solved mid term stock market efficiency

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Department of Business Administration “SOLVED” Mid Term Exam NOV 2011 (MBA 1.5)

Course Title: Stock Market Efficiency Time Allowed: 1 Hour Maximum Marks: 30

Please attempt all questions.

Question No. 01

Suppose that National Bank of Pakistan’s (NBP) share is selling at Rs. 45 per share. You buy a lot of 500 shares using Rs 16,000 of your own money and borrowing the remainder of the purchase price from your broker. The rate on the margin loan is 7%.

a) What is the percentage increase in the net worth of your brokerage account if the price of NBP immediately changes to: (i) Rs. 51; (ii) Rs. 38? Please prepare Margin Trade Account to represents changes in your margin. SOLUTION

Margin Account (At the time of purchase of 500 shares) Shares held as Collateral 500@45=

Rs.

22500

22500

Equity (Initial Margin) Loan (Bal. Fig)

Rs. 16000

6500

22500

Margin Account (If price immediately changes to Rs. 51) Shares held as Collateral 500@51=

Rs.

25500

25500

Equity (Bal. Fig) Loan (Remain constant as in above case)

Rs. 19000

6500

25500

a) % change in Margin = (Rs. 19000 – Rs. 16000) / Rs. 16000 = 18.75%

Margin Account (If price immediately changes to Rs. 38) Shares held as Collateral 500@38=

Rs

19000

19000

Equity (Bal. Fig) Loan (Remain constant as in above case)

Rs 12500

6500

19000

% change in Margin = (Rs. 12500 – Rs. 16000) / Rs. 16000 = -21.8%


b) If the maintenance margin is 24%, how low can NBP’s price fall before you get a margin call after marking to market? Let P be the price per share

Maintenance Margin = (500P-6500) / 500P 0.24 = (500P-6500) / 500P 120P = 500P – 6500 6500 = 380P P = Rs. 17.10

c) How would your answer to (b) change if you had financed the initial purchase with only Rs. 9,000 of your own money? Let P be the price per share (If 9000 is initial margin then Rs. 13500 would be the amount of loan i.e Rs. 22500 – Rs. 9000)


d) What is the rate of return on your margined position (assuming again that you invest Rs. 16000 of your own money) if NBP is selling after one year at: (i) Rs. 51; (ii) Rs. 38? Please prepare Margin Trade Account to represents changes in your margin.

Margin Account (If price changes to Rs. 51, AFTER ONE YEAR) Shares held as Collateral 500@51=

Rs

25500

25500

Equity (Bal. Fig) Loan (Remain constant as in initial case) Interest on Loan @ 7% p.a

Rs 18545

6500

455

25500

% change in Margin = (Rs. 18545 – Rs. 16000) / Rs. 16000 = 15.91% Margin Account (If price changes to Rs. 38, AFTER ONE YEAR)

Shares held as Collateral 500@38=

Rs

19000

19000

Equity (Bal. Fig) Loan (Remain constant as in initial case) Interest on Loan @ 7% p.a

Rs 12045

6500

455

19000

% change in Margin = (Rs. 12045 – Rs. 16000) / Rs. 16000 = -24.72%


e) Continue to assume that a year has passed. How low can NBP’s price fall before you get a margin call after marking to market? Let P be the price per share (Amount of loan after one year would be 6500 (1.07) here 1.07 represents, principal + interest @7% p.a.)


Question No. 02 Assume the total market value of an investor’s portfolio is Rs 300,000. Of that, Rs. 90,000 (i.e. 30% of Rs. 300,000) is invested in the SBP a risk-free asset. The remaining Rs 210,000 (i.e. 70% of Rs. 300,000) is in risky securities, say Rs 113,400 in the Fauji Fertilizers (i.e. 54% of Rs. 210,000) and Rs 96,600 (i.e. 46% of 210,000) in Engro. If y is the percentage of investments in risky securities then 1-y should be the percentage of investment in risk free securities. Further, assume expected return on risky securities = 15%, with the standard deviation of 22%, and risk free return= 7%.

a) If you invest all of your funds in the risky asset, that is, if you choose y= 1.0, what will be the expected return and risk on your complete portfolio?

E(rrp) = 15% σrp = 22%

b) If you invest all of your funds in risk free assets, what will be the expected return and risk of your portfolio?

E(rf) = 7% σf= 0% (Because it is risk free)

c) If you make a portfolio of risky and risky portfolio (according to the situation given in paragraph above) what would be the expected return and risk of the portfolio?

E(rp) = Risk free return (Weight of Risk free asset) + Risky Return (Weight of Risky assets) = 7% (30%) + 15% (70%) = 12.6% σrp = 22% (70%) = 15.4% d) Draw capital market line (CAL) for the above situations.

Risk Free 7%

Risky Return 15%

Risk of Risky Portfolio

70/30 Portfolio Return =12.6%

Portfolio Risk = 15.4%

CAL

www.financecottage.com Question No. 03

a) Define different forms of stock market efficiency

Weak Form Efficiency: Prices of the securities instantly and fully reflect all information of the past prices. This means future price movements cannot be predicted by using past prices.

Semi‐strong Form Efficiency: Asset prices fully reflect all of the publicly available information. Therefore, only investors with additional inside information could have advantage on the market.

Strong Form Efficiency: Asset prices fully reflect all of the public and inside information available. Therefore, no one can have advantage on the market in predicting prices since there is no data that would provide any additional value to the investors.

b) Read the following paragraph (taken from an empirical study on KSE Pakistan) and explain, what type of market efficiency has been tested in this study and what is authors’ conclusion regarding form market efficiency persists in KSE, Pakistan?

Read the highlighted Paragraphs carefully: The author has emphasized KSE as

“WEAK FORM EFFICIENT MARKET”

Empirical Analysis on Stock Market Efficiency in Pakistan

In order for the capital to be allocated to where it makes most use from a public economy point of view, it is important that prices give the right signals, i.e. contain all the important information. Thus, the society needs the market to be efficient (Claesson, 1987). Historically, there has been a large body of academic people, primarily economists and statisticians, who subscribe to the theory of random walks in stock-market prices. Random-walk theorists usually start from the premise that the major security exchanges are good examples of “efficient” markets. In an efficient market, the actions of the many competing participants, leads to actual prices already reflecting the effects of current information and the actual price of a security to wander randomly about its intrinsic value. Thus, a market where successive price changes in individual securities are independent is, by definition, a random-walk market (Fama, 1965).

The empirical studies on Karachi Stock Exchange (KSE), Pakistan lead us to the conclusion that the Random-walk hypothesis can be accepted for both monthly and daily returns in KSE. There is no “day of the week effect” or the ‘month effect’. This is compatible with Fama’s conclusion of existence of random walk phenomena. This result indicates that daily stock market returns are independent and cannot be used to make forecasts of next trading session stock returns. So the market prices quoted at KSE at any point in time, are representing good estimates of intrinsic or fundamental values and are reflecting the judgments of the market participants on stock potential. Therefore, the stock returns in KSE are independent and they cannot be used to predict future returns. Since changes in stock prices are random, we can do no better than to predict that the next period’s price will be somewhere around where it was the last time we knew it. This conclusion is consistent with modern efficient market studies.

The End

solved mid term stock market efficiency

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