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Chapter 18 The Analysis of Equity Risk and the Cost of Capital The Analysis of Equity Risk and the Cost of Capital Link to Previous Chapters Chapter 3 reviewed standard beta technologies to measure the cost of capital. Chapter 13 distinguished operating risk and financing risk. This Chapter This chapter analyzes the fundamental determinants of operating and financing risk in equity investing. It also introduces price risk and outlines ways to incorporate risk when valuing firms and trading in their shares. Link to Next Chapter Chapter 19 analyzes the risk of firms’ debt. Link to Web Page The book’s web site has more discussion of risk. What are the problems with standard beta technologies? What are the fundamental determinants of risk? What is price risk? How is risk incorporated in valuation? What you will learn from this chapter • That precise measures of the cost of capital are difficult to calculate • What risk is • How business investment can yield extreme (high and low) returns • How diversification reduces risk • Problems with using the standard Capital Asset Pricing Model and other beta technologies • The difference between fundamental risk and price risk • The determinants of fundamental risk • The determinants of price risk What you will learn from this chapter (cont.) • How fundamental analysis protects against price risk • How pro forma analysis can be adapted to prepare value-at-risk profiles • How fundamentals help to measure betas • How the investor finesses the problem of not knowing the required return • How to combine value-at-risk profiling and screening analysis The Nature of Risk • Value is determined by expected payoffs discounted for risk • Risk is determined by the likelihood of getting payoffs that are different from the expected payoff • Risk is characterized by the set of possible outcomes that an investor faces and the probabilities of these outcomes: a payoff (or return) distribution Models of the Distribution of Returns: The Normal Distribution Best and Worst Performers, 2004: Wall Street Journal Shareholder Scorecard The Best Performers The Worst Performers One Year Company Return, % Taser International 361.1% Kmart Holding 313.2% Chicago Mercantile Exchange 218.5% Autodesk 209.6% Apple Computer 201.4% American Eagle Outfitters 188.1% TXU. 177.6% Penn National Gaming 161.9% Boyd Gaming 161.3% First Marblehead 157.1% Sepracor 148.1% USG 143.0% Sirius Satellite Radio 141.1% Urban Outfitters 139.7% Wynn Resorts 138.9% OSI Pharmaceuticals 132.1% Cree 126.6% Tesoro 118.7% Southwestern Energy 112.1% VeriSign 106.1% Cytyc 99.2% Valero Energy 97.6% Diamond Offshore Drilling 97.2% Tibco Software 97.0% Monsanto 96.1% One Year Company Return, % Agere System -55.1% Foundry Networks -51.8% Ciena -49.1% PMC-Sierra -44.0% Synopsys -42.3% Chiron -41.5% Level 3 Communications-40.5% UTStarcom -40.2% Rite Aid -39.4% LSI Logic -38.2% Novell -35.9% Millennium Pharmaceuticals -34.9% Inc. Fairchild Semiconductor-34.9% Atmel -34.8% Vishay Intertechnology -34.4% Novellus Systems -33.7% Allied Waste Industries -33.1% Teradyne -32.9% Sanmina-Sci -32.8% Intersil CI A -32.3% Entercom Communications -32.2% CI A Tenet Healthcare -31.6% Icos -31.5% Unisys -31.4% SPX -30.2% The Actual Distribution of Annual Stock Returns Probability -2 sd -100% -47% 0 sd 13% 2 sd 73% 100% Annual Return Diversification and Risk: the Effect on Standard Deviation from Adding More Securities to a Portfolio Portfolio Standard Deviation 1 5 10 15 Number of Securities The Normal Distribution for the S&P 