chapter 6 - keown

systematic risk

(1) the risk related to an investment return that cannot be eliminated through diversification. Systematic risk results from factors that affect all stocks. Also called market risk or nondiversifiable risk. (2) The risk of a project from the viewpoint of a well-diversified shareholder. This measure takes into account that some of the project's risk will be diversified away as the project is combined with the firm's other projects, and, in addition, some of the remaining risk will be diversified away by shareholders as they combine this stock with other stocks in their portfolios.

Average holding-period return

- Because we are using historical return data, we assume each observation has an equal probability of occurrence - Thus, the average holding-period return is found by summing the returns and dividing by the number of months; that is Average holding-period return = (return in month 1 + return in month 2 + ... + return in last month) / number of monthly returns standard deviation calculated - see screenshot

Rates of Return: The Investor's Experience

- Before comparing these returns, we should think about what to expect. - First, we would intuitively expect a Treasury bill (short-term government securities) to be the least risky of the six portfolios. - Because a Treasury bill has a short-term maturity date, the price is less volatile (less risky) than the price of an intermediate- or long-term government security. - In turn, because there is a chance of default on a corporate bond, which is essentially nonexistent for government securities, a long-term government bond is less risky than a long-term corporate bond. - Finally, the common stocks of large companies are more risky than corporate bonds, with small-company stocks being more risky than large-firm stocks. - With this in mind, we could reasonably expect different rates of return to the holders of these varied securities. - If the market rewards an investor for assuming risk, the average annual rates of return should increase as risk increases. A comparison of the annual rates of return for five portfolios and the inflation rate for the years 1926 to 2011 --- Four aspects of these returns are included: (1) the nominal average annual rate of return; (2) the standard deviation of the returns, which measures the volatility, or riskiness, of the returns; (3) the real average annual rate of return, which is the nominal return less the inflation rate; (4) the risk premium, which represents the additional return received beyond the risk-free rate (Treasury bill rate) for assuming risk.

Risk and Diversification - Diversifying away the risk

- If we diversify our investments across different securities rather than invest in only one stock, the variability in the returns of our portfolio should decline. - The reduction in risk will occur if the stock returns within our portfolio do not move precisely together over time—that is, if they are not perfectly correlated. - The unique variability of a single stock tends to be countered by the unique- ness of another security. - However, we should not expect to eliminate all risk from our portfolio. - In practice, it would be rather difficult to cancel all the variations in returns of a portfolio, because stock prices have some tendency to move together. - Thus, we can divide the total risk (total variability) of our portfolio into two types of risk: (1) company-unique risk, or unsystematic risk, (2) market risk, or systematic risk. - Company-unique risk might also be called diversifiable risk, in that it can be diversified away. Market risk is nondiversifiable risk; it cannot be eliminated through random diversification.

To calculate the standard deviation using the following five-step procedure

- STEP 1 Calculate the expected rate of return of the investment, which was calculated above to be 14 percent. - STEP 2 Subtract the expected rate of return of 14 percent from each of the possible rates of return and square the difference. - STEP 3 Multiply the squared differences calculated in step 2 by the probability that those outcomes will occur. - STEP 4 Sum all the values calculated in step 3 together. The sum is the variance of the distribution of possible rates of return. Note that the variance is actually the average squared difference between the possible rates of return and the expected rate of return. - STEP 5 Take the square root of the variance calculated in step 4 to calculate the standard deviation of the distribution of possible rates of return.

Expected cash flow

- The expected cash flow is simply the weighted average of the possible cash flow outcomes such that the weights are the probabilities of the various states of the economy occurring Expected cash flow, CF = (cash flow in state 1 (CF1) x probability of state 1 (Pb1) + (cash flow in state 2 (CF2) x probability of state 2 (Pb2)) + ... + (cash flow in state 3 (CF3) x probability of state 3 (Pb3))

risk-free rate of return

- The rate of return on risk-free investments. - The interest rates on short-term U.S. government securities are commonly used to measure this rate. - the required rate of return, or discount rate, for riskless investments. - typically our measure for the risk-free rate of return is the U.S. Treasury bill rate

line of best fit = characteristic line

- The slope of the characteristic line measures the average relationship between a stock's returns and those of the S&P 500 Index; or stated differently, the slope of the line indicates the average movement in a stock's price in response to a movement in the S&P 500 Index price. - We can estimate the slope of the line visually by fitting a line that appears to cut through the middle of the dots. We then compare the rise (increase of the line on the vertical axis) to the run (increase on the horizontal axis). - Alternatively, we can enter the return data into a financial calculator or in an Excel spreadsheet, which will calculate the slope based on statistical analysis.

