3 - The merits and limitations of the main investment theories

Validity of these CAPM assumptions

Validity of these CAPM assumptions

Diversification can additionally be achieved by:

• Holding different asset classes within a portfolio. Not all assets respond in the same way to changes in the economic cycle. As a general rule: - equities are more likely to do well as the economy grows; - fixed-interest securities tend to outperform equities as recession looms; and - residential property values are related to people's real earnings, although in the previous downturn, property prices generally fell in line with equities. • Choosing companies from different sectors. Diversification within sectors is limited, however, as most shares move up and down in line with the sector as a whole. • Including overseas companies. In order to provide a greater diversification, it might be beneficial for some clients to invest in non-domestic markets.

Limitations to using an efficient frontier

• It assumes standard deviation is the correct measure of risk and assumes assets have normally distributed returns. • It is difficult to say which portfolio investors would prefer based solely on their attitude to risk, as investors may be concerned about other factors in addition to risk and have constraints on how their portfolio is invested. • Inputs for risk and correlation between assets often rely on historical data, which may not be stable. Correlations usually rise in a financial crisis, meaning that less risk will be diversified away than indicated by the model. • The model does not include transaction costs and investors may not be willing to change their portfolios as often as the model might recommend. • It assumes that the underlying portfolios in each asset class are index funds with the same characteristics as the input data.

The EMH was widely accepted until the ..

1990s, when behavioural economists began to question its validity. They argued that markets were far from perfect in terms of processing information and that other factors, such as investor confidence, must be taken into account.

CAPM - Beta

By definition, the market has a beta of one, and the beta of an individual security reflects the extent to which the security's return moves up or down with the market. According to CAPM: • A security with a beta equal to one is expected to move up and down exactly with the market. Therefore, if the market moves by 10%, the security's price will be expected to also move by 10%. • A security with a beta of more than one exaggerates market movement and is more volatile than the market. If the market goes up, the security will go up more (how much more depends on its beta). If the market goes down, the security will go down more. Such securities are often referred to as aggressive securities. • A security with a beta of less than one and more than zero is usually more stable than the market (unless it has a high level of specific risk), and will move less than the market but in the same direction. These securities are often referred to as defensive securities.

Modern portfolio theory

MPT is concerned with the way in which portfolios can be constructed to maximise returns and minimise risks. According to this theory, we cannot simply consider the potential risks and returns of an individual investment; it is important to consider how each investment changes in price relative to the other investments in the portfolio. Essential to portfolio theory is the assumption that investors are risk averse and would choose a less risky investment if they were offered the choice of two that offered the same return. The higher risk investment would only be chosen if it offered a higher return. The implication is that a rational investor would not invest in a portfolio if an alternative portfolio existed with a more favourable risk-return profile. The foundations of MPT were laid down by Professor Harry Markowitz in 1952, when he demonstrated that portfolio diversification could reduce risk and increase returns for investors. The conclusion is that a diversified portfolio of imperfectly correlated asset classes can provide high returns with the least amount of volatility.

Assumptions for the CAPM

The CAPM is based on a set of assumptions that include: • Investors are rational and risk averse, making decisions on the basis of risk and return alone. • All investors have an identical holding period. • The market comprises many buyers and many sellers, and no one individual can affect the market price. • There are no taxes, no transaction costs and no restrictions on short-selling. • Information is free and is simultaneously available to all investors. • All investors can borrow and lend unlimited amounts of money at the risk-free rate. • The quantity of risky securities in the market is fixed, and all are fully marketable (this means the liquidity of an asset can be ignored).

