Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Macroeconomics Chamberlin and Yueh Chapter 6 Lecture.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Financial Markets Efficient Markets: Asset Pricing Models Expected Dividend Model, Gordon Model Uncertainty and the Capital Asset Pricing Model Portfolio Selection: Tobin Model Financial Market Volatility: Efficient and Inefficient Markets Bubbles and Crashes in Financial Markets

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Learning Objectives Understand the nature of financial markets and why they are an important determinant of consumption and investment. Analyse the expected dividends model and the process of arbitrage. Introduce the Capital Asset Pricing Model (CAPM), which is a consumption based model that implies that assets with higher returns offer less opportunity to hedge against income risks. Discuss the Tobin model of portfolio selection, which describes how investors choose the optimal combination of risk and return in their portfolios.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Learning Objectives Investigate the Efficient Markets Hypothesis (EMH) that financial asset prices should reflect all available information and that asset prices follow a random walk process. Evaluate the empirical tests which tend to reject the EMH because the volatility of asset prices is greater than the volatility of news regarding fundamentals. Define and learn about bubbles in financial markets, such as the dotcom bubble in the late 1990s. Learn about crashes, which refer to a large and sudden drop in market values, and the role of traders.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Importance of financial markets We introduced the main features of the money market. In doing so, we only considered two types of assets, money itself and interest bearing bonds. This topic extends the analysis to look at financial markets – by which we predominately mean the stock market. The stock market is where equities, such as stocks and shares, are traded and prices are determined. We have seen that stock market valuations play a very important role in the economy.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Efficient Markets: Asset Pricing Models Financial markets are at the centre of the circular flow of income and play an important allocative role by intermediating between savers and borrowers. We examine both efficient and inefficient financial markets. If financial markets are efficient, then the price of a financial asset should reflect all available information concerning the fundamentals of risk and return. In these circumstances, it would be expected that assets which offer relatively high and certain returns would accordingly be highly priced.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Efficient Markets: Asset Pricing Models We introduce two models of asset price determination. The first is what has been termed the expected dividend model. This relates the price of an asset to the stream of expected future dividends that the asset pays. The Gordon model is a commonly used variant of this mode. The second model we consider is widely used in corporate finance. The Capital Asset Pricing Model, or CAPM, argues that the value of an asset is strongly related to its ability to diversify risks.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Expected Dividend Model Dividends and Expected Discounted Values A firm listed on the stock market has been split into a number of shares, with each share representing ownership of a certain proportion of the company. These shares are marketable so their value is determined by demand and supply. The total value of the company is found by simply calculating its market value, that is, the number of shares multiplied by the price of each share:

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Expected Dividend Model There are two elements that make up the returns from holding shares. The first is the entitlement to a share of the firm’s earnings, which are usually paid as dividends. The second arises from the gains or losses that accrue from the resale value of the share. If the share price rises (falls) in the period of ownership, then a capital gain (loss) is made. These returns, though, are uncertain. The motive for buying or holding a certain share must therefore come from its expected future returns given the information available at the time.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Expected Dividend Model Assume that: P t is the price of the financial asset at time t. I t is the information set available at time t. The expected dividend paid, given this information, is And, also conditional on the information available, the expected asset price next period is

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Expected Dividend Model These values, though, will only be obtained in the next period at time t+1. In order to present them in present (time t) values, they need to be discounted by the interest rate (1+r). The efficient price of the financial asset will therefore be set equal to the expected discounted value of the future dividend payment and resale price: (6.1) If the asset price were to deviate from this, then there would be opportunities for traders to make profits.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Expected Dividend Model The process which drives asset prices to their efficient values is known as arbitrage. When people think of financial markets, they often think of traders who are buying and selling assets in order to achieve trading profits. These traders can be thought of as arbitrageurs, who try and profit from mis-pricings and can trade aggressively to do so, but the outcome will be to drive asset prices toward fundamental values. By combining long and short positions, it is possible for a trader to hold a portfolio that does not cost anything. For example, its long positions in certain assets are funded by short positions in others. For this reason, arbitrage can be a strong phenomenon as traders can take positions in order to profit from expected movements in asset prices.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Expected Dividend Model The expected dividend model implies that the efficient price of an asset can be written in terms of the stream of future expected discounted dividend payments the asset generates. Rewriting solely in terms of future divident payments, the expected price of the asset at time t+1 will be determined in exactly the same fashion as it was in time t: (6.2) If priced efficiently, the expected price of the asset at time t+1 will equal the sum of the expected discounted dividend payment and asset price at time t+2.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Expected Dividend Model If (6.2) is substituted into (6.1), then a new equation for the asset price at time t can be derived: (6.3) Alternatively, this can be written as: (6.4) Therefore, the current price of the asset is equal to the expected discounted dividend payments over the next two years and the expected discounted resale price in two periods’ time. Note that the payments which accrue two periods in the future are discounted twice.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Expected Dividend Model The expected asset price in two periods’ time would be equal to the sum of the expected discounted dividend payment and asset price in time t+3: (6.5) Substituting (6.5) into (6.3) gives the current asset price as a function of dividends over the next three periods and the asset price at time t+3: (6.6)

