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Q: Expected returns & standard deviation of a portfolio ( Answered ,   0 Comments )
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 Subject: Expected returns & standard deviation of a portfolio Category: Business and Money Asked by: hb18-ga List Price: \$5.00 Posted: 23 Jul 2005 08:35 PDT Expires: 22 Aug 2005 08:35 PDT Question ID: 546921
 ```Suppose the expected returns and standard deviations of stocks A & B are E(RA)=0.15, E(RB) = 0.25, ?B = 0.2, respectfully a. Calculate the expected return and standard deviation of a portfolio that is composed of 40 percent A and 60 percent B when the correlation between the returns on A & B is 0.5 b. Calculate the standard deviation of a portfolio that is composed of 40 percent A and 60 percent B when the correlation coefficient between the returns on A & B is 0.5 c. How does the correlation between the returns on A & B affect the standard deviation of the portfolio?```
 ```Hi!! IMPORTANT NOTE: You are missing the STD of the stock A, I will suppose that it is 0.10; I think that you also forgot a minus sign in the statement of part b) (correlation must be -0.5), if not the problem is the same than the part a) and the part c) results not related to this problem. If they are not the case and my assumptions make difficult the understanding of the solution, just let me know using the clarification feature. a.) Calculate the expected return and standard deviation of a portfolio that is composed of 40 percent A and 60 percent B when the correlation between the returns on A & B is 0.5 If we call: E(RP) = expected return on the portfolio E(RA) = expected return on Stock A E(RB) = expected return on Stock B WA = weight of Stock A in the portfolio WB = weight of Stock B in the portfolio E(RP) = (WA)*[E(RA)] + (WB)*[E(RB)] = = (0.40)*(0.15) + (0.60)*(0.25) = 0.21 or 21% Variance = (WA)^2*(STDA)^2 + (WB)^2*(STDB)^2 + + 2*(WA)*(WB)*(STDA)*(STDB)*[Correlation(RA, RB)] = = (0.40)^2*(0.10)^2 + (0.60)^2*(0.20)*2 + + 2*(0.40)*(0.60)*(0.10)*(0.20)*(0.5) = = 0.0208 STDP = sqrt(Variance) = sqrt(0.0208) = 0.1442 or 14.42% b.) Calculate the standard deviation of a portfolio that is composed of 40 percent A and 60 percent B when the correlation coefficient between the returns on A & B is 0.5 In this case we have that: Variance = (WA)^2*(STDA)^2 + (WB)^2*(STDB)^2 + + 2*(WA)*(WB)*(STDA)*(STDB)*[Correlation(rA, rB)] = = (0.40)^2*(0.10)^2 + (0.60)^2*(0.20)*2 + + 2*(0.40)*(0.60)*(0.10)*(0.20)*(-0.5) = = 0.0112 STDP = sqrt(Variance) = sqrt(0.0112) = 0.1058 or 10.58% c.) How does the correlation between the returns on A & B affect the standard deviation of the portfolio? As Stock A and Stock B become more negatively correlated, the standard deviation of the portfolio decreases. That is the portfolio become less volatile or more predictible in its return rate. For example if the correlation is zero the STDP is 12.65% and if it is -1 we will have a STDP equal to 8%. To make a more predictible portfolio you need to use stocks that are negative correlated, this will balance the uncertainty. ----------------------------------------------------------- I hope that this helps you. Feel free to request for a clarification if you need it. Regards. livioflores-ga```
 hb18-ga rated this answer: `Thank you so much. I really appreciate the help.`