Fluent Essays

Professional Assignment 2 – CLO 1, CLO 2, CLO 3, CLO 4, CLO 5, CLO 6 PA 2 included two parts: Part 1 about evaluating beta and WACC, and Part 2 is about data acquisition in preparation of the CLA 2. You need to do both parts to demonstrate your comprehensive evaluation of the companys opportunity cost as well as your skills in retrieving and organizing historical data on securities for the purpose of portfolio formation.  1. Search Yahoo Finance, or any other credible source to retrieve the most recent income statement and balance sheet for a major leveraged corporation.  - Provide these statements in proper format and include a screenshot of the data. - Retrieve the data on the company’s historical data and calculate annual rate of return by using adjusted closing prices for the past 20 years.  - Using the data on the companys stock rate of return and the index’s rate of return estimate beta of the corporation. Compare this value with the value stated by the source.  - Retrieve the risk-free rate of return as the annual interest rate of US treasuries. Based on these values estimate the expected annual rate of return of the corporation’s security. Compare your estimate with the expected rate of return as evaluated based on your data in part b. - Using the financial statements mentioned above estimate the annual rate of interest paid by the corporation (cost of debt). Also, find the tax rate and capitalization ratio (proportions among equity and debt). Using these values that you have found, estimate the annual weighted cost of capital (WACC) of the corporation. 2. This part of the assignment is in preparation for CLA 2. Choose 5 major securities  from different industries, among which one can be the one you chose in part 1 of the question. Retrieve the data on the companies’ historical data and calculate annual rate of return for the past 20 years for each security. Provide your explanations and definitions in detail and be precise. Comment on your findings. Provide references for content when necessary. Provide your work in detail and explain in your own words. Support your statements with six (6) peer-reviewed in-text citation(s) and reference(s). Note: 1. Please stick to the company that you analyzed for PA 1 assignment, which is Walmart. I have also attached the PA 1 assignment which had been done for your reference. 2. The paper needs to be formatted in APA 7th edition 3. Provide your explanations and definitions in detail and be precise. 4. Provide work in detail and explain in your words.  5. Provide references for content when necessary. Support your statement with peer-reviewed in-text citations and references. 6. Need to have at least 6 peer-reviewed articles as the references (Recommend to find the articles from ProQuest), which should include the source of the data. 7. Need to include textbooks as references. 8. Please find the textbook and class PPTs in the attachment section. 9. Comment on your finding. 10.  Textbook Information: Bowerman, B., Drougas, A. M., Duckworth, A. G., Hummel, R. M. Moniger, K. B., & Schur, P. J.  (2019). Business statistics and analytics in practice (9th ed.). McGraw-Hill ISBN 9781260187496 11. Please find the Course Learning Outcome list of this course in the attachment. STOCK VALUATION CHAPTER 8 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.1 Explain how stock prices depend on future dividends and dividend growth Show how to value stocks using multiples Lay out the different ways corporate directors are elected to office Define how the stock markets work Key Concepts and Skills Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› Common Stock Valuation Some Features of Common and Preferred Stocks The Stock Markets Chapter Outline Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› If you buy a share of stock, you can receive cash in two ways: The company pays dividends. You sell your shares, either to another investor in the market or back to the company. As with bonds, the price of the stock is the present value of these expected cash flows. Cash Flows for Stockholders Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.4 Section 8.1 (A) As the text points out, a stock that currently pays no dividends may or may not have value; a stock that will NEVER pay a dividend cannot have any value as long as investors are rational. For a stock that currently pays no dividend, market value derives from (a) the hope of future dividends and/or (b) the expectation of a liquidating dividend. Suppose you are thinking of purchasing the stock of Moore Oil, Inc. You expect it to pay a $2 dividend in one year, and you believe that you can sell the stock for $14 at that time. If you require a return of 20\% on investments of this risk, what is the maximum you would be willing to pay? Compute the PV of the expected cash flows. Price = (14 + 2) / (1.2) = $13.33 Or FV = 16; I/Y = 20; N = 1; CPT PV = -13.33 One-Period Example Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.5 Section 8.1 (A) Note, the calculation can also be done as: FV = 14; PMT = 2; I/Y = 20; N = 1; CPT PV = -13.33 Now, what if you decide to hold the stock for two years? In addition to the dividend in one year, you expect a dividend of $2.10 in two years and a stock price of $14.70 at the end of year 2. Now how much would you be willing to pay? PV = 2 / (1.2) + (2.10 + 14.70) / (1.2)2 = 13.33 Two-Period Example Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.6 Section 8.1 (A) If you have taught students how to use uneven cash flow keys, then you can show them how to do this on the calculator. The notation below is for the TI BA-II+. Calculator: CF0 = 0; C01 = 2; F01 = 1; C02 = 16.80; F02 = 1; NPV; I = 20; CPT NPV = 13.33 Finally, what if you decide to hold the stock for three years? In addition to the dividends at the end of years 1 and 2, you expect to receive a dividend of $2.205 at the end of year 3 and the stock price is expected to be $15.435. Now how much would you be willing to pay? PV = 2 / 1.2 + 2.10 / (1.2)2 + (2.205 + 15.435) / (1.2)3 = 13.33 Three-Period Example Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.7 Section 8.1 (A) Calculator: CF0 = 0; C01 = 2; F01 = 1; C02 = 2.10; F02 = 1; C03 = 17.64; F03 = 1; NPV; I = 20; CPT NPV = 13.33 You could