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Expected Dividend Model This can be seen more clearly by rearranging the above: (6.7) Once again, note that the values which accrue in three periods’ time are discounted three times.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Expected Dividend Model By continuing this repeated substitution to infinity, we can derive a very simple formula for the fundamental value of an asset solely in terms of its dividend stream: (6.8) Payments that arise a substantial time in the future are discounted more heavily, so in present value terms their value will head to zero. Therefore, we would expect that as time goes to infinity that the expected discounted asset price will head towards zero.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Expected Dividend Model This leaves the current asset price as being determined by just the stream of expected future discounted dividend payments: (6.9) Equation (6.9) is the essentially the same as (6.1).

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Expected Dividend Model The expected dividends model is fairly intuitive in that it links asset values according to the returns that the asset produces. If all assets are priced at their efficient levels, then investors will obtain the same rate of return regardless of which asset they buy. This will be the rate of interest, so the investor will also be indifferent between holding any asset and bonds. This model is quite simple, but it can be used to analyse the causes of stock market changes. These broadly fall into two categories.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Expected Dividend Model The first is any factor that is likely to affect the flow of future dividend payments, which are in turn derived from the firm’s earnings. This could be almost anything – a technological breakthrough, changes in the management structure, specific government regulations, the state of the economy and consumer demand, the condition of the firm’s competitors, and so on. The second is the interest rate, which represents the opportunity cost of holding equities, as any investor could always invest in bonds instead. It is easily seen from (6.9) that higher interest rates imply future dividend payments are more heavily discounted, so share prices would be expected to fall.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Gordon growth model A simple variant of the expected dividend model is the Gordon model. This uses exactly the same framework as above, but specifies a rule that describes how dividends grow over time. This model reaches broadly the same conclusions, but is widely used due to its simplicity.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Gordon growth model The most important assumption is that dividends grow at the rate of g each period. Therefore:

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Gordon growth model If we substitute this dividend stream into (6.8), then the current asset price can be written as follows: (6.10) The expression in (6.10) can be simplified further to produce a very simple rule for asset prices.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Gordon growth model The first step is to factorise (6.10) by collecting the common term on the right hand side: (6.11) Next, we need to make an assumption that the growth rate is less than the interest rate:

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Gordon growth model In (6.11), the terms in the square brackets can be simplified by using the rule for finding a sum to infinity: Which, in turn, can be simplified to: Because The Gordon model is:

