Chapter 7-8-9 Principles of Corporate Finance Tenth Edition Ch 7-9 Slides by Matthew Will and Bo...

7-2 Risk and Return Asset pricing: Investors predict future cash flows, and then set the price (today) to get at least an expected required return. (HPR) Stocks. Bonds, etc. whatever... Since there are both buyers and sellers, and everything is voluntary, we expect returns to be = required returns, meaning prices are in equilibrium over time. Risk and Return Investors are risk averse Investors require higher (expected) returns for higher risk, or they pay less for a risky asset compared to a not-so risky, or a risk-free asset.

7-3 Risk and Return The investor looks at the expected (E) return: E(r) = r f + E(risk premium) Asset pricing theories explain how this is done, CAPM, APT etc. Since investors are risk averse they control risk in two steps Diversification in portfolios (Explain how it works) Split their portfolios between a risk free asset and their risky-portfolio (Explain) In the process they find optimal combinations of returns per unit of risk, and the optimum portfolio

7-4 Please forget: All (stupid) stock recomendatuions and trading tips from DI, DN, E24, Affrsvrlden, Privata affrer, etc. Serious investments is about maximizing the return on saving given the risk the investor is willing to take. So, what is risk and return? How should it be measured?

7-5 Look at Historical Returns Holding period Returns A clear pattern between risk and return historically Goods/Inflation Government short-term bonds Corporate bonds Stocks Small firm stocks

7-6 Return and Risk? Historical return Arithemtic mean Geometric mean Expected Future return Arthimetic return (or mean) Scenario return (or mean) Risk? Is the variance (or standard deviation) around the mean. The bigger the variance the bigger the risk

7-7 A little varning If you dont know so much about statistics, people will try to fool you. 2 examples Risk will not go away over time; your stock portfolio does not get less risky over time. Asset returns (and prices) are random variables. Random variables are described by their moments; the mean, the variance, kurtosis, skewness etc. For asset you normally only need the mean and the variance. It is not woorth exploring higher moments (Samuelson 1966) If stock prices jumps now and then, you need more moments. => Predict the jumps by using poission distribution. This is difficult since you dont observe that many jumps historically! Thus, - two moments (mean and variance) are ok to understand how things work and how to invest!

7-8 Measuring Returns Mean, variances (Stand. Deviation), covariances (correlation) Correlation creates the diversification effect Mean can be measured as Arithmetic or geometric mean Mean based on historical values or scenario mean

7-9 Return HPR, for historical analysis/evaluation. Also, think in terms of Expected return: The price today is set on E(P + Div) to give E(r) = expected (required) return.

7-10 Mean Return Artithmetic mean or Geometric mean Rule of thumb: The geometric mean is somewhat better for historical evaluations. The arithmetic mean is somewhat better for predictions.

7-11 Scenario mean The future has a fixed number of possible outcomes (or states), ex 3 outcomes, and each outcome have a probability: Economy goes up (boom = 30% probability) Economy remains the same (no change = 30%) Economy goes down (recession = 40%) Each outcome can begiven a probability, so that all probabilities sum to unity. Set a a return for each scenario outcome, example: Boom r=15%, The same = 5%, Recession = -2%

7-12 Example Scenario Mean E(r) = p 1 *E(r 1 ) + p 2 *E(r 2 ) + p 3 *E(r 3 ) = 0.3*0.15 + 0.3*0.05 + 0.4*(-0.02) = 0.052 or 5.2% When do we use this? When the future is not like the past. And, write down expectations about the future, in trems if risk, as well. Example, I predict that next quarters GDP growt is 4.5%, but what do I think about up and down and the risk of my estimate?

7-13 Variance = risk The variance, and the standard deviation, around the mean measures risk.

7-14 Scenario Variance Scenario variance: there are k possible outcomes (s), all probabilities p(s) sum to 1.0. E(r) is the scenario mean for these k outcomes.

7-15 The Value of an Investment of $1 in 1900

7-16 Real Returns The Value of an Investment of $1 in 1900

7-17 The Pattern... Over history we see High return High volatily Low return low volatility Stocks high return, high volatility, high risk Tbill: low return, low volatlity, low risk Gov. Bonds and corporate bonds - in between And, portfolios of small firms displays higer returns and hiher variance than the average market portfolio.

7-18 The Conclusion People are risk-averse, this explains the pattern When they invest in risky things (high variance around the expected value) they demand higher return to compensate for the risk. The higher the risk - the higher the risk premium. To volutarily hold risky assets (volatile returns) investors demand higher expected returns. When looking at the returns on the market portfolio of stocks over the return on Tbills we see the risk premium investors demand for holding these risky assets.