Evidence to support the EMH

The debate about the efficiency of markets has resulted in hundreds of studies, attempting to determine the validity of the different forms of the hypothesis: • Generally, strong and consistent evidence supports the weak form of the EMH. The vast majority of studies have found that technical analysis (buying and selling securities based on trends in historical market data) does not lead to out-performance after transaction costs are taken into account. • The semi-strong form of the EMH has strong factual support, although it is not conclusive. Research shows that for most types of information, the markets are semi-strong form efficient, although some anomalies indicate they are not completely semi-strong form efficient. • Tests of the strong-form of the EMH have focused on looking at investors who have access to non-public information or an ability to react to new information before other investors. There is evidence that company directors and their advisers can outperform other investors. However, investment managers on average do not. It would therefore appear that the market is not strongly efficient in the strictest sense of the definition. The bulk of the evidence supports the EMH. However, in reality, markets have varying degrees of efficiency, with some markets being more efficient than others. In markets that are less efficient, more knowledgeable investors can outperform less knowledgeable ones: • Government bond markets are considered extremely efficient. • Most researchers consider large capitalised stocks to be very efficiently priced, while the prices of smaller capitalised stocks, or ones which are not widely followed by analysts, are considered to be less efficient. • Venture capital, which does not have a liquid market, is considered less efficient because different participants may have varying amounts and quality of information. The efficient market debate plays an important role in the decision between active and passive investment. If the EMH is correct, instead of picking stocks, it makes sense to invest in tracker or index funds, which will mirror the overall performance of the market. On the other hand, where markets are less efficient, there is the opportunity for outperformance by skilful, knowledgeable investors.

MPT - Correlation

The effectiveness of diversification depends on the degree of correlation, or covariance, between the returns on investments within the portfolio. Correlation is a number between +1 and -1.

Efficient market hypothesis

The efficient market hypothesis (EMH) was developed by Eugene Fama in the 1960s. He put forward the idea that in an open and efficient market, security prices fully reflect all available information and prices rapidly adjust to any new information. For this reason, market prices are always the correct price for any given security and reflect the best estimate of their true intrinsic value. It is therefore not possible to outperform the market by picking undervalued securities, since the EMH indicates that there are no undervalued or overvalued securities. The crux of the EMH is that it should be impossible to achieve returns in excess of average market returns consistently through stock selection. Only new information will move security prices significantly, and since new information is presently unknown and occurs at random, future movements in security prices are also unknown and so move randomly. The only way an investor can possibly obtain higher than average returns is by purchasing riskier investments. If markets are efficient and current prices fully reflect all information, then buying and selling securities in an attempt to outperform the market will effectively be a game of chance rather than skill.

Modern portfolio theory - risk

The most commonly used measure of risk is the volatility of returns, which is called the standard deviation of returns. The standard deviation is calculated by considering the differences between the average or mean return and actual returns, based on past experience. It is a useful tool to identify the range of returns investments are likely to generate in the future. As a rough rule of thumb, the return can be expected to fall within one standard deviation of the average return 68% of the time and within two standard deviations 95% of the time when the data is normally distributed - as shown in Figure 3.1. For example, if the mean is 8% and the standard deviation is 5%: • roughly 68% of returns or events will fall between 3% and 13% (i.e. 8% ± 5%); and • roughly 95% of returns will fall between -2% and 18% (i.e. 8% ± 2 × 5%). Standard deviation is an acceptable measure of risk if the distribution of returns forms what is called a normal distribution. This means that the distribution of expected returns is spread symmetrically around the mean in a bell-shaped distribution. Investment theory often assumes this to be the case and standard deviation is generally accepted as a suitable measurement of risk. You should note that recent research has discovered that financial data is not always symmetrically spread around the mean: it can be skewed, which means it is lopsided with a long tail on one side or it can exhibit fat tails (called excess kurtosis). This increases the probability of extreme events.

MPT - Positive Correlation

The profits and share values of many companies move up and down together. They are affected by the same things: for example, the overall level of consumer demand or interest rates and the overall market performance.

MPT - No correlation

The profits and share values of some companies are not related to each other in any way. For example, there is probably little or no correlation between UK retailers and Japanese banks, unless they are both affected by the same world events.

MPT - Negative Correlation

The profits of some companies move in opposite directions and therefore have negative correlation. For example, companies with a substantial level of imports may benefit from a rise in the value of sterling, while exporters may be hit by the same factor and will need to cut margins to sell the same volumes. The share prices of such companies may or may not be negatively correlated; this is because most shares, if anything, tend to move in the same direction as the market.

Fama and French model

The securities favoured by the Fama and French model tend to be more volatile than the stock market as a whole, and the higher reward should be considered as the compensation for taking on higher risk.

