1 / 36

Introduction to Risk and Return

Introduction to Risk and Return. Where does the discount rate come from?. Today’s learning objective. Introduction to risk How to measure investment performance Rates of Return 73 Years of Capital Market History Measuring risk and risk premium Risk & Portfolio Diversification

beau-shepherd
Download Presentation

Introduction to Risk and Return

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Introduction to Risk and Return Where does the discount rate come from? FIN 351: lecture 6

  2. Today’s learning objective • Introduction to risk • How to measure investment performance • Rates of Return • 73 Years of Capital Market History • Measuring risk and risk premium • Risk & Portfolio Diversification • Two types of risk • How to measure systematic risk • CAPM

  3. How to measure the performance of your investment • Suppose you buy one share of IBM at $74 this year and sell it at the expected price of $102. IBM pays a dividend of $1.25 for your investment • What profit do you expect to make for your investment? • What profit do you expect to make for one dollar investment?

  4. Solution • Profit in total =102-74+1.25=$29.25 • Profit per one dollar=29.25/74=0.395 or 39.5%

  5. Rates of Return

  6. Rates of Return

  7. Rates of Return

  8. Rates of Return Nominal vs. Real Suppose that the inflation rate is1.6%

  9. Market Indexes Dow Jones Industrial Average (The Dow) Value of a portfolio holding one share in each of 30 large industrial firms. Standard & Poor’s Composite Index (The S&P 500) Value of a portfolio holding shares in 500 firms. Holdings are proportional to the number of shares in the issues.

  10. The performance of $0.1 investment

  11. Volatility of portfolios Volatility Year

  12. Why are stock returns so high? • To invest in stocks, investors require a risk premium with respect to relative risk-free security such as government securities. • The expected return on a risky security is equal to the risk-free rate plus a risk premium • Expected return =risk-free rate + risk premium • Risk premium =expected return –risk-free rate • Example • 23.3% (1981 on market portfolio)=14%+9.3% • 14.1% (1999 on market portfolio)=4.8%+9.3%

  13. How to Measure Risk • We can use the variance or the standard deviation of the expected rate of return to measure risk. • Variance or standard deviation measure weighted average of squared deviation of each observation from the mean.

  14. Some formula • Suppose that there are N states, then the expected rate of return (mean) is • The variance of the rate of return is • The standard deviation

  15. Example of risk • Stock A has the following returns depending on the state of the economy next year as follows: Probability of the state Return rate State of economy 0.6 Good 20% 0.3 Average 10% 0.1 -5% Bad

  16. Measure risk (continue) • First, calculate the mean return or the expected rate of return. Here N=3 (three states) • Expected rate of return is r-bar= p1*r1+p2*r2+p3*r3=0.6*0.2+0.3*0.1+0.1*(-0.05) =14.5% • The variance of return is p1*(r1- r-bar)2+p2*(r2- r-bar)2+p3*(r3-r-bar)2 =0.003325 • The standard deviation is 0.0577=5.7%

  17. Two types of risks Unique Risk - Risk factors affecting only that firm. Also called “firm-level risk.” Market Risk - Economy-wide sources of risk that affect the overall stock market. Also called “systematic risk.”

  18. Can we reduce risk? • Yes, we can reduce risk by diversification: that is, we invest our money in different assets or form a portfolio of different assets. • Can we understand intuitively why diversification can reduce risk?

  19. Portfolio weights • Let W be the total money invested in a portfolio, a set of assets. • Let xi be the proportion of total wealth invested in asset i. Then xi is called portfolio weight for asset i. The sum of portfolio weights for all the assets in the portfolio is 1, that is,

  20. Example • You invest $400 of your $1000 in IBM at a price of $74 per share and the other in Dell at a price of $28. • What is the portfolio weight for IBM and Dell respectively? • Are you sure that you are right?

  21. Solution • xIBM=400/1000=0.4 • xDell=600/1000=0.6 • xIBM+xDell=1

  22. Some formula for portfolios • The return of a portfolio is the weighted average of returns of the stocks in the portfolio. That is, • The expected return of a portfolio is the weighted average of expected returns of the stocks in the portfolio. That is,

  23. Risk and Diversification (example) • John puts his money half in stock A and half in stock B, as shown in the following. • What is the mean and variance of the return of John’s portfolio?

  24. My solution • The mean of the return of a portfolio is the weighted average of the returns of the stocks in the portfolio. Thus the mean of the return of John’s portfolio is • The variance of the return of the portfolio is portfolio variance

  25. Risk and Diversification

  26. Measuring Market Risk • Market Portfolio • It is a portfolio of all assets in the economy. In practice a broad stock market index, such as the S&P 500 is used to represent the market portfolio. The market return is denoted by Rm • Beta (β) • Sensitivity of a stock’s return to the return on the market portfolio, • Mathematically,

  27. An intuitive example for Beta Turbo Charged Seafood has the following % returns on its stock, relative to the listed changes in the % return on the market portfolio. The beta of Turbo Charged Seafood can be derived from this information.

  28. Measuring Market Risk (example, continue)

  29. Measuring Market Risk (continue) • When the market was up 1%, Turbo average % change was +0.8% • When the market was down 1%, Turbo average % change was -0.8% • The average change of 1.6 % (-0.8 to 0.8) divided by the 2% (-1.0 to 1.0) change in the market produces a beta of 0.8. β=1.6/2=0.8

  30. Another example • Suppose we have following information: Market Stock A Stock B State -6% -8% -10% bad 24% 32% good 38% a. What is the beta for each stock? b. What is the expected return for each stock if each scenario is equally likely? c. What is the expected return for each stock if the probability for good economy is 20%?

  31. Solution a. b. c.

  32. Portfolio Betas • Diversification reduces unique risk, but not market risk. • The beta of a portfolio will be an weighted average of the betas of the securities in the portfolio. • What is the beta of the market portfolio? • What is the beta of the risk-free security?

  33. Example • Suppose you have a portfolio of IBM and Dell with a beta of 1.2 and 2.2, respectively. If you put 50% of your money in IBM, and the other in Dell, what is the beta of your portfolio Beta of your portfolio =0.5*1.2 +0.5*2.2=1.7

  34. Market risk and risk premium • Risk premium for bearing market risk • The difference between the expected return required by investors and the risk-free asset. • Example, the expected return on IBM is 10%, the risk-free rate is 5%, and the risk premium is 10% -5%=5% • If a security ( an individual security or a portfolio) has market or systematic risk, risk-averse investors will require a risk premium.

  35. CAPM (Capital Asset Pricing Model) • The risk premium on each security is proportional to the market risk premium and the beta of the security. • That is,

  36. Security market line • The graphic representation of CAPM in the expected return and Beta plane Security Market Line Rm rf

More Related