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Gordon growth model There are two factors which determine the price of a financial asset. –The first is the interest rate – as this rises, the efficient asset price falls. –The second is the growth rate of dividend payments. The implication here is that firms which experience higher earnings growth will be valued more. We could reinsert the notion of uncertainty by arguing that it was expected rather than actual growth which mattered. This means that asset prices will be determined by any number of factors. The discounted dividend and Gordon models are essentially the same and relate asset prices to company earnings. However, these basic models do not consider the impact of different risks and uncertainties on asset prices.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Uncertainty and the Capital Asset Pricing Model The expected discounted dividend model is widely used, but lacks one important ingredient. Assets are valued in accordance with their income streams, so assets with a command over higher future dividends will have a greater price. However, there is one important ingredient that is missing in valuing assets this way – risk. We now introduce the Capital Asset Pricing Model (CAPM) in which assets are valued in terms of their ability to diversify risks.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Capital Asset Pricing Model This is a consumption-based model. Asset pricing models of these types are driven by the law of diminishing marginal utility of consumption. This states that as consumption increases, total utility increases but at a declining rate. This has important implications for the pattern of consumption over time. One of the main features of the Permanent Income Hypothesis is that smoothing consumption over time is consistent with utility maximising behaviour.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Capital Asset Pricing Model Under the Permanent Income Hypothesis, consumption can be smoothed over time by using saving and borrowing to offset transitory movements in consumption. It is less obvious how an individual can smooth consumption over different states of the world, although it would be logical to do so from the standpoint of maximising expected utility. This is where financial markets have a role to play. Different assets will generate different returns in different states of the world, giving investors an opportunity to manage risks and uncertainty. Using financial assets to diversify wealth or income uncertainties is the guiding principal behind consumption-based models, which argue that assets should be priced in accordance to their abilities to do this.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning CAPM Model The CAPM model argues that assets should be valued according to their degree of income diversification. The law of diminishing marginal utility of consumption implies that as consumption increases, the marginal utility of an extra unit of consumption falls. In terms of pricing assets, this implies that dividend payments paid in periods of high income, and therefore high consumption, should be weighted less than dividends paid in periods of low income. This is because although they might have similar money values, they have very different values in terms of utility.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning CAPM Model Incorporating this feature into the asset pricing model in (6.9) yields the following: (6.15) The expected dividend model is extended so that the expected discounted dividends in the future are weighted according to the marginal utility of expected consumption in each period. This means that expected dividend payments in times when expected consumption is expected to be high will be weighted less than the same dividend payment in a time where the level of expected consumption is low.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning CAPM Model This relationship underlies the CAPM model. The higher the covariance of an asset’s returns with the marginal utility of consumption, the lower is the value of the asset. An asset where returns are negatively correlated with the marginal propensity to consume will be worth more because it enables the holders to hedge against low consumption.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning CAPM Model The CAPM pricing rule can be derived in the following fashion: the expected return on an certain asset i is the expected return from holding the market portfolio is If R rf is the expected return on a risk-free asset, then it is possible to write the following identity: (6.16) The market portfolio is where the same amount of each asset is held.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning CAPM Model The CAPM relationship can now be written in the following way: (6.17) For each asset, the excess return over the risk-free rate is related to the excess return of the market portfolio over the risk-free rate of return by the coefficient, β i. This is the central element of the CAPM model. Each Beta gives an indication as to how an asset can be used to diversify risks.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning CAPM Model: β If β i =1, then the returns of asset i move directly in line with the market portfolio. In fact, asset i is the market portfolio. As the market portfolio is expected to move in line with the economy as a whole, this asset would not be expected to diversify income. If β i <1, then the returns of asset i move less than the market portfolio. This offers individuals the ability to diversify income shocks. For example, if 0< β i <1, then following a fall in the overall stock market, the fall in the returns of asset i would be correspondingly less.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning CAPM Model: β It is even better in terms of diversification if β i <0, as the asset returns are negatively correlated with movements in the market portfolio, which offers a more complete opportunity to diversify income risks. If β i> 1, then the returns on asset i would be more volatile than movement in the market as a whole. The CAPM relationship in (6.17) is known as the market line.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning CAPM Model: Summary Assets that offer higher expected returns have higher betas, whereas the assets that offer lower returns have lower betas. The market line reflects a trade-off between risk and return from holding different portfolios of assets. Those which offer high expected returns are more risky, as they offer limited ability to diversify income. On the other hand, assets with low expected returns offer the compensation of a low beta, so are better able to hedge against low income.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Portfolio selection: Tobin model The relationship between risk and return, and the optimal amount of each asset that an investor desires to hold, is explained in the Tobin model of portfolio selection. A portfolio represents the combination of different assets that an investor holds. The overall risk and return of the portfolio will reflect the composition of the assets in the portfolio.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Tobin model of portfolio selection Assume for simplicity there are two types of assets. The first is a risk-free asset which offers a guaranteed rate of return R rf with zero variance: The second is a risky asset which offers a higher rate of return, but these returns are uncertain and have a positive variance:

