Discipline of Finance

FINC3017 Investments and Portfolio Management S2-2022

Assignment 1

Due date: Wednesday 7th September, 2022 11:59 pm.

This assignment will require you to build 4 optimal portfolios, using the theory developed in lectures, and

discuss/compare their performance. You will form this discussion with reference to the paper “The Markowitz

Optimization Enigma: Is ‘Optimized’ Optimal?” by Richard Michaud which is available on Canvas. Using

this paper as motivation, you will construct several portfolios and discuss their relative performance. You

have been assigned 15 stocks from the S&P 100 index that you will use to build your portfolios. These

assigned stocks can be found in the file FINC3017 Asmnt 1 stock allocation.xlsx which is available on

Canvas. There is also a risk-free T-Bill available which has a fixed return of rf = 0.

The portfolios you construct will be built using data from 2nd January, 2019 until 31st December, 2020

(training data) and the performance will be tested using data from 4th January, 2021 until 31st December,

2021 (out of sample data). In the file titled FINC3017 Asmnt 1 Data.xlsx, you have been provided close

prices for (almost) all stocks that are listed on the S&P 100, the close level of the S&P 500 index that you

will use as a market proxy and an adjustment factor for each stock which will allow you to account for any

corporate actions (stock splits, etc). This tracks the number of shares that an investor with a single share

would hold at each date. For example, if an investor holds 1 share of a stock at date t and this stock does

a 2-for-1 split, then on date t + 1 you would own 2 stocks, but the price of each stock would half. In this

case the adjustment factor would change from 1 to 2. From this file, you will select data for the 15 stocks

that have been assigned to you to analyse. You may assume that the close prices on 31st December 2020

are equal to the open prices on 4th January, 2021 which is when you will construct your portfolios.

Using the training data, you are to compute simple returns at a daily frequency and use these returns to

compute the sample covariance matrix and mean returns. These will be your proxy for Σ and r respectively.

You are to assume that the investor is the representative market investor from the CAPM.

Using the training data to create inputs, you are to build the following portfolios for investment at the

open on 4th January, 2021:

1. A portfolio of the 15 stocks only that allows short positions.

2. A portfolio of the 15 stocks and the risk-free T-Bill that allows short positions in all assets.

3. A portfolio of the 15 stocks only that does not allow short positions.

4. A portfolio of the 15 stocks and the risk-free T-Bill that does not allow short positions in the stocks

but does allow a short position in the T-Bill.

Once the weights for these portfolios are identified, you are to construct a portfolio where you have

$100,000,000 to invest. Note that you may assume, for simplicity, that you can purchase fractional positions

in all assets and that your portfolio is always re-balanced, at no cost and no profit, back to the weights you

identified at initiation. Following this analysis, you are to write a report addressing the following points:

1. A table listing your stocks that states which GICS sector you believe they operate in (there are 11

sectors and you may choose more than 1 if its appropriate), their mean return (annualised), standard

deviation (annualised) and beta all computed using the training period. You should also provide a

brief discussion (only a few sentences at most) of how you think this spread across industries will aid

diversification.

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2. The same statistics as required above, but computed using the out of sample period. Compare and

contrast your results stating how any differences/similarities could affect portfolio performance.

3. A plot of the portfolio weights (bar chart) and a table outlining the standard deviation and expected

return (all annualised) of each portfolio. Again, these statistics should be computed using training

sample data. Explain what these numbers represent in the context of your portfolio construction.

4. A plot of the dollar value of your portfolios through time (over the out of sample period). You should

also include the dollar value of an investment in the S&P 500 index.

5. A table of performance statistics including the annualised mean daily return, the holding period return

(one year), the annualised standard deviation of daily returns, the Sharpe ratio (computed using both

the annualised daily mean and the holding period return) and the beta of each portfolio. Discuss

how the results you achieved with your portfolios compare across portfolios and also to the portfolio

statistics computed using the training period data.

Your discussion should attempt to relate your results to the findings in the Michaud paper provided.

Your report should not be a list of points that answers each point as a question. Rather it should be a

coherent piece of writing that addresses all the required items. There is a word limit of 1000 words (approx

2 full pages of writing) but I will not impose a page limit as I’d like tables and plots to be clearly formatted.

Remember that any tables and figures appearing in your report should be clearly referenced and discussed

in the report. Please also ensure all tables and figures have captions and axis labels. Finally, you must use

your assigned stocks to complete the assignment. If you choose a different set of stocks all marks

awarded for accurate computation will be forfeited.

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