Question

There are three securities in the market. The following chart shows their possible payoffs:

State	Probability of Outcome	Return on Security 1	Return on Security 2	Return on Security 3
1	.16	.207	.207	.057
2	.34	.157	.107	.107
3	.34	.107	.157	.157
4	.16	.057	.057	.207

a-1.	What is the expected return of each security? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

Security 1 ____ %

Security 2 ____ %

Security 3 ____ %

a-2.	What is the standard deviation of each security? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

Security 1 ____ %

Security 2 ____ %

Security 3 ____ %

b-1.	What are the covariances between the pairs of securities? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answers to 5 decimal places, e.g., 32.16162.)

Security 1 & 2  ____

Security 1 & 3 ____

Security 2 & 3 ____

b-2.	What are the correlations between the pairs of securities? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answers to 4 decimal places, e.g., 32.1616.)

Security 1 & 2 ____

Security 1 & 3 ____

Security 2 & 3 ____

c-1.	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 and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

  Security 1 & 2 ____ %

c-2.	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 and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

   Security 1 & 2 ____ %
  

d-1.	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 and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Security 1 & 3 ____ %

d-2.	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.)

Security 1 & 3 ____

e-1.	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 and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Security 2 & 3 ____ %    

e-2.	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 and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Security 2 & 3 ____ %     

  
      

  
      

  

      

    

Answer 1

Expected Return = [Probability(i) * Return(i)]

Security 1's Expected Return = [0.16 * 0.207] + [0.34 * 0.157] + [0.34 * 0.107] + [0.16 * 0.057]

= 0.03312 + 0.05338 + 0.03638 + 0.00912 = 0.132, or 13.20%

Security 2's Expected Return = [0.16 * 0.207] + [0.34 * 0.107] + [0.34 * 0.157] + [0.16 * 0.057]

= 0.03312 + 0.03638 + 0.05338 + 0.00912 = 0.132, or 13.20%

Security 3's Expected Return = [0.16 * 0.057] + [0.34 * 0.107] + [0.34 * 0.157] + [0.16 * 0.207]

= 0.00912 + 0.03638 + 0.05338 + 0.03312 = 0.132, or 13.20%