continue to push back the year in which you will sell the stock. You would find that the price of the stock is really just the present value of all expected future dividends. So, how can we estimate all future dividend payments? Developing The Model Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.8 Section 8.1 (A) In equilibrium, the required return, R, is the same as the “expected return.” Constant dividend (i.e., zero growth) The firm will pay a constant dividend forever. This is like preferred stock. The price is computed using the perpetuity formula. Constant dividend growth The firm will increase the dividend by a constant percent every period. The price is computed using the growing perpetuity model. Supernormal growth Dividend growth is not consistent initially, but settles down to constant growth eventually. The price is computed using a multistage model. Estimating Dividends: Special Cases Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› Section 8.1 (B) 7.9 If dividends are expected at regular intervals forever, then this is a perpetuity, and the present value of expected future dividends can be found using the perpetuity formula. P0 = D / R Suppose a stock is expected to pay a $0.50 dividend every quarter and the required return is 10\% with quarterly compounding. What is the price? P0 = .50 / (.1 / 4) = $20 Zero Growth Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.10 Section 8.1 (B) Remind the students that if dividends are paid quarterly, then the discount rate must be a quarterly rate. Also, if students have been using a financial calculator for most of their calculations, they often forget to convert the interest rate and they leave it as a percent, i.e., P = .5 / (10/4) = .2. Ask them if this is a reasonable answer – “Would you only be willing to pay $0.20 for an asset that will pay you $0.50 every quarter forever?” Dividends are expected to grow at a constant percent per period. P0 = D1 /(1+R) + D2 /(1+R)2 + D3 /(1+R)3 + … P0 = D0(1+g)/(1+R) + D0(1+g)2/(1+R)2 + D0(1+g)3/(1+R)3 + … With a little algebra and some series work, this reduces to: Dividend Growth Model Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.11 Section 8.1 (B) g is the growth rate in dividends; the subscripts denote the period in which the dividend is paid. This is the formula for a growing perpetuity that was developed in chapter 6. Lecture Tip: The newly instituted tax cuts, all else equal, should increase margins and cash flow. Companies can increase dividends or reinvest more in the firm, which would increase the growth rate. In either case, stock values should increase, which is what has happened to the market – beginning even before the cuts were officially announced. Suppose Big D, Inc., just paid a dividend of $0.50 per share. It is expected to increase its dividend by 2\% per year. If the market requires a return of 15\% on assets of this risk, how much should the stock be selling for? P0 = .50(1+.02) / (.15 - .02) = $3.92 DGM – Example 1 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.12 Section 8.1 (B) The biggest mistake that students make with the DGM is using the wrong dividend. Be sure to emphasize that we are finding a present value, so the dividend needed is the one that will be paid NEXT period, not the one that has already been paid. Suppose TB Pirates, Inc., is expected to pay a $2 dividend in one year. If the dividend is expected to grow at 5\% per year and the required return is 20\%, what is the price? P0 = 2 / (.2 - .05) = $13.33 Why isn’t the $2 in the numerator multiplied by (1.05) in this example? DGM – Example 2 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.13 Section 8.1 (B) Does this result look familiar? The examples used to develop the earlier model were based on a 5\% growth rate in dividends. Stock Price Sensitivity to Dividend Growth, g D1 = $2; R = 20\% Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.14 Section 8.1 (B) As the growth rate approaches the required return, the stock price increases dramatically. Price 0.01 0.02 0.03 0.04 0.05 0.06 7.0000000000000007E-2 0.08 0.09 0.1 0.11 0.12 0.13 0.14000000000000001 0.15 0.16 0.17 0.18 0.19 10.53 11.11 11.76 12.5 13.33 14.29 15.38 16.670000000000002 18.18 20 22.22 25 28.57 33.33 40 50 66.67 100 200 0.01 0.02 0.03 0.04 0.05 0.06 7.0000000000000007E-2 0.08 0.09 0.1 0.11 0.12 0.13 0.14000000000000001 0.15 0.16 0.17 0.18 0.19 0.01 0.02 0.03 0.04 0.05 0.06 7.0000000000000007E-2 0.08 0.09 0.1 0.11 0.12 0.13 0.14000000000000001 0.15 0.16 0.17 0.18 0.19 0.01 0.02 0.03 0.04 0.05 0.06 7.0000000000000007E-2 0.08 0.09 0.1 0.11 0.12 0.13 0.14000000000000001 0.15 0.16 0.17 0.18 0.19 Growth Rate Stock Price Stock Price Sensitivity to Required Return, R D1 = $2; g = 5\% Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.15 Section 8.1 (B) As the required return approaches the growth rate, the price increases dramatically. This graph is a mirror image of the previous one. Lecture Tip: The newly instituted tax cuts, all else equal, should increase margins and cash flow. Companies can increase dividends or reinvest more in the firm, which would increase the growth rate. In either case, stock values should increase, which is what has happened to the market – beginning even before the cuts were officially announced. Price 0.06 7.0000000000000007E-2 0.08 0.09 0.1 0.11 0.12 0.13 0.14000000000000001 0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 200 100 66.67 50 40 33.33 28.57 25 22.22 20 18.18 16.670000000000002 15.38 14.29 13.33 12.5 11.76 11.11 10.53 0.06 7.0000000000000007E-2 0.08 0.09 0.1 0.11 0.12 0.13 0.14000000000000001 0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.06 7.0000000000000007E-2 0.08 0.09 0.1 0.11 0.12 0.13 0.14000000000000001 0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.06 7.0000000000000007E-2 0.08 0.09 0.1 0.11 0.12 0.13 0.14000000000000001 0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 Growth Rate Stock Price Gordon Growth Company is expected to pay a dividend of $4 next period, and dividends are expected to grow at 6\% per year. The required return is 16\%. What is the current price? P0 = 4 / (.16 - .06) = $40 Remember that we already have the dividend expected next year, so we don’t multiply the dividend by 1+g. Example 8.3: Gordon Growth Company - I Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.16 Section 8.1 (B) What is the price expected to be in year 4? P4 = D4(1 + g) / (R – g) = D5 / (R – g) P4 = 4(1+.06)4 / (.16 - .06) = 50.50 What is the implied return given the change in price during the four year period? 