Question

You have reviewed the characteristics and historical prices of two companies (A and B), and have estimated their relations to the wider market, detailed below:

	Company A	Company B
Current dividends per share (just paid)	$0.06	$0.40
Current Beta	1.3	1.5
Growth in dividends	4%	5%

Date	Share Price A	Share Price B
2016	$0.35	$4.13
2017	$0.42	$6.76
2018	$0.40	$5.23
2019	$0.52	$4.88

      

Other information:

• Current risk-free rate of return: 3% p.a.
• Current return on market portfolio: 11% p.a.

1. Calculate the expected return and standard deviation for share A and B.                     

2. Calculate the required return for share A and B, given their risk characteristics.         

3. Calculate the intrinsic value of Company A’s and B’s shares. Based on your calculated intrinsic value, identify whether you would buy or sell the shares, using the 2019 share price for each share as a reference value. Provide justification for your decision.                                        

4. Briefly explain, in your own words, what is likely to occur, in relation to the risk exposure of an investment portfolio, as an investor increases the number of investments in the investment portfolio.                                                                                                                                  

Answer 1

a) The Expected Return of a stock is calculated as the average of the historical return as shown below

Date	Share Price A	Share Price B	Return A	Return B
2016	$0.35	$4.13
2017	$0.42	$6.76	0.2	0.636803874
2018	$0.40	$5.23	-0.047619048	-0.226331361
2019	$0.52	$4.88	0.3	-0.066921606
		Averge Return	0.150793651	0.114516969

So, Expected Return of A = 15.08%

Expected Return of B = 11.45%

Standard deviation of a stock is calculated as

where RAi  are the individual returns of stock A and isthe expected return from Stock A calculated above

So, Standard Deviation of Stock A = sqrt (((0.2-0.1508)^2+(-0.0476-0.1508)^2+(0.3-0.1508)^2)/2)

=0.178957 or 17.90%

Standard Deviation of Stock B = sqrt (((0.6368-0.1145)^2+(-0.2263-0.1145)^2+(-0.0669-0.1145)^2)/2)

=0.459283 or 45.93%

b) From CAPM, Required Return of A = 3%+1.3*(11%-3%) = 13.4%

Required Return of B = 3%+1.5*(11%-3%) = 15%

c) Intrinsic value of A's share = D1/(r-g) (from Gordon's constant growth model)

=D0*(1+g)/(r-g)

=0.06*1.04/(0.134-0.04)

= $0.6683

As the Intrinsic value is higher than the 2019 price of $0.52 , I will buy the stock A

Intrinsic value of B's share = 0.40*1.05/(0.15-0.05)

= $4.2

As the Intrinsic value is lesser than the 2019 price of $4.88 , I will not buy the stock B

d) As an investor increases the number of investments in the investment portfolio, the investor gets diversification benefits. With increase in no of investments, the unsystematic risk is diversified away and only the systematic risk remains. This helps the investor achieve better risk-return profile.