How to calculate Standard Deviation of two stocks?

 Portfolio correlation:

The correlation states that how much one stock is related to other stock. It measure on the scale of +1.0 to -1.0. If the two stocks have +1 correlation it means both the stocks are positively correlated and if the return of one stock decreases then the return of other stock also decreases in same manner. If both the stocks have 0 correlations it means the two stocks are not correlated it means the return of one stock is increases the other stock does not show the same effect. If the two stocks have -1 correlation it means they are negative correlated and if the return of one stock increases then the return of other stock decreases. Correlation shows the degree of relationship between two stocks.

Formula:

R_ij = cov_ij / σ_i σ_j

Where,

cov_ij = co-variance between stock i and j

σ_i = standard deviation of asset i

σ_j = standard deviation of asset j

Portfolio Co-variance: The co-variance states that how two stocks price move in future. If two stocks move in same direction it means the two stocks have positive co-variance. The negative co-variance means the two stocks move in opposite direction. The investors want to invest in those stocks which have negative co-variance which help to reduce the risk level.

Formula:

Co-variance =Ʃ (return_i –Average_i)*(Return_j – Average_j) / Sample size – 1

OR

Co-variance = p_ij * σ_i *σ_j

Standard deviation of two stocks portfolio: Standard deviation shows the risk level of two stocks.

Formula:

σ_p = √(w_i² σ_i² + w_j² σ_j² + 2w_i w_j cov_ij)

or

σ_p = √(w_i² σ_i² + w_j² σ_j² + 2w_i w_j σ_i σ_j p_ij)

Where,

σ_p = standard deviation of portfolio

w_i and w_j = weight of security i and j

p_ij = correlation of security i and j

Example: Suppose Mr. Y has invested in two companies stock that is AB Company and MN Company. Find out the co-variance between AB stock and MN stock.

Stock	Standard deviation	Correlation of stock AB and MN
AB stock	21%	0.25
MN stock	28%

Solution:

Co-variance =p_ij * σ_i *σ_j

= 0.25*21*28

= 1.47

It shows positive co-variance means both stocks prices were move in same direction.

Example: Find out the Correlation if stock A has 24% and stock B has 32% standard deviation. The co-variance between two stocks is 0.18.

Solution: R_ij = cov_ij / σ_i σ_j

= 0.18 / 24*32

= 0.000234%

It shows zero correlation between AB stock and MN stock. So, there is no relationship between these two stocks.

Example: Find out the standard deviation of two stocks with the help of given information:

Stock	Weight of stock	Standard deviation
A	60%	52%
B	40%	45%

 The correlation of stock A and B is 0.32.

Solution:

σ_p = √(w_i² σ_i² + w_j² σ_j² + 2w_i w_j σ_i σ_j p_ij)

= √ (0.60² *52² + 0.40² *45² + 2*0.6 *0.4*52*45*0.32)

= √ (0.36*2, 704 + 0.16*2, 025 + 0.48*748.8)

= √ (973.44 + 324 + 359.42)

= √1, 656.86

= 40.70%

Example: Mr X has invested in stock C and D. The weights of security C and D in a portfolio is 30% and 70% respectively. The co-variance of stock C and D is 0.18. The standard deviation of stock C and D is 26% and 38% respectively. Find out the standard deviation of a portfolio.

Solution:

σ_p = √(w_i² σ_i² + w_j² σ_j² + 2w_i w_j cov_ij)

= √ (0.3²*26² + 0.7²*38² + 2*0.3*0.7*0.18)

= √ (0.09*676 + 0.49*1, 444 + 0.42*0.18)

= √ (60.84 + 707.56 + 0.0756)

= √ 768.48

= 27.72%