Question

Shares for ZCCM Investment Holdings (IH) and ZAFFFICO have the following historical dividend and price data.  

Companies	ZCCM-IH Share		ZAFFICO Share
Year	Dividend	Year-end Price	Dividend	Year-end Price
2012		22.50		43.75
2013	2.00	16.00	3.40	35.50
2014	2.20	17.00	3.65	38.75
2015	2.40	20.25	3.90	51.75
2016	2.60	17.25	4.05	44.50
2017	2.95	18.75	4.25	45.25

Required:
(a) Calculate the realized rate of return (or holding period return) for each share in each year. Assume an equally weighted portfolio. What would the realized rate of return on the portfolio be in each year from 2012 through to 2017? What are the average returns for each share and for the portfolio?

(b) Calculate the standard deviation of returns for each share and for the portfolio.

(c) Based on the extent to which the portfolio has a lower risk than the shares held individually, would you assess that the correlation co-efficient between returns on the two shares is closer to 0.9, 0.0 or -0.9?

(d) If you added more shares at random to the portfolio, what is the most accurate statement of what would happen to σp?

(i) σp would remain constant, or

(ii) σp would decline to somewhere in the vicinity of 15%, or

(iii) σp would decline to zero if enough shares were included.

Answer 1

a]

Holdping period return for each share in each year = (current year price + dividend - previous year price) / previous year price

Return of portfolio in each year = weighted returns of each share in the portfolio, with the weights being the proprotion of each share in the portfolio. As the portfolio is equally weighted, the weight of each share is 0.50.

Average returns for the share and portfolio are the average holding period return during the period.

This is calculated using AVERAGE function in Excel

b]

Standard deviation is calculated using STDEV.S function in Excel

c]

As it can be seen from the calculations, the standard deviation of the portfolio is only slightly lower than the standard deviation of the individuals shares. This means that the prices of the shares move together. Therefore we can conclude that the correlation positive and higher, and is closer to 0.90.

d]

Adding more stocks to the portfolio would decrease systematic risk, but unsystematic risk would remain.  

Total risk, measured by standard deviation, consists of both systematic risk and unsystematic risk.

Therefore, statement (ii) is the most accurate.  

Statement (i) is not accurate. Standard deviation would decrease due to decrease in systematic risk.

Statement (iiii) is not accurate. Systematic risk would decrease, but unsystematic risk would remain. Therefore, standard deviation will not be zero.