Measuring Relative Risk (PDF)

AND SUBJECT TO GAME PLAYING 55 © All Slides | Aswath Damodaran MEASURING RELATIVE RISK: YOU DON’T LIKE BETAS OR MODERN PORTFOLIO THEORY? NO PROBLEM. © All Slides | Aswath Damodaran DON’T LIKE THE DIVERSIFIED INVESTOR FOCUS, BUT OKAY WITH PRICE-BASED MEASURE...

AND SUBJECT TO GAME PLAYING 55 © All Slides | Aswath Damodaran MEASURING RELATIVE RISK: YOU DON’T LIKE BETAS OR MODERN PORTFOLIO THEORY? NO PROBLEM. © All Slides | Aswath Damodaran DON’T LIKE THE DIVERSIFIED INVESTOR FOCUS, BUT OKAY WITH PRICE-BASED MEASURES q Relative Standard Deviation a. Relative Volatility = Std dev of Stock/ Average Std dev across all stocks b. Captures all risk, rather than just market risk q Proxy Models a. Look at historical returns on all stocks and look for variables that explain differences in returns. b. You are, in effect, running multiple regressions with returns on individual stocks as the dependent variable and fundamentals about these stocks as independent variables. c. This approach started with market cap (the small cap effect) and over the last two decades has added other variables (momentum, liquidity etc.) q CAPM Plus Models a. Start with the traditional CAPM (Rf + Beta (ERP)) and then add other premiums for proxies. © All Slides | Aswath Damodaran  DON’T LIKE THE PRICE-BASED APPROACH.. 58 q Accounting risk measures: To the extent that you don’t trust market- priced based measures of risk, you could compute relative risk measures based on a. Accounting earnings volatility: Compute an accounting beta or relative volatility b. Balance sheet ratios: You could compute a risk score based upon accounting ratios like debt ratios or cash holdings (akin to default risk scores like the Z score) q Qualitative Risk Models: In these models, risk assessments are based at least partially on qualitative factors (quality of management). q Debt based measures: You can estimate a cost of equity, based upon an observable costs of debt for the company. a. Cost of equity = Cost of debt * Scaling factor b. The scaling factor can be computed from implied volatilities. © All Slides | Aswath Damodaran  DETERMINANTS OF BETAS & RELATIVE RISK 59 Beta of Equity (Levered Beta) Beta of Firm (Unlevered Beta) Financial Leverage: Other things remaining equal, the greater the proportion of capital that a firm raises from debt,the higher its Nature of product or Operating Leverage (Fixed equity beta will be service offered by Costs as percent of total company: costs): Other things remaining equal, Other things remaining equal the more discretionary the the greater the proportion of Implciations product or service, the higher the costs that are fixed, the Highly levered firms should have highe betas the beta. higher the beta of the than firms with less debt. company. Equity Beta (Levered beta) = Unlev Beta (1 + (1- t) (Debt/Equity Ratio)) Implications Implications 1. Cyclical companies should 1. Firms with high infrastructure have higher betas than non- needs and rigid cost structures cyclical companies. should have higher betas than 2. Luxury goods firms should firms with flexible cost structures. have higher betas than basic 2. Smaller firms should have higher goods. betas than larger firms. 3. High priced goods/service 3. Young firms should have higher firms should have higher betas betas than more mature firms. than low prices goods/services firms. 4. Growth firms should have higher betas. © All Slides | Aswath Damodaran  IN A PERFECT WORLD… WE WOULD ESTIMATE THE BETA OF A FIRM BY DOING THE FOLLOWING 60 Start with the beta of the business that the firm is in Adjust the business beta for the operating leverage of the firm to arrive at the unlevered beta for the firm. Use the financial leverage of the firm to estimate the equity beta for the firm Levered Beta = Unlevered Beta ( 1 + (1- tax rate) (Debt/Equity)) © All Slides | Aswath Damodaran  ADJUSTING FOR OPERATING LEVERAGE… 61 q Within any business, firms with lower fixed costs (as a percentage of total costs) should have lower unlevered betas. If you can compute