Capital Asset Pricing Model Chapter 9 Capital Asset Pricing Model

Chapter 9 Outline 9.1 What You Already Know and What You Want to Know 9.2 The Capital Asset Pricing Model (CAPM)—A Cookbook Recipe Approach 9.3 The CAPM Cost Of Capital in the Present Value Formula 9.4 Estimating the CAPM Inputs 9.5 Empirical Evidence: Is the CAPM the Right Model? Appendix: Certainty Equivalence, CAPM Theory and Background, and CAPM Alternatives 9.6 Application: Certainty Equivalence 9.7 Theory: The CAPM Basis 9.8 Theory: CAPM Alternatives!?

The Capital Asset Pricing Model Introduction If we know risk, then we can find the appropriate cost of capital. If we know cost of capital, then we can find the NPV of a project. If we know NPV, then we can find the value of a project to shareholders. If firms choose the best projects according to their returns and risks, the economy benefits from the improvement in financial decision-making.

The Capital Asset Pricing Model What You Already Know and Want to Know. The NPV discount factor is the opportunity cost of capital. If the project returns as much or more than the investor’s opportunity cost of capital, you should proceed with the project. We assume that investors like greater portfolio expected return for less portfolio risk – either variance or standard deviation. We assume that investors choose to diversify and wish to maximize their wealth in a one-period world. Since investors are concerned with your project’s portfolio risk, then the market beta of the project is the important risk measure. Investors trade between projects to find the most return for the least risk. The Capital Asset Pricing Model (CAPM) indicates the tradeoff of risk for return.

The Capital Asset Pricing Model (CAPM) A Cookbook Recipe Approach CAPM gives the appropriate cost of capital (expected rate of return) for a project, given the relevant risk characteristics. Three inputs are needed for CAPM: The risk-free rate of return The expected market rate of return The market beta Assets with lower risk have lower expected returns. Assets with higher risk have higher expected returns.

The Capital Asset Pricing Model The CAPM Formula

The Capital Asset Pricing Model The Security Market Line If the risk-free rate = 3% and the expected return on the market = 8%: Assets with Betas of 0 should have 3% expected returns. Assets with Betas of 1 should have 8% expected returns. Assets with Betas of 2 should have 13% expected returns. The line that connects the asset expected returns and is plotted with beta on the X-axis is called the Security Market Line. The SML shows the correct risk and expected return relationship, according to CAPM. The slope of the SML is the equity premium  ( ) – rF . The intercept is the risk free rate. Expected Return = rF + Beta [( ) – rF] Real-world data finds a rough linear relationship between the data-estimated expected return and the data-estimated market beta.

The Capital Asset Pricing Model The SML Plot FIGURE 9.1 The Security Market Line

The Capital Asset Pricing Model The SML in an Ideal CAPM World FIGURE 9.2 The Security Market Line in an Ideal CAPM World

The Capital Asset Pricing Model The CAPM Cost of Capital in the PV Formula CAPM estimates the cost of capital. CAPM indicates that assets should have different expected rates of return based on risk. CAPM doesn’t include the default risk so to find a stated rate, default risk will be “added back” to the expected rate of return.

The Capital Asset Pricing Model CAPM and Default Rate Example Consider a bond that pays $200 ninety-five percent of the time and $0 five percent of the time. If the bond has a beta of .25 when the risk free rate is 6% and the expected market return is 10%, then CAPM finds it will have a 7% expected return.  ( ) = rF + [( ) – rF] •  ( ) = 6% + .25 (10% - 6%) = 7% Expected cash flow is $190 with probabilities of 95% for receiving $200 and 5% for receiving $0.  ( BOND) = Prob (No Default) • Promise + Prob (Default) • Nothing  ( BOND) = 95% • $200 + 5% • $0 = $190 To earn a 7% return with a $190 expected outcome, you would pay $177.57. Find the PV of $190 at 7%. PV = $190 / 1.07 = $177.57 Your stated rate is the return of 12.6% on a $177.57 investment that promises $200. $200 / $177.57 – 1 = promised rate of return  12.6%

The Capital Asset Pricing Model Promised, Quoted, Stated Rates and CAPM So in CAPM, you have a time premium of the 6% risk-free rate plus the 1% risk premium to equal the expected return of 7%. The default premium of 5.6% is added to the 7% CAPM expected return to equal the stated rate of 12.6% on the bond investment. Promised Interest Rate = Time Premium + Risk Premium + Default Premium 12.6% = 6% + 1% + 5.6% Summing up: CAPM provides an expected rate of return. This return is not a stated, promised, or quoted rate of return because it does not include a default premium. The probability of default is handled in the NPV numerator by adjusting cash flow, and not in the NPV denominator by adjusting the expected return.

