Question

a. An analyst in a daily business segment broadcasted on the national TV quoted the following statement:   

“Looking at the historical market prices of AB and CD stocks, we find that AB have been on an average traded at Rs. 120 for last three years, indicating low beta because its price moved very little. On the other hand, CD stock showed that it has been traded at a high of Rs. 1050 and a low of Rs. 550 (its current market price) during the same time period as stock AB. Thus, CD stock has shown large variation in terms of its stock prices indicating a high beta.” Do you agree with his statement? Explain.

b. There are two stocks i.e. Stock OP and Stock QP. The beta of Stock OP and Stock QP is 1.35 and 0.80 respectively. Moreover, the expected return of Stock OP is 14 percent and that of Stock QP is 11.5 percent. Assume that the T-bills rate is 4.5 percent and the KSE-100 index’s risk premium is 7.3 percent. Show calculations to check if these two stocks are correctly priced?

c. Assume that a particular fund consists of two assets i.e. Treasury bills and the market portfolio. This fund’s expected rate of return is 07 percent with a standard deviation of 10 percent. The rate of returns on T-bill and the market portfolio is 4 percent and 12 percent respectively. In this investment, CAPM model holds. Calculate the expected rate of return on a security that has a correlation of 0.45 with the market portfolio with the standard deviation of 0.55?

d. Saad have saved Rs. 100,000 and he wants to invest in a fund available in the market as suggested by his stock broker friend. This portfolio is a combination of three types of instrument securities i.e. OGDCL stock, Gadoon Textile stock and T-bills. He must invest the entire money in this find. Saad’s investment objective is to create such a portfolio with these three assets that his Portfolio should earn him an expected return of 11.22 percent but it should have only 96 percent of the risk of the overall market. The expected returns (beta) on OGDCL, Gadoon and T-bills are 15.35 percent (1.55), 9.4 percent (0.7), and 4.5 percent respectively. How much of Saad’s total investment will be invested in OGDCL stock? Also, interpret your answer.

e. You have been given a task by your US based client, to construct a Portfolio for an investor willing to invest $1 million but his portfolio would be as risky as the market. This portfolio will have three stocks and a risk free asset. Stock 1 will use $180,000 and its beta is 0.85, Stock 2 will utilize $290,000 of the total money invested and its beta is 1.40. Stock 3’s beta is 1.45. Find out the amount of money to be invested in Stock 3 and risk free asset.                                                                          

Answer 1

a.) The above statement is incorrect.   

Beta is a measure of the volatility–or systematic risk–of a security or portfolio compared to the market as a whole. Beta is used in the capital asset pricing model (CAPM), which describes the relationship between systematic risk and expected return for assets (usually stocks). CAPM is widely used as a method for pricing risky securities and for generating estimates of the expected returns of assets, considering both the risk of those assets and the cost of capital.

A beta coefficient can measure the volatility of an individual stock compared to the systematic risk of the entire market.

Beta effectively describes the activity of a security's returns as it responds to swings in the market. A security's beta is calculated by dividing the product of the covariance of the security's returns and the market's returns by the variance of the market's returns over a specified period.

The calculation for beta is as follows:

              Beta Coefficient (β) = Covariance (Re, Rm)/Variance (Rm)

where:

Re = the return on an individual stock

Rm = the return on the overall market

Covariance= how changes in a stock’s returns are related to changes in the market’s returns

Variance=how far the market’s data points spread out from their average value

b) To identify if the stocks are correctly priced can be done by comparing the Expected Return (ER) of the stock and Required Return (Re) from the stock.

Required Return (Re) can be calculated by using CAPM ie;

              Re = Rf + β( Rm – Rf)

Where Rf = Risk free rate of return

             Β = Beta value of the investment

       (Rm -Rf) = Market risk premium available

Is the stock underpriced /overpriced/ correctly priced?

· If ER > Re – stock is underpriced

· If ER< Re – stock is overpriced

· If ER= Re – stock is correctly priced

Stock	OP	QP
Expected Return (ER)	14%	11.5%
Risk free Return (Rf)	4.5%	4.5%
Market Risk Premium (Rm-Rf)	7.3%	7.3%
Beta (β)	1.35	0.8
Required Return (Re)	14.36%	10.34%
Conclusion	Overpriced	Underpriced

c) To calculate the expected return, if the CAPM holds good, the Expected Return (ER) = Required Retun (RE)

Required Retun (RE) = Rf + β( Rm – Rf)

Where Rf = Risk free rate of return

             Β = Beta value of the investment

       (Rm -Rf) = Market risk premium available

Here ;     7% = 4% +β(12-4)

                β   = 0.375

Beta (β) = Covariance (Re, Rm)/ Variance (Rm)

0.375 = .45/Variance (Rm)

Therefore Variance of Rm = 1.2

Expected Return of the security :

Beta (β) = Covariance (Re, Rm)/ Variance (Rm)

                =0.45*0.55/1.2

                =0.20625

Expected Return = 4%+ 0.20625(12-4)

                              =5.65%

d) Total Amount to be invested = Rs. 100000

	OGDCI	Gradoon	T Bills
Expected Return	15.35%	9.4%	4.5%
Beta	1.55	.7	0

Required Beta = 0.96

Expected Return = 11.2%

e) The portfolio will have same beta as that of the market. Here it is assumed that market beta is the average of all the stocks.

       Therefore Market Beta (β) = (0.85+ 1.4+ 1.45)/3

                                                   =1.233

So Portfolio Beta (β) = ∑wx/∑w

       Total portfolio value = $1000000

Stock	Weights (W)	Beta (x)	WX
Stock 1	180000	0.85	153000
Stock 2	290000	1.4	406000
Stock 3	a	1.45	1.45a
Risk free Asset		0	0

Portfolio Beta (β) = ∑wx/∑w

            1.233       = (559000+1.45a)/1000000

Therefore a (amount allocated to stock 3) = $ 464828

Amount Invested in Risk free Asset = $ 65172

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