Portfolio Theory

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Formulae sheet has been attached

The historical returns of the stocks of companies A and B during 2015 until 2019 are summarise as follows: A %) B (%) Year 2015 18 22 2016 5 12 5 -4 2017 15 2018 6 -4 2019 20 30 (a) Calculate the mean return and standard deviation on A and B based on the information above. (4 marks) (b) Calculate the coefficient of correlation for these two stocks. Interpret the meaning of it. (4 marks) (C) Plot an efficient frontier. Note that the portfolio weights should range from 0 to 1 by the increment of 0.2. (7 marks) (d) In relation to this question explain the concept of efficient frontier and diversification of risk. (5 marks) (Total: 20 marks) Formulae Sheet Mean and standard deviation - 3R = (R, +R, tu+R) where E is the expectation operator, R is the rate of return; T is the sample size s.d. tR, - E(R)] = \; {R, - E(R)F +[R. - E(R)j + +[R, - E(R)}} - where s.d. stands for the standard deviation Correlation coefficient and covariance Cove R, R) Px.x s.dys.dy where p is the correlation coefficient; Cove) is the covariance between the two stock returns CovRR) R,, - EUR/JIR,, - EXR, )= {[Rr. -E(R)][R,, - E(R)]+[Rx2-E(R)][R, 2-E(R)] +...+[R... - E(R)[R, - E(R,)]} X Rua Portfolio return and standard deviation E(R)=wxE(Rx)+w,E(R) s.dn = wisd + ws.d; + 2wxW5Pxys.dys.d, where P stands for portfolio; w is the proportion of wealth invested in the individual stock