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Risk and Return (Ch. 5)

Risk and Return (Ch. 5). 04/24/06. How Investors View Risk and Return. Investors like return . They seek to maximize return. But investors dislike risk . They seek to avoid or minimize risk. Why?

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Risk and Return (Ch. 5)

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

  2. How Investors View Risk and Return • Investors like return. They seek to maximize return. • 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 • Dollar Return • Ending Value + Distributions – Original Cost OR P1 + D – P0 • Percentage Return • [(Ending Value + Distributions) / Original Cost] – 1 OR (P1 + D – P0) / P0

  4. Holding Period Returns • 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 • 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. • 3-Month Treasury Bill • Long-Term Government Bonds • Large Company Stocks • Small Company Stocks

  6. Historical Returns • 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

  7. Historical risk • 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.

  8. Historical risk • Historical risk of individual financial assets can be measured in two ways: • Standard deviation (σ) of returns Where xiis 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 • 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. • 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. where payoffirepresents the payoff under outcome i,probabilityi 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.

  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.

  14. Risk and Return Tradeoff • Objective: Maximize Return and Minimize Risk • 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? • Must look to individual choice

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