1 Investments: Risk and Return Business Administration 365 Professor Scott Hoover

2 Returns  Return  measure of the benefit received from an investment holding period return  % change in value over the period effective annual return (EAR)  1-year holding period return  includes the effects of compounding. annual percentage rate (APR)  per period rate × # of periods per year  ignores the effects of compounding

3  If r p is the per period rate and m is the # of compounding periods per year,  Putting those together gives  The distinction is important because… Annual discount rates must be EARs Banks quote APRs Bond yield-to-maturities (YTMs) are APRs Credit cards and option valuation models use continuously- compounded interest rates  APRs with m = ∞

4  A few examples… A bank quotes 9% APR, compounded monthly.  Per period rate 9%/12 = 0.75%  EAR = = 9.38% A bond pays 4% interest every six months.  YTM = 4%×2 = 8%  EAR = = 8.16% The continuously-compounded interest rate is 6% per year.  What happens as m gets bigger?  m = 10 → EAR = 6.165%  m = 100 → EAR = 6.182%  m = 1000 → EAR = 6.183%  m = ∞ → EAR = 6.184%

5 Risk  Risk  measure of the potential for loss in an investment How should we measure risk?  Reality: we really don’t know how to best measure risk.  What do we know about risk? Some risk is all but eliminated in well-diversified portfolios   diversifiable risk (aka, idiosyncratic risk, firm-specific risk) Some risk remains no matter how well-diversified we are   non-diversifiable risk (aka, systematic risk, market risk)

6  Capital Asset Pricing Model (CAPM) Intuition: Investors will only be compensated for the level of non-diversifiable risk they take on. Why? Definition: market portfolio ≡ portfolio of all assets weighted according to their market values. Result  Expected return on a well-diversified portfolio is a linear function of the standard deviation of the portfolio’s returns  Why is std. dev. a reasonable measure here?  The line is called the Capital Market Line (CML)  E(R) = R f + (  /  m )(E(R m )-R f )  R  return on portfolio  R m  return on market portfolio  R f  risk-free return    std. dev. of portfolio   m  std. dev. of market portfolio

7 Risk (standard deviation) Expected Return mm E(R m ) RfRf Capital Market Line

8  The CML is useful for well-diversified portfolios, but not for individual assets.  To eliminate diversifiable risk, we extract the portion of the standard deviation that is correlated with the market. This leaves , which is our measure of the non-diversifiable risk of an asset.  ≡ correlation between asset returns and market returns Result: expected return on any asset is a linear function of  This line is called the Security Market Line (SML)  E(R) = R f +  (E(R m )-R f )

9 Risk (beta) Expected Return  E(R m ) RfRf Security Market Line

10  Roughly speaking, beta tells us how the asset price tends to move when the market moves.  e.g., Suppose  =1.5 for some asset. The asset will tend to move by 15% whenever the market moves by 10%.  Do assets with negative betas exist? After all, E(R) < R f  Yes! Such assets provide insurance on the portfolio

11 Miscellaneous Notes  If markets are efficient, investing is nothing more than choosing a  and a method to achieve it.   invest in a combination of the risk-free and a market index  Portfolio betas  The beta of a portfolio is the weighted average of the betas of the individual assets in the portfolio:  p = w A  A + w B  B + …  The weights are the fraction of our money we have invested in each, with short positions having negative weights  example: Suppose we have $10,000 to invest and that we short $6,000 of one asset. We then invest $16,000 into a second asset.  w 1 = -$6,000/$10,000 = -0.6 w 2 = $16,000/$10,000 = 1.6

12  Problems with using the CAPM What is the market portfolio?  can include every conceivable asset (stocks, bonds, baseball cards, ostrich eggs, etc.).  difficult to measure, so we proxy by using a market index (such as the S&P500 or the Russell 3000).  expected return on the market portfolio is difficult to estimate.  def’n: market risk premium (MRP) = E(R m )-R f  One study shows that the MRP was about 7.4% from  Recent evidence suggests that it should be around 4%.

13 Other factors may be important. Historical returns may not be representative of future returns.  See spreadsheet example What if we don’t have historical data for the asset?  find comparables  use common sense  Bottom Line: use the CAPM and common sense to estimate the appropriate discount rate

14 Applying the CAPM  gives the appropriate rate for discounting cash flows to shareholders  used as part of the WACC calculation WACC = w d R d (1-T) + w ps R ps + w e R e Recall that  w i  fraction of firm (using mkt values) financed with type i  T  tax rate  R e  required return on equity  estimated using CAPM  R ps  required return on preferred stock  estimated using D/P  R d  required return on debt

15  Techniques to estimate cost of debt #1: Find the yield-to-maturity on the company’s outstanding debt  Potential problems  1. YTM depends on the maturity of the debt. If the company’s debt has a very long or very short maturity, our estimate may be biased.  2. The YTM does not reflect the expected return to investors.  3. The company’s debt may not be publicly-traded  4. Bonds with embedded options are problematic.

16 #2: Use the company’s debt rating in conjunction with yield spreads to estimate the company’s cost of debt.  yield spread: the difference between the yield on a bond (or class of bonds) and a corresponding Treasury bond with the same maturity  example: Suppose a company’s debt is rated Baa1 by Moody’s. What is our best estimate of the company’s cost of debt?  Suppose we choose to use a ten-year maturity for our estimates.  From we see that the yield spread is 107 basis points, or 1.07%. (Note that this is an old estimate).  From we see that ten-year Treasuries have a yield of 3.89%  Cost of debt estimate = 3.89%+1.07% = 4.96%

17  Potential problems  The company’s debt may not be rated  The bond may not be an average bond within its ratings class. #3: Find the cost of debt on comparable companies