Question

Create a portfolio using the four stocks and information below:

	Expected Return	Standard Deviation	Weight in Portfolio
Stock A	21.00%	21.00%	15.00%
Stock B	5.00%	17.00%	28.00%
Stock C	7.00%	12.00%	11.00%
Stock D	22.00%	22.00%	46.00%
----------------------	----------------------	----------------------	----------------------
Correlation (A,B)	0.7000	----------------------	----------------------
Correlation (A,C)	0.4900	----------------------	----------------------
Correlation (A,D)	0.2500	----------------------	----------------------
Correlation (B,C)	0.4400	----------------------	----------------------
Correlation (B,D)	0.9600	----------------------	----------------------
Correlation (C,D)	0.2000	----------------------	----------------------

(Do not round intermediate calculations. Record your answers in decimal form and round your answers to 4 decimal places. Ex. x.xxxx)

What is the variance of A?

What is the variance of B?

What is the variance of C?

What is the variance of D?

What is the Correlation (A,A)?

What is the Correlation (B,B)?

What is the Correlation (C,C)?

What is the Correlation (D,D)?

What is the Covariance (A,A)?

What is the Covariance (A,B)?

What is the Covariance (A,C)?

What is the Covariance (A,D)?

What is the Covariance (B,A)?

What is the Covariance (B,B)?

What is the Covariance (B,C)?

What is the Covariance (B,D)?

What is the Covariance (C,A)?

What is the Covariance (C,B)?

What is the Covariance (C,C)?

What is the Covariance (C,D)?

What is the Covariance (D,A)?

What is the Covariance (D,B)?

What is the Covariance (D,C)?

What is the Covariance (D,D)?

What is the expected return on the portfolio above?

What is the variance on the portfolio above?

What is the standard deviation on the portfolio above?

please i need the answers to be correct

Answer 1

Before answering the questions, lets revise few important concepts.

Kindly note that all of the concepts involve "Sample" as the common word

1. Sample Variance - It is a measurement of spread or distance of each number from its mean for a given dataset. This is calculated by summing the squared difference between each number and its mean divided by the number of values in the given dataset. Also, it is the square of standard deviation of a given dataset. This is mathematically represented as

Kindly note that standard deviation is squared root of variance

2. Sample Covariance - As per standard definition, covariance is defined as the expected value of the product of the deviations of two random variables from their respective means. This is mathematically represented as

where X and Y are two random variables of two different dataset with a sample size of n.

3. Sample Correlation - Correlation coefficient is the covariance of two variables divided by the product of their sample standard deviations. It is essentially a linear relationship between two variables.

Now this should solve most of the questions easily. Lets try one by one

a. Variance of A = square of standard deviation of A = = 4.41%

b. Variance of B = = 0.25%

c. Variance of C = = 0.49%

d. Variance of D = = 4.84%

According to the concept of correlation, Correlation of two same variables will be always equal to 1 as it is linearly correlated to each other. Students can mathematically try to achieve the same.

e. Covariance (A,A) is similar to variance of A = 4.41%

f. Covariance (B,B) = 0.25%

g. Covariance (C,C) = 0.49%

h. Covariance (D,D) = 4.84%

i. Covariance (A,B) = Correlation (A,B)*(Standard Deviation of A)*(Standard Deviation of B) = 0.7*(0.21*0.05) = 0.735%

j. Covariance (A,C) = 0.49*(0.21*0.07) = 0.7203% = Covariance (C,A) (as the order of representation has no effect on the actual results)

k. Covariance (A,D) = 0.25*(0.21*.22) = 1.155% = Covariance (D,A)

l. Covariance (B,A) = Covariance (A,B) = 0.735% (as the order of representation has no effect on the actual results)

m. Covariance (B,C) = Covariance (C,B) = 0.44*(0.05*0.07) = 0.154%

n. Covariance (B,D) = Covariance (D,B) = 0.96*(0.05*0.22) = 1.056%

o. Covariance (C,D) = Covariance (D,C) = 0.2*(0.07*0.22) = 0.308%

p. Expected Return of the portfolio = weight of each stock in the portfolio * expected return of each stock in the portfolio

Mathematically

Therefore, E(R_P) = 15%*21% + 28%*5% + 11%*7% + 46%*22% = 15.44%

q. Standard deviation of a portfolio is mathematically represented as (kindly remember the following)

Standard Deviation = 11.7173%

r. Variance of the portfolio = 1.3729%