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Risk and Return. FIL 240 – Business Finance Prepared by Keldon Bauer. Risk and Return. Risk is defined as uncertainty of outcomes. In a financial sense, we are uncertain of the outcome of any investment. Formally, uncertainty is measured by variability. I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
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1. Risk and Return FIL 240 – Business Finance Prepared by Keldon Bauer

2. Risk and Return • Risk is defined as uncertainty of outcomes. • In a financial sense, we are uncertain of the outcome of any investment. • Formally, uncertainty is measured by variability. • Statistically that means variance or standard deviation.

3. Risk and Return • Return refers to the gain or loss on an investment. • It is generally stated as a percent of the original investment, and annualized. • The interest rate on a savings account is a form of return.

4. Defining/Measuring Return • Observed return, kt, is calculated as follows:

5. Defining/Measuring Risk • Expected Return as defined in statistics is as follows:

6. Defining/Measuring Risk • Risk in statistics (and financial economics) is measured by standard deviation, which measures the variability of the return.

7. Defining/Measuring Risk • If we assume that the return on two companies would be as follows:

8. Defining/Measuring Risk Widget Manufacturing:

9. Defining/Measuring Risk Bloomington Electric:

10. Defining/Measuring Risk Usingmandsto Approximate a Normal Distribution:

11. Measuring Stand-Alone Risk • If investors have invested everything in one investment, then standard deviation should be standardized by expected return.

12. Measuring Stand-Alone Risk The lower the CV the lower the return adjusted risk.

13. Risk Aversion • Assuming that you need to live off of your investment, and you can only invest in one of the two companies from the previous slides, which would it be? • Widget Manufacturing • Bloomington Electric

14. Risk Aversion • If you chose Bloomington Electric, you are risk averse. • Risk averse investors require higher rates of return to invest in riskier assets. • It is assumed that all investors are risk averse: • If two assets offer the same return, they will opt for the less risky.

15. Risk Premium • The amount of additional return required by a riskier asset to make that asset equally desirable by the market in general is called a risk premium. • When the market perceives that one asset is riskier than another, it requires that the expected return increase to compensate investors for the risk.

16. Portfolio Returns • In the real world, investors can hold more than one investment. • But risk is still important in pricing assets given their expected return.

17. Returns

18. Returns

19. Returns

20. Return Variability

21. Return Variability

22. Return Variability

23. Risk and Return

24. Portfolio Returns • Risk and return should not be evaluated in isolation. Each security should be evaluated in its risk/return trade-off to the portfolio. • Portfolio expected return:

25. Portfolio Returns - Example • Given the following portfolio of stocks:

26. Portfolio Risk • Unlike portfolio return, which is just a weighted average return of all returns in the portfolio, portfolio standard deviation is much more complicated.

27. Portfolio Risk • It depends on the weight (wi) of the new asset to the overall portfolio. • It depends on the standard deviation (si) of the new asset’s returns. • It depends on the correlation (rij) between the new asset and all other assets in the portfolio.

28. Correlation Coefficient • rij is a measure of the degree of relationship between two variables. • It ranges from -1 to +1. • For rij<1, overall portfolio risk decreases. • Which is why risk goes down as number of stocks in a portfolio goes up. • For rij=-1, portfolio risk could be eliminated.

29. Portfolio Risk Reduction • Risk can only be reduced so far. • Almost all stocks are positively correlated. • As the number of stocks increase, the risk approaches sm.

30. Portfolio Risk Reduction

31. Portfolio Risk Reduction

32. Capital Asset Pricing Model • CAPM shows return is a function of only the systematic risk. • Unsystematic risk can be reduced through diversification. • CAPM is used to determine the required rate of return. • Measured by degree of “correlation” with the market.

33. Capital Asset Pricing Model • bj is a measure of a stock’s sensitivity to market fluctuations. • When bj = 1, equal volatility with market. • Only measures systematic risk.

34. Portfolio Risk/Return • Term definitions: RF = Risk-free (US Treasury bill) rate of return. bj = Beta coefficient for stock j. kM = Expected return to the market portfolio. (kM – RF) = Risk premium on the market portfolio.

35. Capital Asset Pricing Model • Risk has two components • Market and firm-specific risks. • Firm specific risk can be eliminated through diversification. • Market risk cannot be eliminated. • Therefore, one must be compensated to hold market (systematic) risk.

36. Capital Asset Pricing Model • The greater the systematic risk, the higher return will be required by the market. • The beta (regression) coefficient measures systematic risk. • Because beta determines how the stock affects the riskiness of a diversified portfolio, beta is the most relevant measure of a stock’s risk!

37. Portfolio Beta Coefficients • Like expected return, the portfolio beta, bp, is a weighted average of individual stock b’s.

38. Portfolio Beta Coefficients • Given the following stocks:

39. Portfolio Risk/Return • We have talked about expected return. • Now we will talk of required return, required by efficient economic markets.

40. Portfolio Risk/Return - Example • If the market portfolio is expected to earn 14%, the risk-free rate is 6% and Wasup Dot.com has a beta of 2.

41. Portfolio Risk/Return - Example • Earlier, we said that this stock had an expected return of 30%. • Based on a required return of 22%, should you buy or sell? • Buy - It is under-priced!!!

42. The Security Market Line - SML • If we allow the x-axis to represent bj, and the y-axis to represent the required return, kj, the resulting graph is called the Security Market Line - SML. • Note that RF is the intercept. • Note that (kM-RF), or market risk premium, is the slope.

43. The Security Market Line - SML

44. The Security Market Line - SML

45. Impact of Inflation on SML • We will find out next chapter that inflationary expectation are embedded in interest rates (as inflation is expected to go up - interest rates go up). • The risk premium is expected to stay constant over time.

46. Impact of Inflation on SML

47. Impact of Inflation on SML

48. Impact of Risk Aversion on SML • If there were no risk aversion, all assets would earn the same return. • As risk aversion increases, the risk premium (the slope of the line) increases.

49. Impact of Risk Aversion on SML

50. Impact of Risk Aversion on SML