7-19 Average Market Risk Premia (by country) Risk premium, % Country

7-20 Rates of Return 1900-2008 Source: Ibbotson Associates Year Percentage Return Stock Market Index Returns

7-21 Measuring Risk Return % # of Years Histogram of Annual Stock Market Returns (1900-2008)

7-22 Equity Market Risk (by country) Standard Deviation of Annual Returns, % Average Risk (1900-2008)

7-23 Understanding Risk Risk aversion leads to diversification Spread your investment among many different assets, => huge reduction in risk in relation to reduction in return Diversification - Strategy designed to reduce risk by spreading the portfolio across many investments. Unique Risk - Risk factors affecting only that firm. Also called diversifiable risk. Market Risk - Economy-wide sources of risk that affect the overall stock market. Also called systematic risk.

7-24 Outcome of diversification. Notice that the figure has the wrong scale. Most diversification is reached around 15-20 assets. Not 5 assets.

7-25 Outcome of Diversification: Risk reduction: only market risk remain in portfolio

7-26 Diversification Diversification works through the covariance (correlation) between assets. Since assets are not perfectly correlated, combination of risky assets gives a bigger reduction in risk compared to reduction in return. To max return: invest all in asset with higest expected return To min risk: invest all in risk free asset Risk averse seeks to max return per risk => diversification

7-27 Adding two random returns Covariance and correlation: Correlation is a number between -1 and +1. Where +1 indicate perfect correlation. (-1) indicate perfect negative correlation.

7-28 The return on a 2-asset portfolio Two assets: 1 and 2 The expected return on 2-asset portfolio: Portfolio weights must sum so unity. The expected return on an N-asset portfolio:

7-29 Variance of 2-asset portfolio When adding two (or more) returns beware of the covariance (correlation), which will affect the outcome Variance or st. dev is measuring risk. Let the correlation coeffcient go from +1 over 0 to -1 and study the outcome (graph)

7-30 The N-asset portfolio The N-asset portfolio involves a large number of covariances (correlations). However, there are short-cuts for people doing this in practice. Use monthly data for the last 5 (or up 10 say a business cycle) years to estimate, means, variances and covariances.

7-31 Two asset: Portfolio Risk Example Suppose you invest 60% of your portfolio in Campbell Soup and 40% in Boeing. The expected dollar return on your Campbell Soup stock is 3.1% and on Boeing is 9.5%. The expected return on your portfolio is:

7-32 Portfolio Risk- Two Assets Suppose you invest 60% of your portfolio in Campbell Soup and 40% in Boeing. The expected annual return on your Campbell Soup stock is 3.1% and on Boeing is 9.5%. The standard deviation of their annualized daily returns are 15.8% and 23.7%, respectively. Assume a correlation coefficient of 1.0 and calculate the portfolio variance.

7-33 The Risk Averse Invesstor To get higher return an investor must accept higher risk The choice between risk and return is the investors own (individual) decision For each choice of risk, the investor wants the highest possible return. When constructing a well diversified portfolio to reduce risk, the correlations among assets are essential.

7-34 Figure Draw a figur that shows expected returns E(r) on the vertical line and risks ( ) on the horizontal line. Illustrate the effects of different possible correlations in a two asset portfolio: Example values: r 1 = 12, =15 r 2 = 8, = 10 Correlation = +1: A straigth line Correlation

7-36 Portfolio Risk two-asset example Example Correlation Coefficient =.4 Stocks % of PortfolioAvg Return ABC Corp2860% 15% Big Corp42 40% 21% Standard Deviation of Portfolio = 28.1: Portfolio variance= (28 2) (.6 2 ) + (42 2 )(.4 2 ) + 2(.4)(.6)(28)(42)(.4) = > St. dev: 28.1 Return : r = (15%)(.60) + (21%)(.4) = 17.4%

7-37 More Portfolio Risk Example Correlation Coefficient =.4 Stocks % of PortfolioAvg Return ABC Corp2860% 15% Big Corp42 40% 21% Standard Deviation = Portfolio = 28.1 Return = weighted avg. = Portfolio = 17.4% Next, add the stock New Corp to the portfolio

7-38 Portfolio Risk Example Correlation Coefficient =.3 Stocks % of PortfolioAvg Return Portfolio28.150% 17.4% New Corp30 50% 19% NEW Standard Deviation of Portfolio = 23.43 NEW Return of Portfolio = 18.20% NOTE: A little higher return and much lower risk How did we do that? Mainly through diversification, the correlation between portfolio and New asset is quite low. Actually 0.3 is the correlation of gold.

