fin 405 chapter 4
market cap formula
# of shares outstanding * share price
beta of cash
0 •$100 mil invested in pharmaceuticals vs. $50 mil in pharmaceuticals and $50 mil in cash - if you run OLS regression on these stocks, the firm 100% invested in pharmaceuticals is going to have a much higher beta because cash is not exposed to systematic risk •drags down levered beta
the purpose of the bottom up beta is to:
1. drive down standard error or the noise in our estimate by using more data - adding cross sectional data (data from other firms as well as the time series data) 2. more forward looking because were building the beta based on assets under management presently, rather than long term history 3. allows us to build division level hurdle rates
beta determinants
1. product type •industry effects: the beta value for a firm depends upon the sensitivity of the demand for its products and services and of its costs to macroeconomic factors that affect the overall market; cyclical companies have higher betas than non-cyclical firms; firms which sell more discretionary (more elasticity of demand) products will have higher betas than firms that sell less discretionary products 2. operating leverage effects: •operating leverage refers to the proportion of the total cost of the firm that are fixed; other things remaining equal, higher operating leverage results in greater earnings variability which in turn results in higher betas b/c even though operating costs are lower, they are fixed (if we go into recession, we still have to make fixed operating cost payments); do you have fixed or variable costs in your production process?; ex: lease you sign, sign 2 year lease - have different (lower cost- more commitment) monthly rent commitment than signing a 1 year lease 3. financial leverage •as firms borrow, they create fixed costs (interest pmts) that make their earnings to equity investors more volatile - this increased earnings volatility increases the equity beta **the beta of equity alone can be written as a function of the unlevered beta and the debt ratio: BL = BU (1 + ((1 - t)(D/E)) where BL = levered or equity beta, BU = unlevered or asset beta, D/E = market value debt to equity ratio, and t = marginal tax rate •earlier, was disneys beta a levered or unlettered beta? levered
2 paths to estimating sovereign default spreads if we didn't have credit ratings or didn't trust Moodys
1. sovereign dollar or euro denominated bonds: the difference between the interest rate on a sovereign US $ bond, issued by the country, and the US treasury bond rate can be used as the default spread; ex: in November 2013, the 10-year Brazil US $ bond, denominated in US dollars (facing US inflation) had a yield of 4.25% and the US 10-year T.Bond rate traded at 2.75% (only difference between these two bonds is the credit spread); default/credit spread = 4.25% - 2.75% = 1.50% 2. average spread: If you know the sovereign rating for a country, you can estimate the default spread based on the rating; in November 2013, Brazil's rating was Baa2, yielding a default spread of 2% **the t bond rate of 2.75% and the default spread of 2% is given from stats
is beta an adequate measure of risk for a private firm? Beta measures the risk added on to a diversified portfolio. The owners of most private firms are not diversified. Therefore, using beta to arrive at a cost of equity for a private firm will: a.) Under estimate the cost of equity for the private firm b.) Over estimate the cost of equity for the private firm c.) Could under or over estimate the cost of equity for the private firm
a.) Under estimate the cost of equity for the private firm - because if the equity holder in the private company is not well diversified, he/she is bearing total risk (includes idiosyncratic risk and systematic)
Assume now that you are the CFO of Disney. The head of the movie business has come to you with a new big budget movie that he would like you to fund. He claims that his analysis of the movie indicates that it will generate a return on equity of 9.5%. Would you fund it? a.) Yes. It is higher than the cost of equity for Disney as a company b.) No. It is lower than the cost of equity for the movie business. c.) What are the broader implications of your choice?
b.) No. It is lower than the cost of equity for the movie business. •9.5% is higher than the cost of equity for disney operations (8.52%) BUT its less than the cost of equity for studio entertainment (9.92%)
equity risk premium formula
base premium for mature equity market + country premium (if any for a specific market)
pure play company
company that derives 100% or nearly 100% from its single segment
firm value formula
market cap + total debt
what happens to the standard error and r squared when an index is broadened
the standard error gets larger and the r squared gets lower
gross D/E formula
total debt / market cap
business unlevered beta/division level beta formula
unlevered beta / (1 - cash/ firm value) •takes out median cash/firm value - takes out cash
real risk free rate
•.5% •use the ten year inflation indexed treasury bond (TIPS) rate of .5% as the risk free rate for any computations done in real terms
Euro risk free rate
•1.75% - risk free rate for euro-based computations •looked at the ten year euro-denominated government bonds and noted that at least 12 different European governments have such bonds outstanding, with wide differences in rates •since the only reason for differences is default risk (since they are denominated in the same currency) you use the lowest of these rates: the German 10 year bond rate of 1.75%
Brazilian risk free rate
•10.18% - risk free rate for R$ computation •in Brazilian R$ •the 10 year Brazilian real (R$) denominated government rate was 12.18% - subtracting out the default spread of 2% estimated for Brazil, based on its sovereign rate of Baa2, yields a risk free rate of 10.18%
US risk free rate
•2.75% - risk free rate in any dollar-based computation •the ten year US treasury bond rate is 2.75%
Chinese risk free rate
•3.50% - risk free rate for yuan •yuan •the Chinese 10 year government bond rate, denominated in yuan, was 4.30% - subtracting out a default spread of .80% based on chinas sovereign rating of Aa3, yields a risk free rate of 3.50%
Indian risk free rate
•6.57% - risk free rate for rupees •in rupees •estimated by subtracting out the default spread of 2.25% (based on Indias sovereign rating of Baa3) from the Indian government bond rate (in rupees) of 8.82% to arrive at a risk free rate of 6.57%
how managers use this expected return
•CAPM tells managers at Disney it needs to make at least 9.95% as a return for their equity investors to break even; this is the hurdle rate for projects, when the investment is analyzed from an equity standpoint •in other words, Disney's cost of equity (COE) is 9.95% •What is the cost of not delivering this cost of equity? -> if disneys management only earned 7% year after year, we can expect an active takeover market to turnover/discipline management
the bottom line on risk free rates