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Tobin model of portfolio selection A portfolio can be constructed by choosing a combination of these two assets, with a proportion w of the risky asset and (1-w) of the risk-free asset. The expected return from the portfolio is derived as follows: (6.18a) As the proportion of the risky asset in the portfolio increases, the expected return also increases.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Tobin model of portfolio selection Equation (6.18a) can be rearranged, (6.18b) The riskiness of the portfolio, though, depends on the relative variances of the two assets. The variance of the portfolio is then: (6.19),

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Tobin model of portfolio selection This can be rearranged so that the weight w can be expressed as the ratio of the standard deviation of the portfolio to the risky asset: (6.20), Substituting this ratio into (6.18) gives us an equation which describes the risk return trade-off that the investor faces: (6.21)

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Tobin model of portfolio selection Equation (6.21) fully describes the risk return trade-off an investor faces. The excess expected return of the portfolio over the risk-free asset increases as the proportion of the risky asset in the portfolio increases. However, the variance of the returns will increase as a result. Plotting (6.21) on a set of axis graphically shows the risk return trade-off, which has a very similar form to the market line derived in the CAPM.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning CAPM vs. Tobin’s model The only difference between the CAPM and Tobin models is how risk is measured. In the CAPM model, risk is determined in terms of the beta – with a higher beta indicating that the portfolio has less ability to hedge against income uncertainties. In Tobin’s model, the risk of a portfolio is defined in terms of the variance or uncertainty of asset returns.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Tobin model of portfolio selection The assumption of there being only two assets is just a simplifying assumption. If there were many assets, the same trade-off between risk and return would exist, but would reflect the minimum variance of each portfolio for every level of expected returns. It would still be the case that as the portfolio becomes more risky, the expected returns would increase to reflecting a risk premium. The Tobin model describes how investors choose the risk and return composition of their portfolio.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Tobin model of portfolio selection It is assumed that each trader has preferences over risk and return which can be represented in a utility function: (6.22) This utility function generates a suite of indifferences curves, which shows the combinations of risks and return that gives the investor a given level of utility. These indifference curves are upward sloping because investors see returns as a good thing, but risk as a bad thing. Therefore, as the investor is forced to hold a portfolio with greater risk, they require higher returns in order to keep their utility at the same level.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Tobin model of portfolio selection The slope of the indifference return reflects the rate at which the investor is prepared to trade-off risk for return. The utility maximising decision of the risk and return structure of the portfolio is found by moving on to the highest possible indifference curve, subject to the market line which determines the feasible risk-return combinations available. The choice of portfolio will be predominately determined by the preferences of the investor. Those who are less risk averse will likely have an optimal portfolio offering higher risks but also higher expected returns. The opposite would apply to more risk adverse investors.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning CAPM vs. Tobin’s model: Summary The CAPM and Tobin model both introduce the element of risk into asset pricing. The expected dividend model implies that assets which offer higher returns should be valued more highly. However, if these greater risks simply reflect the existence of a risk premium, then it is not necessarily the case that investors will choose to hold assets with higher expected returns. If investors are sufficiently risk averse, their optimal portfolio might consist of lower return but safer assets.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Financial Market Volatility: Efficient and Inefficient Markets The Efficient Markets Hypothesis (EMH) has been the central proposition in finance theory since Fama first presented the idea in 1970. In its most basic form, it just implies that prices in financial markets fully reflect the available information as in the expected dividend model in (6.9). The strong implication is that any investor cannot hope to consistently beat the market because arbitrage is strong enough to correct any mis-pricings. Spending vast resources on trying to gain an informational advantage would be wasted as all information will be correctly and quickly incorporated into asset prices; it would be better to passively hold the market portfolio.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning The Theoretical Foundations of the EMH: Arbitrage There are several foundations to the EMH. Firstly, investors are assumed to be rational so that financial assets are valued according to the expected discounted value of future dividends as explained in (6.9). If investors are rational, financial asset prices will reflect all available and relevant information, and market efficiency will prevail as assets are priced according to their fundamental values. To the extent that some traders are irrational, then their trades are assumed to be random and therefore will cancel each other out. Hence, asset prices will continue to trade at prices close to fundamental values.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning The Theoretical Foundations of the EMH: Arbitrage However, it is the force of arbitrage that acts as the ultimate defensive line for the EMH driving asset prices towards their fundamental values. Arbitrage has a further implication. Irrational investors lose money, but as Friedman pointed out in 1953, they cannot continue to lose money forever. Eventually they will become less wealthy and disappear from the market. So, even if arbitrage cannot eliminate their effects on asset prices, market forces will eventually act to eliminate them from the market. Therefore, even if arbitrage is limited, competitive selection means that market efficiency will prevail.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning The Econometrics of the EMH The EMH implies that the prices of financial assets include all the available information regarding the expected future earnings of that asset. Because this new information is unpredictable, financial assets are said to follow a random walk process: (6.23) where ε t is a stochastic term which represents news innovations. The change in asset prices solely reflects the arrival of new news: (6.24)