7-39 Portfolio Risk Example of a covariance matrix for N-asset portfolio construction. The shaded boxes contain variance terms; the remainder contain covariance terms. 1 2 3 4 5 6 N 123456N STOCK To calculate portfolio variance add up the boxes

7-40 Markowitz Mean-Variance theory Markowitz formalised the investment process of a risk-averse investor. Recall that only two moments are necessary to describe a risky asset: mean and variance All people are risk averse They build portfolios to diversify and reduce risk, in order to find their desired combination of maximum return for minimum risk. They are left with market risk in their portfolis which they want compensation for by asking for higher return on the portfolio (=> they bid down relative prices on risky assets). The rational investor estimates construct an efficient frontier of all well-diversified investment portfolios (graph).

7-41 Graph: An intuitive algorthim for an efficient portfolio Estimate expected returns, st,dev and correlations. Look at formula for the portfolio mean and the portfolio variance. Fix a level of risk (st.dev) ask a computer to calculate the weights that leads to the higest return for this level of risk. Fix a new level of risk, find the weights that optimizes the expected return for this risk level, Interpolate between the estimates to get a curve of effecient (well diversified) portfolios. Markowitz: Make your individual choice between risk and return along the line according to taste for risk.

7-42 Be smart - Extent your choices In the graph of the efficent (well-diversified) portfolios, mark the risk free-rate on the vertical axis. Draw a line from the risk-free rate that is tangent to the effcient portfolio. (Tobin 1958) Now, make your (smarter) choices between risk and return along that straight line starting from r f and just touching the effcient frontier portfolio. The tangent with the efficient portfolio is the optimal risky portfolio. These portfolio weights represent the best well diversified portfolio. Invest in the risk-free asset and in therisk portfolio. Thus, allocate w 1 to risk-free and w 2 to risky portfolio. You can borrow money to invest more than 100% of your assets in the risky portfolio, to maximize your utility from returns and risk. (extend graph)

7-43 The Individual Investor From the graph: Investors can controll risk through: 1) Diversification and finding the optimal risky portfolio 2) Mix their investment between the optimal risky portfolio and the risk-free asset. This portfolio is called the complete portfolio = Risk-free + risky assets. (Risky assets = stocks and corporate bonds etc.) Important, learn to be smart investors, think in terms of portfolio returns. 1) and 2) above is THE SEPARATION THEOREM. Find the well-diversified portfolio is a technical problem. Chosing the highest utility combination between risk-free and risk portfolio is the individuals choice.

7-44 Suppose we all are the same: Equilibrium on the markets If everyone behaves like the person Marowitz described => Capital Asset Pricing Model CAPM The optimal risky portfolio is the market porfolio We approximate with stock market index Difference between the return on the market and the risk-free rate is the risk premium people ask for to hold the risky (well-diversified) portfolio. Individual stocks are priced with respect to their contribution to the portfolio return and risk.

7-45 CAPM Notice that all assets, and the market portfolio, is willingly held by the market. It is a free market you can by and sell as you want. If the the expected return is too low, people will sell risky assets. Prices on risky assets go down today and expectd returns will go up. If the expected return is too high (returns give more than compensation for risk), people buy more. Prices go up and expected returns go down. Individual years are not important here, on average all will be as in theory.

7-46 CAPM predicts: That individual stocks are priced according to their expected return, so that investors are compensated for market risk only. Not total risk, only the part that cannot be diversified away needs to be compensated. On average we have, according to CAPM that the expected return r i on asset (i) is E(r i ) = risk-free rate + compensation for asset i:s non-diversifiable risk, E(r i ) = r f + i [E(r m ) r f ].

7-47 And Beta is Beta measures the risk of the individual asset. We can use it calculate the required return on a stock, or a firms equity. Beta is measured as the covariance between the expected return on the asset and the market, divided with the variance of the expected market return i = Cov(r i, r m )/Var(r m ) Or a linear regression r i = a i + i r m + e i Think of r m in terms of the business cycle, as the economy moves up and down, so will the return on individual assets, but to different degrees.

7-48 Estimate Beta Beta for the market = 1.0 (of course), the average of all assets. Individual assets have Betas that are either lower, equal or higher than 1.0 Estimate Beta, decide on the risk free rate and caculate the required return for any risky asset. Risk premium on the market r m r are typically estimated in the range of 4.5 -5.5%. (Sometimes, in historical times, down to 4% or up to 8%), see BMA ch 7. See course web for references CAPM works quite well for corporate finance investments. CAPM is standard.

7-49 CAPM CAPM predicts that the market portfolio is the optimal risky portfolio. Everyone holds a replica of the market portfolio, because we all have the same information. All assets are priced with respect to beta, and the CAPM formula. Any deviations will be eliminated by market forces. (=>arbitrage trading) and the security market Line. Figures 8.6-8.7

7-50 Sharpe Ratio You need compensation for non-diversifiable risk, CAPM allows us to measure this risk and If you compare over time: E(r i ) r f = + i [E(r m )-r f ] You can never earn systematic returns over what CAPM predicts, that means = 0. (Jensens alpha) Another investment performance measure is Sharpes ratio = (r r f )/ Return per unit of risk

7-51 Security Market Line Use the security market line to determine (illustrate) if an asset is overpriced or underprices, or corretly priced, at the moment. Discuss the required cost of capital.