fixed and variable costs for each firm in a sector, you can break down the unlevered beta into business and operating leverage components. Unlevered beta = Pure business beta * (1 + (Fixed costs/ Variable costs)) q The biggest problem with doing this is informational. It is difficult to get information on fixed and variable costs for individual firms. q In practice, we tend to assume that the operating leverage of firms within a business are similar and use the same unlevered beta for every firm. © All Slides | Aswath Damodaran  ADJUSTING FOR FINANCIAL LEVERAGE… 62 q Conventional approach: If we assume that debt carries no market risk (has a beta of zero), the beta of equity alone can be written as a function of the unlevered beta and the debt-equity ratio q bL = bu (1+ ((1-t)D/E)) q In some versions, the tax effect is ignored and there is no (1-t) in the equation. q Debt Adjusted Approach: If beta carries market risk and you can estimate the beta of debt, you can estimate the levered beta as follows: q bL = bu (1+ ((1-t)D/E)) - bdebt (1-t) (D/E) q While the latter is more realistic, estimating betas for debt can be difficult to do. © All Slides | Aswath Damodaran  BOTTOM-UP BETAS 63 Step 1: Find the business or businesses that your firm operates in. Possible Refinements Step 2: Find publicly traded firms in each of these businesses and obtain their regression betas. Compute the simple average across these regression betas to arrive at an average beta for these publicly If you can, adjust this beta for differences traded firms. Unlever this average beta using the average debt to between your firm and the comparable equity ratio across the publicly traded firms in the sample. firms on operating leverage and product Unlevered beta for business = Average beta across publicly traded characteristics. firms/ (1 + (1- t) (Average D/E ratio across firms)) While revenues or operating income Step 3: Estimate how much value your firm derives from each of are often used as weights, it is better the different businesses it is in. to try to estimate the value of each business. Step 4: Compute a weighted average of the unlevered betas of the If you expect the business mix of your different businesses (from step 2) using the weights from step 3. firm to change over time, you can Bottom-up Unlevered beta for your firm = Weighted average of the change the weights on a year-to-year unlevered betas of the individual business basis. If you expect your debt to equity ratio to Step 5: Compute a levered beta (equity beta) for your firm, using change over time, the levered beta will the market debt to equity ratio for your firm. change over time. Levered bottom-up beta = Unlevered beta (1+ (1-t) (Debt/Equity)) © All Slides | Aswath Damodaran  WHY BOTTOM-UP BETAS? 64 q Less Noisy: The standard error in a bottom-up beta will be significantly lower than the standard error in a single regression beta. Roughly speaking, the standard error of a bottom-up beta estimate can be written as follows: Average Std Error across Betas Std error of bottom-up beta = Number of firms in sample q Updated: The bottom-up beta can be adjusted to reflect changes in the firm’s business mix and financial leverage. Regression betas reflect the past. € q Don’t need prices: You can estimate bottom-up betas even when you do not have historical stock prices. This is the case with initial public offerings, private businesses or divisions of companies. © All Slides | Aswath Damodaran ESTIMATING BOTTOM UP BETAS & COSTS OF EQUITY: VALE Sample' Unlevered'beta' Peer'Group' Value'of' Proportion'of' Business' Sample' size' of'business' Revenues' EV/Sales' Business' Vale' Global'firms'in'metals'&' Metals'&' mining,'Market'cap>$1' Mining' billion' 48' 0.86' $9,013' 1.97' $17,739' 16.65%' Iron'Ore' Global'firms'in'iron'ore' 78' 0.83' $32,717' 2.48' $81,188' 76.20%' Global'specialty' Fertilizers' chemical'firms' 693' 0.99' $3,777' 1.52' $5,741' 5.39%' Global'transportation' Logistics' firms' 223' 0.75' $1,644' 1.14' $1,874' 1.76%' Vale' Operations' '' '' 0.8440' $47,151' '' $106,543' 