PORTFOLIO OPTIMIZATION

PORTFOLIO OPTIMIZATION. i need this project done in the next 8hrs
a sample project is attached the data is different so dont copy
if wrongly done or late be sure i will dispute
bid only if you can handle
 
 
 
You will find an Excel workbook called AssignmentData.xlsx which is needed to
 
 
 
 
complete this assignment. It contains weekly index data for five asset classes and one
 
 
 
in-dividual asset (Gold).
 
 
 
Due to the reputation of “Education Institution of America” for producing work-ready
 
 
 
graduates, you are head-hunted by a small asset management company to work parttime
 
 
 
as a portfolio manager whilst you complete your degree.
 
It is your first day on the job and your boss is keen to see how much you really know. She
 
 
 
provides you with a list of five asset classes and tasks you and your team to investigate the
 
 
 
 
efficient asset allocation between these asset classes. Moreover, you are asked to satisfy a
 
 
 
 
 
 
17% expected return target on the portfolio you construct. To get started you decide to
 
 
 
collect historical performance data for the last five years in order to estimate the expected
 
 
 
return and variance-covariance structure of the asset classes (the data in the Excel file).
 
 
 
To perform the asset allocation you decide to construct a minimum variance portfolio. You
 
 
 
recall the 17% expected return target imposed by your boss and note that there was no
 
 
 
mention of short-selling constraints. In order to construct this portfolio you should copy the
 
 
 
assignment data into an Excel workbook and perform the following tasks/answer the
 
 
 
following questions:
 
 
 
 
 
1. (a) Transform the index values into simple weekly returns (you do not need to
 
 
 
report these in your submission).
 
(b) Using the returns data, estimate (and report) the vector of expected returns for
 
 
 
the five asset classes, as well as the variance-covariance matrix of these returns.
 
 
 
These expected returns etc. should be annualized (i.e., in annual units).
 
 
 
 
(c) Report which of the asset classes are efficient and which are inefficient. For each
 
of the inefficient asset classes, find another asset class that dominates it.
 
 
 
 
(d) Compute and report the parameters A, B, C and .
 
 
 
(e) Construct and plot the MVS (with short sales allowed) for expected (annual)
 
 
 
returns ranging between −10% and 35%. Your figure should also indicate the
 
 
 
positions of the five asset classes.
 
 
 
(f) Identify the global minimum variance portfolio (MVP), i.e. report the portfolio
 
 
 
weights (in the five asset classes), expected return, and variance of the MVP.
(g) Determine and report the portfolio weights for the efficient portfolio with 17%
 
 
 
 
expected return.
 
2
 
 
 
 
 
You are eager to impress so you send the results to your new boss just before you
 
 
 
leave for your lunch break. Upon your return, the boss has looked at your report and
 
 
 
notes that the risk of the portfolio is a little higher than she expected and wondered if
 
 
 
adding an additional asset would help reduce the risk. Knowing all about diversification,
 
 
 
you suggest that maybe adding an asset that has a low correlation with the existing five
 
 
 
asset classes might help. “Gold!”, your boss exclaims. You have heard many stories
about gold being a great diversifier and so you offer to do the analysis again with the
 
 
 
 
additional asset (gold) included in the portfolio. Using the additional gold index data in
 
 
 
the Excel spreadsheet, perform the following tasks:
 
 
 
2. (a) Using the same methodology as in Question 1 (simple returns etc.),
 
 
 
reconstruct the vector of (annual) expected returns and the variancecovariance
 
 
 
matrix for the five asset classes plus gold (i.e., six assets in total).
 
 
 
(b) Compute and report the new A, B, C and parameters.
 
(c) Construct and plot the new MVS (with short sales allowed) for expected (annual)
 
 
 
returns ranging between −10% and 35%. You should also plot the MVS from
 
 
 
1.(e) for comparison and indicate the positions of the five asset classes and gold.
 
 
 
 
 
(d) Identify the new global minimum variance portfolio (MVP), i.e. report the port folio
 
 
 
weights (in the six assets), expected return, and variance of the MVP.
(e) Determine and report the new portfolio weights for the efficient portfolio with
 
 
 
 
17% expected return.
(f) Calculate and report the reduction in risk of the 17% returning efficient
 
 
 
 
portfolio that can be achieved by adding gold to the portfolio.
 
 
 
You inform your boss of these findings and she is happy with the addition of gold to the
 
 
 
portfolio and the reduction in risk. However, she informs you that the 15% returning
portfolio you have constructed is not as ‘efficient’ as it might be as you have forgotten all
 
 
 
 
about the risk-free asset… oops! You quickly do some research and determine that the
 
 
 
appropriate risk-free rate to use is 1% per annum. Perform the following tasks to adjust
 
 
 
your portfolio weights:
 
 
 
3. (a) Construct and plot the MVS (with short sales allowed) for the five asset
 
 
 
classes and gold plus the risk-free asset paying 1%.
 
 
 
(b) Identify the tangency portfolio, i.e. report its portfolio weights, expected return,
 
 
 
and variance of returns. Furthermore, illustrate its tangency property
 
 
 
graphically by plotting the MVS from 2.(c) on the same set of axes.
(c) Determine and report the new portfolio weights for the efficient portfolio with
 
 
 
 
17% expected return.
(d) Calculate and report the reduction in risk of the 17% returning efficient
 
 
 
 
portfolio that can be achieved by adding the risk-free asset bond to the
 
 
 
portfolio of six risky assets.
 
3
 
 
 
 
 
A little embarrassed from your mistake of not including the risk-free asset, you send the new
 
 
 
 
updated results to your boss at 4:50pm. She is impressed with your efficiency as well as the
 
efficiency of the portfolio. However, she hasn’t quite finished with you just yet! She is
 
 
 
 
 
 
worried about the need to short sell certain asset classes in the currently proposed
 
 
 
portfolios. Many of the firm’s clients do not like, and some do not allow, short selling in their
 
 
 
 
portfolios. Therefore, your boss wants you to investigate the effect a no short sales
 
 
 
 
 
 
constraint will have on the MVS without a risk-free asset and any subsequent investment
 
 
 
decisions. To do this you are asked to perform the following tasks:
 
 
 
 
 
4. (a) Construct and plot the risky asset only MVS with no short sales allowed for
 
 
 
the five asset classes plus gold. (Recall you will need Solver to do this.)
 
 
 
(b) Plot the MVS for the unconstrained problem—found in 2.(c)—on the same set
 
 
 
of axes. Also, indicate the positions of the five asset classes plus gold.
 
 
 
(c) List the portfolio weights for all the data points used in constructing your no
 
 
 
short sales allowed graph.
 
 
 
(d) Identify and report the range of expected returns for which the short sales
 
 
 
con-straint is not binding.
 
 
 
(e) Discuss the compositions of the portfolios at the end-points of the MVS with
 
 
 
no short sales.
 
4
 
 
 
 
 

PORTFOLIO OPTIMIZATION