•IF the government is default free, using a long-term government rate (even on a coupon bond) as the risk free rate on all of the cash flows in a long-term analysis will yield a close approximation of the true value; for short term analysis, it is entirely appropriate to use a short-term government security as the risk free rate •the risk free rate that you use in an analysis should be in the SAME CURRENCY that your cash flows are estimated in -in other words, if your cash flows are in US dollars, your risk free rate has to be in US dollars as well; if your cashflows are in euros, your risk free rate should be a euro risk free rate - do this because inflation rates differ everywhere •the conventional practice of estimating risk free rates is to use the government bond rate, with the government being the one that is in control of issuing that currency; in nov 2013, for instance, the rate on a ten year US treasury bond (yield of 2.75%) is used as the risk free rate in US dollars •if you have cash flows in US dollars you're going to want a long term US treasury bond to serve as the risk free rate when you're pricing equity because equity is long term
a composite way of estimating ERP for countries
•Step 1: estimate an equity risk premium for a mature market; if your preference is for a forward looking, updated number, you can estimate an implied equity risk premium for the US (assuming that you buy into the contention that it is a mature market) -my estimate: In November 2013, my estimate for the implied premium in the US was 5.5%; that will also be my estimate for a mature market ERP •Step 2: come up with a generic and measurable definition of a mature market -my estimate: any AAA rated country is mature •Step 3: estimate the additional risk premium that you will charge for markets that are not mature; you have two choices: 1. the default spread for the country, estimated based either on sovereign ratings or the CDS market 2. a scaled up default spread, where you adjust the default spread upwards for the additional risk in equity markets
bottom up betas and costs of equity: Tata motors and Baidu
•Tata Motors: We estimated an unlevered beta of 0.8601 across 76 publicly traded automotive companies (globally) and estimated a levered beta based on Tata Motor's D/E ratio of 41.41% and a marginal tax rate of 32.45% for India: -Levered Beta for Tata Motors = 0.8601 (1 + (1-.3245) (.4141)) = 1.1007 -Cost of equity for Tata Motors (Rs) = 6.57% + 1.1007 (7.19%) = 14.49% •Baidu: To estimate its beta, we looked at 42 global companies that derive all or most of their revenues from online advertising and estimated an unlevered beta of 1.30 for the business. Incorporating Baidu's current market debt to equity ratio of 5.23% and the marginal tax rate for China of 25%, we estimate Baidu's current levered beta to be 1.3560 -Levered Beta for Baidu = 1.30 (1 + (1-.25) (.0523)) = 1.356 -Cost of Equity for Baidu (Renmimbi) = 3.50% + 1.356 (6.94%) = 12.91%
regression
•a statistical method used in finance, investing, and other disciplines that attempts to determine the strength and character of the relationship between one dependent variable (usually denoted by Y) and a series of other variables (known as independent variables) •helps investment and financial managers to value assets and understand the relationships between variables, such as commodity prices and the stocks of businesses dealing in those commodities •the capital asset pricing model (CAPM) is an often-used regression model in finance for pricing assets and discovering costs of capital •regression is often used to determine how many specific factors such as the price of a commodity, interest rates, particular industries, or sectors influence the price movement of an asset. The aforementioned CAPM is based on regression, and it is utilized to project the expected returns for stocks and to generate costs of capital. A stock's returns are regressed against the returns of a broader index, such as the S&P 500, to generate a beta for the particular stock. •beta is the stock's risk in relation to the market or index and is reflected as the slope in the CAPM model. The return for the stock in question would be the dependent variable Y, while the independent variable X would be the market risk premium. •additional variables such as the market capitalization of a stock, valuation ratios, and recent returns can be added to the CAPM model to get better estimates for returns. These additional factors are known as the Fama-French factors, named after the professors who developed the multiple linear regression model to better explain asset returns
make adjustment for underestimating the cost of equity: total risk vs. market risk
•adjust beta to reflect total risk rather than market risk; this adjustment is relatively simple, since the regression R squared measures the proportion of the risk that is the market risk -total beta = market beta / correlation of the sector with the market •in the bookscape example, where the market beta is 0.8558 and the median R squared of the comparable publicly traded firms is 26% and the correlation with the market is 50.99% (roughly 51% idiosyncratic risk that's not being captured by the market return) -market beta / square root of R squared = 0.8558 / .5099 = 1.6783 <- measure of total risk -total cost of equity = 2.75 + 1.6783 (5.5%) = 11.98%
what if there is no default free entity? risk free rates in nov 2013
•adjust the local currency government borrowing rate for default risk to get a riskless local currency rate -in nov 2013. the Indian gov rupee bond rate was 8.82% (hurdle rate - has both credit spread and risk free benchmark), the local currency rating from Moodys was Baa3 (barely investment grade - a lot of credit risk) and the default spread for a Baa3 rated country bond was 2.25% (reasonable estimate of credit risk in the Indian government b/c that's the credit rate they have); risk free rate in rupees = 8.82% - 2.25% = 6.57% (suggests quite a bit of inflation in the rupees) -in nov 2013, the Chinese renmimbi government bond rate was 4.30% (less credit risk and inflation than rupee) and the local currency rating was Aa3, with a default spread of 0.8% (credit risk); risk free rate in Chinese renmimbi = 4.30% - 0.8% = 3.5% •Baa3 is the lowest investment grade credit rating •the analysis in an alternate currency, where getting the risk free rate is easier. with vale in 2013, we could choose to do the analysis in US dollars (rather than estimate a risk free rate in R$); the risk free rate is then the US treasury bond rate •do your analysis in real terms, in which case the risk free rate has to be a real risk free rate; the inflation-indexed treasury rate is a measure of a real risk free rate
sovereign credit rating
•an independent assessment of the creditworthiness of a country or sovereign entity •can give investors insights into the level of risk associated with investing in the debt of a particular country, including any political risk
sovereign credit rating
•an independent assessment of the creditworthiness of a country or sovereign entity •investors use sovereign credit ratings as a way to assess the riskiness of a particular country's bonds •represents the likelihood that a government might be unable—or unwilling—to meet its debt obligations in the future •several key factors come into play in deciding how risky it might be to invest in a particular country or region: debt service ratio, growth in its domestic money supply, its import ratio, and the variance of its export revenue •Standard & Poor's gives a BBB- or higher rating to countries it considers investment grade, and grades of BB+ or lower are deemed to be speculative or "junk" grade •Moody's considers a Baa3 or higher rating to be of investment grade, and a rating of Ba1 and below is speculative •obtain rating to attract foreign direct investments
what is your risk premium?
