Finance Part 2

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risk is

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risk refers to uncertainty and is usually described in a two-tailed framework. That is, there is downside risk (the chance of something bad happening) as well as upside risk (the chance of something good happening).

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standard deviation

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the measure of total risk

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The prime driver of market risk or systematic risk is the risk associated with the business cycle, which cannot be diversified away. Firm-specific risk is the risk associated with problems that companies may face because of lawsuits, labor problems, or management decisions, among other factors. Firm-specific risk can be diversified away. Let's take a look at how diversification impacts each type of risk.

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Firm-specific risk can be defined as risk specific to a firm or a handful of firms. As we will discuss shortly, this is risk that can be reduced through diversification.

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Firm specific risk factors are

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A company's labor force goes on strikeA company's top management dies in a plane crashAn oil tank bursts and floods a company's production area

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So, are risks and return really closely related? The answer is yes, but we have to be very careful about how we define risk. Specifically, there are two kinds of risk: market risk (or systematic risk) and firm-specific (or non-systematic risk). Market risk or systematic risk is common to most securities and is the risk inherent in the economy as a whole. Systematic risk cannot be diversified away.

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Diversification, simply put, is the process of "spreading" your money over many different assets. The wisdom behind this is captured nicely in the saying "Don't put all your eggs in one basket." Why don't you want all your eggs in a single basket, or for our purposes, what is the advantage of spreading your wealth over more than one asset?

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The driving principle behind the common wisdom of diversification is correlation. Correlation refers to the way two variables (e.g., the return on two stocks) co-move. Correlation is a unitless measure bounded by +1 and –1. Correlation of +1, or perfect positive correlation, means that the variables move in perfect tandem. Correlation of –1, or perfect negative correlation, means that the variables move in exactly opposite directions.

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shows perfect positive correlation, perfect negative correlation, and imperfect positive (i.e., positive but less than +1) correlation. For the purposes of diversification, if the return on two assets is perfectly positively correlated then there is no benefit to diversification.

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Think of this as buying one share of IBM stock and then trying to "diversify" your investment by buying another share of IBM stock. Since both shares of IBM will vary exactly together, there is no risk reduction. At the other extreme, if two assets are perfectly negatively correlated then we can eliminate all risk. Essentially, if we could find two assets with perfectly negatively correlated returns, we could combine two risky assets to form a riskless portfolio.

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However, most asset combinations have neither perfect negative nor perfect positive correlation. For example, the correlation between two randomly selected large capitalization stocks is typically in the range of .3 to .4. The underlying premise of diversification is to spread an investment over several securities to reduce risk. Hence, when combining assets into a portfolio, we usually get some risk reduction (i.e., the standard deviation of the portfolio falls) but not total risk elimination (since correlation is almost always greater than –1).

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But, the lower the correlation among the assets in the portfolio (i.e., the closer to –1), the greater the risk reduction possibilities for the portfolio. This relationship between risk and correlation is one of the most important principles in investment theory: lower correlation means greater diversification. Stated equivalently, lower correlation leads to lower risk.

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This brings us to an important question: If you owned a share of every stock traded on the NYSE and NASDAQ, would you be diversified?1 In layman's terms, your eggs would be spread over a very large number of baskets. So, the answer is yes—you would be diversified.

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As shown in the figure, as we increase from one to two assets in a portfolio, the risk (measured on the vertical axis) decreases. As we move from two to three assets, the risk falls even further. The reduction in risk from adding an additional asset is substantial for portfolios with small numbers of assets. However, the rate of decrease in risk is falling as we get portfolios with greater numbers of assets.

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Eventually, it looks like the graph of portfolio risk becomes almost horizontal. In other words, at some point it looks like adding more securities to the portfolio has no impact on risk! This insight represents another fundamental principle of investing that we touched on earlier: some risks can be diversified away through diversification, but other risks cannot be diversified away.

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We are now in a position to clearly articulate one of the great lessons of modern finance: total risk, as measured by standard deviation, can be divided into two parts. One part, which can be easily diversified away by simply adding more assets to your portfolio, is called firm-specific risk (aka diversifiable risk). The other part, however, cannot be diversified away. This part is called systematic risk (aka market risk or non-diversifiable risk).

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In this text, we've always asserted that risk and return go together. If you want higher returns, you must be willing to endure greater risks. But now the question becomes which type of risk? While it is a bit of an oversimplification, the key insight to be gained here is that the market does not reward you for accepting risks which can be easily diversified away. Hence, it is market (or systematic) risk which is important in the risk/return relationship (this is sometimes called the Systematic Risk Principle).

