Question

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

Part A:

Expected Price = Sum [ Prob * Price ]

Scenario	Price	Prob	Expected Price
1	$   50.00	30.00%	$            15.00
2	$   35.00	60.00%	$            21.00
3	$   23.00	10.00%	$               2.30
Expected Price	$            38.30

Part B:

Holding Period Ret = [ P1 - P0 + Div ] / P0

= [ $ 38.30 - $ 32 + 0 ] / $ 32

= $ 6.30 / $ 32

= 0.1969 i.e 19.69%

Part C:

Variance = Sum [ Prob * ( X - Avg X)^2 ]

SD = SQRT [ Variance ]

Scenario	Price (X )	Ret	Prob	X - Avg X	(X - Avg X)^2	Prob * ( X- Avg X)^2
1	$   50.00	0.5625	30.00%	0.3656	0.1337	0.0401
2	$   35.00	0.0938	60.00%	-0.1032	0.0106	0.0064
3	$   23.00	-0.2813	10.00%	-0.4782	0.2286	0.0229
Variance	0.0693
SD = SQRT [ Variance ]	0.2633

Part D:

Holding Period Ret = [ P1 - P0 + Div ] / P0

= [ $ 36 - $ 32 + 2.5 ] / $ 32

= $ 6.5 / $ 32

= 0.2031 i.e 20.31%

Capital Gain Return = [ P1 / P0 ] - 1

= [ 36 / 32 ] - 1

= 1.125 - 1

= 0.125

Part e:

Exopected Return is the Return expected from the security in future. Realized Return is the return actuall received from the security.