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 20%
$34 with a probability of 50%
$27 with a probability of 15%
$20 with a probability of 15%
a) Calculate the expected return for holding the share for a year.

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

c) Explain the concept of diversification. Explain the benefit of diversification and how it works.

d) “The standard deviation of a portfolio's return can be reduced to zero by holding all the securities in the market.” True or false? Explain.

Answer 1

a. Expected Return = 6.41 %

b. Variance = 8.59% and Standard Deviation = 29.31%

c. Diversification means investing in more than 1 security/ assets so as to reduce the total risk of the portfolio. With a well constructed portfolio the risk (standard Deviation) can be reduced to zero. The portfolio should be constructed by including those securities which have negative correlation.

d. False. The standard deviation can be reduced to zero by holding those securities which have perfect negative correlation..

Return at various prices will be caluclulated using the formula

Return = ( Price at end - Purchase price)/Purchase price * 100

So Return = (50-32)/32*100 = 56.255 ; Return = (34-32)/32*100 = 6.25%

Return = (27-32)/32*100 = -15.63% ;   Return = (20-32)/32*100 = 37.5%

Now

Expected Return = ∑(Ret * Probability)

Standard Deviation =

Where Pi = Probability

Ret = Return of the stock

Ret Expected = Expected Return

The excel sheet for calculation and formula is attached below:

2 pi* (Ret - Ret expected)