Question

QUESTIONS Consider the performance of two securities and k over the five year period from 2014 to 2018. The annual return earned on each one of them is as provided in the table below Year 379 28.4 -15 a 2014 2015 2016 2017 2018 19.8 128 -208 58.6 -500 31.7 Required: Compute the following: a) Assume your organization had K150 million to invest on 01st January, 2014. If 70% was invested in security J over the holding period, the annual returns would you have earned from a portfolio comprising the two securities 06 Marks) b) The annual valatilities of the portfolio with the above investment proportions: assuming the correlation coefficient between returns on securities J and K remained constant at 0.04 over the holding period [10 Marks] c) Evaluate the performance of the portfolio for each year of the holding period and advise when the performance was satisfactory Assume a risk free rate of 6% (05 Marks] Total 20 Marks

Answer 1

Solution to Qs 5 (a)

Proportionate Investment in Security J = 70%

Proportionate Investment in Security K = 30%

Total Return provided by Security J during holding period = Summation of 5 year return =47.90%

Total Return provided by Security K during holding period = Summation of 5 year return =54.60%

Total Return of the portfolio = 70% x 47.9% + 30% x 54.6% = 49.91%

So, Annual Return from portfolio comprising two securities = 49.91%/ 5 = 9.98%

Solution to 5 (b)

Variance of the Portfolio = (W1^2 x SD1^2) + (W2^2 x SD2^2) + (2 x W1 x W2 x SD1 x SD2 x P_(1,2))

Where, W1 = Portfolio weight of Security J = 70%

W2 = Portfolio weight of Security K = 30%

SD 1 = Standard Deviation of J = 36.36%

SD 2 = Standard Deviation of K = 31.92%

P_(1,2) = Correlation coefficient of J & K = 0.04

So, variance = (70%^2 x 36.36%^2) + (30%^2 x 31.92%^2) + (2 x 70% x 30% x 36.36% x 31.92% x 0.04)

= 7.59%