Criticisms of behavioural finance

The theories of behavioural finance, incorporating behavioural and psychological factors, are now beginning to challenge existing efficient market models in terms of explaining market anomalies. However, they do not appear to be able to predict the effect on the market of human behaviour. There is little doubt that various psychological and behavioural factors impact on investment decisions and can affect the market significantly. However, some believe they have little use in forecasting the markets, since the many factors of human behaviour cannot be quantified and so will not enable an individual investor to earn abnormal returns. Critics of behavioural finance, who typically support the existing efficient market models, contend that behavioural finance is more a collection of explanations of anomalies than a true branch of finance and that these anomalies will eventually be priced out of the market. On the other hand, an understanding of behavioural finance can help investors avoid common mistakes, such as holding on to loss-making positions for too long, and help advisers, who understand their clients' behavioural biases, to communicate with these clients more effectively.

example Hedging a portfolio of UK equities

The value of a portfolio of UK equities can be hedged by: • selling FTSE 100 futures contracts; or • buying FTSE 100 put options.

Three forms of the EMH

There are three forms, or levels, of the EMH, which differ in respect of the information that they consider: • weak form efficiency; • semi-strong form efficiency; and • strong form efficiency.

Systematic risk or market risk

This is risk that affects the markets as a whole and cannot be avoided. It is the risk that markets generally will go up and down as a result of news or events. For example: • changes in interest rates, inflation or other economic factors; • tax changes made by the government; and • terrorist attacks or wars. Some securities will be more sensitive to market factors than others and will have a higher systematic or market risk. This type of risk is measured by beta, which indicates the volatility of a stock relative to the market.

Non-systematic risk or investment-specific risk

This is risk that is unique to a particular company and relates to unexpected pieces of good or bad news concerning the company. It is independent of economic, political and other factors that affect share prices in a systematic way. Examples of non-systematic risk are: • a new competitor begins making essentially the same product; • technological breakthrough makes an existing product obsolete; or • a change in a company's credit rating. While all shares have a similar exposure to market risk, investment-specific risk will vary fro company to company. Therefore, it is unlikely that the prices on all shares will move in exactly the same way at the same time. This means that in a portfolio containing a diversified range of shares, it is likely that as some of the prices are falling, the prices of others will be stable or rising. The result is a steadier overall return when a portfolio of shares is held, with the losses on one being cancelled out by gains on another. The risk reduces as the number of securities in a portfolio rises. Various academic studies suggest that 15 to 20 securities selected randomly are sufficient to eliminate most of the investment-specific risk in a portfolio. However, as Figure 3.3 shows, the rate of reduction diminishes as more securities are added. This is because, although the specific risk relating to the individual securities can be diversified away, the risk relating to the market remains.

Weak form efficiency

This states that current security prices fully reflect all past price and trading volume information, and future prices cannot be predicted by analysing this type of historical data. Therefore, technical analysis, which charts historical trading data and looks for trends, is of no use in determining future prices, and will not be able to consistently produce market-beating returns.

Overconfidence and over and underreaction

A key behavioural factor, and perhaps the most robust finding from research that explains market anomalies, is overconfidence. Extensive evidence shows that people have a tendency to overestimate their own skills and predictions for success, and underestimate the likelihood of bad outcomes over which they have no control. Investors tend to be more optimistic when the market goes up and more pessimistic when the market goes down. They typically give too much weight to recent experience and extrapolate recent trends that often run contrary to long run averages and statistical odds.

The efficient frontier

A key concept of modern portfolio theory is the efficient frontier, which describes the relationship between the return that can be expected from a portfolio and the risk of the portfolio as measured by the standard deviation. The efficient frontier plots the risk-reward profiles of various portfolios and shows the best return that can be expected for a given level of risk, or the lowest level of risk needed to achieve a given expected return. The inputs to the models are the: • return of each asset; • standard deviation of each asset's returns; and • correlation between each pair of assets' returns. The efficient frontier represents the set of portfolios that have the maximum rate of returns for every given level of risk, with each portfolio lying on the efficient frontier offering the highest expected return relative to all other portfolios of comparable risk. A rational investor will only ever hold a portfolio that lies somewhere on the efficient frontier. However, it is not possible to say which portfolio an individual investor would prefer, as this is determined by the maximum level of risk that the investor is prepared to take.

