Question

You know the following information about the possible returns offered by the two stocks, Stock X and Stock Y next year.

Scenario Probability Return from X Return from Y Recession 40% -5% -6% Normal 60% 10% 14%

a. Calculate the expected returns and variances for Stock X, Stock Y. b. From risk-return point of view, which stock, X or Y is a better investment? Why? c. What is the correlation coefficient between returns on stock X and stock Y? d. Calculate the expected returns and standard deviations for a "portfolio" consisting of 40% of stock X and 60% of stock Y. e. If I invest 80% of my money in this “portfolio” (40% in stock X and 60% in stock Y) and 20% of my money in T-bills which offers a rate of return of 2%. What is the expected return and standard deviation of my investment portfolio?

Answer 1

Portfolio Management:

A Portfolio can be defined as different investments tools namely stocks,shares,mutual funds,bonds, cash all combined together depending specifically on the investor's income, budget and the holding period. It is formed in such a way that it stabilizes the risk of non performance of different pools of investments.

Portfolio management is defined as the art and science of making decisions about the investment mix and policy, matching investments to objectives, asset allocation for individuals and institutions, balancing risk against performance.

Answers from parts (a) to (d)

(a)

Calculation of Expected Returns and Variance for stock x and stock y:

Scenario (1)	Probability (2)	Return from Stock X (3)	Return from Stock Y (4)	Expected Return (5)=(2)x(3)	Expected Return (6)=(2)x(4)	Variance of stock X (7)={(3)-(4%)}2x(2)	Variance of stock Y (8)={(4)-(6%)}2x(2)
Recession	0.40	- 5%	- 6%	- 2%	- 2.4%	32.40	57.60
Normal	0.60	10%	14%	6%	8.4%	21.60	38.40
				4%	6%	54	96

For calculating the Expected Returns formula is used as:

Expected Return of Stock X = Return from Stock X x Probability = 4%

Expected Return of Stock Y = Return from Stock Y x Probability = 6%

For calculating The Variance of both Stock formula is used as [(Return - Expected Return)2x probability]  

Variance of Stock X = 54; Standard Deviation = = 7.35

Variance of Stock Y = 96; Standard Deviation = = 9.80

(b)

Stocks	X	Y
Risk	7.35	9.80
Return	4%	6%

As per the calculation, the return of Y is higher than the return of X, although the stock y has higher degree of risk as compared to stock x .But its better to invest in Stock Y.

(c)

For calculating correlation cofficient formula is used as:

Rxy =

where, Covariance of two stocks x and y = P1(Return of stock x - Expected Return of x)(Return of stock y - expected return of stock y) + P2(Return of stock x - Expected Retun of x)(Return of stock y - Expected Return of stock y)

Expected returns are calculated above as 4% of stock x and 6% of stock y

Scenerio	Probability (1)	Return from stock x (2)	Return from stock y (3)	Cvariance (4)= [{(2)-4%}x{(3)-6%}x(1)
Recession	0.40	- 5%	- 6%	0.40[{-5%-4%}{-6%-6%}] =43.20
Normal	0.60	10%	14%	0.60[{10%-4%}{14%-6%}] =28.80
				72

Hence, the covariance of both stock is 72

Correlation cofficient = = = 0.999 or 1 (round off)

(d)

Portfolio Return :

For calculating the return of portfolio of both the stocks formula is used as:

Rp =  Ra* Wa + Rb* Wb

where, Rp = Portfolio Return ; Ra = Expected return of stock x; Rb = Expected return of stock y; Wa = weights of stock x and Wb = weights of stock y

Rp = 0.40 * 4% + 0.60 * 6% = 5.2%

Standard Deviation or we called as Portfolio Risk calculated as:

= (0.40)2 * 54 + (0.60)2 * 96 + 2*7.35*9.80*0.40*0.60*1

=8.64+ 34.56+34.57

=8.82