500 Portfolio Mean annual return = 13% Standard deviation of returns = 20% The Actual Distribution of S&P 500 Portfolio Annual Returns, 1926-98 Number of Times Observed 12 9 6 3 0 -50% -40% -30% -20% -10% 1% 10% 20% 30% Source: Based on data from the Center for Research in Security Prices, University of Chicago 40% 50% The Problems with “Asset Pricing Models” 1. Risk factors are hard to identify 2. Risk premiums on risk factors are very hard to measure 3. Often assume normal distributions of return The CAPM is “Seductively Precise” • Normally distributed stock returns are assumed • The market risk premium is a big guess Is it 3½%, 4½%, 8%, or 9½%? Has the market risk premium declined in the 1990s? • Betas are estimated with error • Estimates of the cost of capital are made from market prices and assume that the market is efficient Fundamental Risk • Risk is determined by a firm’s business activities and so is understood by analyzing those activities • A basic distinction: operating and financing risk Required Return for Equity Required Return for Operations Market Leverage Required Return Spread E F Operating Risk V0D F D V0E Financing Risk A Framework for Analysis of Fundamental Risk V0E RE 1 RE 2 RE 3 CSE 0 2 3 ρE ρE ρE RE t ROCE t ρ E 1CSE t 1 Profitability Risk Growth Risk Risk is the chance of earning poor residual earnings Profitability Risk: The Chance of Getting Poor ROCE Return on Common Equity Return on Net Operating AssetsFinancial Leverage Operating Spread NFO ROCE RNOA CSE RNOA NBC Operating Risk Financing Risk The Analysis of Fundamental Risk Fundamental Risk ROCE Risk FLEV x [ RNOA – NBC ] ROCE = RNOA + Operating Risk 1 Profit Margin Risk Asset Turnover Risk OI/Sales Sales/NOA Expense Risk Operating Leverage Risk Expense Fixed Cost Sales Variable Cost Growth Risk (Operating Risk 2) Growth in NOA = Growth in Sales x 1/ATO Financing Risk Operating Liability Leverage Risk OL/NOA Financial Leverage Risk Borrowing Cost Risk NFO/CSE NFE/NFO The Analysis of Operating Risk RNOA = PM x ATO The Drivers of Operating Risk • PM Risk Expense Risk Operating Leverage Risk • ATO Risk • OLLEV Risk The Analysis of Financing Risk The drivers of the financing premium: • Financial Leverage (FLEV) Risk • Borrowing Cost Risk The Analysis of Growth Risk 1 Growth in NOA Growth in Sales ATO Sales Risk Sales risk is the primary business risk Compounding Risk Factors Produce Extreme Returns A drop in sales is compounded by PM risk, ATO risk, FLEV risk and NBC risk • The effect of a drop in sales is magnified by expense risk • The effect of a drop in sales is magnified by operating leverage risk • The effect of a drop in sales is magnified by asset turnover risk • The effect of a drop in sales is magnified by OLLEV risk • The effect of a drop in sales is magnified by FLEV risk • The effect of a drop in sales is magnified by borrowing cost risk Value-at-Risk Profiles • Value-at-Risk profiles are prepared by developing pro formas for different scenarios. The outcomes in these pro formas are determined by the risk factors. • Steps to prepare Value-at-Risk Profiles 1. Identify economic factors that affect the risk drivers 2. Identify risk protection mechanisms in place within the firm 3. Identify the effect of economic factors on the fundamental risk drivers 4. Prepare pro forma financial statements under alternative scenarios for the fundamental risk drivers 5. Forecast residual operating income for each scenario and, from these forecasts, calculate the set of values from the scenarios Value-at-Risk Profile: Firm A Firm A _____________________________________________________ Scenario 1 2 3 4 5 6 7 1% 0% 1% 2% 3% 4% 5% 0.1 0.1 0.2 0.2 0.2 0.1 0.1 Sales ($ million) 25 50 75 100 125 150 175 Operating expenses ($ million) Fixed costs 20 20 20 20 20 20 20 Variable costs 18 36 54 72 90 108 126 Total expenses 38 56 74 92 110 128 146 6 1 8 15 22 29 52% 12% 1.3% 8.0% 12% 14.7% 16.6% 0.63 1.03 1.30 1.50 1.65 1.77 1.87 32.7% 12.3% 1.7% 12.0% 19.8% 26.0% 30.9% 39.7 48.7 57.7 66.7 75.7 84.7 93.7 15.4 8.9 2.5 4.0 10.5 16.9 23.4 40 49 16 133 251 366 484 Factor: GDP growth Probability of scenario Fundamentals affected Operating income ($ million) Profit margin Asset turnover RNOA Beginning NOA ($ million) ReOI (R=1.06) Value with limited liability 13 _____________________________________________________ PM risk driver: ATO risk driver: Operating expense = 20 + 72% of sales Net operating assets = 30.7 + 36% of sales Value-at-Risk Profile: Firm B Firm B ___________________________________________________ Scenario 1 2 3 4 5 6 7 1% 0% 1% 2% 3% 4% 5% 0.1 0.1 0.2 0.2 0.2 0.1 0.1 25 50 75 100 125 150 175 4 4 4 4 4 4 4 Variable costs 22 44 66 88 110 132 154 Total expenses 26 48 70 92 114 136 158 Operating income ($ million) Profit margin 1 2 5 8 11 14 17 4% 4% 6.7% 8.0% 8.8% 9.3% 9.7% Asset turnover 0.81 1.17 1.37 1.50 1.59 1.65 1.70 12.0% 14.0% 15.4% 16.6% Factor: GDP growth Probability of scenario Fundamentals affected Sales ($ million) Operating expenses ($ million) Fixed costs RNOA Beginning NOA ($ million) ReOI (R=1.06) Value with limited liability 3.3% 4.7% 9.1% 30.7 42.7 54.7 66.7 78.7 90.7 102.7 2.8 0.6 1.7 4.0 6.3 8.6 10.8 31 33 83 133 184 234 283 ___________________________________________________ PM risk driver: ATO risk driver: Operating expense = 4 + 88% of sales Net operating assets = 18.7 + 48% of sales ___________________________________________________________________ Value-at-Risk Profiles: Firm A and B Historical Betas Historical Betas are estimated from past stock returns: i Return on the Market ei Return i Beta Beta estimate Beta is a covariance with the return on the market. This (standardized) covariance is estimated from this timeseries regression. Betas revert towards their average of 1.0 Investors are interested in the future beta over the period they hold the investment. High and low historical betas tend to move closer to 1.0 over time. A rough rule for forecasting future betas from historical betas: Future Beta 0.35 0.65 Historical Beta This adjustment pulls betas towards 1.0. Fundamental Betas: Forecasting Future Betas from Fundamentals Two steps: 1. Estimate relationship between historical betas and fundamental attributes (say, FLEV and OLLEV) in the cross section Historical Beta i b0 b1FLEVi b2 OLEV i ui 2. Use estimates of b0, b1, and b2 to predict future beta for a firm using the most recent measures of the fundamentals for that firm: Predicted Beta i b̂0 b̂1FLEV i b̂ 2 OLEV i Some Fundamental Measures that have been Used to Predict Betas • Earnings variability • Cash flow variability • Size • Growth in earnings or sales • Growth in assets • P/E ratio • P/B ratio • Dividend yield Scenario Planning and Pro Forma Analysis Pro forma analysis can be used to model outcomes for different planning scenarios. Investigate, for example, • Adaptation Options • Growth Options • Strategic Risk Management Options Different future paths can be articulated with pro forma analysis. The value of each path calculated can then be. Price Risk and Fundamental Risk • Fundamental Risk is the risk of value not being realized because of fundamental factors that affect the firm’s