Arbitrage pricing theory

APT is a general theory of asset pricing that has become influential in the pricing of securities. It is based on the idea that a security's returns can be predicted using the relationship between the security and a number of common risk factors, where sensitivity to changes in each factor is represented by a factor-specific beta. The model-derived return can then be used to correctly price the security. If the price diverges, arbitrage activities should bring it back into line (arbitrage is the practice of taking advantage of security mispricing to make a risk-free profit), so that it is not possible for a security to yield better returns than indicated by its sensitivity to the various factors. Like the CAPM, it argues that returns are based on the systematic risk to which a security is exposed, rather than total risk. Unlike the CAPM, however, the APT is based on the belief that asset prices are determined by more than just one type of market risk. According to APT, the expected return on a security is determined by adding the risk-free rate to figures representing the risk premium for each of the risk factors. As in the CAPM, any diversifiable risk is unrewarded, because it can be avoided. However, the APT differs from CAPM in that it assumes that each investor holds a unique portfolio with its own particular degree of exposure to the fundamental economic risks that influence asset returns, as opposed to an identical market portfolio. The APT therefore has more flexible assumption requirements than the CAPM. One difficulty with the APT is its generality, as the model does not tell us which factors are relevant. In addition, the number and nature of those factors is likely to change over time and between economies. The inclusion of multiple factors does, however, mean that more betas have to be calculated, and there is no guarantee that all of the relevant factors have been identified. Multi-factor models are widely used by quantitative model-driven investment managers and in risk management.

Behavioural finance

Behavioural finance is a relatively new area of research that explores how emotional and psychological factors affect investment decisions. It attempts to explain market anomalies and other market activity that is not explained by traditional finance models, such as MPT and the EMH, and offers alternative explanations of the key question of why security prices deviate from their fundamental values. Much of the traditional financial theory is based on the assumption that individuals act rationally and consider all available information when making investment decisions. The key argument of behavioural finance is that psychological factors or behavioural biases affect investors. These limit and distort their information and may cause them to reach incorrect conclusions, even if the information is correct. Behavioural finance highlights certain inefficiencies caused by the irrational way in which investors react to new information as causes of market trends and, in extreme cases, of speculative market bubbles (the dotcom bubble in 1999) and stock market crashes, such as in 1987 and 2008. By looking at bubbles and crashes, it becomes clear that psychology can be as important as finance and economics for the explanation of such phenomena.

Limitations of the CAPM - What to use as the risk-free rate?

Finding a totally risk-free return is difficult. Common practice is to pick the return on UK Government Treasury bills as a representation of a risk-free asset. These are 91-day money market instruments issued by the UK Government; there is virtually no default risk and, because of their short life, the interest rate and inflation risks are minimal.

MPT - Hedging

Hedging means protecting an existing investment position by taking another position that will increase in value if the existing position falls in value. One way that this can be achieved is by using derivatives.

Limitations of the CAPM -The suitability of beta

In order for the CAPM to be useful, the beta of a security must be stable or predictable. Betas are calculated from past experience and do not seem to be stable over time, which brings into question their reliability as a guide to estimating future risk. The CAPM suggests a direct relationship between the excess return on a security over the risk-free rate and its beta, but some studies, particularly in the USA, have not found this relationship. There does, however, appear to be more support for the model over longer periods of time, with some studies seeming to imply that low beta securities earn more than the CAPM would predict, while high beta securities earn less. Despite this, the CAPM is the foundation of many risk-adjusted measures of investment performance. The fact that the model has been criticised because its assumptions are unrealistic (there are some studies that show the market does not perform as the theory suggests) does not invalidate its ability to provide relative data that illustrates expected returns and their relationship to risk.

Limitations of the CAPM - What is the market portfolio?

In theory, the CAPM market portfolio includes all risky investments worldwide, while in practice, this is usually replaced by a market index of shares relating to a particular national share market, e.g. the FTSE All-Share or FTSE 100. However, depending on which index is used, the betas are significantly different. This has brought into question whether these indices represent the true market portfolio, since if the true market portfolio is not used, the correct beta for a security cannot be determined.