•assume that stocks are the only risky assets and that you are offered two investment options: 1. a riskless investment (say a Government Security), on which you can make 3% 2. a mutual fund of all stocks, on which the returns are uncertain •How much of an expected return would you demand to shift your money from the riskless asset to the mutual fund? most common answer: d. Between 7% -9% where risk premium is between 4-6% •risk averse agent: between 3% and over 11%
disneys operating leverage: 1987-2013
•average across entertainment companies: 1.35 •1987-2013: % change in sales = 11.79%; % change in EBIT = 11.91%; operating leverage = 11.91/11.79 = 1.01 •1996-2013 (when disney acquired capital cities): % change in sales = 8.16%; % change in EBIT = 10.20%; operating leverage = 10.20/8.16 = 1.25 •given disneys operating leverage measures (1.01 or 1.25), would you expect disney to have a higher or a lower beta than other entertainment companies?
if you did analysis on every stock listed on an exchange, what would the average Jensens alpha be across all stocks? a. Depend upon whether the market went up or down during the period b. Should be zero c. Should be greater than zero, because stocks tend to go up more often than down
•b. should be zero •some stocks are going to outperform and some stocks are going to underperform
estimating Bookscape levered beta and cost of equity (p. 82)
•because the debt/equity ratios used in computing levered betas are market debt equity ratios, and the only debt equity ratio we can compute for Bookscape is a book value debt equity ratio, we have assumed that Bookscape is close to the book industry median market debt to equity ratio of 24.41% •using marginal tax rate of 40% for Bookscape, we get a levered beta of = 0.7584 [1 + (1 - .40)(.2141)] = 0.8558 •using a risk free rate of 2.75% (US treasury bond rate) and an equity risk premium of 5.5%, the cost of equity = 2.75% + 0.8558 (5.5%) = 7.46% -> b/c capm makes assumption that its only the systematic risk that gets price this is too low of a risk that's actually being born by a marginal investor in a private company
beta: exploring fundamentals
•beta > 2: bulgari = 2.45 -> luxury goods, very good at showing market behavior •beta between 1 and 2: qwest communications = 1.85, Microsoft = 1.25, GE = 1.15 -> less discretionary, buy toilet paper all the time •beta < 1: exxon mobil = 0.70, Altria (philip Morris) = 0.60 -> truly not discretionary products, cogarettes (smoker or not- largely insensitive to price of cigs) •beta < 0: harmony gold mining = -0.15 -> negatively correlated with the market
as a potential investor in Disney, what does this expected return of 9.95% tell you? a. this is the return that I can expect to make in the long term on Disney, if the stock is correctly priced and the CAPM is the right model for risk, b. this is the return that I need to make on Disney in the long term to break even on my investment in the stock c. both assume now that you are an active investor and that your research suggests that an investment in Disney will yield 12.5% a year for the next 5 years. Based upon the expected return of 9.95%, would you buy the stock or sell the stock?
•both •CAPM tells us required returns and is also our expectation if the stock is correctly priced
disneys businesses: the financial breakdown
•businesses •revenues •operating income •Depreciation & Amortization •EBITDA •Selling, General, & Administrative costs •cap ex •identifiable assets (accountants attempt to measure collateral value)
disney cap cities beta estimation step 1
•calculate the unlevered betas for both firms -disney's unlevered beta = 1.15/(1+0.64*0.10) = 1.08 -cap cities unlevered beta = 0.95/(1+0.64*0.03) = 0.93 •calculate the unlevered beta for the combined firm -unlevered Beta for combined firm = 1.08 (34286/53401) + 0.93 (19115/53401)= 1.026 -the weights used are the firm values (and not just the equity values) of the two firms, since these are unlevered betas and thus reflects the risks of the entire businesses (not just the equity)
when the government is default/credit risk free: risk free rates in nov 2013
•countries that got AAA credit ratings: Japanese Yen, Swiss Franc, Euro (German gov), danish krone, Singapore $, Swedish Krona, US $, Canadian $, Norwegian krone, Australian $ •if all are AAA governments/ sovereigns, there's no credit risk •why they pay different % on their debt: the inflation on the currency -higher inflation, higher risk free rate
why do people have a higher rate on 10 year euro government bonds than others?
