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Form a group of 3 members. List your group names in the provided group section 1 to 6. Find out several issues related with Efficient Market Theory or Portfolio Management and Asset Pricing Theory - and discuss which is the most interesting issue for your group. Tqsm

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a.

Expected return:

ER(Pluto Bhd) =  (0.3)(-12) + (0.4)(13)  + 0.3(18)  = 7%

ER (Venus Bhd) = (0.3)(11) + (0.4)(10)  + 0.3(8)   = 9.7%

ER (MTB) = 4%

Standard deviation:

SD(Pluto Bhd)  = SQRT{ (0.3) (-12-7)²  +(0.4)(13-7) ²  +(0.3)(18-7)² }

= 12.61%

SD(Venus Bhd) = SQRT{(0.3)(11—9.7)²  +(0.4) (10-9.7) ² +(0.3)(8-9.7)² }

= 1.19%

SD (MTB) = 0% or ZERO SD

Beta:

Beta Pluto       = 93.25/ (8.13)²= 1.41

Beta Venus     = 58.21/ (8.13)²= 0.88

Beta MTB        = 0% or ZERO Beta

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b)

i. Using the CAPM, evaluate whether the above portfolios are correctly priced.

CAPM (Pluto Bhd)         = 4%+ 1.41  (6.3%-4%) = 7.24%

CAPM (Venus Bhd)       = 4% + 0.88 (6.3%-4%)= 6.02%

CAPM (MTB)                 = 4% + 0.00 (6.3%-4%)  = 4%

Therefore,

Pluto Bhd;
CAPM = 7.24%
ER = 7%
Decision = Overvalued because CAPM > ER

Venus Bhd;
CAPM = 6.02%
ER = 9.7%
Decision = Undervalued because CAPM < ER

MTB;
CAPM = 4%
ER = 4%
Decision = correctly priced because CAPM = ER

ii. Mekar Indah Bhd may invest in Venus Bhd and MTBbecause it is now underpriced and correctly priced respectively.  The price of Venus Bhd would rise in the future. Do not invest in Pluto Bhdbecause it is expensive/overpriced and the price would drop soon.

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c. Beta is the responsiveness of a stock’s return with the return on the market. The magnitude of beta describes the impact of systematic risk on a stock’s return.In this case, Beta Pluto Bhd stock is 1.41 times more responsive or high volatile to systematic riskthan Beta Venus Bhd stock which is 0.88 times indicates that Venus stock is less volatile or less riskier to systematic risk.

d.  Investing in a single stock exposes one to extremely high investment risk, both systematic and unsystematic. By putting all investment in a single stock will increase the riskiness and volatility of a security’s return from its expected return.  A portfolio investment is a better alternative because of the diversification effect.  Diversification occurs when the stocks held in a portfolio result in a reduction in the overall risk.  This happens because if a particular stock suffers a loss, it would be offset by the gains made on the other stocks in the portfolio, and vice-versa.  Thus, there is an elimination of the unsystematic risk which results in less risk in the portfolio.

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a.      Expected Return

RValet                      = (0.2 x 8%) + (0.5 x 12%) + (0.3 x 16%)

=  12.4%

RPrmus                     = (0.2 x 5%) + (0.5 x 15%) + (0.3 x 18%)

=  13.9%

Risk

σValet = stddev[0.20(8%-12.4%)2  + 0.50(12%-12.4%)2 + 0.30(16%-12.4%)²]

= √7.84

= 2.80%

σPrimus  = stddev [0.20(5%-13.9%)2 + 0.50(15%-13.9%)²+ 0.30(18%-13.9%)²]

= √21.49

= 4.64%

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b.      Expected Return Portfolio and Standard Deviation Portfolio consisting of 45% in Valet Bhd and 55% in Primus Bhd.

RPortfolio = (0.45 x12.4%) + (0.55 x 13.9%)

= 13.225%

σPortfolio = std dev= [(0.45)² (2.80)2  + 2(0.45)(0.55) (-0.95)  (2.80)  (4.64) + (0.55)²(4.64)²]

= √1.990816

= 1.411%

c.       Moonbay Bhd should invest in the portolfio investment consisting of 45% in Valet Bhd and 55% in Primus Bhd  because it has lowest risk (1.411%) at reasonable expected return which is 13.225%.

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d.            Portfolio required rate return under CAPM.

RValet         =  Rf  +  β (RM  - Rf)

=  4%  + 0.83 (7%)

= 9.81%

RPrimus   =  Rf  +  β (RM  - Rf)

=  4% + 1.25 (7%)

= 12.75%

RPorfolio  =  0.45 (9.81) +  0.55 (12.75)

= 11.427%

Or

Portfolio Beta = 0.45 (0.83) + 0.55 (1.25)  = 1.061

RPorfolio  =  Rf  +  β (RM  - Rf)

Portfolio RRPorfolio  = 4% + 1.061 (7%) = 11.427%

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e.                Comment on the beta measurement with regards to the sensitivity of each security to a market-wide risk portfolio.

·                  Beta measures the responsiveness of security return to the market return.

·                  In other words, beta measures how sensitive its underlying revenue and cash flows to the general economic conditions.

