that the Section 4 Portfolio Theory 1 Year Stock A Stock B 2007 008 012 002

# That the section 4 portfolio theory 1 year stock a

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Section 4: Portfolio Theory 1 Year Stock A (%) Stock B (%) 2007 0.08 0.12 0.02 2008 0.21 0.27 0.15 2009 -0.27 -0.32 -0.33 2010 0.11 0.18 0.05 2011 0.18 0.24 0.12 Totals 0.31 0.49 Means 0.06 0.10 a. Calculate the expected return for each stock over the 5-year period. expected return = total/number of years Expected return for stock ## b. Calculate the variance for stock A. 0.14868/(5-1) variance = .03717 c. Calculate the standard deviation of the expected return for Stock A. standard deviation = square root variance = square root (3.7170%) You have been given the following sample data, showing average historical re Deviation j R(A) - R(mean A) retuen on portfolio Variance = sum of squared deviations / numbe = 19.28%
d. Calculate the variance for stock B Expected return = total/number of years = 49%/5 Expected return for B 0.10 e. Calculate the standard deviation of the expected return for stock B. variance = (23.1680%/ (5-1) 0.05792 standard deviation = square root (5.7920%) standard deviation for B = 24.07% f. Calculate the expected return for a portfolio of Stock A (60%) and Stock B (40 Expected return for Portfolio = 0.6 x 6.2 + 0.4 x 9.8 = 7.64% g. If the distribution of the expected returns is approximately normal, calculate th The range of expected return for stock A = 6.2% +/- 19.28% = -13.08% ~ 25.4 The range of expected return for stock B = 9.8% +/- 24.07% = -14.27% ~ 33.8

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h. What do the results for the expected returns and standard deviations over the Stock A has a lower return. However, it's risk is lower than Stock B Stock B has a higher return. However, it's risk is higher than Stock A. i. If you were an investor that did not like taking high risks, which stock would yo I would prefer the stock A if I was an investor that did not like taking high risks j. Calculate the covariance between stocks A and B The convariance between stocks A and B = 0.185320 / 5 = 0.037064 k. Calculate the correlation coefficient for stocks A and B. The correlation coefficient for stocks A and B = 0.037064 / (0.192795 x 0.2406 l. Interpret what the correlation coefficient is telling you about the relationship b The correlation coefficient of Stock A and Stock B pretty much the same represent the degree change of between stock A and stock B. This mea
2 Suppose the expected returns and standard deviations of two stocks were: Stock A: E(R) = 9%, standard deviation = 36% Stock B: E(R) = 15%, standard deviation = 62% a) Calculate the expected return of a portfolio that is composed of 35% of stock expected return of portfolio = ((weight of portfolio A * exp 0.129 0.129 0.129 12.90% b) Calculate the standard deviation of this portfolio when the correlation coefficie c) Calculate the standard deviation of this portfolio (same weights in each stock) = (35% *36%) ^2 +( 65% * 62%) 35.71% d) How does changes in the correlation between the returns on A and B affect th lower the correlation rate lower is the standard deviation and higher the corre standard deviation = (weight of A * standard deviation of = (35% *36% = 47.86% standard deviation standard deviation = (weight of A * st

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3 Refer to the table of data below and answer the questions that follow: Probability of Economic State Return on Stock K % Bear 0.25 -0.02 0.034 Normal 0.6 0.138 0.062 Bull 0.15 0.218 0.092 SUM FOR J SUM FOR K a) Calculate the expected return of each stock return on stock J = 0.25(-0.02)+0.6*0.138+0.15*0.218=11.05% return on stock k =0.25*0.034+0.6*0.062+0.15*0.092=5.95% b) If a portfolio was created with from 30% of stock J and 70% of stock K, what i return of portfolio = 11.05*0.3 +0.7 *5.95 = 7.58% c) Calculate the standard deviation of each stock the standard deviation of stock J = 0.00644475^0.5 = 0.0802792
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