50.50 = 40(1+return)4; return = 6\% PV = -40; FV = 50.50; N = 4; CPT I/Y = 6\% The price is assumed to grow at the same rate as the dividends. Example 8.3: Gordon Growth Company - II Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.17 Section 8.1 (B) Point out that the formula is completely general. The dividend in the numerator is always for one period later than the price we are computing. This is because we are computing a Present Value, so we have to start with a future cash flow. This is very important when discussing supernormal growth. We know the dividend in one year is expected to be $4 and it will grow at 6\% per year for four more years. So, D5 = 4(1.06)(1.06)(1.06)(1.06) = 4(1.06)4 Lecture Tip: In his book, A Random Walk Down Wall Street, pp. 82 – 89, (1985, W.W. Norton & Company, New York), Burton Malkiel gives four “fundamental” rules of stock prices. Loosely paraphrased, the rules are as follows. Other things equal: -Investors pay a higher price, the larger the dividend growth rate -Investors pay a higher price, the larger the proportion of earnings paid out as dividends -Investors pay a higher price, the less risky the company’s stock -Investors pay a higher price, the lower the level of interest rates Suppose a firm is expected to increase dividends by 20\% in one year and by 15\% in two years. After that, dividends will increase at a rate of 5\% per year indefinitely. If the last dividend was $1 and the required return is 20\%, what is the price of the stock? Remember that we have to find the PV of all expected future dividends. Nonconstant Growth Example - I Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› Section 8.1 (B) 7.18 Compute the dividends until growth levels off. D1 = 1(1.2) = $1.20 D2 = 1.20(1.15) = $1.38 D3 = 1.38(1.05) = $1.449 Find the expected future price. P2 = D3 / (R – g) = 1.449 / (.2 - .05) = 9.66 Find the present value of the expected future cash flows. P0 = 1.20 / (1.2) + (1.38 + 9.66) / (1.2)2 = 8.67 Nonconstant Growth Example - II Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.19 Section 8.1 (B) Point out that P2 is the value, at year 2, of all expected dividends year 3 on. The final step is exactly the same as the 2-period example at the beginning of the chapter. We can look at it as if we buy the stock today and receive the $1.20 dividend in 1 year, receive the $1.38 dividend in 2 years and then immediately sell it for $9.66. Calculator: CF0 = 0; C01 = 1.20; F01 = 1; C02 = 11.04; F02 = 1; NPV; I = 20; CPT NPV = 8.67 What is the value of a stock that is expected to pay a constant dividend of $2 per year if the required return is 15\%? What if the company starts increasing dividends by 3\% per year, beginning with the next dividend? The required return stays at 15\%. Quick Quiz – Part I Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.20 Section 8.1 (B) Zero growth: 2 / .15 = 13.33 Constant growth: 2(1.03) / (.15 - .03) = $17.17 Start with the DGM: Using the DGM to Find R Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.21 Section 8.1 (C) Point out that D1 / P0 is the dividend yield and g is the capital gains yield. Suppose a firm’s stock is selling for $10.50. It just paid a $1 dividend, and dividends are expected to grow at 5\% per year. What is the required return? R = [1(1.05)/10.50] + .05 = 15\% What is the dividend yield? 1(1.05) / 10.50 = 10\% What is the capital gains yield? g = 5\% Example: Finding the Required Return Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› Section 8.1 (C) 7.22 Another common valuation approach is to multiply a benchmark PE ratio by earnings per share (EPS) to come up with a stock price. Pt = Benchmark PE ratio × EPSt The benchmark PE ratio is often an industry average or based on a company’s own historical values. The price-sales ratio can also be used. Stock Valuation Using Multiples Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› Section 8.1 (D) The price-sales ratio is often used to value newer companies that do not pay dividends and are not yet profitable (meaning that earnings are negative). 7.23 Suppose a company had earnings per share of $3 over the past year. The industry average PE ratio is 12. Use this information to value this company’s stock price. Pt = 12 × $3 = $36 per share Example: Stock Valuation Using Multiples Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› Section 8.1 (D) 7.24 Table 8.1 – Stock Valuation Summary (1) Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› Section 8.1 7.25 Table 8.1 – Stock Valuation Summary (2) Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› Section 8.1 7.26 Voting Rights Proxy voting Classes of stock Other Rights Share proportionally in declared dividends Share proportionally in remaining assets during liquidation Preemptive right – first shot at new stock issue to maintain proportional ownership if desired Features of Common Stock Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.27 Section 8.2 (A) Shareholders have the right to vote for the board of directors and other important issues. Cumulative voting increases the likelihood of minority shareholders getting a seat on the board. Proxy votes are similar to absentee ballots. Proxy fights occur when minority owners are trying to get enough votes to obtain seats on the Board or affect other important issues that are coming up for a vote. Different classes of stock can have different rights. Owners may want to issue a nonvoting class of stock if they want to make sure that they maintain control of the firm. Lecture Tip: Large institutions, such as mutual funds and pension funds, used to remain on the sidelines when it came to corporate control. However, several institutions have become much more active in recent years and have worked to force companies to operate in the shareholders’ best interests. CalPERS, the pension plan for California public employees, has been at the forefront of the corporate governance movement. For more information, see http://www.calpers-governance.org/principles/home. Dividends