Standard Deviation & Variance

- We can quantify the risk of an investment by computing the variance in the possible investment returns and its square root, the standard deviation (s). - the riskiness of an investment is of primary concern to an investor, where the standard deviation is the conventional measure of an investment's riskiness. - For the case where there are n possible returns (that is, states of the economy), we calculate the variance as follows: Variance in rates of return = [(rate of return for state 1 (r1) - expected rate of return r)^2 x probability of state 1 (Pb1)] + [(rate of return for state 2 (r2) - expected rate of return r)^2 x probability of state 1 (Pb2)] + ... + [(rate of return for state n (rn) - expected rate of return r)^2 x probability of state n (Pbn)] - Although the standard deviation of returns provides us with a quantitative measure of an asset's riskiness, how should we interpret the result? - What does it mean? - Is the 11.14 percent standard deviation for the publishing company investment good or bad? - First, we should remember that statisticians tell us that two-thirds of the time, an event will fall within 1 standard deviation of the expected value (assuming the distribution is normally distributed; that is, it is shaped like a bell). - Thus, given a 14 percent expected return and a standard deviation of 11.14 percent for the publishing company investment, we can reasonably anticipate that the actual returns will fall between 2.86 percent and 25.14 percent (14, { 11.14,) two-thirds of the time. - In other words, there is not much certainty with this investment. - A second way of answering the question about the meaning of the standard deviation comes by comparing the investment in the publishing firm against other investments. - Obviously the attractiveness of a security with respect to its return and risk cannot be determined in isolation. - Only by examining other available alternatives can we reach a conclusion about a particular investment's risk. - For example, if another investment, say, an investment in a firm that owns a local radio station, has the same expected return as the publishing company, 14 percent, but with a standard deviation of 7 percent, we would consider the risk associated with the publishing firm, 11.14 percent, to be excessive. - In the technical jargon of modern portfolio theory, the radio station investment is said to "dominate" the publishing firm investment. - In commonsense terms, this means that the radio station investment has the same expected return as the publishing company investment but is less risky. - What if we compare the investment in the publishing company with one in a quick oil- change franchise, an investment in which the expected rate of return is an attractive 24 percent but the standard deviation is estimated at 13 percent? - Now what should we do? Clearly, the oil- change franchise has a higher expected rate of return, but it also has a larger standard deviation. - In this example, we see that the real challenge in selecting the better investment comes when one investment has a higher expected rate of return but also exhibits greater risk. - Here the final choice is determined by our attitude toward risk, and there is no single right answer. - You might select the publishing company, whereas I might choose the oil-change investment, and neither of us would be wrong. - We would simply be expressing our tastes and preferences about risk and return.

The Investor's Required Rate of Return - Measuring the Required Rate of Return

- We have seen that (1) systematic risk is the only relevant risk—the rest can be diversified away (2) the required rate of return, k, equals the risk-free rate plus a risk premium. - We will now examine how we can estimate investors' required rates of return. - The finance profession has had difficulty in developing a practical approach to measure an investor's required rate of return; however, financial managers often use a method called the capital asset pricing model (CAPM). - The capital asset pricing model is an equation that equates the expected rate of return on a stock to the risk-free rate plus a risk premium for the stock's systematic risk. - Although certainly not without its critics, the CAPM provides an intuitive approach for thinking about the return that an investor should require on an investment, given the asset's systematic or market risk. - Equation (6-11) above provides the natural starting point for measuring the investor's required rate of return and sets us up for using the CAPM. - Rearranging this equation to solve for the risk premium we have Risk Premium = investor's required rate of return, r - risk-free rate of return, rf -which simply says that the risk premium for a security equals the investor's required re- turn less the risk-free rate existing in the market - For example, if the required return is 12 percent and the risk-free rate is 3 percent, the risk premium is 9 percent. - Also, if the required return for the market portfolio is 10 percent, and the risk-free rate is 3 percent, the risk premium for the market would be 7 percent. - This 7 percent risk premium would apply to any security having systematic (nondiversifiable) risk equivalent to the general market, or a beta (b) of 1. - In this same market, a security with a beta (b) of 2 should provide a risk premium of 14 percent, or twice the 7 percent risk premium existing for the market as a whole. - Hence, in general, the appropriate required rate of return for a given security should be determined by Required return on security, r = risk free rate of return, rf + beta for security, B x (required return on the market portfolio, rm - risk-free rate of return, rf) --> this equation is the CAPM, designates the risk-return trade-off existing in the market, where risk is measured in terms of beta