•credit risk causes this •inflation is the same because same currency •Greece (the higher risk free rate- 8.30%) does not default on its debt as frequently as Germany (the lower risk free rate- 1.75%) - they still both default though •the risk free rate in euros is the 1.75% - lowest AND issued by a government that has a AAA credit rating by Moodys and S&P (not all are AAA) -still 1.75% for Austria (2.10%) and France (2.15%) etc due to credit spread •**if you needed to know the credit spread, the credit risk premium the market is charging Greece: 8.3% - 1.75% •the reason Greece is paying 8.30% is because of credit risk
setting up for the estimation of regression model
•decide on an estimation period -services use periods ranging from 2 to 5 years for the regression (teacher says 10 years, best way to decrease standard error is to increase sample size- but if company changes a lot then data is less relevant) -longer estimation period provides more data, but firms change -shorter periods can be affected more easily by significant firm-specific event that occurred during the period •decide on a return interval - daily, weekly, monthly (teacher says weekly, if its high volume trade use daily, if not traded a lot use monthly) -shorter intervals yield more observations, but suffer from more noise -noise is created by stocks not trading and biases all betas towards one •estimate returns (including dividends) on stock -return = (Price at end - price at beginning + dividends at period)/price at beginning -included dividends only in ex-dividend month (so you don't underestimate returns) •choose a market index, and estimate returns (inclusive of dividends) on the index for each interval for the period
risk free rate in practice
•difficult to get government bonds issued by a risk free government with zero coupons - because interest rates change over time, what you really need to do is maturity match your cash flows •the risk free rate is the rate on a zero-coupon default-free bond matching the time horizon of the cash flow being analyzed •theoretically, this translates into using different risk free rates for each cash flow - the 1 year coupon rate for the cash flow in year 1, the 2-year zero coupon rate for the cash flow in year 2.. •want zero coupon bond for 1 year duration to serve as the risk free rate for the first cash flow of project; then, want to look back at the government bond yield curve, find the zero coupon risk free rate for the 2 year note, and use that government rate as the risk free rate for the 2nd cash flow of project - but not practically going to do this •practically speaking, if there is a substantial uncertainty about expected cash flows, the present value effect of using time varying risk free rates is small enough that it may not be worth it - focus on finding a default risk free issuer (likely gov) then try to maturity match (if we have a long term project we want a long term gov bond), not require/worry about it to be zero coupon
the disney/cap cities merger (1996): pre-merger
•disney: the acquirer -equity beta: 1.15 -debt = $3186 mil -market value of equity = $31,100 mil -debt + equity = firm value = $31,100 + $3186 = $34,286 mil -D/E ratio = 3186/31100 = .10 + •capital cities: the target -equity beta: 0.95 -debt = $615 mil -market value of equity = $18,500 + $615 = $19,115 mil -D/E ratio = 615/18500 = 0.03 •need to know what the plans are for the capital structure of the merged firm: strip away levered to get to an unlevered beta and then strip away leverage from the target using the homoda equation to get an estimated asset beta/unlevered beta for the target - then do weighted average of the asset values to come up with an unlevered beta of the merged firm - then lever up beta of the merged firm, depending not on the pre-merger lever of the bidder or the target but the post merger leverage of the merged firm
disneys unlevered beta: operations and entire company
•do a weighted average of business unlevered betas/asset betas based on the relative size of these divisions inside disney - then reapply Hamada equation •estimating market/enterprise value of each of the divisions: reported revenues * median EV/sales ratio -> get for all divisions to come up with the proportion of total value inside disney that is not driven exclusively by revenues, but is driven by value -> do this because some sales are more valuable than others •beta of Disney = beta of operating assets (Value of operating assets / (value of operating assets + value of cash)) + beta of cash (value of cash (value of operating assets + value of cash)) •= 0.9239(135,132/ 135,132 + 3,931) + 0.0(3,931/ 135,132 + 3,931) = 0.8978
disney has a positive Jensens alpha of 9.02% a year between 2008 and 2013 (incredible performance). this can be viewed as a sign that management in the firm did a good job managing the firm during the period
•does entire managerial team deserve a giant bonus? maybe, maybe not •before giving credit to management, you want to estimate Jensens alpha for entire entertainment sector because its possible that the market is overvaluing entertainment - if they all have high alpha, its not that management did really well, its just that there is a pricing bubble - but if not then management has done a good job
firm betas versus divisional betas
•firm betas are weighted averages: the beta of a firm is the weighted average of the betas of its individual projects •firm betas and business betas: at a broader level of aggregation, the beta of a firm is the weighted average of the betas of its individual division •can't go right to divisional because they aren't publicly traded
Deutsche Bank and Baidu: Index Effects on Risk Parameters
•for Deutsche Bank, a widely held European stock, we tried both the DAX (German index) and the FTSE European index -the standard error is lower and the r squared for the DAX is higher than in FTSE because it is included in the DAX -the high r squared is more indicative of the narrowness of the index rather than the quality of the regression •for Baidu, a NASDAQ listed stock b/c the company does not have a local listing in china, we ran regressions against both the S&P 500 and the NASDAQ - emphasize S&P 500 because it is more diversified
the easy route: outsourcing the measurement of default risk
•for those firms that have bond rating from global rating agencies, use those ratings •if you want to estimate vale's cost of debt in $R terms, we can again use the differential inflation approach we used for the cost of equity: -cost of debt of R$ = (1 + cost of debt of US$) ((1 + expected inflation of R$) / (1 + expected inflation of US$)) - 1 = 1.0405 ((109)/(102)) - 1 = 11.19%
what is debt?
•generally has the following characteristics: -commitment to make fixed payments in the future -the fixed payments are tax deductible -failure to make the payments can lead to either default or loss of control for the firm to the party to whom payments are due •as a consequence, debt should include: -any interest-bearing liability, whether short term or long term -any lease obligation, whether operating or capital
what about historical premiums for other markets?
