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%

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 Pluto       = 93.25/ (8.13)²= 1.41

Beta Venus     = 58.21/ (8.13)²= 0.88 

Beta MTB        = 0% or ZERO Beta

 

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. 

 

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

                              =  12.4% 

 

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

                              =  13.9% 

 

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

                              = √7.84

= 2.80% 

 

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

= √21.49

= 4.64% 

 

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

= 13.225%

 

σ_Portfolio = 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%. 

 

R_Valet         =  R_f  +  β (R_M  - R_f)

=  4%  + 0.83 (7%)

= 9.81%

 

R_Primus   =  R_f  +  β (R_M  - R_f)

=  4% + 1.25 (7%)

= 12.75%

 

R_Porfolio  =  0.45 (9.81) +  0.55 (12.75) 

= 11.427%

 

Or

 

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

 

R_Porfolio  =  R_f  +  β (R_M  - R_f)

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

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.  

 

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. 

 

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.

 

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%

=   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.

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 .

 

                     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. 

 

 

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

 

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. 

 

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.