Question

If the Formula for the variance of volatility in the returns a portfolio of 2 shares is as follows:

??2=(?2??2+(1−?)2???2+2?(1−?)??????)

where

?? = standard deviation of returns to portfolio

??= standard deviation of returns to Vodafone shares

??? = standard deviation of returns to BP shares

? = the proportion we invest in Vodafone

(1−?) = the proportion we invest in BP

? = The correlation coefficient between returns on the two shares

Then if:

??=0.35

???=0.4

?=0.3

What is the value of ? that minimises the variance in this portfolio?

Answer 1

Using Minimum variance portfolio formula

w = weight in Vodafone = (Standard deviation of BP^2 - Correlation * Standard deviation of BP * Standard deviation of Vodafone) / (Standard deviation of Vodafone^2 + Standard deviation of BP^2 - 2 * Standard deviation of Vodafone * Standard deviation of BP * Correlation)

weight in Vodafone = (0.40^2 - 0.30 * 0.40 * 0.35) / (0.35^2 + 0.40^2 - 2 * 0.35 * 0.40 * 0.30)

weight in Vodafone = 0.118 / 0.1985

weight in Vodafone = 59.45%

at w = 59.45% the portfolio variance will be at minimum