1. Risk and Return (Ch. 5) 04/24/06

2. How Investors View Risk and Return Investors like return. They seek to maximize return. Investors like return. They seek to maximize return. But investors dislike risk. They seek to avoid or minimize risk. Why? But investors dislike risk. They seek to avoid or minimize risk. Why? –Because human beings possess the psychological trait of “risk aversion” which is a dislike for taking risks.

3. Returns Calculating a return Calculating a return –Dollar Return Ending Value + Distributions – Original Cost Ending Value + Distributions – Original CostOR P 1 + D – P 0 P 1 + D – P 0 –Percentage Return [(Ending Value + Distributions) / Original Cost] – 1 [(Ending Value + Distributions) / Original Cost] – 1OR (P 1 + D – P 0 ) / P 0 (P 1 + D – P 0 ) / P 0

4. Holding Period Returns Holding Period Returns (HPR) Holding Period Returns (HPR) –The return for the length of time that investment is held –Need to convert to annual basis for comparison Annualized return = (1 + HPR) n – 1 Annualized return = (1 + HPR) n – 1 Warning on extrapolation of holding period returns for less than a year Warning on extrapolation of holding period returns for less than a year –Compounding requires each additional investment period with same holding period return

5. Historical Returns We examine the returns that the following four investments have generated historically. We examine the returns that the following four investments have generated historically. 3-Month Treasury Bill 3-Month Treasury Bill Long-Term Government Bonds Long-Term Government Bonds Large Company Stocks Large Company Stocks Small Company Stocks Small Company Stocks

6. Historical Returns We find We find –Stocks tend to have the largest swings from year to year but also have the highest average returns. –The 3-Month Treasury provides the most consistent return but it is the lowest average return of the four choices. Relationship of average return and standard deviation – first look at risk and return tradeoff Relationship of average return and standard deviation – first look at risk and return tradeoff

7. Historical risk Historical risk represents the variation or change in value from one period to the next of a financial asset. Historical risk represents the variation or change in value from one period to the next of a financial asset. Historical risk measures are ex-post measures but may be used as proxies for the expected risk associated with a particular asset. Historical risk measures are ex-post measures but may be used as proxies for the expected risk associated with a particular asset.

8. Historical risk Historical risk of individual financial assets can be measured in two ways: Historical risk of individual financial assets can be measured in two ways: –Standard deviation (σ) of returns Where x i is the return in time i, n is the number of periods and average is the average return over the period calculated as:

9. Historical risk –Coefficient of variation (CV) Measure the relative dispersion of an asset and is useful for comparing risks of assets Measure the relative dispersion of an asset and is useful for comparing risks of assets The normal distribution is useful in describing the probability that the actual return will end up in a given range. The normal distribution is useful in describing the probability that the actual return will end up in a given range. –68% (95%) chance that the return will be within 1 (2) standard deviation from the average.

10. Risk as Uncertainty Risk can also be defined as the uncertainty in the outcome of an future event. Risk can also be defined as the uncertainty in the outcome of an future event. An event where the outcome is known before the event is free of uncertainty or risk-free. An event where the outcome is known before the event is free of uncertainty or risk-free.

11. Calculating expected payoffs The expected payoff is forward looking and represents the predicted outcome from investing in an asset. The expected payoff is forward looking and represents the predicted outcome from investing in an asset. where payoff i represents the payoff under outcome i, probability i represents the probability of outcome i occurring, and n represents the number of possible outcomes.

12. Calculating expected returns The expected return represents the expected value generated by investing in this asset. The expected return represents the expected value generated by investing in this asset.

13. Calculating expected standard deviation Expected standard deviation provides us with a measure of expected risk of an asset and is calculated using possible payoff outcomes and their associated probabilities. Expected standard deviation provides us with a measure of expected risk of an asset and is calculated using possible payoff outcomes and their associated probabilities.

14. Risk and Return Tradeoff Objective: Maximize Return and Minimize Risk Objective: Maximize Return and Minimize Risk Must tradeoff increases risk and return with decreasing risk and return Must tradeoff increases risk and return with decreasing risk and return –Investment Rule #1 – Two assets with same expected return, pick one with lower risk –Investment Rule #2 – Two assets with the same risk, pick one with higher return What to do when one investment has both higher return and more risk versus another asset? What to do when one investment has both higher return and more risk versus another asset? –Must look to individual choice