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning The Econometrics of the EMH As new information is always arriving in the market, we would expect prices to be continuously changing. Therefore, volatility in financial asset prices shouldn’t necessarily be unexpected or regarded as unfavourable. As new information is always coming to markets, the quick and continuous reaction of asset prices is part of the efficient pricing process. Volatility in financial asset prices is not at in conflict with the predictions of the EMH.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning The Econometrics of the EMH It is clear that daily changes in prices are indeed volatile. We see that stock market prices, although volatile on a daily basis, tend to trend upward over time. This reflects the fact that economies grow over time and this growth is reflected in the fundamental values of assets.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning The Econometrics of the EMH Because of this, a better description of the process driving asset prices is a random walk with drift: (6.25) This states that the change in asset prices is equal to a constant and an innovative factor. A random walk with drift process will be a series that is volatile, but fluctuates around a trend line, so will grow over time.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Efficient Markets Hypothesis: A Critique In the first decade after its inception, the EMH was an enormous empirical and theoretical success. However, over the course of the following 20 years, there have been a growing number of challenges to the theoretical foundation of the EMH and the evidence supporting it. The key forces by which markets are supposed to attain efficiency, such as arbitrage, are likely to be less powerful than efficient markets theorists first believed. With new theory and evidence, behavioural finance has emerged to provide an alternative view of financial markets. Systematic and significant deviations from efficient prices can therefore be expected to persist for long periods of time.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Efficient Markets Hypothesis: A Critique A simple empirical/econometric test for the EMH is simply to test asset prices for the presence of a random walk. From the above, it must be true that if the EMH holds, then the variance of stock market changes should equal the variance of the innovations that underlie them. This presents an intuitive way to test the ramifications of the EMH: can changes in asset prices be related to changes in news about fundamentals?

