Question

Consider two securities, one from the Bellville Stock Exchange and the other from the Brackenfell Stock Exchange (both with normally distributed returns) have same expected rate of return. Suppose the standard deviations of the rates of returns are v1 = .18 and v2 = .24, and that the correlation between the two rates of returns is ρ = .25. Then, calculate the optimal fraction of one’s investment capital that should be used to purchase the security 1 from the Bellville Stock Exchange.

please help me with the financial Mathematics question

Answer 1

Optimal weight in security 1 to be calculated as follows-

Given in question:

standard deviation of 1 = 18%

standard deviation of 2 = 24%

P(correlation coefficient between 1&2)= 0.25

Workings

First we need to calculate covariance between two securities, which is calculated as below:

Cov(1,2)= P(1,2)×V1×V2

= .25×18×24

= 108

Optimal weight in security 1=

(√security 2^2) - cov(1,2) ÷ [(√security 1^2) + (√security 2^2)- {2 × cov(1,2)}]

= 24^2 - 108 ÷ [18^2+ 24^2- (2×108)]

= 576 - 108 ÷ [324+ 576- 216]

= 468 ÷ 684

= 0.6842

Out of total investment capital, 68.42% to be used to purchase security 1 from the bellville stock exchange.