•historical data for markets outside the United States is available for much shorter time periods; the problem is even greater in emerging markets •the historical premiums that emerge from this data reflects this data problem and there is much greater error associated with the estimates of the premiums •want to see if the market outside the US is developed or emerging; if the market is developed, there is no reason ; if Moodys rates it the same as US, assume they have the same credit quality and market risk premium •any sovereign with AAA: developed market
disneys cap cities beta estimation: step 2
•if Disney had used all equity (100%) to buy Cap Cities equity, while assuming Cap Cities debt, the consolidated numbers would have looked as follows: -debt = $ 3,186+ $615 = $ 3,801 million -equity = $ 31,100 + $18,500 = $ 49,600 m (Disney issues/raises $18.5 billion in equity in order to complete the transaction) -D/E Ratio = 3,801/49600 = 7.66% -new Beta = 1.026 (1 + 0.64 (.0766)) = 1.08 •since Disney borrowed $ 10 billion to buy Cap Cities/ABC, funded the rest with new equity and assumed Cap Cities debt: -the market value of Cap Cities equity is $18.5 billion. If $ 10 billion comes from debt, the balance ($8.5 billion) has to come from new equity -debt = $ 3,186 + $615 million + $ 10,000 = $ 13,801 million -equity = $ 31,100 + $8,500 = $39,600 million-D/E Ratio = 13,801/39600 = 34.82% -new Beta = 1.026 (1 + 0.64 (.3482)) = 1.25
when estimating equity risk premiums, choose:
•if predictive power is critical or market neutrality is a prerequisite, use the current implied equity risk premium •if you are skeptical about markets, choices are broader, but usually choose average implied equity risk premium over a long period of time having the strongest predictive power •historical risks are poor predictors of both short term movements in implied premiums or long term returns on stocks
estimating the cost of debt
•if the firm has bonds outstanding, and the bonds are traded, the yield to maturity on a long-term, straight (no special features) bond can be used as the interest rate •if the firm is rated, use the rating a a typical default spread on bonds with that rating to estimate the cost of debt •if the firm is not rated: -and it has recently borrowed long term from a bank, use the interest rate on the borrowing OR -estimate a synthetic rating for the company, and use the synthetic rating to arrive at a default spread and a cost of debt •the cost of debt has to be estimated in the same currency as the cost of equity and the cash flows in the valuation
risk aversion and risk premiums
•if this were the entire market, the risk premium would be a weighted average of the risk premiums demanded by each and every investor •the weights will be determined by the wealth that each investor brings to the market; thus, Warren Buffett's risk aversion counts more towards determining the "equilibrium" premium than yours or mine •as investors become more risk averse, you would expect the "equilibrium" premium to increase
ERP: a historical snapshot
•if you are going to use a historical risk premium, make it: -long term (because of the standard error): use the longest range of years, use t bonds as benchmark -consistent with your riskfree rate -a "compounded" average: use the geometric average (good years are more likely to be followed by poor years, and vice versa) over the arithmetic average (measures the simple mean of the series of annual returns) •no matter which estimate you use, recognize that it is backward looking, noisy & may reflect selection bias
one solution for emerging markets if Moodys does not rate it AAA: bond default spreads as CRP in nov 2013
•in November 2013, the historical risk premium for the US was 4.20% (geometric average, stocks over T.Bonds, 1928-2012) •using the default spread on the sovereign bond or based upon the sovereign rating and adding that spread to the mature market premium (4.20% for the US) gives you a total ERP for a country •use US risk premium for all AAA ratings, then just add country risk premium •if you prefer credit default swap spread: the higher the prob of default, the more expensive the CDS contract •Moodys sovereign policy: no issuer of debt inside a country can have a credit rating higher than the sovereign government
estimating expected returns for disney in November 2013
•inputs to the expected return calculation -Disney's Beta = 1.25 -riskfree Rate = 2.75% (U.S. ten-year T.Bond rate in November 2013) -risk Premium = 5.76% (Based on Disney's operating exposure) •Expected Return = Riskfree Rate + Beta (Risk Premium) = 2.75% + 1.25 (5.76%) = 9.95% (CAPM says disney has to return 9.95%)
measures of operating leverage
•inside the company: fixed cost measure = fixed costs / variable costs -this measures the relationship between fixed and variable costs; the higher the proportion, the higher the operating leverage •outside the company: EBIT variability measure = % change in EBIT / % change in revenues -this measures how quickly the earnings before interest and taxes changes as revenue changes - the higher this #, the greater the operating leverage -when your revenues double, your cost doubles, and your EBIT stays pretty stable -100% fixed costs, when your revenues double, your costs stay constant and your EBIT doubles
analyzing disneys performance
•intercept = 0.712% -this is an intercept based on monthly returns. Thus, it has to be compared to a monthly riskfree rate -between 2008 and 2013: --average Annualized T.Bill rate = 0.50% --monthly Riskfree Rate = 0.5%/12 = 0.042% --riskfree Rate (1-Beta) = 0.042% (1-1.252) = -.0105% •the comparison is then between -intercept versus Riskfree Rate (1 - Beta) -0.712% versus 0.0105% -jensen's Alpha = 0.712% - (-0.0105)% = 0.723% •disney did 0.723% better than expected, when expectations are based on CAPM, on a monthly basis between October 2008 and September 2013 -annualized, Disney's annual excess return = (1 + monthly excess return)^12 - 1 = (1.00723)^12 - 1= 9.02% (earned 9% more than the CAPM said it had to)
the dirty secret of "standard error"
•many firms have much higher standard error is beta estimate than .10 •most standard errors are closer to .3 -> have to add and subtract .6 from point estimate •because of standard errors, beta coefficients really aren't that reliable
