Problem 11-35 Covariance and Portfolio Standard Deviation What is the expected r
ID: 2779633 • Letter: P
Question
Problem 11-35 Covariance and Portfolio Standard Deviation
What is the expected return of each security? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places (e.g., 32.16).)
What is the standard deviation of each security? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places (e.g., 32.16).)
What are the covariances between the pairs of securities? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your final answers to 5 decimal places (e.g., 32.16161).)
What are the correlations between the pairs of securities? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your final answers to 4 decimal places (e.g., 32.1616).)
What is the expected return of a portfolio with half of its funds invested in Security 1 and half in Security 2? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places (e.g., 32.16).)
What is the standard deviation of a portfolio with half of its funds invested in Security 1 and half in Security 2? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places (e.g., 32.16).)
What is the expected return of a portfolio with half of its funds invested in Security 1 and half in Security 3? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places (e.g., 32.16).)
What is the standard deviation of a portfolio with half of its funds invested in Security 1 and half in Security 3? (Leave no cells blank - be certain to enter "0" wherever required. Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places (e.g., 32.16).))
What is the expected return of a portfolio with half of its funds invested in Security 2 and half in Security 3? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places (e.g., 32.16).)
What is the standard deviation of a portfolio with half of its funds invested in Security 2 and half in Security 3? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places (e.g., 32.16).)
There are three securities in the market. The following chart shows their possible payoffs:
Explanation / Answer
A B C D E=A*B F=A*C G=A*D State Probability Return on Security 1 Return on Security 2 Return on Security 3 Probability Probability Probability of Outcome *Return Security 1 *Return Security 2 *Return Security 3 1 0.16 0.21 0.21 0.06 0.0336 0.0336 0.0096 2 0.34 0.16 0.11 0.11 0.0544 0.0374 0.0374 3 0.34 0.11 0.16 0.16 0.0374 0.0544 0.0544 4 0.16 0.06 0.06 0.21 0.0096 0.0096 0.0336 TOTAL 0.1350 0.1350 0.1350 a1 Expected Return of each security Expected return of a security=Sum of (Return of security*Probability of outcome) Expected Return Security1 13.50% Security2 13.50% Security3 13.50% a2 Calculation of Standard Deviation: Security :1 A B C=B-13.5 D=C^2 E=D*A State Probability Return on Security 1(percent) Deviation=Return minus Deviation Deviation square* of Outcome Expected return Squared Probability 1 0.16 21.00 7.50 56.25 9.00 2 0.34 16.00 2.50 6.25 2.13 3 0.34 11.00 (2.50) 6.25 2.13 4 0.16 6.00 (7.50) 56.25 9.00 TOTAL 22.25 VARIANCE of Security 1=Sum of (Deviation from expected return squared*Probability)=22.25 Standard Deviation =Square Root (Variance) Standard deviation of Security 1= 4.716990566 Standard deviation of Security 1= 4.72% Security :2 A B C=B-13.5 D=C^2 E=D*A State Probability Return on Security 1(percent) Deviation=Return minus Deviation Deviation square* of Outcome Expected return Squared Probability 1 0.16 6.00 (7.50) 56.25 9.00 2 0.34 11.00 (2.50) 6.25 2.13 3 0.34 16.00 2.50 6.25 2.13 4 0.16 21.00 7.50 56.25 9.00 TOTAL 22.25 VARIANCE of Security 1=Sum of (Deviation from expected return squared*Probability)=22.25 Standard Deviation =Square Root (Variance) Standard deviation of Security 1= 4.716990566 Standard deviation of Security 1= 4.72% Security :3 A B C=B-13.5 D=C^2 E=D*A State Probability Return on Security 1(percent) Deviation=Return minus Deviation Deviation square* of Outcome Expected return Squared Probability 1 0.16 21.00 7.50 56.25 9.00 2 0.34 11.00 (2.50) 6.25 2.13 3 0.34 16.00 2.50 6.25 2.13 4 0.16 6.00 (7.50) 56.25 9.00 TOTAL 22.25 VARIANCE of Security 1=Sum of (Deviation from expected return squared*Probability)=22.25 Standard Deviation =Square Root (Variance) Standard deviation of Security 1= 4.716990566 Standard deviation of Security 1= 4.72% Standard Deviation Security 1 4.72% Security 2 4.72% Security 3 4.72% b1 Calculation of Covariance between Securities 1,2 A B C D= E G State Probability Return on Security 1 Return on Security 2 Security 1Deviation=Return minus Security 2Deviation=Return minus Deviation Security1*Deviation of Outcome Expected return Expected return Security2*Probability 1 0.16 21 21 7.50 7.50 9 2 0.34 16 11 2.50 (2.50) -2.125 3 0.34 11 16 (2.50) 2.50 -2.125 4 0.16 6 6 (7.50) (7.50) 9 TOTAL 13.75 Calculation of Covariance between Securities 1,3 A B C D= E G State Probability Return on Security 1 Return on Security 3 Security 1Deviation=Return minus Security 3Deviation=Return minus Deviation Security1*Deviation of Outcome Expected return Expected return Security3*Probability 1 0.16 21 6 7.50 (7.50) -9 2 0.34 16 11 2.50 (2.50) -2.125 3 0.34 11 16 (2.50) 2.50 -2.125 4 0.16 6 21 (7.50) 7.50 -9 TOTAL -22.25 Calculation of Covariance between Securities 2,3 A B C D= E G State Probability Return on Security 2 Return on Security 3 Security 2Deviation=Return minus Security 3Deviation=Return minus Deviation Security2*Deviation of Outcome Expected return Expected return Security3*Probability 1 0.16 21 6 7.50 (7.50) -9 2 0.34 11 11 (2.50) (2.50) 2.125 3 0.34 16 16 2.50 2.50 2.125 4 0.16 6 21 (7.50) 7.50 -9 TOTAL -13.75 Covariance Security 1&2 13.75 Security 1&3 -22.25 Security 2&3 -13.75 b2 Correlation between pairs of securities Correlation(x,y)=Covariance(x,y)/((Standard deviation x)*(standard Deviation y)) Covariance Standard Deviation 1 Standard Deviation 2 Standard Deviation 3 Correlation Security 1&2 13.75 4.72 4.72 0.617189744 Security 1&3 -22.25 4.72 4.72 -0.998725223 Security 2&3 -13.75 4.72 4.72 -0.617189744 Correlation Security 1&2 0.6172 Security 1&3 -0.9987 Security 2&3 -0.6172