are not a liability of the firm until a dividend has been declared by the Board. Consequently, a firm cannot go bankrupt for not declaring dividends. Dividends and Taxes Dividend payments are not considered a business expense; therefore, they are not tax deductible. The taxation of dividends received by individuals depends on the holding period. Dividends received by corporations have a minimum 70\% exclusion from taxable income. Dividend Characteristics Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.28 Slide 8.2 (A) Dividend exclusion: If corporation A owns less than 20\% of corporation B stock, then 30\% of the dividends received from corporation B are taxable. If A owns between 20\% and 80\% of B, then 20\% of the dividends received are taxable. If A owns more than 80\%, a consolidated statement can be filed and dividends received from B are essentially untaxed. Dividends Stated dividend that must be paid before dividends can be paid to common stockholders Dividends are not a liability of the firm, and preferred dividends can be deferred indefinitely. Most preferred dividends are cumulative – any missed preferred dividends have to be paid before common dividends can be paid. Preferred stock generally does not carry voting rights. Features of Preferred Stock Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.29 Section 8.2 (B) Point out that there are a lot of features of preferred stock that are similar to debt. In fact, many new issues have sinking funds that effectively convert what was a perpetual security into an equity security with a definite maturity. However, for tax purposes, preferred stock is equity and dividends are not a tax deductible expense, unless they meet specific characteristics as discussed in the text. Corporations that own stock in other corporations are permitted to exclude 50 percent of the dividend amounts they receive and are taxed on only the remaining 50 percent (the 50 percent exclusion was reduced from 70 percent by the Tax Cuts and Jobs Act of 2017). Real-World Tip: Here’s a gruesome-sounding security – the “death spiral.” Actually, the name refers to convertible preferred shares that have a floating conversion ratio. That is, the conversion ratio varies with the price of the firm’s common stock. Also known as “toxic convertibles,” The Wall Street Journal reports that, when the issuer’s common stock falls, more shares must be issued to redeem the convertible securities, so this dilution pushes the common stock price down further. Hence, the “death spiral” appellation. Dealers vs. Brokers New York Stock Exchange (NYSE) Largest stock market in the world License holders (1,366) Designated market makers (DMMs) Floor brokers Supplemental liquidity providers (SLPs) Operations Floor activity Stock Market Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.30 Section 8.3 (A) and (B) DMMs, formerly known as “specialists,” act as dealers in particular stocks. A DMM maintains an inventory and stands ready to trade at quoted bid (DMM posts the price at which they will buy) and ask (DMM posts the price at which they will sell) prices. They make their profit from the difference between the bid and ask prices, called the bid-ask spread. The smaller the spread, the more competition and the more liquid the stock. The move to decimalization allows for a smaller bid-ask spread. There will be more discussion of this later. Floor broker: a broker matches buyers and sellers. They perform the search function for a fee (commission). They do not hold an inventory of securities. SLPs: investment firms that agree to be active participants in stocks assigned to them. They trade purely for their own accounts. Unlike DMMs and floor brokers, SLPs do not operate on the floor of the stock exchange. Lecture Tip: Some students find it hard to grasp the relative importance of primary and secondary market transactions. Suggest that they consider automobile sales rather than stocks. New automobiles are sold through a network of dealers and salesman (brokers) to the public. In any given year, however, the majority of transactions are between people buying and selling existing automobiles, i.e., the secondary (used) car market. As with secondary market transactions in stocks, used car purchases do not directly benefit the issuer/manufacturer. You can also introduce the notion of information asymmetry and signaling at this point, see the classic article by George Akerlof titled “Market for Lemons.” www: Check out the NYSE by clicking on the embedded link. Students are often amazed at all of the information that is available. Not a physical exchange – computer-based quotation system Multiple market makers Electronic Communications Networks Three levels of information Level 1 – median quotes, registered representatives Level 2 – view quotes, brokers, and dealers Level 3 – view and update quotes, dealers only Large portion of technology stocks NASDAQ Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.31 Section 8.3 (C) Point out that the NASDAQ market site in Times Square is NOT an exchange. It is just offices and basically a place for reporters to report on what is happening with Nasdaq stocks. Electronic Communications Networks provide trading in NASDAQ securities. To see more detail, visit Instinet. Work the Web Example Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› Section 8.3 (C) 7.32 Reading Stock Quotes What information is provided in the stock quote? You can go to Bloomberg for current stock quotes. