Question

Question 14

Compare the following securities: a treasury bill, FTSEALL Index (market portfolio), HighSpeed PLC (a telecommunication company stock), WaterField PLC (a utility company stock) and Metal-Gold PLC (a counter-cyclical company stock). You have collected annual stock prices of each of them and calculated the realized returns for 6 years. You report all realized returns in Table 1 below.

year	Treasury bill	FTSEALL	HighSpeed PLC	WaterField PLC	Metal-Gold PLC
2009	3%	-4%	-3%	5%	14%
2010	2%	-2%	2%	6%	6%
2011	1%	3%	7%	4%	3%
2012	1%	7%	12%	5%	-5%
2013	1%	11%	12%	6%	-7%
2014	1%	12%	14%	7%	-11%

a) Calculate the excess return of each realized return for each security in Table 1.?
b) Use the excess returns in part a) to calculate the historical average excess returns and volatilities of each security.?Show your calculations through the exercise and briefly comment on the results. (You make the assumption that each historical average excess return is a good proxy of the expected return of each security) ?
c) Now using the information in part b), calculate the beta of each security. Briefly interpret the results. ?
d) Once you have calculated the required rate of return of each security using the CAPM formula, indicate whether each security is undervalued or overvalued and explain why.

e) Describe what each of the following pairs of asset pricing models has in common, and how they differ:

APT and CAPM
CAPM and F-F-C (Fama-French-Carhart) model
F-F-C model and APT

Answer 1

Calculation of realised return on portfolio during 2009 to 2014

	High speed PLCstock				Water field PLC stock
Year	Proportion	Return	Net return	Proportion	Return	Net return	Total Return
2009	0.5	-3	1.5	0.5	5	2.5	4
2010	0.5	2	1	0.5	6	3	4
2011	0.5	7	3.5	0.5	4	2	5.5
2012	0.5	12	6	0.5	5	2.5	8.5
2013	0.5	12	6	0.5	6	3	9
2014	0.5	14	7	0.5	7	3.5	10.5
			25			16.5	41.5

Average rate of return = 41.56 = 6.92%

Note: Assume that proportin of two securities taken as equal

Computation of Beta of security

Period(	Rm	Rh	Deviation on market(Dm)- 27/6=4.5	Deviatin on stock(Dh) (44/6=7.33)	Covariance (DmDh)	Dm2	Dh2
2009	-4	-3	-8.5	-10.33	15.495	2.25	106.71
2010	-2	2	-6.5	-5.33	2.665	0.25	28.41
2011	3	7	-1.5	-0.3	0.15	0.25	0.09
2012	7	12	2.5	4.7	2.35	0.25	22.09
2013	11	12	6.5	4.7	2.35	0.25	22.09
2014	12	14	7.5	6.7	3.35	0.25	44.89
	27	44			24.015

Variance = 3.56 = 0.583

co variance = 24.0156 = 4

Beta = covariancevariance = 40.583 = 6.86

Cosr of Equity calculation under CAPM

K_e = R_{f +} (R_m-R_f)

= 1.5+6.86(4.5-1.5) =21.99

e) 1. APT and CAPM formulas are looking identical

2. the differnce between APT and CAPM Different in Expected return and Risk free return.