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Efficient Markets Hypothesis: A Critique Shiller’s (1981) work on stock market volatility, which showed that stock market prices are far more volatile than can be justified by a simple model in which prices are equal to the expected net present value of future dividends. This suggests that financial markets may react to non- information. The most salient piece of evidence concerning this is the 1987 stock market crash. The surprising feature of this crash is that no news or announcements could be identified as the source of this crash. In fact, many sharp movements in asset prices seem not to appear to accompany significant news.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Efficient Markets Hypothesis: A Critique An interesting and similar conclusion was reached by Roll (1988). He calculates the share variation in the returns of large stocks explained by aggregate economic influences, the contemporary returns on other stocks in the same industry, and public firm-specific news events. He finds that only 35% of the total volatility in share prices can be accounted for by this information on monthly data, and only 20% on daily data. This again implies that movements in stock prices are largely unaccounted for by public news.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Efficient Markets Hypothesis: A Critique According to the EMH, changes in asset prices should be unpredictable from past data. This is simply because past information will have already been incorporated into asset prices if traders are rational and markets are efficient. In this case: (6.26) For the EMH to describe asset prices, it is required that β=0, i.e., no past changes in prices are significant determinants of current price changes.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Efficient Markets Hypothesis: A Critique Work by DeBondt and Thaler (1985) finds against the notion that past information cannot be used to predict future asset prices, implying that β  0. They compare the performance of two groups of companies: extreme losers and extreme winners. For each year since 1933, they form portfolios of the best and the worst performing stocks over the previous three years. They then compute the returns of these portfolios over the following five years and find that the extreme loser portfolio does significantly better than the extreme winner portfolio. The explanation is that stock prices overreact; extreme losers become too cheap and bounce backwards, whereas the extreme winners become too expensive and must subsequently fall.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Efficient Markets Hypothesis: A Critique The upshot is that there is substantial empirical evidence which points towards a rejection of the EMH. Volatility analysis (event studies) implies that financial asset prices appear to have larger variance than the fundamentals they claim to be built upon. Also, changes in asset prices may not be totally unpredictable, with past price changes being an indicator of current and future movements.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Theoretical Challenges to the EMH There are countless examples of where contagion, mimicking or herding may be important in financial markets. It can also offer an intuitive explanation as to why financial asset prices may be excessively volatile. It is now no longer the case that financial market participants just react to news about fundamentals; they must also react to the reactions of other financial agents. Ultimately though, the theoretical case for efficient markets depends upon the effectiveness of arbitrage. Even if irrational traders lead asset prices away from fundamental values, arbitrageurs will seek to profit from the mis-pricings and in so doing reinforce efficient pricing. However, a central concept of behavioural finance is that arbitrage is risky, and therefore limited. The finite risk bearing capacity of arbitrageurs reduces their ability to bring prices fully into line.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Noise Trader Risk in Financial Markets and the EMH Arbitrage is an important feature of financial markets, as its effect is to bring prices towards fundamentals and keep markets efficient. The most common explanation for complete arbitrage is the presence of transaction costs or imperfect substitutes. The type of risk we are concerned with here is mis-pricing that can worsen in the short run. These types of movements are very important for short horizon investors engaged in arbitrage against noise traders: this is the risk that noise traders’ beliefs become more extreme before reverting to the mean.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Noise Trader Risk in Financial Markets and the EMH If noise traders are pessimistic about an asset and have driven its price downwards, an arbitrageur who buys this asset must accept the possibility that in the near future noise traders may become even more pessimistic and drive the price down further. If the arbitrageur is forced to liquidate his asset holding before the price recovers, then they face a loss. Fear of this loss may limit the original arbitrage position. It is the risk of further movements in noise traders’ beliefs away from the mean (this is what noise trader risk is defined by) that must limit the willingness to bet against noise traders.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Noise Trader Risk in Financial Markets and the EMH The result of limited arbitrage is that substitute assets may end up selling at two different prices, an outright contradiction of the EMH. Mis-pricing can lead to enormous inefficiencies that in the absence of arbitrage behaviour can be sustained. As a result large deviations of prices from fundamental values may arise from risky arbitrage that takes some time to correct.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Example: U.S. Stocks An example may help to illuminate the idea of risky and limited arbitrage. Consider the case of American stocks in the late 1990s. At the end of 1998, large U.S. corporations were trading at some of their historically highest market values relative to most measures of their profitability. For example, the ratio of market value of the S&P 500 relative to the aggregate earnings of the underlying companies stood at 32, compared to the post war average of 15. However, there are not many good substitutes for the whole S&P 500 market. In fact, any arbitrageur that tried to exploit this apparent mis-pricing would probably have gone out of business.