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	.194	.194	.044
2	.34	.144	.094	.094
3	.34	.094	.144	.144
4	.16	.044	.044	.194

  

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

Security 1
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(A)^2* probability
1	0.16	19.4	3.104	8.0104	0.001026664
2	0.34	14.4	4.896	3.0104	0.000308125
3	0.34	9.4	3.196	-1.9896	0.000134589
4	0.044	4.4	0.1936	-6.9896	0.00021496
	a.1 Expected return %=	sum of weighted return =	11.39	Sum=Variance Security 1=	0.00168
			a.2 Standard deviation of Security 1%	=(Variance)^(1/2)	4.1
Security 2
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(B)^2* probability
1	0.16	19.4	3.104	8.0104	0.001026664
2	0.34	9.4	3.196	-1.9896	0.000134589
3	0.34	14.4	4.896	3.0104	0.000308125
4	0.044	4.4	0.1936	-6.9896	0.00021496
	a. 1Expected return %=	sum of weighted return =	11.39	Sum=Variance Security 2=	0.00168
			a. 2Standard deviation of Security 2%	=(Variance)^(1/2)	4.1
Security 3
Scenario	Probability	Return%	=rate of return% * probability	Actual return -expected return(A)%	(C)^2* probability
1	0.16	4.4	0.704	-5.2496	0.000440933
2	0.34	9.4	3.196	-0.2496	2.11821E-06
3	0.34	14.4	4.896	4.7504	0.000767254
4	0.044	19.4	0.8536	9.7504	0.000418309
	a. 1 Expected return %=	sum of weighted return =	9.65	Sum=Variance Security 3=	0.00163
			a. 2Standard deviation of Security 3%	=(Variance)^(1/2)	4.04
Covariance Security 1 Security 2:
Scenario	Probability	Actual return% -expected return% for A(A)	Actual return% -expected return% For B(B)	(A)*(B)*probability
1	0.16	8.0104	8.0104	0.001026664
2	0.34	3.0104	-1.9896	-0.000203643
3	0.34	-1.99	3.0104	-0.000203643
4	0.044	-698.96%	-6.9896	0.00021496
			b.1 Covariance=sum=	0.00083
		b. 2Correlation A&B=	Covariance/(std devA*std devB)=	0.4954
Covariance Security 1 Security 3:
Scenario	Probability	Actual return% -expected return% for A(A)	Actual return% -expected return% for C(C)	(A)*(C)*probability
1	0.16	8.0104	-5.2496	-0.000672822
2	0.34	3.0104	-0.2496	-2.55475E-05
3	0.34	-198.96%	4.7504	-0.000321347
4	0.044	-6.9896	9.7504	-0.000299866
			b. 1 Covariance=sum=	-0.001312
		b. 2 Correlation A&C=	Covariance/(std devA*std devC)=	-0.7967
Covariance Security 2 Security 3:
Scenario	Probability	Actual return% -expected return% For B(B)	Actual return% -expected return% for C(C)	(B)*(C)*probability
1	0.16	8.0104	-5.2496	-0.000672822
2	0.34	-1.9896	-0.2496	1.68845E-05
3	0.34	3.0104	4.7504	0.000486221
4	0.044	-6.9896	9.7504	-0.000299866
			b. 1 Covariance=sum=	-0.00047
		b. 2 Correlation B&C=	Covariance/(std devB*std devC)=	-0.2835

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