Question

Considering the following information of three stocks Stock Expected rate of return Standard deviation ABC 13% 20% XYZ 14% 20% MNO 15% 20% The correlation between ABC and XYZ is 0.36 The correlation between ABC and MNO is 0.52 The correlation between XYZ and MNO is 0.68 You decide to invest only in two stocks out of these three stocks. You want to choose a combination of two stocks that will create lower standard deviation. Half of your money will be invested in the first stock and the rest in the second stock, what will be the standard deviation of your portfolio? If your answer is 20%, type 20.

Answer 1

Stock	Expected rate of return	Standard deviation
ABC	13%	20%
XYZ	14%	20%
MNO	15%	20%

Variance of the portfolio is calculated using the formula:

Portfolio Variance = σP2 = w12*σ12 + w22*σ22 + 2*ρ*w1*w2*σ1*σ2

where ρ is the correlation coefficient between two stocks

Standard deviation of ABC, XYZ, MNO is 20%. So we will choose the pair for which the correlation is lower and hence, it will create a portfolio of lower standard deviation

Correlation between ABC and XYZ = 0.36

Correlation between ABC and MNO = 0.52

Correlation between XYZ and MNO= 0.68

We see that the correlation between ABC and XYZ is lowest. Hence we will choose ABC and XYZ to create the portfolio. The portfolio consists of ABC and XYZ. Half of the money is invested in ABC and half in XYZ.

Portfolio

Weight of ABC in the portfolio = WABC = 0.5

Weight of XYZ in the portfolio = WXYZ = 0.5

Standard deviation of ABC = σABC = 20%

Standard devaition of XYZ = σXYZ = 20%

Correlation between ABC and XYZ = ρ = 0.36

Variance of portfolio = σP2 = W2ABC*σ2ABC + W2XYZ*σ2XYZ + 2*ρ*WABC*WXYZ*σABC*σXYZ

Portfolio Variance = σP2 = 0.52*(20%)2 + 0.52*(20%)2 + 2*0.36*0.5*0.5*20%*20% = 0.01 + 0.01 + 0.0072 = 0.0272

Standard deviation is sqyare root of variance

Standard deviation of portfolio = σP = (0.0272)1/2 = 16.4924225024706% ~ 16.49% (Rounded to two decimals)

Answer (%) -> 16.49