Assignment One
In Question 1 you will use the mean-variance approach and data on returns for two shares for the period January 2019–January 2022 to form a portfolio. You will then examine the performance of your portfolio in the period January 2022–January 2023. In Question 2 you will use the single-index model to develop a more complete understanding of this performance. In Question 3 you will consider changing bond yields in the Eurozone between August and September 2022, and predict the effect on bond prices.
Explain and illustrate your answers to these questions, which are based on Units 1 to 3, in no more than 2,500 words. This limit includes tables and captions but excludes footnotes, endnotes, tables of figures and references. Answers that exceed this limit will result in a loss of marks. Full details of penalties for late submission, exceeding the word limit and other information can be found at the end of this assignment.
Your assignment should be submitted via the Virtual Learning Environment (VLE) to The Centre for Financial and Management Studies no later than 16th May 2023. Full instructions are available on the VLE.
Question 1
The tab-delimited text file M423_A1_S3_2023_Q1_Q2.txt contains weekly data on the share prices of the Nvidia Corporation (denoted NVDA) and Qualcomm (QCOM), the American multinational technology companies; and the Standard and Poor’s 500 share index (SP500). The file also includes the simple weekly return on Nvidia shares (R1), the weekly return on Qualcomm shares (R2), and the weekly return on the S&P 500 index (RM). The data are from 21/1/2019 to 23/1/2023. The share prices and index are in US dollars. The data are from finance.yahoo.com.
1(a) Using the share returns for the period 28 January 2019 to 24 January 2022, and the methods you have studied in Unit 1, construct a portfolio consisting of Nvidia shares and Qualcomm shares. Justify
your choices. [30% of total marks]
1(b) For the portfolio you formed in part 1(a), examine the performance over the period 31 January 2022 to 23 January 2023. Comment on
your results. [10% of total marks]
Question 2
2(a) Using the share returns and the return on the market index for the period 28 January 2019 to 24 January 2022, estimate the parameters of the single-index model for Nvidia and for Qualcomm as shown in equation (2.1)
Ri i i Rm ei
(2.1)
where Ri is the return on asset i (i = 1 for Nvidia and i = 2 for Qualcomm), Rm
is the return on the market index, and ei
is a random disturbance.
Comment on your results. [25% of total marks]
2(b) Historical betas are acknowledged to be biased predictors of future betas. Explain this bias, and Blume’s method for transforming historical betas to address the bias. Apply this transformation to the estimated betas you obtained in Q2(a), and comment on your results. [10% of total marks]
Question 3
At the start of August 2022 the yield on ten-year government bonds issued by the German federal government was 0.8 per cent. Towards the end of September 2022 the yield was 2.3 per cent (source: bundesbank.de). Predict the effect of these changes in yield on the price of the ten-year government bonds. [25% of total marks]
Student Assignment Guidelines
There is no single right way to answer these questions; rather there are a number of approaches, and different students will have their own view of what is expected and how much weight to give any particular element, within the mark weighting for each question. Whatever your approach, you will need to plan your answers carefully, in order to provide a focused and succinct answer to the questions, within the word-limit.
In your answers, you should demonstrate your knowledge of and ability to explain and apply economic and financial models. You must justify any conclusion you reach on the basis of evidence provided by you by reference to, or quotation from, the course notes, textbooks, other course readings, or any other source you choose to use. As long as your answers give a good justification and demonstrate your reasoning ability and your knowledge, you can obtain a good grade.
At all stages you should explain your reasoning in a way that shows your understanding of the theory and empirical studies of Units 1, 2 and 3. You can also introduce knowledge you have gained from other parts of the course, where appropriate, or from other courses, or elsewhere. But remember that the assignment is designed to focus on the subjects you studied in Units 1, 2 and 3.
Your answers should be written in an academic manner, presenting your view carefully, justifying your view with rigour and discussion. When you present a relevant theory, in your justification it is good, where possible, to demonstrate your understanding of it by using a simple equation or diagram. In presenting your arguments, you should also comment on possible weaknesses and limitations.
The questions are intended to develop your understanding of the relevant materials, and to assess your understanding of this material. Therefore the point of the questions is not just to get the numerical answers. You should explain what is being calculated,
how it is calculated, the results at appropriate stages of the calculation, and what the final answer represents. It is not advisable to present only your final numerical answer with no explanation, interpretation, or comment.
Question 1(a)
This question requires you to choose the weights to assign to the two securities in your portfolio; the question is not concerned with the overall size of the portfolio. To help you decide on these weights you should use the methods you have studied in Unit 1, and the share returns for the dates indicated, 28/1/2019 to 24/1/2022. (For simplification, it might be advisable if you do not consider the possibility of short- selling, or of borrowing and lending at a risk-free rate. If you do consider this possibility, you will need to decide on an appropriate risk-free rate for January 2022.) You do not need to do any other research on the two companies concerned, and you do not need to download any additional share price or share index data – you should use only the information provided and the methods you have studied in Unit 1.
The tab-delimited text file can be opened from Excel (or similar spreadsheet software). Excel will allocate the data to the relevant columns. You may need to increase the width of the date column to see the dates. These are closing prices. For reference, for the week beginning 21/1/2019 the share price for Nvidia (NVDA) is 40.04, Qualcomm (QCOM) is 51.30, SP500 is 2,664.76, and there are no values for R1, R2 and RM (the calculation of the returns uses the share price or index in the previous period). For 28/1/2019 NVDA is 36.18, QCOM is 49.61, SP500 is 2,706.53, R1 is -0.096404, R2 is -0.032943, and RM is 0.015675. And for 23/1/2023 NVDA is 203.65, QCOM is 133.40, SP500 is 4,070.56, R1 is 0.141600, R2 is 0.085435, and RM is 0.024656.
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