Discipline of Finance
FINC3017 Investments and Portfolio Management S1-2024
Assignment 1
Due date: Wednesday 27th March, 2024
You are a junior analyst working for a large fund manager. One of your early tasks, provided to familiarise
yourself with the processes of the fund, is to compute some portfolios and compare their performance. Upon
completion of these computations, you are to summarise your results into a short document. You should
think of this as a professional document that could be distributed internally. It should be short and concise
but professional in presentation. You may even use dot points if you wish. Note that if a closed form solution
is available for your problem then that is the expected answer as it is the most accurate choice. If a close
form solution isn’t possible, a numerical solution should be used.
You will have been emailed two files. These are:
ˆ Return Data SID.csv: A file containing daily returns for a set of 20 stocks assigned to you. These
returns are adjusted to account for dividends and corporate actions such as stock splits.
ˆ Price Data SID.csv: A file containing raw, end of day prices for a set of 20 stocks assigned to you.
These are not adjusted for corporate actions, they are the prices listed on a given day.
All files contain daily data. Note that dates for these data sets are formatted as YYYYMMDD. If you wish
to convert these to Excel based dates see the video on the assignment 1 module.
You will also find on Canvas a file containing the daily risk-free rate and market return. All returns are
expressed in decimals (5% = 0.05) and represent the return over a single day. Using this data you, are to
compute the following items and place your answers, as numerical values only, into the stated sheet-[cell]
locations. See Canvas for a video demonstrating how to complete your solution template.
1. Using the returns provided, compute the average daily return for each stock only using data over the
period 20190102 to 20211231. These will be your estimates for the expected return vector.
Inputs & Portfolios-[B2:U2]
2. Using the returns provided, compute the daily sample covariance matrix of returns using data over the
period 20190102 to 20211231. This will be your estimate of the covariance matrix.
Inputs & Portfolios-[B5:U24]
3. Using the inputs computed in parts 1 and 2, compute the allocation vectors:
(a) The GMVP with short sales allowed.
Inputs & Portfolios-[B32:B51]
(b) The GMVP where the minimum allocation is 1% of the investors wealth.
Inputs & Portfolios-[C32:C51]
(c) The optimal portfolio, composed of risky assets only and with short sales allowed, for an investor
with risk aversion A = 5.
Inputs & Portfolios-[D32:D51]
(d) The optimal portfolio, composed of risky assets only and with a minimum allocation of 1% of the
investors wealth, for an investor with risk aversion A = 5.
Inputs & Portfolios-[E32:E51]
1
4. Using the risk-free rate as of 20211231 and the inputs computed in parts 1 and 2, compute the risk
aversion parameter for the tangency portfolio assuming short sales are allowed.
Inputs & Portfolios-[B27]
5. Compute the allocation vector for the tangency portfolio, assuming short sales are allowed, using the
inputs computed in 1, 2 and 4.
Inputs & Portfolios-[F32:F51]
6. Compute the allocation vector for a portfolio, of risky assets only, with maximum Sharpe ratio that
requires a minimum position of 1% of an investors capital using the risk-free rate available on 20211231.
Inputs & Portfolios-[G32:G51]
7. Using the allocations computed in 3, 5 and 6, compute daily simple returns earned on these portfolios
from 20220103 to 20231229 assuming that the portfolio is always rebalanced, at no cost, back to the
weights you initially computed. Place each series returns in the column with the corresponding heading.
Returns-[B3:G503]
8. Using the allocations computed in 3, 5 and 6, compute the daily simple returns earned on these portfo-
lios from 20220103 to 20231229 assuming that the portfolios are not altered after they are constructed.
This is called a static allocation. You may assume that you can buy fractional units of shares and that
the price paid for shares is that listed on 20211231. Place each series returns in the column with the
corresponding heading.
Returns-[I3:N503]
9. Using the allocations computed in 3, 5 and 6 and the inputs computed in 1 and 2, compute, for each
of the 6 allocation vectors and the market portfolio,
(a) Their expected return at construction.
Performance Stats-[B2:H2]
(b) Their expected standard deviation at construction
Performance Stats-[B3:H3]
(c) Their expected Sharpe ratios.
Performance Stats-[B4:H4]
Express all figures as annualised values assuming 252 trading days per year and place your answers
using the corresponding headings.
10. Using your returns computed in 7, compute for the 6 rebalanced portfolios and the market,
(a) Their realised average return over the examination period (20220103-20231229)
Performance Stats-[B7:H7]
(b) Their realised standard deviation over the examination period (20220103-20231229).
Performance Stats-[B8:H8]
(c) Their realised Sharpe ratios over the examination period (20220103-20231229).
Performance Stats-[B9:H9]
Express all figures as annualised values assuming 252 trading days per year and place your answers
using the corresponding headings.
11. Using your returns computed in 8, compute for the 6 static portfolios and the market,
(a) Their realised average return over the examination period (20220103-20231229)
Performance Stats-[B12:H12]
(b) Their realised standard deviation over the examination period (20220103-20231229).
Performance Stats-[B13:H13]
(c) Their realised Sharpe ratios over the examination period (20220103-20231229)..
Performance Stats-[B14:H14]
2
Express all figures as annualised values assuming 252 trading days per year and place your answers
using the corresponding headings.
Following your computations, you are to produce a summary document that provides:
1. A table containing the results computed in questions 9, 10 and 11.
2. A plot of the dollar value of the two best and two worst portfolios (defined by realised Sharpe ratio)
together with the market, assuming you start with an initial investment of $10,000 at the end of the
day on 20211231. All series should be on the same plot.
3. A brief discussion that compares and contrasts your portfolios based on:
ˆ The difference between expected and realised performance.
ˆ The impact that constraining the portfolio to have minimum allocations has on realised vs ex-
pected performance
ˆ The impact that daily rebalancing has on the portfolio.
Your discussion should identify any observed systematic differences along the dimensions stated above and
provide a explanation for the source of this observed difference. The entire summary document (table, plot
and discussion) must be no longer than 1 page and the text must be a minimum of 11 point font with
standard 1-inch margins (the table and plot can be shrunk to fit but should be easily legible). You do not
need to cite any academic research for your discussion (though you may find it helpful to interpret your
findings) and should base all findings on your computed results.
Marking
Your calculation accuracy will contribute 2/3 of your grade and your summary document will contribute 1/3.
Calculations will be graded via a computer program that takes into account previous errors. This means
that you must use prior answers to compute later answers. This requirement is stated in each question. Your
report will be graded based on your insight as to the differences between the portfolios you have constructed.
A high quality answer would accurately identify differences and provide a valid justification which highlights
a deep understanding of the portfolio construction process. Your findings should align with your results. If
there are inconsistencies between your findings and your discussion this will be penalised.