enterprise value (EV) formula
•market cap + debt - cash •market value of the enterprise •market value of the assets that are actually invested in productive assets •cash is not invested in productive assets
bottom line on equity risk premiums in nov 2013
•mature markets: in November 2013, the number that we chose to use as the equity risk premium for all mature markets was 5.5%; this was set equal to the implied premium at that point in time and it was much higher than the historical risk premium of 4.20% prevailing then (1928-2012 period) •for emerging markets, we will use the melded default spread approach (where default spreads are scaled up to reflect additional equity risk) to come up with the additional risk premium that we will add to the mature market premium; thus, markets in countries with lower sovereign ratings will have higher risk premiums that 5.5% -emerging market ERP = 5.5% + country default spread * (standard dev of equity / standard dev of country bond)
jensen's alpha
•measures investment performance as the raw portfolio return less the return predicted by the capital asset pricing model •the difference between the intercept and Rf (1 - β) •if it is positive, your stock did perform better than expected during the period of regression
page 71: backing into a pure play beta: studio entertainment
•movie business value = 97.04, beta = 1.0993; debt value = 21.3, debt beta = 0 (its not riskless, but it is idiosyncratic/firm specific) •cash business value = 2.96, beta = 0 (cash is riskless); equity value = 78.7, equity beta = 1.24 •movie company value = 1.0, beta = 1.658 1. Start with the median regression beta (equity beta) of 1.24 (from p. 72) 2. Unlever the beta (Hamada equation), using the median gross D/E ratio of 27.06% -Gross D/E ratio = 21.30/78.70 = 27.06% -Unlevered beta (hamada equation) = 1.24/ (1+ (1-.4) (.2706)) = 1.06683 3. Take out the cash effect, using the median cash/value of 2.96 -(.0296) (0) + (1-.0296) (Beta of movie business) = 1.0668 -> weighted average of cash and assets that are invested in movie production -Beta of movie business = 1.0668/(1-.0296) = 1.0993 •teacher recommends against: making assumption that corporate debt has the same risk as cash and making the assumption that cash and debt have the same tax consequences: you could have used the net debt to equity ratio -Net D/E ratio = (21.30-2.96)/78.70 = 23.30% -Unlevered beta for movies = 1.24/ (1+(1-.4)(.233)) = 1.0879
the risk free rate and time horizon
•on a risk free asset, the actual return is equal to the expected return; therefore, there is no variance around the expected return •for an investment to be risk free, ie to have an actual return be equal to expected return, two conditions have to be met: 1. there has to be *no default risk*, which generally implies that the security has to be issued by the government; note however that not all governments can be viewed as default free 2. there can be no uncertainty about reinvestment rates (be free from), which implies that it is a zero coupon security with the same maturity as the cash flow being analyzed •we want government bonds issued by a risk free government with zero coupons
choosing the parameters: disney
•period used: 5 years •return Interval = monthly •market Index: S&P 500 Index •for instance, to calculate returns on Disney in December 2009, -price for Disney at end of November 2009 = $ 30.22 -price for Disney at end of December 2009 = $ 32.25 -dividends during month = $0.35 (It was an ex-dividend month) -return =($32.25 - $30.22 + $ 0.35)/$30.22= 7.88% •to estimate returns on the index in the same month (low because coming out of recession) -index level at end of November 2009 = 1095.63 -index level at end of December 2009 = 1115.10 -dividends on index in December 2009 = 1.683 -return =(1115.1 - 1095.63+1.683)/ 1095.63 = 1.78% •Disneys historical beta: return on disney = .0071 + 1.2517 return on market (.10 : standard error of beta coefficient, tells us how much confidence we have in beta coefficient to measure confidence interval) - put in excel; r^2 (what percentage of the total risk/movement of disney stock is explained by the movement on the market) = 0.73386 (quite high - 73.4% of the movement in disney stock can be explained by movement in the S&P 500 - disney stock (73.4%) is largely systematic risk -beta is likely greater than 1 (the 1.25 in equation) because when the market earns, disney earns more and when the market loses, disney loses more -the alpha is .0071 - when the market is flat (has a 0% return) we expect disney to earn 71 basis points (1/100th of a percent)
test for determining beta
•phone service is close to being non-discretionary in the United States and Western Europe. however, in much of Asia and Latin America, there are large segments of the population for which phone service is a luxury •given our discussion of discretionary and non-discretionary products, which of the following conclusions would you be willing to draw: -emerging market telecom companies should have higher betas than developed market telecom companies -developed market telecom companies should have higher betas than emerging market telecom companies -the two groups of companies should have similar betas
Go back to the previous example. Assume now that you are making the same choice but that you are making it in the aftermath of a stock market crash (it has dropped 25% in the last month). Would you change your answer? a. I would demand a larger premium b. I would demand a smaller premium c. I would demand the same premium
•professors answer: I would demand a smaller premium - stocks are on sale so more likely to buy •most would prefer larger premium because the uncertainty after a stock market crash is elevated
breaking down disneys risk
•r squared = 73% •this implies that: 73% of the risk at disney comes from market sources (systematic) and 27% therefore comes from firm-specific sources (idiosyncratic- could be diversified away) •the firm specific risk if diversifiable and will not be rewarded •the r squared for companies, globally, has increased significantly since 2008. why might this happen? •what are the implications for investors?
