Question

Create a portfolio using the three stocks and information below:

	Expected Return	Standard Deviation	Weight in Portfolio
Stock A	6.00%	18.00%	31.00%
Stock B	6.00%	29.00%	19.00%
Stock C	22.00%	22.00%	50.00%
----------------------	----------------------	----------------------	----------------------
Correlation (A,B)	0.2700	----------------------	----------------------
Correlation (A,C)	0.3700	----------------------	----------------------
Correlation (B,C)	0.2600	----------------------	----------------------

(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 Correlation (A,A)?

What is the Correlation (B,B)?

What is the Correlation (C,C)?

What is the Covariance (A,A)?

What is the Covariance (A,B)?

What is the Covariance (A,C)?

What is the Covariance (B,A)?

What is the Covariance (B,B)?

What is the Covariance (B,C)?

What is the Covariance (C,A)?

What is the Covariance (C,B)?

What is the Covariance (C,C)?

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?

Answer 1

Given:

	Expected Return	Standard Deviation	Weight in Portfolio	Variance
Stock A	6.00%	18.00%	31.00%	3.24%
Stock B	6.00%	29.00%	19.00%	8.41%
Stock C	22.00%	22.00%	50.00%	4.84%
Correlation (A,B)	0.27
Correlation (A,C)	0.37
Correlation (B,C)	0.26

Formula: Variance of an asset = (standard deviation of the asset)^2

Correlation matrix (filled in using the given correlation numbers):

Correlation	A	B	C
A	1.00	0.27	0.37
B	0.27	1.00	0.26
C	0.37	0.26	1.00

Formula: Correlation(A,B) = Covariance(A,B)/standard deviation of A*standard deviation of B

Covariance(A,B) = Correlation(A,B)*standard deviation of A*standard deviation of B

Covariance matrix (using the formula above and the variance of assets):

Variance/covariance	A	B	C
A	3.24%	1.41%	1.47%
B	1.41%	8.41%	1.66%
C	1.47%	1.66%	4.84%

This covariance matrix can now be used to find the portfolio return, variance and standard deviation, using matrix calculation, as shown below:

Note: The covariance(A,A) = variance of A; correlation(A,A) = 1

Remember to press CTRL+SHIFT+ENTER when using MMULT() function.