1. 5-1 Risk and Rates of Return Stand-alone risk Portfolio risk Risk & return: CAPM / SML

2. 5-2 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: Taka Percentage Terms

3. 5-3 Investment returns The rate of return on an investment can be calculated as follows: (Amount received – Amount invested) Return = ________________________ Amount invested For example, if $1,000 is invested and $1,100 is returned after one year, the rate of return for this investment is: ($1,100 - $1,000) / $1,000 = 10%.

4. 5-4 Return Income received change in market price beginning market price Income received on an investment plus any change in market price, usually expressed as a percent of the beginning market price of the investment. D t P t - P t-1 D t + (P t - P t-1 ) P t-1 R =

5. 5-5 Return Example $10 $9.50 $1 dividend The stock price for Stock A was $10 per share 1 year ago. The stock is currently trading at $9.50 per share, and shareholders just received a $1 dividend. What return was earned over the past year?

6. 5-6 Return Example $10 $9.50 $1 dividend The stock price for Stock A was $10 per share 1 year ago. The stock is currently trading at $9.50 per share, and shareholders just received a $1 dividend. What return was earned over the past year? $1.00 $9.50$10.00 $1.00 + ($9.50 - $10.00 ) $10.00 R R = 5% = 5%

7. 5-7 What is investment risk? Two types of investment risk Stand-alone risk Portfolio risk Investment returns are not known with certainty. Investment risk is related to the probability of earning a low or negative actual return. The greater the chance of lower than expected or negative returns, the riskier the investment.

8. 5-8 Investment alternatives EconomyProb. ABCDE Recession 0.18.0%-22.0%28.0%10.0%-13.0% Below avg 0.28.0%-2.0%14.7%-10.0%1.0% Average 0.48.0%20.0%0.0%7.0%15.0% Above avg 0.28.0%35.0%-10.0%45.0%29.0% Boom 0.18.0%50.0%-20.0%30.0%43.0%

9. 5-9 Return: Calculating the expected return for each alternative

10. 5-10 Summary of expected returns for all alternatives Exp return B 17.4% E 15.0% D 13.8% A 8.0% C 1.7% B has the highest expected return, and appears to be the best investment alternative, but is it really? Have we failed to account for risk?

11. 5-11 How to Determine the Expected Return and Standard Deviation K i P i (K i )(P i ) -.15.10 -.015 -.03.20 -.006.09.40.036.21.20.042.33.10.033.090 Sum 1.00.090 The expected return, R, for Stock is.09 or 9%

12. 5-12 Risk: Calculating the standard deviation for each alternative

13. 5-13 Standard deviation calculation

14. 5-14 How to Determine the Expected Return and Standard Deviation K i P i (K i )(P i ) (K i -K) 2 (P i ) -.15.10 -.015.00576 -.03.20 -.006.00288.09.40.036.00000.21.20.042.00288.33.10.033.00576.090.01728 Sum 1.00.090.01728

15. 5-15 Determining Standard Deviation (Risk Measure)   =  ( K i - K ) 2 ( P i )  =.01728 .131513.15%  =.1315 or 13.15%

16. 5-16 Comments on standard deviation as a measure of risk Standard deviation (σ i ) measures total, or stand-alone, risk. The larger σ i is, the lower the probability that actual returns will be closer to expected returns. Difficult to compare standard deviations, because return has not been accounted for.

17. 5-17 Determining Expected Return (Continuous Dist.) K =  ( K i ) / ( n ) K is the expected return for the asset, K i is the return for the ith observation, n is the total number of observations.

18. 5-18 Determining Standard Deviation (Risk Measure)   =  ( K i - K ) 2 ( n )

19. 5-19 9.6%, -15.4%, 26.7%, -0.2%, 20.9%, 28.3%, -5.9%, 3.3%, 12.2%, 10.5% Calculate the Expected Return and Standard Deviation

20. 5-20 Comparing risk and return SecurityExpected return Risk, σ A8.0%0.0% B17.4%20.0% C1.7%13.4% D13.8%18.8% E15.0%15.3%

21. 5-21 Coefficient of Variation (CV) A standardized measure of dispersion about the expected value, that shows the risk per unit of return.

22. 5-22 Risk rankings, by coefficient of variation CV A0.000 B1.149 C7.882 D1.362 E 1.020 C has the highest degree of risk per unit of return. B, despite having the highest standard deviation of returns, has a relatively average CV.

23. 5-23 Investor attitude towards risk Risk aversion – assumes investors dislike risk and require higher rates of return to encourage them to hold riskier securities. Risk premium – the difference between the return on a risky asset and less risky asset, which serves as compensation for investors to hold riskier securities.

24. 5-24 Portfolio construction: Risk and return Assume a two-stock portfolio is created with $50,000 invested in both HT and Collections. Expected return of a portfolio is a weighted average of each of the component assets of the portfolio. Standard deviation is a little more tricky and requires that a new probability distribution for the portfolio returns be devised.

25. 5-25 Calculating portfolio expected return

26. 5-26 An alternative method for determining portfolio expected return EconomyProb.BCPort. Recession0.1-22.0%28.0%3.0% Below avg0.2-2.0%14.7%6.4% Average0.420.0%0.0%10.0% Above avg0.235.0%-10.0%12.5% Boom0.150.0%-20.0%15.0%

27. 5-27 Calculating portfolio standard deviation and CV

28. 5-28 Comments on portfolio risk measures σ p = 3.3% is much lower than the σ i of either stock (σB = 20.0%; σ C. = 13.4%). σ p = 3.3% is lower than the weighted average of B and C’s σ (16.7%).  Portfolio provides average return of component stocks, but lower than average risk.