100.00%' © All Slides | Aswath Damodaran  EMBRAER’S BOTTOM-UP BETA 66 Business Unlevered Beta D/E Ratio Levered beta Aerospace 0.95 18.95% 1.07 q Levered Beta = Unlevered Beta ( 1 + (1- tax rate) (D/E Ratio) = 0.95 ( 1 + (1-.34) (.1895)) = 1.07 q Can an unlevered beta estimated using U.S. and European aerospace companies be used to estimate the beta for a Brazilian aerospace company? a. Yes b. No q What concerns would you have in making this assumption? © All Slides | Aswath Damodaran  GROSS DEBT VERSUS NET DEBT APPROACHES 67 q Analysts in Europe and Latin America often take the difference between debt and cash (net debt) when computing debt ratios and arrive at very different values. q For Embraer, using the gross debt ratio q Gross D/E Ratio for Embraer = 1953/11,042 = 18.95% q Levered Beta using Gross Debt ratio = 1.07 q Using the net debt ratio, we get q Net Debt Ratio for Embraer = (Debt - Cash)/ Market value of Equity = (1953-2320)/ 11,042 = -3.32% q Levered Beta using Net Debt Ratio = 0.95 (1 + (1-.34) (-.0332)) = 0.93 q The cost of Equity using net debt levered beta for Embraer will be much lower than with the gross debt approach. The cost of capital for Embraer will even out since the debt ratio used in the cost of capital equation will now be a net debt ratio rather than a gross debt ratio. © All Slides | Aswath Damodaran  THE COST OF EQUITY: A RECAP 68 Preferably, a bottom-up beta, based upon other firms in the business, and firmʼs own financial leverage Cost of Equity = Riskfree Rate + Beta * (Risk Premium) Has to be in the same Historical Premium Implied Premium currency as cash flows, 1. Mature Equity Market Premium: Based on how equity and defined in same terms Average premium earned by or market is priced today (real or nominal) as the stocks over T.Bonds in U.S. and a simple valuation cash flows 2. Country risk premium = model Country Default Spread* ( σEquity/σCountry bond) © All Slides | Aswath Damodaran COST OF DEBT © All Slides | Aswath Damodaran  ESTIMATING THE COST OF DEBT 70 q The cost of debt is the rate at which you can borrow at currently, It will reflect not only your default risk but also the level of interest rates in the market. q The two most widely used approaches to estimating cost of debt are: q Looking up the yield to maturity on a straight bond outstanding from the firm. The limitation of this approach is that very few firms have long term straight bonds that are liquid and widely traded q Looking up the rating for the firm and estimating a default spread based upon the rating. While this approach is more robust, different bonds from the same firm can have different ratings. You have to use a median rating for the firm q When in trouble (either because you have no ratings or multiple ratings for a firm), estimate a synthetic rating for your firm and the cost of debt based upon that rating. © All Slides | Aswath Damodaran  ESTIMATING SYNTHETIC RATINGS 71 q The rating for a firm can be estimated using the financial characteristics of the firm. In its simplest form, the rating can be estimated from the interest coverage ratio Interest Coverage Ratio = EBIT / Interest Expenses q For Embraer’s interest coverage ratio, we used the interest expenses from 2003 and the average EBIT from 2001 to 2003. (The aircraft business was badly affected by 9/11 and its aftermath. In 2002 and 2003, Embraer reported significant drops in operating income) Interest Coverage Ratio = 462.1 /129.70 = 3.56 © All Slides | Aswath Damodaran  INTEREST COVERAGE RATIOS, RATINGS AND DEFAULT SPREADS: 2004 72 If Interest Coverage Ratio is Estimated Bond Rating Default Spread(2004) > 8.50 (>12.50) AAA 0.35% 6.50 - 8.50 (9.5-12.5) AA 0.50% 5.50 - 6.50 (7.5-9.5) A+ 0.70% 4.25 - 5.50 (6-7.5) A 0.85% 3.00 - 4.25 (4.5-6) A– 1.00% 2.50 - 3.00 (4-4.5) BBB 1.50% 2.25- 2.50 (3.5-4) BB+ 2.00% 2.00 - 2.25 ((3-3.5) BB 2.50% 1.75 - 2.00 (2.5-3) B+ 3.25% 1.50 - 1.75 (2-2.5) B 4.00% 1.25 - 1.50 (1.5-2) B– 6.00% 0.80 - 1.25 (1.25-1.5) CCC 8.00% 0.65 - 0.80 (0.8-1.25) CC 10.00% 0.20 - 0.65 (0.5-0.8) C 12.00% < 0.20 (