estimating disneys beta
•slope of the regression of 1.25 is the beta •regression parameters are always estimated with error; the error is captured in the standard error of the beta estimate, which in the case of disney is 0.10 •assume that I asked you what disneys true beta is, after this regression -what is your best point estimate? -> slope of regression of 1.25 is beta -what range would you give me, with 67% confidence? -> can say with 67% confidence that the beta is somewhere between 1.15 and 1.35; but will you do it with only 65% confidence? -what range would you give me, with 95% confidence? -> the beta is somewhere between 1.05 and 1.45 (add and subtract twice the standard error); not comforting because very different numbers
hamada equation
•strips away financial leverage •method of analyzing a firm's cost of capital as it uses additional financial leverage, and how that relates to the overall riskiness of the firm. •the higher the Hamada equation beta coefficient, the higher the risk associated with the firm βL = βU [1 + (1−T) (D / E)] where: βL = Levered beta, βU = Unlevered beta*, T = Tax rate, D/E = Debt to equity ratio* •unlevered beta is the market risk of a company without the impact of debt •debt-to-equity ratio is a measure of a company's financial leverage
estimating risk premiums in practice
•survey investors on their desired risk premiums and use the average premium from these surveys •assume that the actual premium delivered over long time periods is equal to the expected premium - i.e., use historical data -downside: requires a lot of data •estimate the implied premium in today's asset prices
the survey approach
•surveying all investors in a market place is impractical; however, you can survey a few individuals and use these results •the limitations of this approach are: -there are no constraints on reasonability (the survey could produce negative risk premiums or risk premiums of 50%) -the survey results are more reflective of the past than the future -they tend to be short term; even the longest surveys do not go beyond one year
beta estimation: using bloomburg
•the beta and Standard dev are what we got before •the alpha coefficient gets biased downwards because Bloomberg does not consider dividends •uses an adjusted beta = raw beta (.67) + 1 (.33)
betas are weighted averages
•the beta of a portfolio is always the market value weighted average of the betas of the individual investments in that portfolio •if you have both a publicly traded bidder and a publicly traded target, then your estimated beta coefficient for the merged firm is simply a function of the relative size; if they are the same size, then the forecasted beta for the merged firm is simply the average of the two •thus, -the beta of a mutual fund is the weighted average of the betas of the stocks and other investment in that portfolio -the beta of a firm after a merger is the market value weighted average of the betas of the companies involved in the merger
estimating betas for non-traded assets
•the conventional approaches of estimating betas from regressions do not work for assets that are not traded. there are no stock prices or historical returns that can be used to compute regression betas •two ways in which betas can be estimated for non-traded assets: 1. using comparable firms - bottom up beta ; recommended 2. using accounting earnings
from cost of equity to cost of capital
•the cost of capital is a composite cost to the firm of raising financing to fund its projects •in addition to equity, firms can raise capital from debt
the historical premium approach
•the default approach used by most to arrive at the premium to use in the model •in most cases, this approach does the following: 1. defines a time period for the estimation (1928-Present, last 50 years...) 2. calculates average returns on a stock index during the period 3. calculates average returns on a riskless security over the period 4. calculates the difference between the two averages and uses it as a premium looking forward •limitations of this approach are: -it assumes that the risk aversion of investors has not changed in a systematic way across time (the risk aversion may change from year to year, but it reverts back to historical averages) -it assumes that the riskiness of the "risky" portfolio (stock index) has not changed in a systematic way across time
estimating performance
•the intercept (α) of the regression provides a simple measure of performance during the period of the regression, relative to the capital asset pricing model •CAPM (what the stock is supposed to do): Rj = Rf + β (Rm - Rf); = Rf (1-β) + β Rm (change format so it can compare to the regression) •regression equation (what the stock actually did): Rj = α + β Rm •if α > Rf (1 - β) the stock did better than expected during regression period •if α = Rf (1 - β) the stock did as well as expected during regression period •if α < Rf (1 - β) the stock did worse than expected during regression period
effects of leverage on betas: disney
•the regression beta for disney is 1.25 (based on monthly stock returns over a 5 year period starting in 2008); this beta is a levered beta (because it is based on stock prices, which reflect leverage) and the leverage implicit in the beta estimate is the average MARKET debt equity ratio during the period of regression (2008 - 2013) •the average debt equity ratio during this period was 19.44% •the unlevered beta for disney can then be estimated (using a marginal tax rate of 36.1%) - current beta / (1 + (1 - tax rate)(average debt-equity)) -> = 1.25 / (1 + (1 - 0.361)(1.1944)) = 1.1119: if disney were more conservatively financed, without any debt in its capital structure, its beta would be closer to 1.11 than 1.25 •the COE is sensitive, but not linear( because the benchmark/risk free rate is not changing): -with debt = 2.75% + 1.25 (5.7%) = 9.875% -without debt = 2.75% + 1.11 (5.7%) = 9.007%
measurement of the risk premium
•the risk premium is the premium that investors demand for investing in an average risk investment, relative to the riskfree rate •as a general proposition, this premium should be: -greater than 0 -increase with the risk aversion of the investors in that market -increase with the riskiness of the "average" risk investment
estimating beta