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.33 Section 8.3 (D) This quote is the Costco quote from the text. 52 week high = 169.59 52 week low = 138.57 Company is Costco Wholesale Annual dividend = $1.80 per share Dividend yield = 1.12\% P/E ratio = 29.31 Most recent price = 160.63 Lecture Tip: A useful assignment is to require students to obtain a recent Wall Street Journal and examine the financial section. Have the students examine the dividend column for various stocks and point out the number of non-dividend paying stocks. Also have them identify the information available in each quote. This allows them to see more information at once than they would normally see with online quotes. You observe a stock price of $18.75. You expect a dividend growth rate of 5\%, and the most recent dividend was $1.50. What is the required return? What are some of the major characteristics of common stock? What are some of the major characteristics of preferred stock? Quick Quiz – Part II Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.34 Section 8.4 r = [1.5(1.05)/18.75] + .05 = 13.4\% The status of pension funding (i.e., over- vs. under-funded) depends heavily on the choice of a discount rate. When actuaries are choosing the appropriate rate, should they give greater priority to future pension recipients, management, or shareholders? How has the increasing availability and use of the internet impacted the ability of stock traders to act unethically? Ethics Issues Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.35 XYZ stock currently sells for $50 per share. The next expected annual dividend is $2, and the growth rate is 6\%. What is the expected rate of return on this stock? If the required rate of return on this stock were 12\%, what would the stock price be, and what would the dividend yield be? Comprehensive Problem Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 7.36 Section 8.4 Expected return = 2/50 + .06 = .10 Price = 2/ (.12 - .06) = $33.33 Dividend yield = 2 / 33.33 = 6\% End of Chapter Chapter 8 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8-‹#› 8-‹#› g-R D g-R g)1(D P 1 0 0    g P D g P g)1(D R g-R D g - R g)1(D P 0 1 0 0 1 0 0       RETURN, RISK, AND THE SECURITY MARKET LINE CHAPTER 13 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 1-‹#› Show how to calculate expected returns, variance, and standard deviation Discuss the impact of diversification Summarize the systematic risk principle Describe the security market line and the risk-return trade-off Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Key Concepts and Skills 1-‹#› Expected Returns and Variances Portfolios Announcements, Surprises, and Expected Returns Risk: Systematic and Unsystematic Diversification and Portfolio Risk Systematic Risk and Beta The Security Market Line The SML and the Cost of Capital: A Preview Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Chapter Outline 1-‹#› 11.3 Lecture Tip: You may find it useful to emphasize the economic foundations of the material in this chapter. Specifically, we assume: -Investor rationality: Investors are assumed to prefer more money to less and less risk to more, all else equal. The result of this assumption is that the ex ante risk-return trade-off will be upward sloping. -As risk-averse return-seekers, investors will take actions consistent with the rationality assumptions. They will require higher returns to invest in riskier assets and are willing to accept lower returns on less risky assets. -Similarly, they will seek to reduce risk while attaining the desired level of return, or increase return without exceeding the maximum acceptable level of risk. Expected returns are based on the probabilities of possible outcomes. In this context, “expected” means average if the process is repeated many times. The “expected” return does not even have to be a possible return. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Expected Returns 1-‹#› 11.4 Section 13.1 (A) Use the following example to illustrate the mathematical nature of expected returns: Consider a game where you toss a fair coin: If it is Heads, then student A pays student B $1. If it is Tails, then student B pays student A $1. Most students will remember from their statistics that the expected value is $0 (=.5(1) + .5(-1)). That means that if the game is played over and over then each student should expect to break-even. However, if the game is only played once, then one student will win $1 and one will lose $1. Suppose you have predicted the following returns for stocks C and T in three possible states of the economy. What are the expected returns? State Probability C T___ Boom 0.3 0.15 0.25 Normal 0.5 0.10 0.20 Recession ??? 0.02 0.01 RC = .3(15) + .5(10) + .2(2) = 9.9\% RT = .3(25) + .5(20) + .2(1) = 17.7\% Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Example: Expected Returns 1-‹#› 11.5 Section 13.1 (A) What is the probability of a recession? 1- 0.3 - 0.5 = 0.2 If the risk-free rate is 4.15\%, what is the risk premium? Stock C: 9.9 – 4.15 = 5.75\% Stock T: 17.7 – 4.15 = 13.55\% Variance and standard deviation measure the volatility of returns. Using unequal probabilities for the entire range of possibilities Weighted average of squared deviations Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Variance and Standard Deviation 1-‹#› 11.6 Section 13.1 (B) It’s important to point out that these formulas are for populations, unlike the formulas in chapter 12 that were for samples (dividing by n-1 instead of n). Further, the probabilities that are used account for the division. Remind the students that standard deviation is the square root of the variance. Consider the previous example. What are the variance and standard deviation for each stock? Stock C 2 = .3(0.15-0.099)2 + .5(0.10-0.099)2 + .2(0.02-0.099)2 = 0.002029  = 4.50\% Stock T 2 = .3(0.25-0.177)2 + .5(0.20-0.177)2 + .2(0.01-0.177)2 = 0.007441  = 8.63\% Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Example: Variance and Standard Deviation 1-‹#› 11.7 Section 13.1 (B) It is helpful to remind students that the standard deviation (but not the variance) is expressed in the same units as the original data, which is a percentage return in our example. Consider the following information: State Probability ABC, Inc. Return Boom .25 0.15 Normal .50 0.08 Slowdown .15 0.04 Recession .10 -0.03 What is the expected return? What is the variance? What is the standard deviation? Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Another Example 1-‹#› 11.8 Section 13.1 (B) E(R) = .25(0.15) + .5(0.08) + .15(0.04) + .1(-0.03) = 8.05\% Variance = .25(.15-0.0805)2 + .5(0.08-0.0805)2 + .15(0.04-0.0805)2 + .1(-0.03-0.0805)2 = 0.00267475 Standard Deviation = 5.17\% A portfolio is a collection of assets. An asset’s risk and return are important in how they affect the risk and return of the portfolio. The risk-return trade-off for a portfolio is measured by the portfolio expected return and standard deviation, just as with individual assets. