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CHAPTER 10 – Risk and Return

CHAPTER 10 – Risk and Return. Questions to be addressed. Differentiate between standalone risk and risk in a portfolio. How are they measured? What is market risk? How many stocks must a portfolio contain to be well diversified?

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CHAPTER 10 – Risk and Return

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  1. CHAPTER 10 – Risk and Return

  2. Questions to be addressed • Differentiate between standalone risk and risk in a portfolio. How are they measured? • What is market risk? How many stocks must a portfolio contain to be well diversified? • What is risk aversion? How is risk aversion related to the return of a stock? • What is CAPM? What is SML (security market line) in CAPM?

  3. What are investment returns? • Investment returns measure the financial results of an investment. • Returns may be historical or prospective (anticipated). • Returns can be expressed in: • Dollar terms. • Percentage terms.

  4. An investment costs $1,000 and is sold after 1 year for $1,100. Dollar return: $ Received - $ Invested $1,100 - $1,000 = $100. Percentage return: $ Return/$ Invested $100/$1,000 = 0.10 = 10%.

  5. What is investment risk? • Typically, investment returns are not known with certainty. • Investment risk pertains to the probability of earning a return less than that expected. • The greater the chance of a return far below the expected return, the greater the risk.

  6. Stand-Alone Risk • Standard deviation measures the stand-alone risk of an investment. • The larger the standard deviation, the higher the probability that returns will be far below the expected return.

  7. Stand-Alone: Risk Probability Distribution: Which stock is riskier? Why?

  8. ^ r = expected rate of return. ^ n ∑ r = riPi. i=1 Stand-Alone: Calculate the expected rate of return

  9. σ = Standard deviation σ = √ Variance = √ σ2 = √ n ^ ∑ (ri – r)2 Pi. i=1 Stand-Alone: What is the standard deviation of returns?

  10. Stand-Alone: Coefficient of Variation (CV) • CV = Standard deviation / expected return • CV shows the risk per unit of return. Thus, the lower the CV, the better investment.

  11. ^ rp is a weighted average (wi is % of portfolio in stock i): n ^ ^ rp = Σ wi ri i = 1 Portfolio Expected Return r sp depends on the correlations between stocks:

  12. Two-Stock Portfolios • Two stocks can be combined to form a riskless portfolio if r = -1.0. • Risk is not reduced at all if the two stocks have r = +1.0. • In general, stocks have r≈ 0.35, so risk is lowered but not eliminated. • Investors typically hold many stocks. • What happens when r = 0?

  13. Adding Stocks to a Portfolio • What would happen to the risk of an average 1-stock portfolio as more randomly selected stocks were added? • sp would decrease because the added stocks would not be perfectly correlated, but the expected portfolio return would remain relatively constant.

  14. s1 stock ≈ 35%sMany stocks ≈ 20%

  15. p Company Specific (Diversifiable) Risk 35% Stand-Alone Risk, p 20% 0 Market Risk 10 20 30 40 2,000 stocks Risk vs. Number of Stock in Portfolio

  16. Stand-alone risk = Market risk + Diversifiable risk • Market risk is that part of a security’s stand-alone risk that cannot be eliminated by diversification. • Firm-specific, or diversifiable, risk is that part of a security’s stand-alone risk that can be eliminated by diversification.

  17. Conclusions • As more stocks are added, each new stock has a smaller risk-reducing impact on the portfolio. • sp falls very slowly after about 40 stocks are included. The lower limit for sp is about 20%=sM . • By forming well-diversified portfolios, investors can eliminate about half the risk of owning a single stock. • Investors are compensated for bearing risk (beta, not s)

  18. Can an investor holding one stock earn a return commensurate with its risk? • No. Rational investors will minimize risk by holding portfolios. • They bear only market risk, so prices and returns reflect this lower risk. • The one-stock investor bears higher (stand-alone) risk, so the return is less than that required by the risk.

  19. How is market risk measured for individual securities? • Market risk, which is relevant for stocks held in well-diversified portfolios, is defined as the contribution of a security to the overall riskiness of the portfolio. • It is measured by a stock’s beta coefficient. For stock i, its beta is: • bi = (ri,Msi) / sM =COVi,M / VARIANCEM • Correlation of two sets of data: CORREL(cell1 of group1:cell2 of group1, cell1 of group2:cell2 of group2).

  20. How are betas calculated? • Beta is the measure of a stock’s risk, not standard deviation. • In addition to measuring a stock’s contribution of risk to a portfolio, beta also which measures the stock’s volatility relative to the market.

  21. Using a Regression to Estimate Beta • Run a regression with returns on the stock in question plotted on the Y axis and returns on the market portfolio plotted on the X axis. • The slope of the regression line, which measures relative volatility, is defined as the stock’s bta coefficient, or b. • Beta: slope (cell1 of group1:cell2 of group1, cell1 of group2:cell2 of group2).

  22. Calculating Beta for PQU

  23. Calculating Beta in Practice • Many analysts use the S&P 500 to find the market return. • Analysts typically use four or five years’ of monthly returns to establish the regression line. • Some analysts use 52 weeks of weekly returns.

  24. How is beta interpreted? • If b = 1.0, stock has average risk. • If b > 1.0, stock is riskier than average. • If b < 1.0, stock is less risky than average. • Most stocks have b in the range of 0.5 to 1.5. • Can a stock have a negative b?

  25. Web Sites for Beta • Go to http://finance.yahoo.com • Enter the ticker symbol for a “Stock Quote”, such as IBM or Dell, then click GO. • When the quote comes up, select Key Statistics from panel on left.

  26. Calculate beta for a portfolio bp = Weighted average of beta = w1b1 + w2b2+…+wnbn

  27. CAMP and SML (security market line) – Has the CAPM been completely confirmed or refuted? • No. The statistical tests have problems that make empirical verification or rejection virtually impossible. • Investors’ required returns are based on future risk, but betas are calculated with historical data. • Investors may be concerned about both stand-alone and market risk.

  28. EXCEL Command Summary: • Average: average(cell1, cell2 ) • Standard Deviation: stdve (cell1, cell2) • Correlation of two sets of data: CORREL(cell1 of group1:cell2 of group1, cell1 of group2:cell2 of group2). • Regression b: slope (cell1 of group1:cell2 of group1, cell1 of group2:cell2 of group2).

  29. Equations:Portfolio

  30. Equations: individual stock

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