·                  A relatively low beta (less than 1) indicated by Hearsay Bhd (0.42) and Valet Bhd (0.83) means the average stock price tends to move up and down less sensitive to the systematic risks.  Thus, it is more stable and insensitive to fluctuation in the overall market.

·                  The extreme stocks that has higher beta (more than 1) indicated by Primus Bhd (1.25) and Intel Bhd (2.38), means, its return is affected by the strength of the economy;  boom and busts of the economy as a whole or more sensitive to systematic risks.  The average stock price tends to rise more than one as much as the market rise and when market is plummet, it tends to fall more than one as well.

Alternative:

·        Beta of less than 1 as in Hearsay Bhd (0.42) and Valet Bhd (0.83) means that the stock ia 58% and 17% less volatile than the market; less sensitive and less risky.

·        Beta of more than 1 as shown by Primus Bhd (1.25) and Intel Bhd (2.38) means the stock is 25% and 138% more volatile than the market; highly sensitive and risky.

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i.
In a semi-strong form efficiency, the underlying rationale for the efficient market hypothesis is the presence of information that is available to all investors, which includes information from technical analysis (past info) and in corporate press release (public info).   It implies that the securities will be fairly or correctly price, given all information that is available to investors in a semi strong form efficiency.

As the shares of Apple are moving downward trend which lost 11.7% in last month shown by the chart plus the announcement made in corporate letter by the Apple CEO on the revenue shortfall from $89-$93 billion to $84 billion, has resulted the share price further down by another 6% since the end of December.  The reaction of stock price plunged instantaneously in responded to the bad information released indicates that the market is efficient in the semi-strong form efficiency.   Thus, consistent with other analysts who have cut their price targets on Apple over the last month, the prediction of the new share price would be drop but only in the short-term.  The profit opportunities should be a normal profit  only as the investors have no time to trade on it to beat the stock market.

ii.
It is suggests the investors buy the Apple sharesas the stock price has brought the valuation down to a cheap level and it’s believed that it would drop temporarily. Further, the management has confidence that Apple is still one of the most valuable brands in the world and trusted brand by its customer, it possibly make the stock price rebound again and worth considering right now and in the future in view of company’s long-term growth potential.

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i.       The timing of decision

If financial markets are efficient, securities are always correctly priced.Efficiency implies that stock is sold for its true worth, so the timing decision becomes unimportant.

ii.      Speculation

If financial markets are efficient, managers should not waste their time trying to forecast the movement of interest rates and foreign currencies to make borrowing. Their forecast will likely be no better than chance as the price of the borrowing will always be at correctly priced.

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a. CAPM required rate of return

Acer                             :   4  +  1.00  (12 - 4)  =   12%

Bacs                            :   4  +  1.65  (12 - 4)   =   17.2%

Core                            :   4  +  1.40  (12 - 4)   =   15.2%

Dell                             :   4  +  0.80  (12 - 4)  =   10.4%

Risk-free (MTB)          :   4  +  0.00  (12 - 4)   =   4%

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Based on the evaluation in (a) and (b) above, only two stocks are correctly priced; Acer and MTB whilst Bacs and Dell are underpriced.  Thus, Mr. Yosef could invest in all combinations of the portfolio except for Core  because the price would drop soon  when it is overpriced since the average return below the SML @ required return at CAPM.  Mr. Yosef should buy more Stocks Bacs and Dell which is now underpriced because the price would rise  in the future.

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d.

Portfolio beta :             0.2 (1.00) +0.2(1.65)+0.2(1.40)+0.2(0.80)+0.2 (0.00)

=   0.97

Portfolio’s RR :            0.2 (12)+0.2(17.2)+0.2(15.2)+0.2(10.4) +0.2 (4)

=    11.76

Or

Portfolio’s RR :            4 % + 0.97 (12- 4)  =11.76%

e.
i.          Is it possible to have zero-beta portfolio of risky assets and;

Yes, it is possible, in theory, to construct a zero beta portfolio. Because such a portfolio’s value does not fluctuate as a result of market movement and therefore, would have zero correlation with the market movement.

ii.                Relates to (a), what would be its expected return for zero-beta portfolio?

A zero beta portfolio would have the expected return as the risk-free rate . In this case, it is 4%.  Since it would have zero correlation with the market movement, the expected would be either equal to risk-free rate or relatively low rate of return  compared to higher beta portfolio.

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The premise of efficient market hypothesis:

Efficient market hypothesis is one in which the stock prices fully reflect available information .  On the arrival of new information, the prices would immediately adjust to this information.  Prices change rapidly to knowable information and information disseminates rapidly. It implies that the stocks will be fairly priced  and day to day price changes will follow in a “random walk”  over time. As a result, investors cannot beat the market and cannot obtain an extraordinary profit .

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The empirical evidences on the efficient market hypothesis:

i.                 The weak form

Serial correlation  – which involves only one security. A positive coefficient of serial correlation for a particular stocks indicates a tendency towards continuation.  A negative coeffiecient of serial correlation indicates a tendency toward reversal. If price changes are truly random, it is a contradict situation if  so many believe that process follows pattern.

ii.               The semi strong form

Event studies  – according to the EMH, a stock’s abnormal returns at time should reflect the information at the same time.   Any information released before then should have no effect on abnormal returns in this period because all of its influence would already have incorporated in the prices.

