Question

Using the data in the following table, answer questions.

Year	Stock X	Stock Y
2012	-11%	-5%
2013	15%	25%
2014	10%	15%
2015	-5%	-15%
2016	5%	-5%
2017	8%	-2%
2018	7%	10%
2019	5%	15%
Average return
Standard deviation
Correlation between Stock X and Stock Y	0.7567

1.Calculate the standard deviation of returns for Stocks X and Y.

2.For a portfolio that is 75% weighted in Stock X, and 25% weighted in Stock Y, calculate the expected return of the portfolio.  

3.Calculate the standard deviation of your portfolio based on the weights of Stocks X and Y stated in part (2).    

4.Suppose the correlation between Stocks X and Y has reduced to 0.35, does it increase or reduce the standard deviation of your portfolio based on the weights of Stocks X and Y stated in part (2). Explain your answer.         

Answer 1

Q1)Using financial calculator to calculate the standard deviation of stock X and stock Y

First press '2nd' and then 'Data'

Inputs: X01= -11% Y01= -5%

X02= 10% Y02= 25%

X03= 15% Y03= 15%

X04= -5% Y04= -15%

X05= 5% Y05= -5%

X06= 8% Y06= -2%

X07= 7% Y07= 10%

X08= 5% Y08= 15%

After putting in these values, Press '2nd' and then 'STAT' . USE the arrow button to scroll down to see the answer for standard deviation.

Standard deviation of X = 7.822%

Standard deviation of Y= 12.617%

Q2) Return from stock X = -11% + 10% + 15% - 5% + 5% + 8% + 7% + 5% / 8

= 34% / 8

= 4.25%

Return from stock Y = -5% + 25% + 15% -15% - 5% - 2% + 10% + 15% / 8

= 38% / 8

= 4.75%

Return from portfolio= weight of stock X × return from stock X + weight of stock Y × return from stock Y

= 0.75 × 4.25% + 0.25 × 4.75%

= 3.1875% + 1.1875%

= 4.375%

Q3) standard deviation of portfolio

= √ (weight of X)^2 × (std deviation of X)^2 + (weight of Y)^2 × (std deviation of Y)^2 + 2 × weight of X × weight of Y × std deviation of X × std deviation of Y × correlation

= √ (0.75)^2 (0.0782)^2 + (0.25)^2 (0.12617)^2 + 2 × 0.75 × 0.25 × 0.0782 × 0.12617 × 0.7567

= √ (0.5625) (0.0061) + (0.0625) (0.0159) + 0.0028

= √ 0.0034 + 0.0099 + 0.0028

= √ 0.0161

= 0.1269 or 12.69%

Note:- Answer might differ due to rounding off

Q4) As the correlation between Stock X and stock Y decreases, it reduces the standard deviation of the protfolio. There is a direct relationship between risk and correlation. Higher the correlation, higher will be the risk and vice versa.