MPT - Diversification of risk

Investors can reduce the risk on their portfolio by holding a range of different types of assets. Each type of investment tends to perform well in certain market conditions and by broadening the portfolio's exposure across a range of asset classes, the fluctuations caused by most economic and financial events can be smoothed out. You should note that diversification within a portfolio can remove investment specific risk but not market risk. It is clearly riskier to invest in a single security than in a collection of securities. When a portfolio is made of a number of securities, the problems associated with one particular security will not have such a major impact on the overall value of the portfolio: • Diversification reduces risk because combining different asset classes or securities in a portfolio reduces the overall risk to less than the average risk of the individual securities. The downside risk of one investment would be offset by the upside potential of another investment. This offsetting would not occur if the investments all moved in the same direction at the same time. Diversification is effective where individual stocks move in opposite directions

Regret

Investors may be less willing to sell a losing investment because it is showing a loss. People tend to feel sorrow and grief after having made an error of judgment. Investors deciding whether to sell a security are typically emotionally affected by whether the security was bought for more or less than the current price. Investors therefore avoid selling stocks that have gone down to avoid the pain and regret of having made a bad investment. It is the fear of regret that causes investors to hold losing positions too long in the hope that they will become profitable, or sell too soon to lock in profits in case they turn into losses.

MPT - Reduction of risk

One way to construct a low-risk portfolio is simply to buy low-risk assets, but this will usually lead to low returns. A more attractive way is to buy risky assets, which on average will give higher returns, and then reduce the risk in one of two ways: • either by diversification of the portfolio holdings;or • more specifically, by hedging out risk.

Effect of overconfidence

Overconfidence has been found to cause investors to overestimate the reliability of their knowledge, underestimate risks and exaggerate their ability to control events, which can lead to excessive trading volumes and speculative bubbles.

The efficient frontier graph and portfolio comparisons

Portfolio A v portfolio B - Portfolio A is a better choice because it offers the same return as portfolio B, but at a lower level of risk. Portfolio B v portfolio C - Portfolio C is a better choice because it offers a higher return for the same level of risk as portfolio B. Portfolio C v portfolio D - Portfolio C is a better choice because it offers the same return as portfolio D, but at a lower level of risk. Portfolio D v portfolio E - Portfolio E is a better choice because it offers a higher return for the same level of risk as portfolio D. Portfolio A v portfolio C v portfolio E - It is difficult to choose between these portfolios. Portfolio A offers a low risk, low return strategy, while both portfolios C and E offer higher levels of risk but with higher returns. The portfolio selected will depend on the risk preference of the individual investor.

Prospect theory/loss aversion

Prospect theory deals with the idea that people do not always behave rationally, in particular in respect to their risk tolerance when they are facing a loss or have made a profit. The theory suggests that there are persistent biases that influence people's choices under different conditions of uncertainty. Research has shown that investors place different weights on gains and losses, and on different ranges of probability. Individuals are much more distressed by prospective losses than they are made happy by equivalent gains, and responded differently to equivalent situations depending on whether that situation is presented in the context of a loss or a gain. Research has also found evidence that people play safe when protecting gains, but if faced with the possibility of losing money, they often take riskier decisions aimed at loss aversion. This may include a reluctance to realise losses, so people hold on to losing investments longer than they should in the hope that, given time, the loss will be recouped. If they were to sell they would realise the loss, otherwise it is just a paper loss.

Psychological factors or behavioural biases

Psychological factors and behavioural biases can be categorised in many ways, although these often overlap and can be indistinguishable from one another. The following sections consider some of the principal theories within behavioural finance that often contradict the basic assumptions of traditional financial theory.

Influences on security returns

Research suggests that there are four important factors that influence security returns: • unanticipated inflation; • changes in the expected level of industrial production; • changes in the default risk premium on bonds; and • unanticipated changes in the return of long-term government bonds over Treasury bills (shifts in the yield curve).

Modern portfolio theory - Standard deviation

Standard deviation measures how widely the actual return on an investment varies around its average or expected return. The greater the standard deviation, the greater the volatility and therefore, the associated risk: • An investment with returns staying close to its expected return is said to be low risk and has a low standard deviation. • An investment with returns fluctuating wildly may have the same expected return, but is described as high risk. It has a higher standard deviation of returns. • The greater the standard deviation around the expected return, the more volatile and hence risky the investment.

