Question

Assume you are a portfolio manager at JS Global Capital Ltd. Recently you came across three attractive stocks and want to create a portfolio investment in these three stocks. The details of the stocks are given below:
Company name Volatility
(Standard deviation) Weight in Portfolio Correlation with the market portfolio
Meezan Bank Ltd 0.25 12% 0.40
Lucky Cement Ltd 0.35 25% 0.60
KE Ltd 0.40 13% 0.50

The expected return on the market portfolio is 8% and its volatility is 10%. The risk-free rate based on central bank’s discount rate is 3%. (1.5 marks each)

a. Calculate each of the stock’s expected return and risk (beta) as compared to the market.
b. What should be the expected return of the portfolio based on values calculated in part a.
c. Calculate the beta of the portfolio? what does it tells regarding the riskiness of the portfolio?
d. Using the values from part c, can you calculate the expected return of the portfolio? Is it similar to your answer in part b? Why or why not?

Answer 1

Since the values in the question are not arranged properly, we would first arrange the values in a table for systematic calculations.

Given:

Company Name	Weight	Volatility	Correlation
Meezan Bank ltd	0.25	12%	0.40
Lucky cement ltd	0.35	25%	0.60
KE Ltd	0.4	13%	0.50

Expected return on Market Portfolio = 8%

Market Volatility = 10%

Risk free rate = 3%

Part (a) The expected return of each stock can be calculated using the CAPM Model formula, which is:

where,

Re = Expected return os the stock

Rf = Risk free rate

Rm = Expected market return

B = Beta of the stock  

BETA OF THE STOCKS

where,

B = Beta

Cov(r,rm) = Covariance between security and market returns calculated as

i.e Correlation* Standard deviation of stock* Standard deviation of market

= variance of market return which is 0.1*0.1= 0.01

Meezan ltd Beta = 0.4* 0.12* 0.1/ 0.01

= 0.48

Lucky ltd. Beta = 0.6* .25* .1 / .01

= 1.5

KE Ltd Beta = 0.5* .13* .1/ .01

=0.65

STOCK RETURNS

Meezan Ltd = 0.03 + ( 0.08 - 0.03) * 0.48

= 0.054 or 5.4%

Lucky Ltd = 0.03 + (0.08- 0.03) * 1.5

=0.105 or 10.5%

KE Ltd = 0.03 + (0.08- 0.03) * 0.65

0.0625 or 6.25%

Part (b) EXPECTED PORTFOLIO RETURN

It is calculated as :

Rp = Wa * Ra + Wb * Rb + Wc * Rc

where, Rp = Return on portfolio

Wa = weight of security a

Ra = return on security a

Wb = weight of security b

Rb = return on secutiry b

Wc = weight of security c

Rc = Return on security c

Rp = 0.25 * 5.4% + 0.35 * 10.5% + 0.4 * 6.25%

= 1.35% + 3.675% + 2.5%

=7.525%

Part (c) PORTFOLIO BETA

Where W are the weights and B is beta

0.25 * 0.48 + 0.35 * 1.5 + 0.4* 0.65

=0.12+ 0.525 + 0.26

=0.905

Part (d) EXPECTED RETURN ON PORTFOLIO

Where,

Rpe= Expected portfolio return

Rf = Risk free rate

Rm= Expected market return

B= Beta of portfolio

Rpe= 0.03+ (0.08- 0.03) 0.905

= 0.07525 or 7.525%

Yes, the answer is same as found in part (b). This is because a portfolio is a basket of securities which is used to diversify the unsystematic risk. The portfolio's returns and risk is nothing but a summation of the returns and risk of all the securities into it according to their assigned weights. Which is why the answer was same.