Assessment 2 aims to provide students with an opportunity to analyse various inv
ID: 2757518 • Letter: A
Question
Assessment 2 aims to provide students with an opportunity to analyse various investment alternatives based on the respective risk and return so as to choose the most appropriate investment opportunity. You are expected to read beyond textbooks and able to apply the knowledge gain from real life examples either from your working environment or/and case studies read, and are able to demonstrate your competence in the areas indicated in the questions. You are encouraged to provide specific in-depth comments instead of general comments.
Instructions to students:
Download stock prices for any two different companies – 5 years of monthly closing prices for each company. You can use any database to obtain the prices e.g. datastream, yahoo finance (click the Investing tab followed by the Historical Prices tab) etc. Use data from December 2008 to December 2013 to generate average monthly returns. Calculate the annualised mean return, standard deviation and correlation of the stocks.
Use investment proportions for the two stocks ranging from 0% to 100% using intervals of 5%. Tabulate the investment opportunity set of the two stocks. Plot the investment opportunity set of the two stocks.
Calculate the weights on the optimal risky portfolio consisting of the two stocks, which we denote by stock 1 and stock 2, using the following formulae:
Calculate the expected return and standard deviation of this optimal risky portfolio. Plot the optimal risky portfolio on the diagram determined in (b) above.
Calculate the weights on the minimum variance portfolio consisting of the two stocks, which we denote by stock 1 and stock 2, using the following formulae:
Calculate the expected return and standard deviation of this minimum variance portfolio (MVP). Plot the minimum variance portfolio on the same graph in (b) above. Identify the MVP and efficient frontier consisting of the portfolios made up of these two assets. Label them clearly on the graph.
Discuss in your report diversification referring to the efficient frontier and comparing the expected return and standard deviation of the optimal risky portfolio to the minimum-variance portfolio in your answer.
Explanation / Answer
Investment(Rs) Portfolio weight Stock return
H 1000 .25 .02
D 3000 .75 .03
4000 1.0
Return of the portfolio = .25(.02) + .75(.03) = 2.75%
State of world Prob. of state Conditional return
stock I stock J
1 .2 -.18 -.04
2 .25 .16 -.02
3 .3 .12 .21
4 .25 .40 .20
E (RI) = .14 E (RJ) = .10
Cov (I,J) = (-.18-.14)(-.04-.10)(.2)+(.16-.14)(-.02-.10).25+ ........
= .0142
covariance between assets I and J is .0142 and their standard deviations are .193 and .116 respectively, correlation coefficient is as follows :
= 0.63
Forming Efficient Portfolios
(the allocation of asset weights in forming efficient portfolios)
Consider forming a two asset portfolio P from assets B and C with weights P(x,y)
BC = the locus of all possible portfolio combinations
MV = the minimum variance portfolio
Calculating the weights of the minimum variance portfolio
Suppose the investor is interested in forming a two-asset portfolio that will provide the minimum risk (standard deviation). How does he determine the appropriate amount to invest in A and B (the portfolio weights)?
E(Rp) = wA RA + wB RB
s2p = + 2 wAwBCOV(A,B)
wA + wB = 1
s2p = + 2 wA(1-wA)COV(A,B)
minimize the portfolio variance with respect to the portfolio weight, WA
= 0
solving,