activities • Price Risk is the risk of value not being realized in prices because of factors other than fundamentals Price Risk Market Inefficiency Risk The market price may not reflect the “fundamental value” • Scenario A risk • Scenario B risk Fundamental analysis reduces Scenario A risk, but Scenario B risk can still affect a diligent fundamental investor Price Risk: Scenario A and Scenario B Scenario A: Price gravitates to fundamental value Cum-dividend Value PTC = VTC Normal return, PTC V0 Actual return, PTC P0 V0 Abnormal return, V0 P0 P0 Time 0 1 2 3 4 T Scenario B: Price deviates from fundamental value Cum-dividend Value PTC Abnormal return, PTC VTC Actual return, VTC PTC P0 Normal return, VTC V0 P 0 = V0 Time 0 1 2 3 4 T Liquidity Risk Liquidity Risk is the risk of not finding a buyer or seller at the fundamental price •Liquidity discounts •Mechanisms to reduce liquidity risk – Brokers – Market makers – Investment banks (“deal makers”) The fees of these specialists are the costs of reducing the liquidity discount Inferring the Expected Return from Market Prices Reverse engineering to estimate the expected reurn: P0 CSE 0 RE 1 RE 2 RE T RE 2 T T 1 /ρ TE ρE ρE ρE ρ E g Given an estimate of growth (g), the expected return can be estimated from prices and forecasts of earnings P0 AEG 2 AEG 3 AEG T 1 T Earn ... ρE 1 2 ρ g ρ ρE E 1 E E 1 If market is efficient, expected return = cost of capital Implied Expected Returns and Valueat-Risk Profiles 1. Group firms with similar Value-at-Risk profiles 2. Rank firms within each group on implied expected returns 3. Buy those with high expected returns, sell those with low expected returns Holding risk constant Relative Value Analysis: Evaluation firms within a Risk Class Relative value ratios for firms in same risk class: Relative Value Ratio V0E 1/P0 1 V0E 2 /P0 2 V0E 1 and V0E 2 are calculated by discounting expected residual earnings (or capitalizi ng earnings and growth) at the risk-free rate. P0 1 and P0 2 are the market prices for the two investments. A relative value ratio of 1.0 implies no arbitrage Perceived Risk Name of Stock Perceived Risk Mean Asset Size Financial Leverage Variance Variability in Earnings _____________________________________________________________________________________________ AT&T 1.89 1.22 11.83 0.165 1.09 Procter & Gamble 2.36 1.74 8.85 0.318 2.79 IBM 2.39 1.52 10.30 0.338 1.95 General Electric 2.69 1.64 9.95 0.468 1.29 Exxon 2.70 1.97 11.33 0.277 2.25 Commonwealth Edison 3.20 2.40 9.32 0.620 1.76 Dow Jones & Co. 3.57 2.38 6.28 0.477 2.96 McDonalds 3.87 2.36 7.97 0.413 2.32 Sears Roebuck 3.91 1.69 10.24 0.573 1.42 DuPont 4.11 1.91 10.08 0.508 1.64 Safeway 4.28 3.27 8.21 0.691 2.01 Citicorp 4.30 2.37 11.69 Dr. Pepper 4.32 2.03 5.11 0.215 General Motors 4.59 2.43 10.57 0.422 Xerox 4.69 2.45 8.95 0.397 1.04 American Broadcasting 4.86 1.83 7.37 0.370 0.47 Holiday Inns 5.13 1.86 7.43 0.536 1.34 Tandy 5.54 2.00 6.84 0.225 3.27 Litton Industries 5.66 1.78 8.21 0.552 2.52 RCA 5.67 2.02 8.97 0.855 Georgia Pacific 5.88 2.51 8.53 0.450 3.13 Emery Air Freight 5.92 2.58 5.62 0.697 2.28 E.F. Hutton 6.37 2.75 8.64 1.80 U.S. Homes 7.23 2.60 6.63 20.18 International Harvester 8.78 0.41 8.58 1.52 2.26 0.704 Source: G.E. Farrelly, K.R. Ferris and W.R. Reichenstein,” Perceived Risk, Market Risk, and Accounting Determined Risk measures,” Accounting Review, April 1985, pp. 278-288. Building in a Margin of Safety 1. Use a high discount rate in evaluating a BUY; use a low discount rate in evaluating a SELL 2. Be conservative (for a BUY) or optimistic (for a SELL) in forecasting