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Recall that we started this topic with a desire to understand the relationship between risk and return. We're now to the point where we know that it is systematic risk, not total risk, which is important in this relationship. However, to make this insight useful we need to be able to quantify systematic risk.

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Recall that we started this topic with a desire to understand the relationship between risk and return. We're now to the point where we know that it is systematic risk, not total risk, which is important in this relationship. However, to make this insight useful we need to be able to quantify systematic risk.

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Different firms have differing amounts of systematic risk. Think back to the historical market crash in 2008. If you had owned all the publicly traded stocks in the market, you would have been well diversified and still seen a dramatic fall in the value of your stock portfolio. However, this doesn't mean that all stocks went down by the same amount. For instance, you are probably familiar with Apple products. Apple is known as the producer of high-quality, high-cost technology and computer gadgetry. In particular, many of Apple's products are considered luxury items.

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Typically, when the economy is strong and the market is high, Apple's sales and Apple's stock returns are also very high. Conversely, when the economy stumbles, Apple's stock falls. Apple is a good example of a firm with lots of systematic risk. That is, when the market goes up, Apple goes up (probably in exaggerated fashion); when the market falls, Apple falls as well.

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Now, contrast Apple with your local electric utility company. Changes in the overall market or economy do have some impact on the returns to the typical utility firm. But, the impact of market changes on a utility firm is usually much less dramatic. Utility companies are good examples of firms with low systematic risk. That is, as the market moves up or down utility firms will probably move up and down also, but in a diminished way.

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Now, contrast Apple with your local electric utility company. Changes in the overall market or economy do have some impact on the returns to the typical utility firm. But, the impact of market changes on a utility firm is usually much less dramatic. Utility companies are good examples of firms with low systematic risk. That is, as the market moves up or down utility firms will probably move up and down also, but in a diminished way.

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Both of these firms are exposed to market risk (or the risk that company performance will be affected by happenings in the market), but to different degrees. In general, providers of luxury goods are going to have a lot of market risk; their performance will vary greatly even with small changes in the market. For example, if the market is up 5 percent, a luxury good provider like Apple may have stock returns of 10 percent.

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The opposite is also true: a 10 percent decline in the market could lead to a 20 percent decrease in the value of the company. On the other hand, providers of staple or essential goods such as your local electric utility will have relatively low performance variability, regardless of what happens in the market.

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What's important to understand here is that different firms have different levels of systematic risk. Since systematic risk is the important type of risk in the risk/return relationship, we need to be able to measure the systematic risk for the securities we are considering for our portfolio. As we will see in the next section, we measure the amount of systematic risk in an asset as beta.

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We measure the amount of systematic risk inherent in an asset as beta. Specifically, beta is a measure of how an individual stock's returns vary with market returns. Think of beta as a measure of the sensitivity of an individual stock's returns to changes in the market. Consider the graph in Figure 8-3, which plots the returns of XYZ Company versus the returns of the S&P 500 (i.e., "the market").

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Each point on the scatter graph represents the returns of XYZ versus the returns of the S&P 500 over some time period, say, one month. As you examine the graph, it is clear that there is an upward trend or a positive relationship between the market and the company because most of the points plot in the top right and bottom left quadrants of the graph. Generally, when the market is up, XYZ tends to be up as well. Conversely, when the market is down, XYZ tends to be down. If you were to perform regression analysis on the

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As you examine this graph, you are observing both the systematic risk and the firm-specific risk inherent in XYZ. The line of best fit is the "average" relationship from the data set: as the market goes up, we can expect that XYZ also will go up. That is, the slope of the line of best fit represents the systematic risk inherent in XYZ.

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In this example, the slope of the line of best fit is 1.2, which is XYZ's beta. This beta can be directly interpreted as a factor for the return on XYZ as the market moves. For example, if the market is up by 10%, XYZ would be expected to go up by 12% (10% × 1.2). We can also see firm-specific risk in Figure 8-4. The firm-specific risk is represented by the dispersion around the line. As we learned earlier, diversification will reduce the distribution about the line. In other words, as we add more securities to the portfolio the dispersion will "tighten" or move closer to the line of best fit.

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In this example, the slope of the line of best fit is 1.2, which is XYZ's beta. This beta can be directly interpreted as a factor for the return on XYZ as the market moves. For example, if the market is up by 10%, XYZ would be expected to go up by 12% (10% × 1.2). We can also see firm-specific risk in Figure 8-4. The firm-specific risk is represented by the dispersion around the line. As we learned earlier, diversification will reduce the distribution about the line. In other words, as we add more securities to the portfolio the dispersion will "tighten" or move closer to the line of best fit.