The Capital Asset Pricing Model Estimating the CAPM Inputs: Equity Premium The equity premium is the most difficult to estimate. There are five methods to estimate the equity premium. Historical Averages recent average as good guess at future Historical Averages and Bubbles high returns indicate lower future return Current Predictive Ratios regress dividend or earnings yield Philosophical Prediction guess what is reasonable vs. bond return Consensus Survey ask investors what is reasonable No one method has absolute certainty. Some methods lead to nonsense results. We believe the premium is between 1% and 8%. Be consistent and use a reasonable estimate in CAPM. Note: Most use the S&P500 as their market proxy (simple and available).

The Capital Asset Pricing Model The Risk-Free Rate and Multiyear Considerations We can look at Treasury bonds for the risk-free rate. Accepted convention is to match the maturity of the Treasury bond with the length of time for the investment project. Theory doesn’t help much here. You may even match risk-free rates by year to the year’s corresponding expected cash flow. If the project is likely to exist for 10 years, then a 10 year risk-free bond rate seems more appropriate than a 3-month T-Bill rate. Since no one knows exactly how risk-free rates, equity premiums, and project values interact, there are many reasonable estimates for the risk-free rate If you match Treasury bond rates to the investment horizon, you do have economic intuition in your favor if asked about your assumptions. Of course, reasonable is in the eye of the beholder -- or at least one’s boss.

The Capital Asset Pricing Model Investment Projects’ Market Betas While the risk-free rate and the expected rate of return of the market are the same regardless of the project, the beta will differ for each project or firm. Beta gives you a point on the Security Market Line that is an expected return. Market beta also suggests something about standard deviation. Zero beta assets should have low or no risk. High (absolute) beta assets’ returns will vary more. Negative beta assets have good returns in down markets. Positive beta assets have good returns in up markets. Negative beta assets are a form of insurance against overall market movements. Insurance assets usually have a high value and low expected returns.

The Capital Asset Pricing Model Beta Estimation Four Methods to Estimate Equity Betas: Look up on a financial website for public firms Use a regression to estimate return of firm vs. the market index Use an average beta of comparable firms to estimate a firm’s beta Use intuition to guess at equity beta Firms have asset betas, debt betas, and equity betas. The equity beta can be adjusted to find the firm’s asset beta. The asset beta is the risk of the firm’s projects.

The Capital Asset Pricing Model Debt Adjustments: Asset Betas and Equity Betas Firms use their overall cost of capital, the weighted average cost of capital, to value projects. The WACC uses the asset beta to find a cost of capital. Beta of the firm’s assets = average of debt beta and equity beta The risk of a firm’s assets is the same no matter how it is financed (perfect market). WACC is the same while the weights and rates and required returns on debt and equity change. WACC is the same whether the firm has 0% debt or 90% debt in a perfect market. WACC of the firm = average of debt and equity cost of capital.

The Capital Asset Pricing Model Empirical Reality If a stock offered too high a return compared to its appropriate expected return, investors would buy the stock until its expected return fell to the CAPM return. If a stock offered too low a return compared to its appropriate expected return, investors would sell until its expected return rose to the CAPM return. If we test beta and CAPM, we should find that: Beta has a linear relationship with expected return (high expected return associated with high beta). Risky assets should have higher expected returns than the risk-free asset. Beta should be the only factor: market capitalization should not matter.

The Capital Asset Pricing Model The SML in non-CAPM Worlds FIGURE 9.4 The Security Market Line in Non-CAPM Worlds

The Capital Asset Pricing Model Does CAPM Work? CAPM isn’t perfect (to borrow a really bad finance pun). The relationship between beta and expected return is reasonably linear. There’s a better-than-predicted return for the lower beta stocks. Beta doesn’t work as well for small capitalization stocks compared to large capitalization stocks. Small cap outperforms. Beta doesn’t work as well for growth stocks when compared to value stocks. Value outperforms. Beta doesn’t work as well for stocks with positive momentum in past returns. Momentum outperforms. The underperformance of growth stocks surprises most investors.

The Capital Asset Pricing Model Historical Firm Types, Beta, and Returns FIGURE 9.6 Historical Firm Types Locations in Plot of Rates of Return against Historical Market Beta, 1970–2003.

The Capital Asset Pricing Model Strengths and Weaknesses CAPM and market beta are still useful to CFOs and financial managers. Knowing beta does give a relative return that makes sense. CAPM is correct for stressing the importance of diversification and for defining opportunity costs for investors according to levels of risk. CAPM is a simple-to-use model that works well enough in most situations. CAPM is widely accepted in corporations; it works because no one has found a method to consistently beat those using it for business decisions. CAPM is the “gold standard” of corporate finance, even if not precise. CAPM is not useful for stock trading or stock selection with its simple assumptions. Most of the estimation risk is in the beta and market risk premium, and this matters more for longer-term projects.

The Capital Asset Pricing Model CFO Valuation Approaches TABLE 9.1 CFO Valuation Techniques

Chapter 9 Appendix and Additional Chapter Art Certainty Equivalence, CAPM Theory and Background, and CAPM Alternatives

FIGURE 9.3 More Perspectives on Beta

FIGURE 9.5 Average Historical Rates of Return against Historical Market Betas, 1970–2003.

TABLE 9.2 Efficient and Inefficient Portfolios