Example - Correlation of returns

Suppose an investor buys shares in two companies, an ice cream manufacturer and an umbrella manufacturer. Like all businesses, these two companies have risky returns in that their profits vary from year to year. For the sake of this example, we will assume that the profits of the two companies are only affected by the weather and nothing else. In particular, the weather affects profitability in opposite ways: • In good weather, the demand for ice cream increases and the profits of the ice cream manufacturer rise, but in bad weather, the demand for ice cream falls. • In contrast, in bad weather, the demand for umbrellas increases and the profits of the umbrella manufacturer rise, but in good weather, demand for umbrellas falls. • One prospers when the other does badly. By investing equally in both companies, the variability of their returns is reduced or eliminated, because they are affected by changes in their environment in opposite ways. The risk has been diversified away because the returns are negatively correlated.

CAPM equation

The CAPM is a model that derives the theoretical expected return for a security as a combination of the return on a risk-free asset and compensation for holding a risky asset, i.e. a risk premium.

Objective of portfolio management

The objective of portfolio management is to find the optimal portfolio for an investor. The more risk averse an investor is, the lower the optimum portfolio on the risk-reward spectrum will be, as defined by the efficient frontier.

Multi-factor models

The CAPM expresses a simple relationship between risk and return. It indicates the expected return on a security as the return on a risk-free asset, plus a risk premium. This risk premium is simply determined by the level of the security's systematic (non-diversifiable) risk relative to the average level of systematic risk on a stock market. Hence, the model is often referred to as a single factor model - it is concerned with only one factor, the security's sensitivity to the market, as measured by its beta. However, as we have seen, there are some problems with this theory. The relationship between risk and return can be far too complex to describe by the relationship with a single market index, as other factors may also determine the return on a security. Different securities have different sensitivities to different types of market wide shocks: inflation, business cycles, interest rates, etc. Multi-factor models allow for different sensitivities to different factors and the identification of each factor's contribution to the security's return. A multi-factor model attempts to describe security returns as a function of a limited number of factors. However, when constructing a multi-factor model, it is difficult to decide how many and which factors to include. The Fama and French model expanded the CAPM by adding factors for company size and value in addition to the market risk factor of CAPM. Fama and French identified two types of company securities that tended to do better than the market as a whole, they found that: • small cap stocks tended to outperform large cap stocks; and • value stocks (those with a high book value to price ratio) tended to outperform growth stocks. One of the best-known multi-factor asset pricing models, based on arbitrage pricing theory (APT), was developed by Stephen Ross. He suggested a more general multi-factor structure, which is based on the idea that there are a few major macro-economic factors or indices that influence security returns. Additional factors can be added that relate to the fundamentals of the company being analysed, such as earnings growth, return on equity, dividend yield, etc. Multi-factor models are able to make a more detailed prediction of risk and return, and improve our understanding of security returns.

Capital asset pricing model

The concept of MPT derives a relationship between the risk and return of financial assets. To invest in a risky asset, an investor requires a return that is equal to the risk-free return plus a risk premium for taking on the additional risk of that asset. As explained in section A, the total risk of a security can be divided between systematic or market risk and non-systematic or investment-specific risk. The non-systematic risk relates to risks that are unique to the security and which can be diversified away as increasing numbers of securities are added to a portfolio. However, no matter how many securities are held in the portfolio, systematic risk remains. Some securities are more sensitive to market factors than others and will therefore have a higher systematic or market risk, while others will not be as sensitive and will have a lower systematic risk. CAPM says that because non-systematic risk can be eliminated by diversification, it is not rewarded. It is the sensitivity of the security to the market that is the appropriate measure of risk.

Semi-strong form efficiency

This states that security prices adjust to all publicly available information very rapidly and in an unbiased way, so that no excess returns can be earned by trading on that information. Public information includes not only past prices, but also information reported in a company's financial statements, company announcements and economic factors. This indicates that a company's financial statements are of no help in forecasting future price movements and securing excess returns. Semi-strong form efficiency implies that neither fundamental analysis, which looks at the historical financial performance of a company, nor technical analysis, which charts historical trading data, will reliably be able to help identify whether a security is over or undervalued.

Strong form efficiency

This states that security prices reflect all information that any investor can acquire. In this form, all information includes not only public information, but also private information, typically held by corporate insiders such as officers or executives of a company, or their advisers.

Although there are differences between multi-factor models, they all share two basic ideas:

• investors require extra return for taking risk; and • they appear to be predominantly concerned with the risk that cannot be eliminated by diversification.