Business Finance (MGT 232) Lecture 14

Risk and Return

Overview of the Last Lecture Risk and Return Stand Alone Expected return Stand alone risk Coefficient of variance

Risk Attitudes Certainty Equivalent (CE) is the amount of cash someone would require with certainty at a point in time to make the individual indifferent between that certain amount and an amount expected to be received with risk at the same point in time.

Risk Attitudes Certainty equivalent > Expected value Risk Preference Certainty equivalent = Expected value Risk Indifference Certainty equivalent < Expected value Risk Aversion Most individuals are Risk Averse.

Risk Attitude Example You have the choice between (1) a guaranteed rupee reward or (2) a coin-flip gamble of Rs.100,000 (50% chance) or Rs.0 (50% chance). The expected value of the gamble is Rs.50,000. Mariam requires a guaranteed Rs.25,000, or more, to call off the gamble. Ali is just as happy to take Rs.50,000 or take the risky gamble. Sameer requires at least Rs.52,000 to call off the gamble.

What are the Risk Attitude tendencies of each? Risk Attitude Example What are the Risk Attitude tendencies of each? Mariam shows “risk aversion” because her “certainty equivalent” < the expected value of the gamble. Ali exhibits “risk indifference” because his “certainty equivalent” equals the expected value of the gamble. Sameer reveals a “risk preference” because his “certainty equivalent” > the expected value of the gamble.

Portfolio Risk & Return “Don’t Put all your eggs in one basket” Portfolio is a group of two or more stocks

Expected return on a Portfolio Expected return on a portfolio is the weighted average of expected return on individual asset in a portfolio, with weights being fraction of wealth invested in each asset

Determining Portfolio Expected Return ^ rP = S ( Wj )( rj ) rP is the expected return for the portfolio, Wj is the weight (investment proportion) for the jth asset in the portfolio, rj is the expected return of the jth asset, m is the total number of assets in the portfolio. ^ j=1 ^ ^

Expected return on a Portfolio Shares ri wi A 12% B 11.5 C 10 D 9 Total wealth invested = Rs. 100,000 equally distributed

Expected return on a Portfolio

Risk of a Portfolio sP = S S Wj Wk sjk m m sP = S S Wj Wk sjk Wj is the weight (investment proportion) for the jth asset in the portfolio, Wk is the weight (investment proportion) for the kth asset in the portfolio, sjk is the covariance between returns for the jth and kth assets in the portfolio. j=1 k=1

Correlation Coefficient A standardized statistical measure of the linear relationship between two variables. The tendency of two variables to move together is called correlation and is represented by greek letter ρ

Correlation Coefficient The range is from -1.0 to + 1.0 -1.0 (perfect negative correlation) 0 (no correlation) +1.0 (perfect positive correlation)

Correlation Coefficient Average Correlation of two randomly selected stocks is 0.6 Range is +0.5 to 0.7 Adding more stocks to portfolio…risk keeps declining Acc. To a study; Single asset investment standard deviation is 35% Market portfolio standard deviation is 20%

Summary of the Portfolio Return and Risk Calculation Stock C Stock D Portfolio Return 9.00% 8.00% 8.64% Stand. Dev. 13.15% 10.65% 10.91% CV 1.46 1.33 1.26 The portfolio has the LOWEST coefficient of variation due to diversification.

Diversification and the Correlation Coefficient Combination E and F SECURITY E SECURITY F INVESTMENT RETURN TIME TIME TIME Combining securities that are not perfectly, positively correlated reduces risk.

Portfolio Risk and Expected Return Example You are creating a portfolio of Stock D and Stock BW (from earlier). You are investing Rs.2,000 in Stock BW and Rs.3,000 in Stock D. Remember that the expected return and standard deviation of Stock BW is 9% and 13.15%, respectively. The expected return and standard deviation of Stock D is 8% and 10.65%, respectively. The correlation coefficient between BW and D is 0.75. What is the expected return and standard deviation of the portfolio?

Determining Portfolio Expected Return WBW = Rs.2,000 / Rs.5,000 = .4 WD = Rs.3,000 / Rs.5,000 = .6 RP = (WBW)(RBW) + (WD)(RD) RP = (.4)(9%) + (.6)(8%) RP = (3.6%) + (4.8%) = 8.4%

Determining Portfolio Standard Deviation Two-asset portfolio: Col 1 Col 2 Row 1 WBW WBW sBW,BW WBW WD sBW,D Row 2 WD WBW sD,BW WD WD sD,D This represents the variance - covariance matrix for the two-asset portfolio.

Determining Portfolio Standard Deviation Two-asset portfolio: Col 1 Col 2 Row 1 (.4)(.4)(.0173) (.4)(.6)(.0105) Row 2 (.6)(.4)(.0105) (.6)(.6)(.0113) This represents substitution into the variance - covariance matrix.

Determining Portfolio Standard Deviation Two-asset portfolio: Col 1 Col 2 Row 1 (.0028) (.0025) Row 2 (.0025) (.0041) This represents the actual element values in the variance - covariance matrix.

Determining Portfolio Standard Deviation sP = .0028 + (2)(.0025) + .0041 sP = SQRT(.0119) sP = .1091 or 10.91% A weighted average of the individual standard deviations is INCORRECT.

Determining Portfolio Standard Deviation The WRONG way to calculate is a weighted average like: sP = .4 (13.15%) + .6(10.65%) sP = 5.26 + 6.39 = 11.65% 10.91% = 11.65% This is INCORRECT.

Summary Risk attitudes Portfolio return Portfolio Risk Coefficient of correlation Risk diversification