Find the optimal risky portfolio

Assignment Help Portfolio Management

Reference no: EM131021393

The associated data files are attached. Please check in detail and answer the questions

Portfolio Management Seminar

Part -1:

You have been given, in the file "Data for 1st computer lab.xlsx", end of month return index data (index that accounts for capital gains and dividends) from 1999-2008 for 7 UK stocks, the FTSE All share Index (proxy for the market portfolio), and the 3-month T-Bill (proxy for the risk free rate); downloaded from the Datastream.

a) Answer all the questions and submit your solutions to the tutor's email at least a day before the Lab.

b) Please save the original (i.e. untreated) data in a disk and take with you in the computer lab. So that you can start from the beginning with your tutor following his instructions. Questions

Questions

(1) Calculate returns for
(i) Each company
(ii) The FTSE All-Share Index

(2) Create descriptive statistics for the returns of
(i) Each company
(ii) The FTSE All-Share Index Discuss the findings

(3) Estimate the correlations for all the companies and the index. Comment on them.

(4) Estimate the 1st, 2nd, 4th, 6th and 12th order autocorrelations. Comment on them.

(5) Create an equally weighted portfolio consisting of all 7 stocks.

(6) Create descriptive statistics for the Portfolio above

(7) Compare the descriptive statistics with the ones for the market portfolio. Is your portfolio less or more risky than the Market one? To answer please see

(i) The standard deviations

(ii) The Beta of the Portfolio (To estimate the beta, please use the simple Market model

R_P,t = α + β × R_M,t + ∈_P,t

(8) Compare the average return and risk of all 7 individual companies with the portfolio risk and returns. What do you find?

(9) Estimate the market model for each individual company.

(i) Based on the betas are all companies equally sensitive to changes in the Market? What does standard error tell us with respect to the beta estimation?

(ii) What information do we get from the constant (alpha) of the model?

(iii) What information do we get from the R² with respect to the system- atic and unsystematic risk of each of the companies?

(10) Using the first five years of data estimate the CAPM parameters for each stock

(11) Using the parameters obtained above; estimate the required rate of return for each of the companies for the next five years, and compare the predicted with the actual values.

Part -2:

Based on the data of the previous computer lab and the market value data of data for 7 UK stocks given in the file "Data for 2nd computer lab.xlsx":

a) Answer all the questions and submit your solutions to the tutor's email at least a day before the Lab.

b) Please save the original (i.e. untreated) data in a disk and take it with you in the computer lab.

So that you can start from the beginning with your tutor following his instructions.

Questions

(1) The universe of available securities includes two risky stock funds A and B and T-bills. The expected return for funds A and B are 10% and 30%, respectively. The standard deviations for fund A is 20% whereas for fund B is 60%. The correlation coefficient between funds A and B is -0.2. The T-bills rate is 5%.

(i) Calculate expected returns and standard deviations for different port- folios using different weights invested in each fund (i.e. starting from 100% invested in fund A and 0% in fund B, 95% invested in fund A and 5% in fund B, 90% invested in fund A and 10% in fund B, . . . , ending to 0% invested in fund A and 100% in fund B).

Prepare a graph of the possible risk return combinations and discuss your findings.

(ii) Find the optimal risky portfolio and its expected return and standard deviation.

(iii) How much an investor with A = 5 will invest in the optimal risky portfolio (i.e. funds A and B) and in T-bills?

(2) Create a value weighted portfolio (based on the market value of each firm measured at the end of the calendar year) consisting of 7 stocks (the ones in your sample) that will rebalance annually (i.e. the weights will change each year, and at the beginning of the year one can use the market value of last year to allocate funds check that the weights sum to 100%)

(3) Create descriptive statistics for the returns of the value weighted portfolio

(i) Compare and contrast the descriptive statistics for the value weighted and the equally weighted portfolios

(ii) Using the 7 stocks create the efficient frontier and find the optimal risky portfolio in line with Markowitz methodology (Hint: You may use the Excel Solver to solve the various optimization problems for the appropriate weights Example 8.4 in BKM).

Discuss the findings, i.e. which of the 3 portfolios seems to be better and why it is so?

Attachment:- Data.rar

Reference no: EM131021393

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