Portfolio Theory (M32252/1)

Assessment  2

The assessment 2 for the module comprises a 2500-word written assignment worth 60% of the final grade. The written 2500-word assignment is due on  Thursday 15th January 2026 at 1pm.

Assignment 2 Details

Hand in Date: Thursday 15th January 2026, 1pm.

Requirements:

•    Individual Assignment

•    Maximum of 2500 words (excluding the appendix and tables)

•    You need to make 2 submissions. You must submit

a.one copy of the word report that includes tables and appendix (not excel files) in the Turnitin dropbox.  and

b.should store one copy of all relevant workings, formulas and/or calculations used in an excel file  in the Moodle dropbox

We regret that it may not be able to mark work submitted without the excel workfile.

Part 1. Performance Measurement (60%, 1200 words)

Overview

You have £1 million to invest in a portfolio of eight (8) shares. Four of them are from companies that constitute Dow Jones Index and the other four from companies that constitute FTSE-100 index. You are an English investor, so all your computations and cash have to be in GBP.   Analysts’ target prices may be used to compute ‘expected returns’, while 12 months expected T-bill rates would be used to compute ‘risk-free rate.'

You are required to compute the efficient frontier under three scenarios:

•    a.Short selling is allowed with a risk-free rate equal to your estimate of the one-year risk-free rate in the UK.

•    b.Short selling is allowed but there is no risk-free rate.

•    c.Short selling is not allowed

You need to do these using the following expected return models:

•     1.CAPM

•    2.Market Model

You must then compare these six portfolios (a1, b1, c1, a2, b2 and b3) to the returns generated by your portfolio over that one year and critically discuss the models used and the forecasting issues  that have arisen.

Step 1

Take a list ofFTSE-100 and Dow Jones Index companies   from the respective file available in this unit on moodle and choose seven (8) companies. Justify your selection, as this should not just be random.

Step 2

You are constructing the efficient frontier and your time period is one year.

For each share you need the expected annual return (for the coming year), the standard deviation of returns for each share (annualized standard deviation), and the correlation coefficient (or equivalently, the covariance), between each pair of shares.

Note that this is a forecasting problem. You want the expected returns, standard deviations and co-variances for the coming year. Initially you need to use five years of historical data (so October 2020 to September 2025) to do this. However this may be changed once you have reflected upon your results.

Step 3

Once you have your forecasts, use Solver on Excel to solve the optimisation problem. This will be covered in the lectures, so it is a good idea if you are up-to-date with the computations ofthe previous steps so you can fully benefit from these classes.

You are required to compute the efficient frontier under three scenarios:

•    Short  selling is allowed with a risk-free rate equal to your estimate of the  one-year riskfree rate in the UK.

•    Short selling is allowed but there is no risk-free rate.

•    Short selling is not allowed

You need to do these using the two following expected return models:

•    CAPM

•    Market Model

Step 4

You need to examine the weights given by the optimizer. Critically discuss the advantages and disadvantages ofthe method you chose to get your forecasts. Critically discuss the advantages and dis-advantages of using this technique as a solution to the general asset allocation problem. Refer to possible solutions, in a context that refers to current literature (books, papers examined). The critical discussion must be integrated with the particular quantitative results you have obtained, i.e. you must demonstrate that you understand the issues you talk about by relating them to and illustrating them with your own results. Critical discussion should include, ideally but not necessarily, reference to both (a) at least three (3) books and (b) at least five (5) papers published in 3-star or 4-star journals in 2021, 2022, 2023, 2024 and 2025. Published papers can be retrieved by using google scholar. An indicative list of 4star journals under the ABS AJG ranking is provided in the appendix.

In other words, you are standing back from all the computations you have done, and are asking the question about the value of this technique in practical applications.

Part 2. IPS

Limit 700 words, 20%. (Hint: See Ch.2 MTPM and Handout: Investment Policy)

You have been recently appointed as an asset manager.   You  have  three  new  customers. Johnathan  is  a  confident  investor  who  may  undertake  limited  risk.  Amrita  is  a  young entrepreneur who is a risk-taker. Benjamin is a gentleman that is, to a large extent, financially independent. Categorise your customers according to the life-cycle view, the Bailard, Biehl and Kaiser model and the Barnewall model. (5 marks)

Judging from the income and the personality, what strategy (Income, growth, Income and growth, Total Return Policy) will you follow for each of your customers, and why? (5 marks)

Write a concise Investment Policy Statement (IPS) for each of them (10 marks). See Appendix for details.

Part 3. Asset Allocation

Limit 200 words, 7%. (Hint: See Ch.5 MTPM and Handout: Asset Allocation)

Now assuming that you followed a constant weight monthly rebalancement (or constant mix strategy), by using only the shares of one company and a hypothetical zero-coupon 12-month T-bill price  for the last  12  months  (assume  the  price of T-bill is not  affected by market conditions), show on a table what is the development of the following

Pstockt,  Pbondt, At-1,t, Bt-1,t, Vt, At, Bt,  Given that

Pstockt denotes the stock price at time t

Pbondt, the bond price, Vt is the total value of the portfolio at time t

At, Bt is value of stock and bond portfolio, respectively, after rebalancing.

At-1,t, Bt-1,t is value of stock and bond portfolio, respectively, before rebalancing.

You follow a 60:40 constant mix strategy, the risk free rate is 5% and you initially invest £1,000. Transaction cost is 0.2%. (4 marks)

Compare your finding with a hypothetical buy and hold strategy during the same period. (3 marks)

Part 4. Performance Measurement

Limit 350 words, 13%.

Compute the Sharpe, Treynor, and  Jensen metrics for the same portfolio, by using analysts expectations for expected returns. (6 marks)

Which metrics is the most appropriate for your portfolio and why? (2 marks)

Use the Merton-Henriksson attribution analysis, based on the betas computed during the first four years  (48  monthly  observations  during  the  period  year-5  to year-1), to  evaluate  the performance of a portfolio of your selection during the last  12 months of a 5-yr period. (5 marks).