Expected rate of return

- a weighted average of all the possible returns, weighted by the probability that each return will occur. Expected rate of return r = (rate of return for state 1 (r1) x probability of state 1 (Pb1)) + (rate of return for state 2 (r2) x probability of state 2 (Pb2)) + ... + (rate of return for state 3 (r3) x probability of state 3 (Pb3))

capital asset pricing model (CAPM)

- an equation stating that the expected rate of return on an investment (in this case a stock) is a function of (1) the risk-free rate (2) the investment's systematic risk (3) the expected risk premium for the market portfolio of all risky securities.

asset allocation

- identifying and selecting the asset classes appropriate for a specific investment portfolio and determining the proportions of those assets within the portfolio.

The Investor's Required Rate of Return - The Required Rate of Return Concept

- investors required rate of return: the minimum rate of return necessary to attract an investor to purchase or hold a security --> this definition considers the investor's opportunity cost of funds of making an investment in the next-best investment. - his forgone return is an opportunity cost of undertaking the investment and, consequently, is the investor's required rate of return. - In other words, we invest with the intention of achieving a rate of return sufficient to warrant making the investment. - The investment will be made only if the purchase price is low enough relative to expected future cash flows to provide a rate of return greater than or equal to our required rate of return. - To help us better understand the nature of an investor's required rate of return, we can separate the return into its basic components: the risk-free rate of return plus a risk premium. - Expressed as an equation: Investor's required rate of return = risk-free rate of return + risk premum

risk and diversification demonstrated

- look briefly on how risk and return change as we (1) diversify between two different types of assets—stocks and bonds, and (2) increase the length of time that we hold a portfolio of assets. - Notice that when we previously spoke about diversification, we were diversifying by holding more stock, but the portfolio still consisted of all stocks. - Now we examine diversifying between a portfolio of stocks and a portfolio of bonds. - Diversifying among different kinds of assets is called asset allocation, compared with diversification within the different asset classes, such as stocks, bonds, real estate, and commodities. - the benefit we receive from diversifying is far greater through effective asset allocation than from astutely selecting individual stocks to include within an asset category - moving from an all-stock portfolio to a mixture of stocks and bonds and finally to an all-bond portfolio reduces the variability of returns (our measure for risk) significantly along with declining average rates of return --- stated differently: if we want to increase our expected returns, we must assume more risk --> that is, there is a clear relationship between risk and return (risk requires a reward) - the market rewards the patient investor

slope is called beta

- measures the average relationship between a stock's returns and the market's returns.

required rate of return

- minimum rate of return necessary to attract an investor to purchase or hold a security.

Risk Defined and Measured

- risk is vitally important in almost all dimensions of our life - potential variability in future cash flows - the wider the range of possible events that can occur, the grater the risk example 1. The first investment is a U.S. Treasury bond, a government security that matures in 10 years and promises to pay an annual return of 2 percent. If we purchase and hold this security for 10 years, we are virtually assured of receiving no more and no less than 2 per- cent on an annualized basis. For all practical purposes, the risk of loss is nonexistent. 2. $The second investment involves the purchase of the stock of a local publishing com- pany. Looking at the past returns of the firm's stock, we have made the following esti- mate of the annual returns from the investment:

risk premium

- the additional return expected for assuming risk. - as the level of risk increases, we will demand additional expected returns. - Even though we may or may not actually receive this incremental return, we must have reason to expect it; otherwise, why expose ourselves to the chance of losing all or part of our money? - To illustrate, assume you are considering the purchase of a stock that you believe will provide a 10 percent return over the next year. - If the expected risk-free rate of return, such as the rate of return for 90-day Treasury bills, is 2 percent, then the risk premium you are demanding to assume the additional risk is 8 percent (10% − 2%).