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Example: Royal Dutch Shell Fundamentally identical assets should trade at identical prices; this is just the workings of arbitrage. However, this is not always the case, and the presence of noise trader risk appears to explain price divergences. A 1907 alliance between Royal Dutch and Shell Transport in which the two companies agreed to merge their interests on a 60:40 basis, while remaining separate and distinct entities. The only real difference between the two firms is that Royal Dutch trades in Holland and on the U.S. S&P 500, whilst Shell trades predominately in the UK on the FTSE.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Example: Royal Dutch Shell Between September 1980 and September 1995, there was a tremendous amount of deviation, from an underpricing of 35% to an overpricing of 10% of Royal Dutch relative to Shell. It takes about 4 years for the 30% mis-pricing of Royal Dutch and Shell that was prevalent in September 1980 to eventually disappear. In return for bearing this risk, the arbitrageur earns about 7% per year. For reasons such as the costs of leveraging, and the presence of possible liquidation should further mis-pricing occur, arbitrageurs may have found it unattractive to arbitrage in September 1980, even with a 30% mis-pricing of two identical securities.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Noise Trader Risk in Financial Markets and the EMH Therefore, mis-pricing can be seen to take a while to correct, and so enormous inefficiencies can be maintained without aggressive arbitrage activity coming in to correct them. From the point of view of the EMH, this is crucial as it suggests that even with identical securities noise trader risk may be large enough to cause large and sustained price deviations from fundamental values.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Professional Arbitrage Effectively, so far we have considered arbitrageurs who use their own wealth to trade, and therefore are limited by their own risk aversion. In reality, arbitrage is conducted by relatively few professional, highly specialised investors who combine their knowledge with the resources of outside investors to take large positions. In this respect, traders and financers are separated by an agency relationship. When the arbitrageur is managing other people’s money, and his investors do not fully understand what he is doing, they can only observe him losing money if prices happen to move further out of line from fundamental values.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Performance based arbitrage The responsiveness of funds under management to past returns is referred to as performance based arbitrage (PBA). Investors may rationally allocate funds based on the past returns of arbitrageurs, and withdraw funds after poor performance. Consequently, arbitrageurs become less aggressive in betting against mis-pricing. Performance based arbitrage is extremely ineffective in extreme circumstances when prices are substantially out of line and arbitrageurs are fully invested. In such panics, arbitrageurs may bail out of the market, voluntarily or not, exactly at the point of time where their participation is most needed.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Bubbles and crashes in financial markets Much volatility in financial markets thus results because herding behaviour or irrational investors are allowed to influence market prices, as their actions will not be corrected by arbitrage. This means that trading on noise rather than fundamentals may come to drive market prices. We now turn to look at two important cases of financial market volatility – bubbles and crashes.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Bubbles and crashes in financial markets A bubble sees long sustained rises in prices away from fundamental values. Bubbles are characterised by their self-fulfilling nature. Even if investors know that prices are over-valued, the anticipation that prices will rise further makes further acquisition of the asset profitable. Therefore, prices can rise in a marked fashion for a considerable period of time. Crashes refer to sudden and sharp drops in market prices. This need not be at odds with market rationality. It could be the case that a crash results from the arrival of very bad news. Also, a crash may manifest itself in a collapsing bubble, which should just be seen as a correction in market prices.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Bubbles and crashes in financial markets However, there are also examples of sharp asset price drops that cannot be related to either of these explanations; therefore, there may be something inherently irrational about them in that prices are driven down to unjustifiably low levels. The October 1987 stock market crash is a recent example which will form the basis of some brief analysis. The next figure plots the recent history of the NASDAQ and the S&P500 stock market indices since 1990.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Dot Com Mania There is clear evidence of a dramatic rise in U.S. share prices during the period 1995-2000, followed by a large collapse over the following two years, a pattern which is highly indicative of a bubble and its bursting. Between 1995 and 2000, it is possible to see that the S&P 500 doubled in value, but this trend is hard to observe when it is pitted against the almost 10-fold increase in the NASDAQ. The NASDAQ is the index on which the new technology shares are traded. Because the dramatic rise in the stock market was driven by IT companies, and especially those involved in internet technologies, this period has been widely christened as Dot Com Mania.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Bubbles and crashes in financial markets When stock prices start to increase quickly, further price rises are fuelled by others who jump on the bandwagon through fear of missing out on easy profits. However, for this process to begin, there has to be something that justifies an initial strong rise in prices. These reasons will also provide comfort for those who continue to buy at higher and higher prices who can be convinced that stock markets offer a one-way bet. Two of the arguments put forward justifying the strong rise in share prices were as follows.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Bubbles and crashes in financial markets Firstly, the New Economy over the late 1990s. This galvanised the strong belief that the U.S. was at the outset of a new golden economic era and asset prices should rise to reflect this. The second relates to the idea that it takes time for new technology to be represented in asset prices. Information technology began to emerge in the 1960s; the sharp rise in asset prices during the 1990s simply reflects the New Economy firms replacing the Old Economy firms in the stock market listings.