The Basics of Risk 04/08/08 Ch.3

2 One of the major tenets of finance The higher the risk, the higher the return required. In the corporate finance context: A project should generate a return that is appropriate for the level of risk of that project

3 How do we define risk? Risk in general is the uncertainty of a future event or outcome where there is some peril of loss or injury. For stocks, it is the potential to either make or lose money on the investment over time. For stocks, risk is often measured as the variability or volatility of stock returns and thus includes both potential worse-than- expected as well as better-than-expected returns.volatility

4 Types of Risk in a Finance World Project Specific Risk Misestimated cash flow…risk or model problems or both? Competitive Risk How does competition impact outcomes? Industry Specific Risk Why do companies share similar risks? International Risk Market Risk

5 A closer examination of risk types Actions/Risk that affect only one firm Actions/Risk that affect all investments Firm-specificMarket Projects may do better or worse than expected Competition may be stronger or weaker than anticipated Entire Sector may be affected by action Exchange rate and Political risk Interest rate, Inflation & news about economy Figure 3.5: A Break Down of Risk Affects few firms Affects many firms Firm can reduce by Investing in lots of projects Acquiring competitors Diversifying across sectors Diversifying across countries Cannot affect Investors can mitigate by Diversifying across domestic stocksDiversifying across asset classes Diversifying globally

6 One way to measure risk? Variance of returns: _ Where R t is the return for period t, R is the average return and n is the number of periods.

7 Is variance an appropriate measure of risk for all investors? No… variance is total risk of the asset but many investors do not “carry” the total risk because… The risk calculated in the variance of returns for a stock includes both firm-specific risk and market risk. An investor can eliminate all the firm-specific risk by holding a diversified portfolio. Example of diversification as you add additional assets…rolling the die One die…all the risk Two dice…central tendency starts and large outcomes (12) or small outcomes (2) less likely Three…four…five...six dice…what is happening to the distribution

8 Moments of a distribution Moment one: mean Moment two: variance (standard deviation) Moment three: skewness Moment four: kurtosis Mean-Variance World Bell-shaped curve (normal distribution) Mean and variance completely describe the distribution of the returns Adding Moments to the bell-shaped curve

9 Which one do you prefer? *The mean and variance of the returns are approximately the same

10 Downside Only Risk? Semi-variance of returns: _ Where R is the average return over all periods, R t is the return for period t when less than the average, and n is the number of periods where the actual return is less than the average return.

11 Is variance an appropriate measure of risk for all investors? No, for the diversified investor, only market risk is important. The firm’s beta is the appropriate measure of this market risk. What is Beta? Covariance of the individual assets return with the return of the market… Statistically measured with historical returns What we really want is the relationship going forward Future Beta? What does it mean if a firm’s beta is 0? Beta of 1? Beta of 2? Beta of zero…risk-less asset Beta of one…average risk asset Beta of 2, If the “market” goes up by 1% today, on average, the firm’s stock price will go up by 2%.

12 Asset Pricing Models CAPM Two parameter model, mean and variance E(r i ) = r f + β i (E(r m ) - r f ) Arbitrage Pricing Theory (APT) Multiple factors E(r i ) = r f + β 1 x F 1 + β 2 x F 2 + β 3 x F 3 + … Multifactor Models (same as APT) Proxy Models E(r i ) = 1.77% ln (MV) ln (BV/MV)

13 Is Beta the right risk for others? Debt lenders? Where is there risk? No potential upside above the required repayment of principal and interest Downside is not getting paid back…default How do you measure the probability of default? In theory…distribution of cash flows and promise to lender In practice…bond rating agencies

14 Bond Ratings Who? What? When? Where? Why? How? Firms “apply” for rating Provide information to rating agencies AAA to D ratings…(page 81)

15 Determining hurdle rates (required rates of return) A simple representation of the hurdle rate is as follows: Hurdle rate = Risk-free Rate + Risk Premium What we should use is the weighted average cost of capital for that project… WACC = E/V x R e + D/V x R d (1 – T c ) This shows the risk assumed by debt lenders and equity owners proportional to their investment in the project

16 Practice Problems for Thursday Problem 7 – Standard Deviation of a Portfolio Problem 12 – Beta of a stock Problem 13 – Correlation between market and stock Problem 14 – APT (called APM) Problem 15 – Multifactor Model Problem 16 – Fama – French Model