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Q: Expected Returns & Stocks ( Answered ,   0 Comments ) Question
 Subject: Expected Returns & Stocks Category: Business and Money > Accounting Asked by: bladehulk-ga List Price: \$13.00 Posted: 12 Nov 2006 02:14 PST Expires: 12 Dec 2006 02:14 PST Question ID: 782033
 ```STATE OF ECONOMY RETURN ON STOCK a(%) RETURN ON STOCK B(%) a. Bear 6.30 -3.70 b. Normal 10.50 6.40 c. Bull 15.60 25.30 1. Calculate the expected return on each stock 2 Calculate the standard deviation of returns on each stock 3. Calculate the covariance and correlation between the returns on the two stocks.``` Subject: Re: Expected Returns & Stocks Answered By: livioflores-ga on 12 Nov 2006 06:45 PST Rated: ```Hi!! Let me start defining the variables: E(RA) = expected return on Stock A E(RB) = expected return on Stock B STDA = standard deviation of stock A STDB = standard deviation of stock B VarA = variance of stock A VarB = variance of stock B Cor(RA,RB) = correlation between RA and RB Cov(RA,RB) = covariance between RA and RB - Part a). Since it is not stated we can consider the same probability for each possible state of the economy, that is 1/3, then: E(RA) = (1/3)*(0.063) + (1/3)*(0.105) + (1/3)*(0.156) = = 0.1080 = = 10.80% So the expected return on Stock A is 10.80%. E(RB) = (1/3)*(-0.037) + (1/3)*(0.064) + (1/3)*(0.253) = = 0.0933 = = 9.33% The expected return on Stock B is 9.33%. - Part b). For definition and formulas of variance and standard deviation see "Standard Deviation and Variance: Common Measures of Variability" http://davidmlane.com/hyperstat/A16252.html VarA = (1/3)*(0.063 - 0.108)^2 + (1/3)*(0.105 - 0.108)^2 + + (1/3)*(0.156 - 0.108)^2 = = 0.001446 STDA = sqrt(0.001446) = = 0.0380 = = 3.80% The standard deviation of returns of Stock A is 3.80%. VarB = (1/3)*(-0.037 - 0.0933)^2 + (1/3)*(0.064 - 0.0933)^2 + + (1/3)*(0.253 - 0.0933)^2 = = 0.014447 STDB = sqrt(0.014447) = = 0.1202 = = 12.02% The standard deviation of returns of Stock B is 12.02%. - Part c). For formulas and definitions see "Covariance and correlation" http://www.ncbi.nlm.nih.gov/books/bv.fcgi?rid=mga.section.2685 or "Statistical Review with formula of, and rules for the mean, variance, covariance, correlation coefficient": http://www.kaspercpa.com/statisticalreview.htm Cov(RA,RB) = (1/3)*(0.063 - 0.108)*(-0.037 - 0.0933) + + (1/3)*(0.105 - 0.108)*(0.064 - 0.0933) + + (1/3)*(0.156 - 0.108)*(0.253 - 0.0933) = = 0.004539 The covariance between the returns of the two stocks is 0.004539. Cor(RA,RB) = Cov(RA,RB) / (STDA * STDB) = 0.004539 / (0.0380 * 0.1202) = = 0.9937 The correlation between the returns of the two stocks is 0.9937. Search strategy: variance formula covariance correlation formula I hope this helps you. Feel free to request foe a clarification if you need it. Regards, livioflores-ga```
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