Expected Return Defined and Measured

- the expected benefits, or returns, an investment generates come in the form of cash flows - cash flow, not accounting profit, is the relevant variable the financial manager uses to measure returns - this principle holds true regardless of the type of security, whether it is a debt instrument, preferred stock, common stock, or any mixture of these (such as convertible bonds) - the risk-return trade-off that investors face on a day-to-day basis is based not on realised rates of return but on what the investor expects to earn on an investment in the future - We can think of the rate of return that will ultimately be realised from making a risky investment in terms of a range of possible return outcomes, much like the distribution of grades for this class at the end of the term. - To describe this range of possible returns, it is customary to use the average of the different possible returns. - We refer to the average of the possible rates of return as the investment's expected rate of return.

portfolio beta

- the relationship between a portfolio's returns and the market returns. - It is a measure of the portfolio's nondiversifiable risk. - As it works out, the portfolio beta is merely the average of the individual stock betas. - It is a weighted average of the individual securities' betas, with the weights being equal to the proportion of the portfolio invested in each security. - whenever the general market increases or decreases 1 percent, our new portfolio's returns would change 1.3 percent on average, which means that our new portfolio has more systematic, or market, risk than the market has as a whole. -We can conclude that the beta of a portfolio is determined by the betas of the individual stocks. - If we have a portfolio consisting of stocks with low betas, then our portfolio will have a low beta. - The reverse is true as well. - Before leaving the subject of risk and diversification, we want to share a study that demonstrates the effects of diversifying our investments, not just across different stocks but also across different types of securities.

unsystematic risk

- the risk related to an investment return that can be eliminated through diversification. - Unsystematic risk is the result of factors that are unique to the particular firm. - Also called company-unique risk or diversifiable risk

Ibbotson Associates publishes the long-term historical annual rates of return for the following types of investments beginning in 1926 and continuing to the present

1. Common stocks of large companies 2. Common stocks of small firms 3. Long-term corporate bonds 4. Long-term U.S. government bonds 5. Intermediate-term U.S. government bonds 6. U.S. Treasury bills (short-term government securities)

historical or realised rate of return (also called holding-period return

Holding-period dollar gain, DG = price end of period + cash distribution (dividend) - pricebeginning of period Holding-period rate of return, r = dollar gain/price beginning of period = (priceend of period + dividend - price beginning of period) / price beginning of period

measuring a portfolio's Beta (the beta (b) of a portfolio consisting of n stocks is equal to)

Portfolio beta = (percentage of portfolio invested in asset 1 x beta for asset 1 (B1)) + (percentage of portfolio invested in asset 2 x beta for asset 2 (B2) + ... + (percentage of portfolio invested in asset n x beta for asset n (Bn))

Monthly holding return or holding period returns

monthly holding return = [(price end of month - price beginning of month) / price beginning of month] = (price end of month / price beginning of month) - 1

market risk

see systematic risk systematic risk: (1) the risk related to an investment return that cannot be eliminated through diversification. Systematic risk results from factors that affect all stocks. Also called market risk or nondiversifiable risk. (2) The risk of a project from the viewpoint of a well-diversified shareholder. This measure takes into account that some of the project's risk will be diversified away as the project is combined with the firm's other projects, and, in addition, some of the remaining risk will be diversified away by shareholders as they combine this stock with other stocks in their portfolios.

nondiversifiable risk

see systematic risk (1) the risk related to an investment return that cannot be eliminated through diversification. Systematic risk results from factors that affect all stocks. Also called market risk or nondiversifiable risk. (2) The risk of a project from the viewpoint of a well-diversified shareholder. This measure takes into account that some of the project's risk will be diversified away as the project is combined with the firm's other projects, and, in addition, some of the remaining risk will be diversified away by shareholders as they combine this stock with other stocks in their portfolios.

company-unique risk

see unsystematic risk unsystematic risk: the risk related to an investment return that can be eliminated through diversification. Unsystematic risk is the result of factors that are unique to the particular firm. Also called company-unique risk or diversifiable risk.

diversifiable risk

see unsystematic risk unsystematic risk: - the risk related to an investment return that can be eliminated through diversification. - Unsystematic risk is the result of factors that are unique to the particular firm. - Also called company-unique risk or diversifiable risk

security market line

the return line that reflects the attitudes of investors regarding the minimum acceptable return for a given level of systematic risk associated with a security.