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Portfolios 1-‹#› 11.9 Section 13.2 Lecture Tip: Each individual has their own level of risk tolerance. Some people are just naturally more inclined to take risk, and they will not require the same level of compensation as others for doing so. Our risk preferences also change through time. We may be willing to take more risk when we are young and without a spouse or kids. But, once we start a family, our risk tolerance may drop. Suppose you have $15,000 to invest and you have purchased securities in the following amounts. What are your portfolio weights in each security? $2000 of C $3000 of KO $4000 of INTC $6000 of BP Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Example: Portfolio Weights C: 2/15 = .133 KO: 3/15 = .2 INTC: 4/15 = .267 BP: 6/15 = .4 1-‹#› 11.10 Section 13.2 (A) C – Citigroup KO – Coca-Cola INTC – Intel BP – BP Show the students that the sum of the weights = 1 The expected return of a portfolio is the weighted average of the expected returns of the respective assets in the portfolio. You can also find the expected return by finding the portfolio return in each possible state and computing the expected value as we did with individual securities. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Portfolio Expected Returns 1-‹#› Section 13.2 (B) 11.11 Consider the portfolio weights computed previously. If the individual stocks have the following expected returns, what is the expected return for the portfolio? C: 19.69\% KO: 5.25\% INTC: 16.65\% BP: 18.24\% E(RP) = .133(19.69\%) + .2(5.25\%) + .267(16.65\%) + .4(18.24\%) = 15.41\% Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Example: Expected Portfolio Returns 1-‹#› Section 13.2 (B) 11.12 Compute the portfolio return for each state: RP = w1R1 + w2R2 + … + wmRm Compute the expected portfolio return using the same formula as for an individual asset. Compute the portfolio variance and standard deviation using the same formulas as for an individual asset. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Portfolio Variance 1-‹#› 11.13 Section 13.2 (C) Consider the following information on returns and probabilities: Invest 50\% of your money in Asset A. State Probability A B Portfolio Boom .4 30\% -5\% 12.5\% Bust .6 -10\% 25\% 7.5\% What are the expected return and standard deviation for each asset? What are the expected return and standard deviation for the portfolio? Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Example: Portfolio Variance 1-‹#› 11.14 Section 13.2 (C) If A and B are your only choices, what percent are you investing in Asset B? 50\% Asset A: E(RA) = .4(30) + .6(-10) = 6\% Variance(A) = .4(30-6)2 + .6(-10-6)2 = 384 Std. Dev.(A) = 19.6\% Asset B: E(RB) = .4(-5) + .6(25) = 13\% Variance(B) = .4(-5-13)2 + .6(25-13)2 = 216 Std. Dev.(B) = 14.7\% Portfolio (solutions to portfolio return in each state appear with mouse click after last question) Portfolio return in boom = .5(30) + .5(-5) = 12.5 Portfolio return in bust = .5(-10) + .5(25) = 7.5 Expected return = .4(12.5) + .6(7.5) = 9.5 or Expected return = .5(6) + .5(13) = 9.5 Variance of portfolio = .4(12.5-9.5)2 + .6(7.5-9.5)2 = 6 Standard deviation = 2.45\% Note that the variance is NOT equal to .5(384) + .5(216) = 300 and Standard deviation is NOT equal to .5(19.6) + .5(14.7) = 17.17\% What would the expected return and standard deviation for the portfolio be if we invested 3/7 of our money in A and 4/7 in B? Portfolio return = 10\% and standard deviation = 0 Portfolio variance using covariances: COV(A,B) = .4(30-6)(-5-13) + .6(-10-6)(25-13) = -288 Variance of portfolio = (.5)2(384) + (.5)2(216) + 2(.5)(.5)(-288) = 6 Standard deviation = 2.45\% Consider the following information on returns and probabilities: State Probability X Z Boom .25 15\% 10\% Normal .60 10\% 9\% Recession .15 5\% 10\% What are the expected return and standard deviation for a portfolio with an investment of $6,000 in asset X and $4,000 in asset Z? Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Another Example: Portfolio Variance 1-‹#› 11.15 Section 13.2 (C) Portfolio return in Boom: .6(15) + .4(10) = 13\% Portfolio return in Normal: .6(10) + .4(9) = 9.6\% Portfolio return in Recession: .6(5) + .4(10) = 7\% Expected return = .25(13) + .6(9.6) + .15(7) = 10.06\% Variance = .25(13-10.06)2 + .6(9.6-10.06)2 + .15(7-10.06)2 = 3.6924 Standard deviation = 1.92\% Compare to return on X of 10.5\% and standard deviation of 3.12\% And return on Z of 9.4\% and standard deviation of .49\% Using covariances: COV(X,Z) = .25(15-10.5)(10-9.4) + .6(10-10.5)(9-9.4) + .15(5-10.5)(10-9.4) = .3 Portfolio variance = (.6 × 3.12)2 + (.4 × .49)2 + 2(.6)(.4)(.3) = 3.6868 Portfolio standard deviation = 1.92\% (difference in variance due to rounding) Lecture Tip: Here are a few tips to pass along to students suffering from “statistics overload”: -The distribution is just the picture of all possible outcomes. -The mean return is the central point of the distribution. -The standard deviation is the average deviation from the mean. -Assuming investor rationality (two-parameter utility functions), the mean is a proxy for expected return and the standard deviation is a proxy for total risk. Realized returns are generally not equal to expected returns. There is the expected component and the unexpected component. At any point in time, the unexpected return can be either positive or negative. Over time, the average of the unexpected component is zero. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Expected vs. Unexpected Returns 1-‹#› Section 13.3 (A) 11.16 Announcements and news contain both an expected component and a surprise component. It is the surprise component that affects a stock’s price and therefore its return. This is very obvious when we watch how stock prices move when an unexpected announcement is made or earnings are different than anticipated. