, by definition, is the market). An asset with a beta of 0.5 has half as much systematic risk asan average asset and an asset with a beta of zero has no systematic risk.8Beta tells us the percentage change in an asset’s return that we expect for each 1% change in themarket’s return. For example, if we expect the market to increase in the coming year by 10%: the returns on an asset with a beta of 2.0 would be expected to increase by 20% (2 x 10%); the returns on an asset with a beta of 1 would be expected to increase by 10%; the returns on an asset with a beta of 0.5 would be expected to increase by 5% (0.5 x 10%);and the returns on an asset with a beta of 0 would not be expected to change.What about an asset with a beta of –0.5? The interpretation of the magnitude of change would bethe same as for the asset with a beta of 0.5 but the direction of the change would be opposite. So ifwe expect the market increase by 10%, the returns on an asset with a beta of –0.5 would beexpected to decrease by 5%.The security market line (SML)The Security Market Line (SML) describes the relationship between risk and return predicted bythe CAPM and so can be used to estimate an asset’s expected return:?(??) = ?? + ??(?(??) – ??)where ?? = the risk-free rate of return, ?? = the asset’s beta, ?(??) = the expected return on themarket portfolio and (?(??) – ??) is known as the market risk premium (sometimes symbolisedby RPm), which applies to an asset with a beta of 1. The whole term ??(?(??) – ??) is the asset’srisk premium over the risk-free rate and is sometimes symbolised by RPi.The SML and CAPM provide a useful, simple and intuitive conceptual framework for themeasurement and appraisal of the riskiness of individual assets and asset portfolios. It has becomethe standard against which other risk-return models are judged. It is also widely used in financialmarkets and in corporate financial policy-making. For example, KPMG (2015) has reported that83% of a sample of Big 4 accounting firms, investment banks, funds and large corporates usedCAPM to estimate the cost of equity for valuations. The model can also provide useful guidance onappraising the risk of company investment projects and evaluating the cost of capital for a firm.Partly because of this, the CAPM has attained the status of required knowledge for anyoneattempting a study of business finance. Of course, as with all theories, CAPM is not without its flaws.Like all models, it relies upon several assumptions that may or may not hold.Market equilibrium and the efficient markets hypothesisTwo key assumptions of the CAPM are that: markets are dominated by risk averse investors securities markets are very competitive and efficient and all relevant information is quicklyabsorbed into security prices.9The new field of behavioural finance, based heavily on ideas from psychology, has cast doubt onCAPM’s assumption about risk averse investors by its explorations of a concept called loss aversion.Loss aversion suggests people have a strong desire to avoid realising losses, which results in losseshaving more weight in decisions than gains.We touched on the idea of efficient markets in our first topic when discussing the valuemaximisation objective assumed in most corporate finance models. When we talk about marketefficiency, we are really asking whether security prices rapidly reflect new information that comesto the market. If markets are efficient in this sense, can prices of actively traded shares differsignificantly from their ‘true’ values?One of the reasons that the market is efficient, or at least behaves in an orderly manner, is thenumber of highly trained professional analysts and traders operating in the market. These analystsand traders are constantly searching for ‘bargains’ in the stock market and they have millions ofdollars at their disposal to take advantage of any ‘bargains’. As new information becomes available,these analysts and traders evaluate it immediately and thus share prices adjust rapidly to any newdevelopments. However, behavioural finance researchers are looking at a number of concepts thatmight change the traditional view of market efficiency, such as anchoring bias (focussing too muchon recent events when predicting the future) and herding behaviour,.Textbook readingRead Chapter 6 and Chapter 7 of your text. Again, we recommend you try to replicatesome of the more complex calculations in examples as you go using this topic’sspreadsheet template or by hand for the simpler calculations. The spreadsheet alsoincludes the example shown in Table 5.2 presented earlier in this document.SummaryIn this topic, we examined the concepts of return and risk, and learnt how some asset specificsources of risk may be diversified away in the construction of asset portfolios. We found that thisleads to a focus on systematic risk.A further important part of our treatment of risk was the examination of the nature of the trade-offbetween risk and return. Market history clearly shows the risk-return trade-off: riskier assetclasses have generated higher average returns. Risk premiums for individual assets are not linkedto total risk; rather they are linked to systematic risk. CAPM attempts to capture this linkage and,through the SML equation, provides us with a useful tool for estimating the expected return onindividual assets. Despite the development of more complex models of risk and return, the CAPMremains the most widely used model for asset pricing and cost of equity estimation in practice.Furthermore, although the EMH has been questioned, particularly through behavioural finance andin light of asset pricing bubbles, we can conclude that many liquid, transparent asset markets arereasonably efficient most of the time. This means we can usually assume that the expected returnestimated through CAPM is also the required return. Therefore, the CAPM is useful in establishingthe prices of stock market securities, aiding in the selection of assets for inclusion in a securityportfolio, estimating appropriate costs of capital and determining required rates of return fordecisions involving investments in capital projects. We will consider the latter two applicationsduring our study of investment in capital projects.10ReferencesBrailsford, T., Handley, J.C. & Maheswaran, K. 2012, ‘The historical equity risk premium inAustralia: post-GFC and 128 years of data’, Accounting & Finance, 52, pp. 237-247.Grenfell, CR 2013, ‘Australian investment performance 1959 to 2013 (and investmentassumptions for stochastic models), Institute of Actuaries of Australia, available athttp://www.actuaries.asn.au/Library/Events/Insights/2013/GrenfellInvestmentPerformance.pdf, accessed 13/8/2015.KPMG 2015, Australian Valuation Practices Survey 2015, available athttp://www.kpmg.com/AU/en/IssuesAndInsights/ArticlesPublications/valuation-practicessurvey/Documents/valuation-practices-survey-2015.pdf, accessed 14/8/2015.
