Finance

1. Finance Chapter 5 Risk & rates of return

2. No pain no gain • What is risk? • How is risk measured? • How can risk be minimized or at least compensated for bearing it? • Investors like returns and dislike risk • Investors will invest in risky assets only if they expect to receive higher returns

3. Risk in perspective • The riskiness of an asset can be considered in two ways: • Stand-alone—an assets cash flows are analyzed by themselves • Portfolio context—cash flows from a number of assets are combined (consolidated) and analyzed

4. Risk analysis considerations • Portfolio context • Diversifiable risk—risk that is eliminated through diversification (irrelevant) • Market risk—cannot be eliminated thru diversification (relevant) • An asset with a high degree of market risk (relevant) must provide a high rate of return to attract investors • Remember that investors are averse to risk

5. Investment returns • Measuring rates of return problem: • Scale (size of investment) • Timing problem • Solution: • Rates of return or percentage of return for a one year investment • ROR = (amount rec’d - amount invested) / amount invested

6. Stand-alone risk • Risk—the chance that some unfavorable event will occur • Stand-alone risk—the risk an investor would face if s/he held only one asset • Probability—the chance an event will occur • Probability distribution—a listing of all possible outcomes (events) with a chance of occurrence (probability) assigned to each outcome • Probabilities must add up to 100% • See Table 5-1, pg. 172

7. Expected rate of return • Expected rate of return, k (k-hat)—the rate of return expected to be realized from an investment; the weighted average of the probability distribution of possible results (payoff matrix)

8. Stand-alone risk • The tighter the probability distribution of expected future returns, the smaller the risk of a given investment (see figure 5-2, page 174) • Standard deviation (sigma)—the smaller the standard deviation, the tighter the probability distribution, and the lower the riskiness of a stock. • Standard deviation is essentially a weighted average of the deviations from the expected value.

9. Stand-alone risk • Coefficient of variation (CV)—the standard deviation divided by the expected return. • CV = Standardized measure of the risk per unit of return used for investments that have the same expected returns but different standard deviations.

10. Risk Aversion • Most investors are risk averse. • The higher a security’s risk the lower its price and the higher its required return. • Risk Premium (RP)—the difference between the expected rate of return on a given risky asset and that on a less risky investment = increased compensation required for a risky investment

11. Portfolio returns & risk • Expected return on a portfolio kp (k-hat p)= the weighted average of the expected returns on assets held in the portfolio • Realized rate of return k (k-bar) = the return that was actually earned during some past period. K-bar usually is different from the expected (k-hat) except for riskless assets.

12. Correlation coefficients • Correlation = the tendency of 2 variables to move together • Correlation coefficient, r = measures the degree of relationship between 2 variables (the tendency to correlate movements) • r can range from +1.0 (perfectly positive correlation - move up and down together) to -1.0 (perfectly negative correlation - move in opposite directions) while 0 means they are independent of one another. • Diversification means nothing if all stocks are perfectly correlated

13. Diversifiable risk vs. market risk • Almost half the riskiness of an average stock can be eliminated if the stock is held in a diversified portfolio containing at least 40 stocks • Market risk—that part of security’s risk that cannot be eliminated by diversification. • Capital Asset Pricing Model (CAPM)—a stock’s required ROR is equal to the risk-free rate of return plus a risk premium that reflects only the risk remaining after diversification. • Relevant risk—the risk remaining after diversification that cannot be diversified away (aka, market risk)

14. The concept of Beta (b) • Beta coefficient, b—a measure of market risk, which is the extend to which the returns on a given stock move with the stock market. • b measures the volatility of a stock, e.g., 1.0 (high beta)stocks will move up and down with the broad market averages. 0.5 (low beta) stocks are half as volatile as the market averages. A negative b means the stock will move in the opposite direction as the market average.

15. Market risk premium • RPm –the additional return over the risk-free rate needed to compensate investors for assuming an average amount of risk. • Security Market Line (SML)—the relationship between a security’s market risk and its required rate of return. The return required for any security is equal to the risk-free rate plus the market risk premium times the security’s beta:ki = krf + (km – krf )bi

16. Factors effecting RROR • Risk-free rate change (real rates or inflation) • Change in a stock’s beta • Investors’ aversion to risk can change • Global diversification may result in lower risk for multinational companies and globally diversified portfolios.