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Announcements and News 1-‹#› 11.17 Section 13.3 (B) Lecture Tip: It is easy to see the effect of unexpected news on stock prices and returns. Consider the following two cases: (1) On November 17, 2004 it was announced that K-Mart would acquire Sears in an $11 billion deal. Sears’ stock price jumped from a closing price of $45.20 on November 16 to a closing price of $52.99 (a 7.79\% increase) and K-Mart’s stock price jumped from $101.22 on November 16 to a closing price of $109.00 on November 17 (a 7.69\% increase). Both stocks traded even higher during the day. Why the jump in price? Unexpected news, of course. (2) On November 18, 2004, Williams-Sonoma cut its sales and earnings estimates for the fourth quarter of 2004 and its share price dropped by 6\%. There are plenty of other examples where unexpected news causes a change in price and expected returns. Efficient markets are a result of investors trading on the unexpected portion of announcements. The easier it is to trade on surprises, the more efficient markets should be. Efficient markets involve random price changes because we cannot predict surprises. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Efficient Markets 1-‹#› Section 13.3 (B) 11.18 Risk factors that affect a large number of assets Also known as non-diversifiable risk or market risk Includes such things as changes in GDP, inflation, interest rates, etc. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Systematic Risk 1-‹#› 11.19 Section 13.4 (A) Risk factors that affect a limited number of assets Also known as unique risk and asset-specific risk Includes such things as labor strikes, part shortages, etc. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Unsystematic Risk 1-‹#› 11.20 Section 13.4 (A) Lecture Tip: You can expand the discussion of the difference between systematic and unsystematic risk by using the example of a strike by employees. Students will generally agree that this is unique or unsystematic risk for one company. However, what if the UAW stages the strike against the entire auto industry. Will this action impact other industries or the entire economy? If the answer to this question is yes, then this becomes a systematic risk factor. The important point is that it is not the event that determines whether it is systematic or unsystematic risk; it is the impact of the event. Total Return = expected return + unexpected return Unexpected return = systematic portion + unsystematic portion Therefore, total return can be expressed as follows: Total Return = expected return + systematic portion + unsystematic portion Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Returns 1-‹#› Section 13.4 (B) 11.21 Portfolio diversification is the investment in several different asset classes or sectors. Diversification is not just holding a lot of assets. For example, if you own 50 Internet stocks, you are not diversified. However, if you own 50 stocks that span 20 different industries, then you are diversified. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Diversification 1-‹#› 11.22 Section 13.5 Video Note: “Portfolio Management” looks at the value of diversification. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Table 13.7 1-‹#› Section 13.5 (A) 11.23 Diversification can substantially reduce the variability of returns without an equivalent reduction in expected returns. This reduction in risk arises because worse than expected returns from one asset are offset by better than expected returns from another. However, there is a minimum level of risk that cannot be diversified away and that is the systematic portion. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. The Principle of Diversification 1-‹#› 11.24 Section 13.5 (B) A discussion of the potential benefits of international investing may be helpful at this point. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Figure 13.1 1-‹#› Section 13.5 (B) 11.25 The risk that can be eliminated by combining assets into a portfolio. Often considered the same as unsystematic, unique or asset-specific risk If we hold only one asset, or assets in the same industry, then we are exposing ourselves to risk that we could diversify away. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Diversifiable Risk 1-‹#› Section 13.5 (C) 11.26 Total risk = systematic risk + unsystematic risk The standard deviation of returns is a measure of total risk. For well-diversified portfolios, unsystematic risk is very small. Consequently, the total risk for a diversified portfolio is essentially equivalent to the systematic risk. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Total Risk 1-‹#› Section 13.5 (D) 11.27 There is a reward for bearing risk. There is not a reward for bearing risk unnecessarily. The expected return on a risky asset depends only on that asset’s systematic risk since unsystematic risk can be diversified away. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Systematic Risk Principle 1-‹#› 11.28 Section 13.6 (A) A discussion of diversification via mutual funds and ETFs may add to the students’ understanding. How do we measure systematic risk? We use the beta coefficient. What does beta tell us? A beta of 1 implies the asset has the same systematic risk as the overall market. A beta < 1 implies the asset has less systematic risk than the overall market. A beta > 1 implies the asset has more systematic risk than the overall market. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Measuring Systematic Risk 1-‹#› 11.29 Section 13.6 (B) Lecture Tip: Remember that the cost of equity depends on both the firm’s business risk and its financial risk. So, all else equal, borrowing money will increase a firm’s equity beta because it increases the volatility of earnings. Robert Hamada derived the following equation to reflect the relationship between levered and unlevered betas (excluding tax effects): L = U(1 + D/E) where: L = equity beta of a levered firm; U = equity beta of an unlevered firm; D/E = debt-to-equity ratio Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Table 13.8 – Selected Betas 1-‹#› 11.30 Section 13.6 (B) Lecture Tip: Students sometimes wonder just how high a stock’s beta can get. In earlier years, one would say that, while the average beta for all stocks must be 1.0, the range of possible values for any given beta is from - to +. Today, the Internet provides another way of addressing the question. Go to the Yahoo! Finance stock screener site. This site allows you to search many financial markets by fundamental criteria. Consider the following information: Standard Deviation Beta Security C 20\% 1.25 Security K 30\% 0.95 Which security has more total risk? Which security has more systematic risk? Which security should have the higher expected return? Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Total vs. Systematic Risk 1-‹#› 11.31 Section 13.6 (B) Security K has the higher total risk. Security C has the higher systematic risk. Security C should have the higher expected return. Many sites provide betas for companies. Yahoo! Finance provides beta, plus a lot of other information under its Key Statistics section. Enter a ticker symbol and get a basic quote. Click on Key Statistics. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Work the Web Example 1-‹#› Section 13.6 (B) 11.32 Consider the previous example with the following four securities. Security Weight Beta C .133 1.685 KO .2 0.195 INTC .267 1.161 BP .4 1.434 What is the portfolio beta? .133(1.685) + .2(.195) + .267(1.161) + .4(1.434) = 1.147 Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Example: Portfolio Betas 1-‹#› 11.33 Section 13.6 (C) Which security has the highest systematic risk? C Which security has the lowest systematic risk? KO Is the systematic risk of the portfolio more or less than the market? more Remember that the risk premium = expected return – risk-free rate. The higher the beta, the greater the risk premium should be. Can we define the relationship between the risk premium and beta so that we can estimate the expected return? YES! Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Beta and the Risk Premium 1-‹#› Section 13.7 (A) 11.34 Example: Portfolio Expected Returns and Betas Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Rf E(RA) A 1-‹#› 11.35 Section 13.7 (A) Based on the example in the book: Point out that there is a linear relationship between beta and expected return. Ask if the students remember the form of the equation for a line. Y = mx + b E(R) = slope (Beta) + y-intercept The y-intercept is = the risk-free rate, so all we need is the slope Lecture Tip: The example in the book illustrates a greater than 100\% investment in asset A. This means that the investor has borrowed money on margin (technically at the risk-free rate) and used that money to purchase additional shares of asset A. This can increase the potential returns, but it also increases the risk. Expected Return 0 0.4 0.8 1.2 1.6 2 2.4 0.08 0.11 0.14000000000000001 0.17 0.2 0.23 0.26 0 0.4 0.8 1.2 1.6 2 2.4 0 0.4 0.8 1.2 1.6 2 2.4 0 0.4 0.8 1.2 1.6 2 2.4 Beta Expected Return The reward-to-risk ratio is the slope of the line illustrated in the previous example. Slope = (E(RA) – Rf) / (A – 0) Reward-to-risk ratio for previous example = (20 – 8) / (1.6 – 0) = 7.5 What if an asset has a reward-to-risk ratio of 8 (implying that the asset plots above the line)? What if an asset has a reward-to-risk ratio of 7 (implying that the asset plots below the line)? Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Reward-to-Risk Ratio: Definition and Example 1-‹#› 11.36 Section 13.7 (A) Ask students if they remember how to compute the slope of a line: rise / run. If the reward-to-risk ratio = 8, then investors will want to buy the asset. This will drive the price up and the expected return down (remember time value of money and valuation). When will the flurry of trading stop? When the reward-to-risk ratio reaches 7.5. If the reward-to-risk ratio = 7, then investors will want to sell the asset. This will drive the price down and the expected return up. When will the flurry of trading stop? When the reward-to-risk ratio reaches 7.5. In equilibrium, all assets and portfolios must have the same reward-to-risk ratio, and they all must equal the reward-to-risk ratio for the market. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Market Equilibrium 1-‹#› Section 13.7 (A) 11.37 The security market line (SML) is the representation of market equilibrium. The slope of the SML is the reward-to-risk ratio: (E(RM) – Rf) / M But since the beta for the market is always equal to one, the slope can be rewritten. Slope = E(RM) – Rf = market risk premium Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Security Market Line 1-‹#› 11.38 Section 13.7 (B) Based on the discussion earlier, we now have all the components of the line: E(R) = [E(RM) – Rf] + Rf Lecture Tip: Although the realized market risk premium has on average been approximately 8.5\%, the historical average should not be confused with the anticipated risk premium for any particular future period. There is abundant evidence that the realized market return has varied greatly over time. The historical average value should be treated accordingly. On the other hand, there is currently no universally accepted means of coming up with a good ex ante estimate of the market risk premium, so the historical average might be as good a guess as any. In the late 1990’s, there was evidence that the risk premium had been shrinking. In fact, Alan Greenspan was concerned with the reduction in the risk premium because he was afraid that investors had lost sight of how risky stocks actually are. Investors had a wake-up call in late 2000 and 2001 (and again in 2008 and 2009). The capital asset pricing model defines the relationship between risk and return. E(RA) = Rf + A(E(RM) – Rf) If we know an asset’s systematic risk, we can use the CAPM to determine its expected return. This is true whether we are talking about financial assets or physical assets. Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. The Capital Asset Pricing Model (CAPM) 1-‹#› Section 13.7 (B) 11.39 Pure time value of money: measured by the risk-free rate Reward for bearing systematic risk: measured by the market risk premium Amount of systematic risk: measured by beta Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Factors Affecting Expected Return 1-‹#› Section 13.7 (B) 11.40 Consider the betas for each of the assets given earlier. If the risk-free rate is 4.15\% and the market risk premium is 7.5\%, what is the expected return for each? Security Beta Expected Return C 2.685 3.15 + 1.685(7.5) = 15.79\% KO 0.195 3.15 + 0.195(7.5) = 4.61\% INTC 2.161 3.15 + 1.161(7.5) = 11.86\% BP 2.434 3.15 + 1.434(7.5) = 13.93\% Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Example - CAPM 1-‹#› 11.41 Section 13.7 (B) Lecture Tip: Students should remember …