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Irrational exuberance The emergence of ICT and the New Economy may certainly have provided some grounds for an increase in stock market prices. However, was the scale of this rise justified when compared to fundamentals such as earnings? The price-earnings ratio is the price of a share divided by the level of corporate earnings per share. The next figure plots the price-earnings ratio for the S&P 500 index over a 120 year period. It is clear that this ratio grows dramatically during the latter half of the 1990s, indicating that share prices had risen substantially compared to earnings.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Irrational exuberance It is justifiable for current share prices to rise without seeing an increase in current earnings? This is because the current share price will reflect the present discounted value of future earnings, so the expectation of strong future earnings would lead to an increase in current prices. However, with hindsight, it appears that share prices had been driven to values way in excess of fundamentals. Alan Greenspan famously referred to this as irrational exuberance. The large downward correction in share prices between 2000 and 2002 acted to bring the price-earnings ratio back towards its long run average.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Crashes: The 1987 Stock Market Crash and the Trading Mechanism While financial markets are intrinsically volatile, some of the sharper movements are harder to explain in terms of existing models. The crash on October 19th, 1987 led to losses of around $700 billion, amounting to about 20% of the total pre-crash stock value of $3.5 trillion. This dramatic fall, though, was brought on by a much smaller amount of selling in comparative terms. Although trading on this day was three times the average, only $6 billion (0.2% of total equity value) worth of trades were responsible for this huge collapse in prices. The curiosity was how such a small amount of selling could explain such a large decline in stock prices.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Fundamentals vs. the market mechanism According to the predictions of the EMH, the large decline in asset values should be associated with announcements of bad news concerning the fundamental values of equities. Preceding the crash, there were pieces of bad economic news: –Press speculation concerning the Federal Reserve raising the discount rate. –Fed announced decision to depreciate the $ against the DM –U.S. bombing of an Iranian oil platform in the Gulf –Trade deficit was worse than expected by about $1.5 billion However, none of these could be deemed significant enough to match the huge fall in asset prices.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Fundamentals vs. the market mechanism In financial markets a wide variety of order types can be found. The most common are price contingent orders. In the years preceding the crash, two important changes occurred in the U.S. and also in other global stock exchanges. Firstly, trading became electronic. Secondly, over the course of the 1980s, trading came to be dominated by large institutional investors. The execution of one stop order could create a cascade of similar executions.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Summary Financial markets are where financial assets are traded. The value of financial assets is an important determinant of consumption and investment. The expected dividends model implies that the value of an asset is equal to the expected present discounted value of its earnings (such as dividends). This can be thought of as the fundamental value of an asset. The Gordon model is a simplified version of the expected dividends model which relates asset valuations to the growth in dividend payments. The process of arbitrage- where traders act to profit from the over or under pricing of financial assets- acts to drive asset prices towards fundamental values.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Summary Assets with higher returns might be riskier- and therefore asset pricing models ought to value both risk and return. The Capital Asset Pricing Model (CAPM) is a consumption based model which implies that assets with higher returns offer less opportunity to hedge against income risks. The CAPM beta reflects the covariance between an asset’s returns and those of the market portfolio. The higher the beta, the lower the ability to hedge. The Tobin model of portfolio selection describes how investors choose the optimal combination of risk and return in their portfolios.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Summary The Efficient Markets Hypothesis (EMH) states that financial asset prices should reflect all available information. As a result, whenever new information arrives at the market asset prices will change quickly to reflect it. This implies that asset prices follow a random walk process. Empirical tests tend to reject the EMH as the volatility of asset prices is greater than the volatility of news regarding fundamentals. One of the explanations for this is the presence of noise trader risks. Because asset prices might become more mis-priced before moving to fundamental values the power of arbitrage is less than the EMH suggests. Therefore, financial market mis-pricings (inefficiencies) can be sustained for long periods of time.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Summary A bubble refers to the self-fulfilling process where asset prices are driven upwards by the expectation of further increases in prices. As a result asset prices can rise to levels far in excess of fundamentals. The strong rise in US stock markets (particularly the NASDAQ) during the second half of the 1990s is an example relating to the boom in the share prices of new technology firms. A crash refers to a large and sudden drop in market values. These can result from a sudden deterioration in fundamentals, but also through the sharp unwinding of a bubble. The October 1987 crash demonstrates the roles that the market-mechanism and the strategies of traders can play in precipitating a sudden collapse in prices.

Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Macroeconomics Chamberlin and Yueh Chapter 6 Lecture.

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Use with Macroeconomics by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1 © 2006 Cengage Learning Macroeconomics Chamberlin and Yueh Chapter 6 Lecture.

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