7-52 Company Cost of Capital A companys cost of capital can be compared to the CAPM required return Required return Project Beta 0.5 Company Cost of Capital 3.8 0.2 0 SML

7-53 Portfolio Risk Market Portfolio - Portfolio of all assets in the economy. In practice a broad stock market index, such as the S&P Composite, is used to represent the market. Beta - Sensitivity of a stocks return to the return on the market portfolio.

7-54 Portfolio Risk The return on Dell stock changes on average by 1.41% for each additional 1% change in the market return. Beta is therefore 1.41.

7-55 Dells Beta The return on Dell stock changes on average by 1.41% for each additional 1% change in the market return. Beta is therefore 1.41.

7-56 Market Risk Beta Covariance with the market Variance of the market

7-57 Cost of Capital CAPM gives us the cost of equity, the required return (discount rate) for stocks. The cost of debt is measured by the YTM on the companys debt. (Given from ratings and peers in practice) Beta gives us a companys cost of equity, and the required return on investments financed with equity. A company has both debt and equity => Weighted average cost of captal WACC

7-58 WACC Assume a mix of debt and equity in a firm. Required return on debt and equity together. Use YTM on new debt to set r D and CAPM (and BETA) to set r E Use market value of debt and equity, not book values. Only amatures refers to return on book value of equity, yes even if they are CEO:s for big companies.

7-59 Estimate Beta Debt is YTM on new debt (not old), for this type of firm and level of debt. Risk-free plus default risk rating. Beta is estimated typically from monthly data five years back. Industry standard. Adjusted Beta, adjust the estimate especially for younf firms. Equity Beta and Asset Beta Equity Beta (=levered Beta) is what you estimate, includes finaning risk from debt. Recalculate to construct a Beta value as if the firm was all equity = Asset Beta = Unlevered Beta. http://www.wikiwealth.com/wacc-analysis:azn http://www.wikiwealth.com/wacc-analysis:azn

7-60 Beta is affected by If you estimate Beta from market returns it reflects both the financial risk and the business risk of the firm An all-equity firm has only business risk With both debt and equity financing there is both busines risk and financial risk in Beta. Thus, Beta must be unlevered if we want to compare firms and if we want to calculate an average sector beta. In addition Adjusted Beta values - the estimate is usually biased away from 1.0. Therefore Adjusted Beta values adjusts estimates of equity Betas to come closer to 1.0.

7-61 What Beta to use? Adjusted Betas are especially important for young firms. Equity Betas = Levered Betas vs Asset Betas = Levered Betas For a correct estimation of WACC we look for estimated future returns. For firm valuation in particuar, and sometimes project valuation, use sector YTM and sector Beta values. Sector Betas, are typically unlevered and then relevered for the (Debt/equity ratio) of firm or the project. Typically, analyse the effects of debt financing by varying the debt/equity ratio.

7-62 After CAPM I The APT model Arbitrage Pricing Theory : Ross (1976) basically breaks down one single risk premium (r m r f ) into several macro economic risk factors; and different risk premiums. Risk factors example: economic growth, inflation, interest rates, energy prices. It does not tells us which these risks are, only that investors compare portfolios and returns to create an efficient market portfolio. In CAPM all risks are priced in the market risk premium. APT splits into several risk premiums.

7-63 After CAPM II 3 Factor Model Fama and French discovered that a three factor version of the APT usually works better than CAPM for predicting returns, and seem to work all over the world. The three factors are r i = B 1 * Market factor (return on market r m ) B 2 * Size factor (small firms are special) B 3 * Book-to-market factor (growth opportunities)

7-64 CAPM or Not? CAPM is heavily critized. Bad at predicting returns, not good for investments. But for understanding it is very good. If you dont understand CAPM you understand nothing! It is a very robust theory. Change an underlying assumption and the model still holds, perhaps with an additional parameter in the equation. It does not break down as other theories. Everyone who has tried to explain asset pricing has the CAPM as a special case of their theory. Works for NPV and valuation in corporate finannce because you can usually change things in the future (with new information).

7-65 Web Resources Click to access web sites Internet connection required www.globalfindata.com http://www.gacetafinanciera.com/TEORIARIESGO/MPS.pdf

Chapter 7-8-9 Principles of Corporate Finance Tenth Edition Ch 7-9 Slides by Matthew Will and Bo...

Documents

Transcript of Chapter 7-8-9 Principles of Corporate Finance Tenth Edition Ch 7-9 Slides by Matthew Will and Bo...