The record of mutual funds  - refers to studies comparing mutual fund performance against the performance of a broad based index.  Research findings found that mutual funds were unable to beat the market index consistently since mutual fund managers use publicly available information. Therefore, it is consistent with week form and semi-strong form efficiency.

iii.                 The strong form

Insider trading  - even in the strongest adherents to the EMH, it is not a suprised to find markets are inefficient in the strong form.  This is due to insider trading. Insiders in the firms have across to information that is not generally available. However if the EMH holds, they should not be able to profit by trading the information.

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a.     Beta individual securities

Beta United       = (Cov United,mkt) /Var mkt

= 20.57 / 4.14²

= 1.20

Beta City           = (Cov City,mkt) /Var mkt

= 15.43 / 4.14²

= 0.90

b.     Expected return and Standard deviation of portfolios.

Option 1

Expected return, R(Option 1)   = 0.5(12%) +0.5(9.70)

= 10.85%

Standard deviation, σ(Option 1) = sqroot{(0.5)²(7.50%)²  + (0.5)²(9.30%)² + 2(0.5)(0.5)(47.43)}

= 7.71%

Option 2

Expected return, R(Option 2)   = 0.75(12%) +0.25(9.7%)

= 11.425%

Standard deviation, σ(Option 2) = sqroot{(0.75)²(7.50%)² + (0.25)²(9.30%)2 + 2(0.75)(0.25)( 47.43)}

= 7.40%

Option 3

Expected return, R(Option 3)   = (25k/40k)(12%) + (15k/40k)(4%)

= 9%

Standard deviation, σ(Option 3) = sqroot{(0.625)²(7.50%)²  + (0.375)²(0%)² + 2(0.625)(0.375)(0)}

= 4.69%

Beta Portfolio

Beta (option 1)= 0.50(1.20) +0.50(0.90)

= 1.05

Beta (option 2) = 0.75(1.20) +0.25(0.90)

= 1.125

Beta (option 3) = 0.625(1.20) + 0.375(0)

= 0.75

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c.
Decision: Choose Option 3: As risk averse investors, the best suited investment is option 3 because it has lowest risk  Beta = 0.75 and the standard deviation = 4.69%.  The expected return of 9.0% is considered as reasonable (not too low). In addition to standard deviation, the best measure of risk of a security in a large and well diversified portfolio is the beta of the security.

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a.     Yes, agree.   Normally when investors hold more than two securities or invest in many possible combinations of securities, investors are attempted to benefit from diversification of portfolio investments either to have the lowest possible standard deviation of a portfolio inter alia minimum variance portfolio (MV) or highest expected return  depending on the investors attitude towards risk averse (invest in point MV) or risk tolerance (invest in point X) as per illustration of graph below.  The diversification effects occurs whenever the correlation (p) between the two securities is below 1 or perfectly negatively correlated.  The diversification effect is illustrated in the figure because the curved line is always to the left of the straight line and where many securities available (denote by 1,2,3,4), it will formed different curve for different correlation and this indicates that the diversification effect rises as (p) declines.  When investors hold many securities, the feasible set would no longer be a line, instead it would be a confined region shown by the shaded area.  No security or combination of securities can fall outside the efficient frontier or shaded area to avoid less expected return with high standard deviation or vice versa.   Apparently, the investors will want to be somewhere on the upper edge between MV and X point which is known as the “efficient set or efficient frontier”.

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A.               The appropriate test in weak form efficiency is the use of serial correlation to find a correlation between the current return on one security and the return on the same security over a later period.  The correlation will indicate whether there are relationship between yesterday’s returns and today’s returns.

The evidence found a positive coefficient of serial correlation for a particular stock indicates tendency towards continuation. (if yesterday’s return higher, today’s return also higher). A negative coefficient indicates tendency towards reversal. (if yesterday’s return higher, today’s return will be lower).  Both significantly positive and negative serial correlation are indications of market being inefficient; return today can be used to predict future return.  Why? It is cheap and easy to find patterns in stock prices.  Serial correlation coefficients for stock returns near zero would be consistent with the random walk hypothesis where the stock price is not predictable from past prices.  Hence, it is strongly consistent with weak-form efficiency.

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B.               Justify whether the following statements are true or false:

i.                 False.  Aman cannot make abnormal return by analyzing the historical stock price movement if a capital market is weak form efficient. Technical analysis is useless because if it were possible to make big money simply by finding “the pattern” in the stock price movements, everyone would do it and the profits would be competed away. ü

ii.                True. Mr. William is getting private information from the insider Mr. Rajhi a business partner of Rail Works Bhd whom can be a trusted source of information. As Transport Ministry has yet to make an official announcement to the public, these is very big opportunities for Mr. William to make abnormal return by trading the shares before the information make known to the other investor.

iii.               True. In semi-strong form efficient market, prices respond instantaneously to new information and fully reflect that information. The speed and accuracy of share price movement do effect by the arrival of new information.