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However, in this case the four stocks are SDIX1, PDFS2, CRIS3 and CSCD4 with annual possible rate of returns of 22.37%, 19.40%, -35.04% and 10.87%. In addition their last sale prices rated at $ 2.63, $ 5.96, $ 2.795 and $ 6 respectively but would not be used since the stocks do not have information on their dividends. The third step is to divide the expected dividend per share by selling price for each selected stock (Not used in this illustration).Instead the annual return rates; 22.37%, 19.40%, -35.04% and 10.87% are then converted into decimal by dividing each by 100 to give the rate of return for SDIX, PDFS, CRIS and CSCD as 0.2237, 0.1940, -0.3504 and 0.1087 respectively. Once the possible rates of returns are obtained, the next step is to assign individual probabilities for each stock and which must add up to 100.This is in accordance to "givens" conditions in the calculation of ERR (Damon, 2010). Therefore, let us say the probability of SDIX stocks bringing 22.37% return is 30, PDFS stocks bringing 19.40% return is 20, CRIS stocks bringing -35.04% returns is 15 and CSCD stocks D bringing 10.87% returns is 35, the Expected Rate of Return for the four portfolios could then be calculated with the formula
ERR = ? (Return Rates x Return Probability) from i to ‘n' where i=Stocks (Damon, 2010). In our case, ‘i‘- ‘n' represents SDIX, PDFS, CRIS and CSCD respectively. It then follows that ERR= {(0.2237x30) + (0.1940x 20) + (-0.3504 x 15) + (0.1087x 35)} = 6.771 + 3.88 - 5.256 + 3.8045 = 9.1995.Thus the expected rate of return as in this illustration is approximately 9.2 % for the entire portfolio selected from NASDAQ.
To calculate Beta, The first step is the conversion of associated ERR values into decimals since they are normally given in percentages. For instance, 9.2 % would translate to 0.092. In addition, it would require us to have values for risk-free rate and market premium rate since the formula states ERR=(Risk free rate)+(beta x (Market premium rate)).Let us say the risk free rates and market premium rates are 1% and 5% respectively, it thus implies 0.01955 = 0.01 + (beta)x (.05).This brings 0.05Beta= 0.01955 - 0.01 = 0.00955 thus by making beta the subject of the formula yield its value to Beta = 0.191 (How to calculate Beta, 2010)
To calculate the value of standard deviation, we use the formula described as (Calculating Standard Deviation).Where x and x-bar are the stock closing prices values and their weighted respectively, and n = number of days. For our case we have SDIX, PDFS, CRIS and CSCD with their respective closing prices as $1.86, $4.80, $ 2.28 and $ 5.10 and weights of 15%, 30% 35% and 20% respectively. Also ‘n' will be a month span of approximately 30 days. Rows for closing price, closing price minus the weighted value, and the square value of middle row are created. The individual weights (x-bar) 0.15, 0.30, 0.35 and 0.20 are subtracted from individual closing price(x) (NASQAD Stocks Exchange).thus (1.86 - 0.15), (4.80 - 0.3), (2.28 - 0.35) and (5.10 -0.2), thus we get 1.71, 4.5, 1.93 and 4.9. These values are then squared to give 2.9241, 20.25, 3.7249 and 24.01 respectively. The result is then divided by (30-1) i.e. 29 to give 0.100, 0.698, 0.128 and 0.827 respectively. These values are finally square-rooted to give the approximate values of standard deviation as 0.316, 0.835, 0.357 and 0.909 for securities SDIX, PDFS, CRIS and CSCD respectively. Practically Beta, also known as Beta coefficient, predicts the systematic risk volatility in a given portfolio compared with the entire market. Such that, Beta values of greater than 1 predicts higher price volatility, Beta equals to 1 means the stock price is consistent with market and Beta less than 1 means it is less volatile. For me I would choose those stocks with high Beta values due to their higher returns though more risky.
2. Capital Asset Pricing Model (CAPM) and Securities Market Line
CAPM is for pricing individual securities or portfolio. In the case of individual portfolios, it applies values for Security Market Line (SML) in respect to the expected returns and Beta values so as to dictate respective security market prices depending on the category of risk they fall into. Thus the ratio between the returns to risk is determined in comparison with the general market. Thus a Beta coefficient resulting in the decrease of ERR of a security would result in the ratio value equal to the ratio of market return to risk. This can be summarized as [[E(Ri) - R f] /Betai] = [E(Rm) –Rf ], where E(Ri) is expected return rate, E(Rm ) is expected market return and Rf = risk free rate (Basu, 2010)
The weakness of this model attributes to its many assumptions on information access, models theory, taxation and transaction (Roll, 1977).Its assumptions implicate real life explanations especially if conditions are very dynamic. For instance, it assumes that there will be no arbitrage and that all investors are rational and there is an efficient operation of capital markets. The model further assumes that all actors have same level to access market information. As much as this may be a strength by being consistent with exact world of business, it is also a weakness as it markdown those investors who are privileged to more information. In addition, the economic theories supporting this model were based on particular environment and people thus not applicable to the real dynamic business world (Roll, 1977).The assumption that the model neither reflects on taxation or costs makes it solely to help in acknowledging the problems faced by economic models and this is a great weakness(Roll, 1977).
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