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You Can't Become Rich In Your Pocket Until You Become Rich In Your Mind | ||||
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The greater this variance, the more risky an investment is perceived to beTHE BASICS OF RISK When valuing assets and firms, we need to use discount rates that reflect the riskiness of the cash flows. In particular, the cost of debt has to incorporate a default spread for the default risk in the debt and the cost of equity has to include a risk premium for equity risk. But how do we measure default and equity risk, and more importantly, how do we come up with the default and equity risk premiums? In this chapter, we will lay the foundations for analyzing risk in valuation. We present alternative models for measuring risk and converting these risk measures into acceptable hurdle rates. We begin with a discussion of equity risk and present our analysis in three steps. In the first step, we define risk in statistical terms to be the variance in actual returns around an expected return. The greater this variance, the more risky an investment is perceived to be. The next step, which we believe is the central one, is to decompose this risk into risk that can be diversified away by investors and risk that cannot. In the third step, we look at how different risk and return models in finance attempt to measure this non-diversifiable risk. We compare and contrast the most widely used model, the capital asset pricing model, with other models, and explain how and why they diverge in their measures of risk and the implications for the equity risk premium. In the second part of this chapter, we consider default risk and how it is measured by ratings agencies. In addition, we discuss the determinants of the default spread and why it might change over time. By the end of the chapter, we should have a methodology of estimating the costs of equity and debt for any firm. What is risk? Risk, for most of us, refers to the likelihood that in lifes games of chance, we will receive an outcome that we will not like. For instance, the risk of driving a car too fast is getting a speeding ticket, or worse still, getting into an accident. Websters dictionary, in fact, defines risk as exposing to danger or hazard. Thus, risk is perceived almost entirely in negative terms. In finance, our definition of risk is both different and broader. Risk, as we see it, refers to the likelihood that we will receive a return on an investment that is different from the return we expected to make. Thus, risk includes not only the bad outcomes, i.e, returns that are lower than expected, but also good outcomes, i.e., returns that are higher than expected. In fact, we can refer to the former as downside risk and the latter is upside risk; but we consider both when measuring risk. In fact, the spirit of our definition of risk in finance is captured best by the Chinese symbols for risk, which are reproduced below: first symbol is the symbol for danger, while the second is the symbol for opportunity, making risk a mix of danger and opportunity. It illustrates very clearly the tradeoff that every investor and business has to make - between the higher rewards that come with the opportunity and the higher risk that has to be borne as a consequence of the danger. Much of this chapter can be viewed as an attempt to come up with a model that best measures the danger in any investment and then attempts to convert this into the opportunity that we would need to compensate for the danger. In financial terms, we term the danger to be risk and the opportunity to be expected return. What makes the measurement of risk and expected return so challenging is that it can vary depending upon whose perspective we adopt. When analyzing Boeings risk, for instance, we can measure it from the viewpoint of Boeings managers. Alternatively, we can argue that Boeings equity is owned by its stockholders and that it is their perspective on risk that should matter. Boeings stockholders, many of whom hold the stock as one investment in a larger portfolio, might perceive the risk in Boeing very differently from Boeings managers, who might have the bulk of their capital, human and financial, invested in the firm. In this chapter, we will argue that risk in an investment has to be perceived through the eyes of investors in the firm. Since firms like Boeing often have thousands of investors, often with very different perspectives, we will go further. We will assert that risk has to be measured from the perspective of not just any investor in the stock, but of the marginal investor, defined to be the investor most likely to be trading on the stock at any given point in time. The objective in corporate finance is the maximization of firm value and stock price. If we want to stay true to this objective, we have to consider the viewpoint of those who set the stock prices, and they are the marginal investors. Equity Risk and Expected Return To demonstrate how risk is viewed in corporate finance, we will present risk analysis in three steps. First, we will define risk in terms of the distribution of actual returns around an expected return. Second, we will differentiate between risk that is specific to one or a few investments and risk that affects a much wider cross section of investments. We will argue that in a market where the marginal investor is well diversified, it is only the latter risk, called market risk that will be rewarded. Third, we will look at alternative models for measuring this market risk and the expected returns that go with it. I. Defining Risk Investors who buy assets expect to earn returns over the time horizon that they hold the asset. Their actual returns over this holding period may be very different from the expected returns and it is this difference between actual and expected returns that is source of risk. For example, assume that you are an investor with a 1-year time horizon buying a 1-year Treasury bill (or any other default-free one-year bond) with a 5% expected return. At the end of the 1-year holding period, the actual return on this investment will be 5%, which is equal to the expected return. The return distribution for this investment is shown in Figure 4.1. This is a riskless investment. To provide a contrast to the riskless investment, consider an investor who buys stock in Boeing. This investor, having done her research, may conclude that she can make an expected return of 30% on Boeing over her 1-year holding period. The actual return over this period will almost certainly not be equal to 30%; it might be much greater or much lower. The distribution of returns on this investment is illustrated in Figure 4.2. In addition to the expected return, an investor now has to consider the following. First, note that the actual returns, in this case, are different from the expected return. The spread of the actual returns around the expected return is measured by the variance or standard deviation of the distribution; the greater the deviation of the actual returns from expected returns, the greater the variance. Second, the bias towards positive or negative returns is represented by the skewness of the distribution. The distribution in Figure 4.2 is positively skewed, since there is a higher probability of large positive returns than large negative returns. Third, the shape of the tails of the distribution is measured by the kurtosis of the distribution; fatter tails lead to higher kurtosis. In investment terms, this represents the tendency of the price of this investment to jump (up or down from current levels) in either direction. In the special case, where the distribution of returns is normal, investors do not have to worry about skewness and kurtosis. Normal distributions are symmetric (no skewness) and defined to have a kurtosis of zero. Figure 4.3 illustrates the return distributions on two investments with symmetric returns. When return distributions take this form, the characteristics of any investment can be measured with two variables - the expected return, which represents the opportunity in the investment, and the standard deviation or variance, which represents the danger. In this scenario, a rational investor, faced with a choice between two investments with the same standard deviation but different expected returns, will always pick the one with the higher expected return. In the more general case, where distributions are neither symmetric nor normal, it is still conceivable that investors will choose between investments on the basis of only the expected return and the variance, if they possess utility functions1 that allow them to do so. It is far more likely, however, that they prefer positive skewed distributions to negatively skewed ones, and distributions with a lower likelihood of jumps (lower kurtosis) to those with a higher likelihood of jumps (higher kurtosis). In this world, investors will trade off the good (higher expected returns and more positive skewness) against the bad (higher variance and higher kurtosis) in making investments. 1 A utility function is a way of summarizing investor preferences into a generic term called utility on the basis of some choice variables. In this case, for instance, we state the investors utility or satisfaction as a function of wealth. By doing so, we effectively can answer questions such as - Will an investor be twice as happy if he has twice as much wealth? Does each marginal increase in wealth lead to less additional utility than the prior marginal increase? In one specific form of this function, the quadratic utility function, the entire utility of an investor can be compressed into the expected wealth measure and the standard deviation in that wealth. In closing, we should note that the expected returns and variances that we run into in practice are almost always estimated using past returns rather than future returns. The assumption we are making when we use historical variances is that past return distributions are good indicators of future return distributions. When this assumption is violated, as is the case when the assets characteristics have changed significantly over time, the historical estimates may not be good measures of risk. In Practice 4.1: Calculation of standard deviation using historical returns: Boeing and the Home Depot We will use Boeing and the Home Depot as our investments to illustrate how standard deviations and variances are computed. To make our computations simpler, we will look at returns on an annual basis from 1991 to 1998. To begin the analysis, we first estimate returns for each company for each of these years, in percentage terms, incorporating both price appreciation and dividends into these returns: n Price Price at at the beginning beginning of of year year n ??Dividend in year n n We compute the average and standard deviation in these returns for the two firms, using the information in the table (there are 8 years of data): Average Return on Boeing91-98 = 67.00%/8 = 8.38% Average Return on The Home Depot91-98 = 398.70%/8 = 49.84% variance is measured by looking at the deviations of the actual returns in each year, for each stock, from the average return. Since we consider both better-than-expected and worse-than-expected deviations in measuring variance, we square the deviations2. Table 4.2: Squared Deviations from the Mean Following the standard practice for estimating the variances of samples, the variances in returns at the two firms can be estimated by dividing the sum of the squared deviation columns by (n-1), where n is the number of observations in the sample. The standard deviations can be computed to be the squared-root of the variances. Based upon this data, the Home Depot looks like it was two times more risky than Boeing between 1991 and 1998. What does this tell us? By itself, it provides a measure of how much each these companies returns in the past have deviated from the average. If we assume that the past is a good indicator of the future, the Home Depot is a more risky investment than Boeing. optvar.xls: There is a dataset on the web that summarizes standard deviations and variances of stocks in various sectors in the United States. II. Diversifiable and Non-diversifiable Risk Although there are many reasons that actual returns may differ from expected returns, we can group the reasons into two categories: firm-specific and market-wide. The risks that arise from firm-specific actions affect one or a few investments, while the risk arising from market-wide reasons affect many or all investments. This distinction is critical to the way we assess risk in finance. The Components of Risk When an investor buys stock or takes an equity position in a firm, he or she is exposed to many risks. Some risk may affect only one or a few firms and it is this risk that we categorize as firm-specific risk. Within this category, we would consider a wide range of risks, starting with the risk that a firm may have misjudged the demand for a product from its customers; we call this project risk . For instance, in the coming chapters, we will be analyzing Boeings investment in a Super Jumbo jet. This investment is based on the assumption that airlines want a larger airplane and are will be willing to pay a higher price for it. If Boeing has misjudged this demand, it will clearly have an impact on Boeings earnings and value, but it should not have a significant effect on other firms in the market. The risk could also arise from competitors proving to be stronger or weaker than anticipated; we call this competitive risk. For instance, assume that Boeing and Airbus are competing for an order from Quantas, the Australian airline. The possibility that Airbus may win the bid is a potential source of risk to Boeing and perhaps a few of its suppliers. But again, only a handful of firms in the market will be by it. Similarly, the Home Depot recently launched an online store to sell its home improvement products. Whether it succeeds or not is clearly important to the Home Depot and its competitors, but it is unlikely to have an impact on the rest of the market. In fact, we would extend our risk measures to include risks that may affect an entire sector but are restricted to that sector; we call this sector risk. For instance, a cut in the defense budget in the United States will adversely affect all firms in the defense business, including Boeing, but there should be no significant impact on other sectors, such as food and apparel. What is common across the three risks described above project, competitive and sector risk - is that they affect only a small sub-set of firms. There is other risk that is much more pervasive and affects many if not all investments. For instance, when interest rates increase, all investments are negatively affected, albeit to different degrees. Similarly, when the economy weakens, all firms feel the effects, though cyclical firms (such as automobiles, steel and housing) may feel it more. We term this risk market risk. Finally, there are risks that fall in a gray area, depending upon how many assets they affect. For instance, when the dollar strengthens against other currencies, it has a significant impact on the earnings and values of firms with international operations. If most firms in the market have significant international operations, it could well be categorized as market risk. If only a few do, it would be closer to firm-specific risk. Figure 4.4 summarizes the break down or the spectrum of firm-specific and market risks. |
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