•the standard procedure for estimating betas is to regress stock returns (Rj) against market returns (Rm): Rj = α + β Rm where Rj is a time series of historical stock returns over a historical stock period for stock j, α is the intercept (the point at which the return on stock j crosses the axis for the return on stock m) and β is the slope of the regression (slope of the line that fits the stock returns to the market returns), and Rm is a vector of historical returns to the stock market •going to need a proxy (S&P 500, Dax, vespa) for the overall market because the true market portfolio is a valuated portfolio with exposure to every conceivable risky investment (not just every stock in Us and planet, but also all the corporate bonds and real estate, commodities markets) so its just not tractable to try to estimate the return on the true market portfolio •contemporaneous vector: over the same time period; say we choose Rj to be monthly, then Rm has to be monthly too - have to be measured over the same time period •Rj and Rm are the INPUTS, α + β are the OUTPUTS •the slope of the regression corresponds to the beta of the stock, and measures the riskiness of the stock -if the market goes up by 1 unit and the return on the stock goes up by more than 1 unit, then you have a steeper slope than if they went up the same •the R squared of the regression provides an estimate of the proportion of the risk (variance) of a firm that can be attributed to market risk; the balance (1 - R squared) can be attributed to firm specific risk -the fit of the model -tells you what percentage of the overall movement/volatility of returns to stock j is explained by returns to the market OR what proportion of the total risk of Rj is systematic (the market risk that can't be diversified away) -if the R squared is very high, the risk in Rj is mostly systematic risk and cannot be diversified -if R squared is 55% then we say 55% of the variation of stock j is being explained in the variation of the market or systematic risk - 45% of stock j is not systematic and can be diversified away
bottom up vs. top down beta
•the top down beta for a firm comes from a regression •the bottom up beta can be estimated by doing the following: -find out the businesses/divisions that a firm operates in -find the unlevered betas of other firms in these businesses -take a weighted (by sales or operating income) average of these unlevered betas -lever up using the firms debt/equity ratio •the bottom up beta is a better estimate than the top down beta because: -the standard error of the beta estimate will be much lower -the betas can reflect the current (and even expected future) asset mix of businesses that the firm is in rather than the historical mix -do this at divisional level: division level beta coefficients, which will translate into division level cost of equity which will translate into division level hurdle rates rather than using 1 hurdle rate across all divisions
estimating bottom up betas and cost of equity: vale
•to convert a discount rate in one currency to another, all you need are expected inflation rates in the two currencies = (1 + $cost of equity) ((1 + inflation rate of Brazil) / (1 + inflation rate of US)) - 1 •from US$ to R$: if we use 2% as the inflation rate in US dollars and 9% as the inflation ratio in Brazil, we can convert vale's US dollar cost of equity of 11.23% to a $R cost of equity: - cost of equity of nominal R$ = (1 + cost of equity of US$) ((1 + expected inflation of R$) / (1 + expected inflation of US$) - 1 - = 1.1123 (1.09/1.02) - 1 = 18.87% •alternatively, you can compute a cost of equity, starting with the $R risk free rate of 10.18% - cost of equity in $R = 10.18% + 1.15 (7.38%) = 18.67%
the levered beta: disney and its divisions (p. 75)
•to estimate the debt ratios for division, we allocate disneys total debt ($15,961 million) to its divisions based on identifiable assets •we use the allocated debt to compute D/E ratios and levered betas
what type of yield curve do government/treasury bonds have?
•upward sloping •even though we view the government as being risk free, the US gov has to pay higher yields on 10 year bonds than 5 year notes and it has to pay higher yields on 5 year notes than on 30 day t-bills - the reason is the risk free rate compensates the investor for delayed consumption and for lost purchasing power - the longer the duration of the bond the more you have to compensate for delayed consumption, similarly you have to compensate the investor for lost purchasing power because the longer you wait the higher the effect on the inflation rate
regression diagnostics for tata motors
•uses Sensex index (alternative index based on Indian companies) •based on high inflation currency •monthly •beta = 1.83; 67% range; 1.67-1.99 •69% market risk •31% firm specific •Jensen's alpha= 2.28% - 4%/12 (1-1.83) = 2.56% -annualized = (1+.0256)^12 - 1= 35.42% (great but based on high inflation currency - not quite same if it was US) -average monthly riskfree rate (2008-13) = 4% •expected return (in Rupees)= Riskfree Rate+ Beta*Risk premium= 6.57%+ 1.83 (7.19%) = 19.73% •a better beta? -> vale; still monthly returns over 5 years, right side uses S&P 500 and left uses bovespa (index return on Brazilian stocks); the raw data, alpha, correlation, and standard error are very different - which is right? not a math class so no right answer BUT choose index where you believe the marginal investor would invest - if investor is 100% invested in bovespa, then choose that - if marg investor is vanguard, then use S&P 500 - index depends on marginal investor, not necessarily home country
implied ERP in nov 2013
•watch what I pay, not what I say •instead of asking people what they think, we can instead look at what they are willing to pay •does not require historical data or adjustments for country risk but does assume that the overall stock market is correctly priced •if you can observe what investors are willing to pay for stocks, you can back out an expected return from that price and an implied equity risk premium •benefit: forward looking and easy to update
bottom up betas and costs of equity: Deutsche bank
•we break deutche bank down into two businesses - commercial and investment banking •we not not unloved or relever betas, because estimating debt and equity for banks is an exercise in futility. using a risk free rate of 1.75% (euro risk free rate) and deutche's ERP of 6.12%: - commercial banking cost of equity = 1.75% + 1.0665 (6.12%) = 8.28% -investment banking cost of equity = 1.75% + 1.2550 (6.12%) = 9.44$ -deutche bank cost of equity = 1.75% + 1.1516 (6.12%) = 8.80%
beyond the default spread? equities are riskier than bonds
•while default risk spreads and equity risk premiums are highly correlated, one would expect equity spreads to be higher than debt spreads; one approach to scaling up the premium is to look at the relative volatility of equities to bonds and to scale up the default spread to reflect this: country risk premium = country default spread (standard dev of equity / standard dev of country bond) •Brazil: the annualized standard deviation in the Brazilian equity index over the previous year is 21 percent, whereas the annualized standard deviation in the Brazilian C-bond is 14 percent (standard dev of equity market scale it by the government bond): Brazils total risk premium = 4.20% + 2.0% (21%/14%) = 7.20% •using the same approach for China and India: ERP of India = 4.20% + 2.25% (24%/17%) = 7.80%; ERP of china = 4.20% + .80% (18%/10%) = 5.64%
inputs required to use the CAPM
•yields the following expected return: expected return = risk free rate + beta* (expected return on the market portfolio - risk free rate) OR expected return = risk free rate + equity risk premium ERP OR expected return = risk free rate + (beta* MRP) •to use, we need 3 inputs: 1. the current risk free rate 2. the expected market risk premium, the premium expected for investing in risky assets, ie the market portfolio, over the riskless asset 3. the beta (systematic risk) of the asset being analyzed
