Question

a) “The standard deviation of a portfolio's return cannot be reduced to zero by holding all the securities in the market.” True or false? Explain. (2 mark)

An investor buys 1 share of ABC Ltd at the price of $32 on December 1, 2019. The firm is not expected to pay any dividends. Consider the following three possible scenarios for the share price on December 1, 2020:

$50 with a probability of 30%
$35 with a probability of 60%
$23 with a probability of 10%
b) Calculate the expected return for holding the share for a year. (2 mark)

c) Calculate the variance of return and standard deviation of return.

d) On December 1, 2020, the share is worth $36 and the investor just received a dividend of $2.50. Calculate the total holding period return and capital gains return over the one-year period.

e) Explain the difference between expected return and realised return.

Answer 1

a) This statement is true because all the securities in the market have some risk and these securities do not necessarily negate the risk of each other because they do not necessarily have perfect negative corelatin among each other.

b) Calculation of expected return for holding the security for one year:

Price after one year	Purchase Price	Return	Probability	Expected Ret=Ret*Prob
50	32	18	0.3	5.4
35	32	3	0.6	1.8
23	32	-9	0.1	-0.9
Expected Return	6.3

c)Calculation of Variyance of return:

Return	Expected Ret	Deviation(D)	D2	Probability(P)	D2*P
18	6.3	11.7	136.89	0.3	41.067
3	6.3	-3.3	10.89	0.6	6.534
-9	6.3	-15.3	234.09	0.1	23.409
Variyance=total of D2*P	71.01
SD=Square root of Variyance	8.426743

d) Calculation of total holding period return:

Total Holding period return=[(Closing period-Buy Price)+Dividend]/Buy Price

=[(36-32)+2.5]/32

=.203125 or 20.3125%

e) Difference between Expected and realised return=14.0125% (i.e.20.3125-6.3)