1. slide no.: 1 Prof. Dr. Rainer Stachuletz – Berlin School of Economics Betriebswirtschaftliche Bewertungsmethoden Grundlagen der Gestaltung effizienter Wertpapierportfolios -Grundelemente der finanzwirtschaftlichen Portfoliotheorie- und politik Prof. Dr. Rainer Stachuletz Corporate Finance

2. slide no.: 2 Prof. Dr. Rainer Stachuletz – Berlin School of Economics Measuring Risk Variance - Average value of squared deviations from mean. A measure of volatility. Standard Deviation – Square root of the average value of squared deviations from mean (Variance).

3. slide no.: 3 Prof. Dr. Rainer Stachuletz – Berlin School of Economics Measuring Risk Coin Toss Game-calculating variance and standard deviation

4. slide no.: 4 Prof. Dr. Rainer Stachuletz – Berlin School of Economics Measuring Risk 68% mean - 1  + 1  Statistically the mean return from the coin-toss-game will be 10% at a standard deviation of 21,2 % (i.e. 10% +/- 21,2%).

5. slide no.: 5 Prof. Dr. Rainer Stachuletz – Berlin School of Economics Measuring Portfolio Return

6. slide no.: 6 Prof. Dr. Rainer Stachuletz – Berlin School of Economics Measuring Risk Diversification - Strategy designed to reduce risk by spreading the portfolio across many investments. Unique Risk - Risk factors affecting only that firm. Also called “diversifiable risk.” Market Risk - Economy-wide sources of risk that affect the overall stock market. Also called “systematic risk.”

7. slide no.: 7 Prof. Dr. Rainer Stachuletz – Berlin School of Economics Measuring Portfolio Risk Diversifiable Risks Undiversi- fiable Risks

8. slide no.: 8 Prof. Dr. Rainer Stachuletz – Berlin School of Economics Portfolio Risk The variance of a two stock portfolio is the sum of these four boxes

9. slide no.: 9 Prof. Dr. Rainer Stachuletz – Berlin School of Economics Portfolio Risk Example Suppose you invest 65% of your portfolio in Coca-Cola and 35% in Reebok. The expected dollar return on your CC is 10% x 65% = 6.5% at a standard deviation of 31.5% and on Reebok it is 20% x 35% = 7.0% at a standard deviation of 58,5%. The expected return on your portfolio is 6.5 + 7.0 = 13.50%. Assume a correlation coefficient of 1. % Portf.ReturnRisk Coca Cola 65 %10 %31.5 % Reebok 35%20 %58.5 %

10. slide no.: 10 Prof. Dr. Rainer Stachuletz – Berlin School of Economics Portfolio Risk Example Suppose you invest 65% of your portfolio in Coca-Cola and 35% in Reebok. The expected dollar return on your CC is 10% x 65% = 6.5% at a standard deviation of 31.5% and on Reebok it is 20% x 35% = 7.0% at a standard deviation of 58,5%. The expected return on your portfolio is 6.5 + 7.0 = 13.50%. Assume a correlation coefficient of 1.

11. slide no.: 11 Prof. Dr. Rainer Stachuletz – Berlin School of Economics Portfolio Risk Example Suppose you invest 65% of your portfolio in Coca-Cola and 35% in Reebok. The expected dollar return on your CC is 10% x 65% = 6.5% at a standard deviation of 31.5% and on Reebok it is 20% x 35% = 7.0% at a standard deviation of 58,5%. The expected return on your portfolio is 6.5 + 7.0 = 13.50%. Assume a correlation coefficient of 1.

12. slide no.: 12 Prof. Dr. Rainer Stachuletz – Berlin School of Economics Possible Outcomes at a Return- Correlation of +1.0. Portfolio Risk & Return (Cola/Reebok-Case)

13. slide no.: 13 Prof. Dr. Rainer Stachuletz – Berlin School of Economics Portfolio Risk & Return (Cola/Reebok-Case) Possible Out- comes at a Return-Cor- relation of +1.0.

14. slide no.: 14 Prof. Dr. Rainer Stachuletz – Berlin School of Economics Portfolio Risk & Return (Cola/Reebok-Case) Possible Outcomes at a Return- Correlation of – 0.5

15. slide no.: 15 Prof. Dr. Rainer Stachuletz – Berlin School of Economics Portfolio Risk & Return (Cola/Reebok-Case) Possible Outcomes at a Return- Correlation of – 0.5

16. slide no.: 16 Prof. Dr. Rainer Stachuletz – Berlin School of Economics Portfolio Risk & Return (Cola/Reebok-Case) Possible Outcomes at a Return- Correlation of – 1.0

17. slide no.: 17 Prof. Dr. Rainer Stachuletz – Berlin School of Economics Portfolio Risk & Return (Cola/Reebok-Case) Possible Outcomes at a Return- Correlation of – 1.0

18. slide no.: 18 Prof. Dr. Rainer Stachuletz – Berlin School of Economics The Correlation Determines The Riskiness of a Portfolio

19. slide no.: 19 Prof. Dr. Rainer Stachuletz – Berlin School of Economics Portfolio Risk The shaded boxes contain variance terms; the remainder contain covariance terms. 1 2 3 4 5 6 N 123456N STOCK To calculate portfolio variance add up the boxes

20. slide no.: 20 Prof. Dr. Rainer Stachuletz – Berlin School of Economics Beta and Unique Risk beta 10% -+ - 10%+10% Copyright 1996 by The McGraw-Hill Companies, Inc -10% 1. Total risk = diversifiable risk + market risk 2. Market risk is measured by beta, the sensitivity of a stock`s return to market changes Expected stock return Expected market return

21. slide no.: 21 Prof. Dr. Rainer Stachuletz – Berlin School of Economics Beta and Unique Risk Market Portfolio - Portfolio of all assets in the economy. In practice a broad stock market index, such as the S&P Composite, is used to represent the market. Beta - Sensitivity of a stock’s return to the return on the market portfolio.

22. slide no.: 22 Prof. Dr. Rainer Stachuletz – Berlin School of Economics Beta and Unique Risk

23. slide no.: 23 Prof. Dr. Rainer Stachuletz – Berlin School of Economics Exercise: Portfolio of Pfizer and E.on - stocks Based on monthly data (return and risk) we can annualize that figures: Return (e.)Risk (e.) Pfizer 41,6 %44,80 % E.on 10,8 %16,42 % Stock pricesReturnsDeviation from mean

24. slide no.: 24 Prof. Dr. Rainer Stachuletz – Berlin School of Economics Exercise: Portfolio of Pfizer and E.on - stocks

25. slide no.: 25 Prof. Dr. Rainer Stachuletz – Berlin School of Economics Exercise: Portfolio of Pfizer and E.on – stocks Risk and Return Combinations

26. slide no.: 26 Prof. Dr. Rainer Stachuletz – Berlin School of Economics Portfolio Risk and Return Combinations at Correlation of -1

27. slide no.: 27 Prof. Dr. Rainer Stachuletz – Berlin School of Economics Portfolio Risk and Return Combinations at Correlation of -1

28. slide no.: 28 Prof. Dr. Rainer Stachuletz – Berlin School of Economics Portfolio Risk and Return Combinations at Correlation of +1

29. slide no.: 29 Prof. Dr. Rainer Stachuletz – Berlin School of Economics Portfolio Risk and Return Combinations at Correlation of +1