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The assumption that only systematic risk matters in determining return depends critically on the idea that the investor can diversify away all firm-specific risk. How does the CAPM relate to investors who cannot diversify? Since the CAPM assumes that the only risk inherent in a security is market risk,

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the CAPM is not a good model for poorly diversified investors, such as young entrepreneurs. The reason for this is because undiversified investors cannot eliminate firm-specific risk. Hence, the required rate of return or cost of equity may be much higher for investors in this predicament. Since the CAPM is not applicable in this situation, we need another approach to determine required return.

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The Build-Up Method is an alternative to the CAPM and is used commonly in small businesses. In essence, we will "build up" the required rate of return or cost of equity by adding various risk premiums. The following is a basic formula for the Build-Up Method:

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Bond yield+Equity risk premium+Micro-cap risk premium+Start-up risk premiumRequired rate of return

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Let's examine the inputs of the Build-Up Method. First, you would start with the bond yield for a large company and add an equity risk premium. The bond yield and the equity risk premium added together would be the equivalent of the CAPM for a security with a beta of approximately 1. If, for example, we were to analyze IBM we could get an acceptable estimate of IBM's required rate of return by adding its bond yield to its equity risk premium.

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The micro-cap risk premium would be added to the bond yield and the equity risk premium if the company is small (i.e., less than, say, $1 billion in sales). Consider, for example, Tahitian Noni Inc. In terms of financial performance the firm has done great as it has had strong growth in sales and profitability.

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However, Tahitian Noni can by no means be compared to IBM, Ford, or any other large companies because the firm does not have the same market penetration, asset base, or recognition. Furthermore, Tahitian Noni probably does not have a fully integrated supply chain like the other large companies. If we were going to estimate Tahitian Noni's required rate of return we would have to add a micro-cap risk premium to the large cap bond yield and equity premium.

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Finally, if we are examining a start-up company we would have to consider the additional risk associated with the firm and add another premium. For example, let us assume that you have started a company and have been in business for the last 16 months. You have funded this venture with some money you have been saving over the last couple of years. Your company sells widgets and only has one supplier.

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Finally, if we are examining a start-up company we would have to consider the additional risk associated with the firm and add another premium. For example, let us assume that you have started a company and have been in business for the last 16 months. You have funded this venture with some money you have been saving over the last couple of years. Your company sells widgets and only has one supplier.

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Furthermore, your company's revenue is highly dependent on 3 customers and has had cumulative sales over the last 16 months of $180,000. Would your company be considered risky? Quite simply, the answer is yes. Since your company has "start-up" risk attributes you would have to add a start-up risk premium to the bond yield, equity premium, and micro-cap risk premium in order to calculate your company's required rate of return. In the end, the Build-Up Method is another recognized approach to estimating a company's required rate of return. The methodology and logic is summarized thus:

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Let's work an example to solidify the idea of the Build-Up Method. Consider the following data:Bond yield6%Equity risk premium5%Micro-Cap Risk Premium4%Start-Up Risk Premium4%

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If we were going to calculate the required rate of return on a large cap stock we would simply add the bond yield to the equity risk premium. Therefore, we would expect the required rate of return for a large cap stock to be about 11 percent (.06 + .05). The sum of the bond yield and the equity risk premium is also known as the base equity rate.

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If we were going to analyze a small but well-established company, we would simply add the micro-cap risk premium to the base equity rate. We would expect that a small or mid cap stock's required rate of return would be about 15 percent (.11 + .04). The sum of the base equity rate and the micro-cap risk premium is known as the micro-cap equity rate.

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Finally, if we were going to solve for your cousin's start-up company's required rate of return, we would add the start-up risk premium to the micro-cap equity rate, which would be 19 percent (.15 + .04). Therefore, we would expect this start-up company's required rate of return to be about 19 percent. Generally, start-up companies have required rates of return between 17 and 25 percent, or higher. What does this all mean?

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For an investment in the typical young entrepreneur's firm, an investor will need to earn a return much greater than the return on IBM or other well-known firms to be appropriately compensated for investing in a start-up firm. You should also keep in mind that this is the low end of the range!

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Is there a point to all of this? Yes! If you plan on starting your own firm, don't make the mistake of thinking that equity is free or the mistake of assuming that investing in your company at 11 percent is as good as investing in a well-diversified portfolio at 11 percent. Greater risks always demand greater returns.