Question

Please show working for all parts.

1. The annual returns of two stocks are given as follows. Year Stock A Stock B 2011 -10% 21% 2012 2013 20% 5% 7% 30% 2014 -5% -3% 2015 2% -8% 2016 9% 25% (a) Estimate the expected return and volatility of each stock. (b) Estimate the covariance and correlation between two stocks. (c) Find the expected returns and volatilities of portfolios that maintain 100.6% investment in Stock A and 100(1-x)% in Stock B, where r is given in the following table. volatility expected return 0 0.1 0.6 0.8 0.9 1.0 (d) Create the minimum variance portfolio by investment of these two stocks. (e) Sketch the efficient frontier

Answer 1

12 13 ar A 14 B -10 20 15 16 17 2011 2012 2013 2014 2015 2016 18 21 9 19 25 20 21 23 Expected return Standard deviation Covariance correlation 3.51 12 10.59716943 15.6460858 8.666666667 0.062724579 24 25 26 27 28 29 (1-x) 0 30 31 0.1 0.2 0.3 32 33 0.4 volatility Expected Return 15.6460858 12 14.1764241 11.15 12.8038015 10.3 11.5628284 9.45 10.5002857 8.6 9.67513996 7.75 9.15183042 6.9 8.98326221 6.05 9.18897891 5.2 9.74530656 4.35 10.5971694 3.5 34 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0.5 0.6 35 36 37 0.7 0.8 0.9 11 38 39 40 41 Minimum vari. portfolio 42 0.694986756 0.305013244 43 |(1-x)

Formulas used :-

expected return A =AVERAGE(D14:D19)

Volatility A =STDEV(D14:D19)

Covariance =COVAR(D14:D19,E14:E19)

Correlation =CORREL(D14:D19,E14:E19)

Volatility of portfolio =((C29^2*$D$23^2)+(D29^2*$E$23^2)+(2*$D$24*C29*D29))^(1/2)

Expected return on portfolio =(C29*$D$22)+(D29*$E$22)

Minimum variance portfolio (x).   =((E23^2-D24)/(D23^2+E23^2-(2*D24)))

(e) Diagram of efficient frontier given below

Expected Return 0 5 10 — Expected Return 15 20

I hope my efforts will be fruitful to you...☺️