Question

QUESTION 2 (27 MARKS) Currently you are considering two stocks before you decide to invest. Since the market will volatile after the 14th General Election, you have the follwing data to analyse: Probability of State of economy Rate of return Stock Genuine Rate of return Stock Lobaloba (56) occurrence 10 0.1 Boom 0.6 Normal Recession Required: b. Calculate the expected return and standard deviation for each of two stocks. (10 marks) Suppose an investor has 25,000 shares and invests 15.000 in Stock Genuine and remainder in Stock Lobaloba. Stock Genuine currently is selling at RM1.50 per share and Stock Lobaloba at RM3 per share. Compute the expected return and standard deviation of the portfolio. (14 marks) From part a and b, which is the best choice to invest either in Stock Genuine. Stock Lobaloba or portfolio? Why? (3 marks) FORMULA: E(Ri) - PRI + P R + ....... P.R. o'i-P(RA-ECRA)+P (R24 - (RA)*+...+ PRAE(R) Con-PIR- B(R2)][P-ER..)] +PRAE(R2)][P20-E(R) +...+ P.R. E(Rp) - Wix E(R1) + w x E(R) +...+w.x E(R.) o'p-WA0A+W, 2 WA W. Covan

Answer 1

a. Calculation of expected return

Probability (p)	Return of Genuine (g)	Return of Lobaloba (l)	p * g	p * l
0.1	10%	25%	1%	2.5%
0.6	5%	12%	3%	7.2%
0.3	-10%	3%	-3%	0.9%
Expected Return			G = 1%	L = 10.6%

Expected Return of Genuine = 1%

Expected Return of Lobaloba = 10.6%

Calculation of standard deviation

Probability (p)	g - G	(g - G)^2	l - L	(l - L)^2	p * (g - G)^2	p * (l - L)^2
0.1	9	81	14.4	207.36	8.1	20.736
0.6	4	16	1.4	1.96	9.6	1.176
0.3	-11	121	-7.6	57.76	36.3	17.328
Variance					54.00	39.24

Standard deviation = Variance^1/2

Standard deviation of Genuine = 54^1/2 = 7.35

Standard deviation of Lobaloba = 39.24^1/2 = 6.26

b. Amount invested in Genuine = 15,000 shares * RM 1.5 = RM 22,500

Amount invested in Lobaloba = 10,000 shares * RM 3 = RM 30,000

Total investment = RM 22,500 + RM 30,000 = RM 52,500

% of investment in Genuine = (RM 22,500 / RM 52,500) * 100 = 42.86%

% of investment in Lobaloba = (RM 30,000 / RM 52,500) * 100 = 57.14%

Expected return of portfolio = Expected Return of Genuine * % of investment in Genuine + Expected Return of Lobaloba * % of investment in Lobaloba

= 1 * 42.86% + 10.6 * 57.14%

= 6.49%

In order to find risk of portfolio we need to calculate covariance between the two stocks. Covariance is calculated as follows:

Probability (p)	g - G	l - L	(g - G) * (l - L)	p * (g - G) * (l - L)
0.1	9	14.4	129.6	12.96
0.6	4	1.4	5.6	3.36
0.3	-11	-7.6	83.6	25.08
Covariance				41.40

Variance of portfolio = Variance of Genuine * (% of investment in Genuine^2) + Variance of Lobaloba * (% of investment in Lobaloba^2) + 2 * % of investment in Genuine * % of investment in Lobaloba * Covariance

= 54 * (0.4286^2) + 39.24 * (0.5714^2) + 2 * 0.4286 * 0.5714 * 41.40

= 54 * 0.1837 + 39.24 * 0.3265 + 20.2779

= 9.9198 + 12.8119 + 20.2779

= 43.0095

Standard deviation of portfolio = Variance of portfolio^1/2

= 43.0095^1/2

= 6.56

c. Decision of investment

	Return	Standard Deviation
Genuine	1	7.35
Lobaloba	10.6	6.26
Portfolio	6.49	6.56

From the table, it can be seen that stock Lobaloba has the highest return and the lowest standard deviation (risk). Hence it is the best choice to invest.