Digital Finance Coursework
Module name: Digital Finance Module code: COMP0164 Academic year: 2023-24 Term 1, 2 or 3 Term 1
Nature of assessment Group Section Content
A. Core Information
B. Coursework Brief and Requirements C. Assessment of This Coursework
D. Group Instructions
Section B: Coursework Brief and Requirements
This assignment will require you to apply what you have learnt in the lectures, tutorials and covered in the reading materials to answer six questions.
You should submit your answers as both a Jupyter Notebook written in python of your code and markdown, as well as an exact pdf copy.
For each question where a numerical answer is required, you should show the python code that you used to compute the answer and the relevant formulas and working steps to solve the problem. If you do not include each of these in your answers, you will only gain partial marks.
For any mini-essay question, you should write your answers in markdown and in full sentences (not bullet points). Any answers over the word limit of a question part will not be marked beyond the word limit.
[5 marks] are available for the structure, clarity, language, mathematical notion and overall presentation of your coursework.
Question 4 [13 marks]
Suppose that you want to build a portfolio with the stocks (with tickers of) AAPL, GOOG, AMZN and META. You plan to retrieve the relevant Yahoo Finance data with the yfinance Python module from the 1st of Jan. 2017 to 31st of Dec. 2020 (inclusive).
a.) Calculate the daily returns of these stocks. You should use the adjusted daily closing price. [1 mark] b) Based on a.), find the covariance matrix of these stocks. [1 mark]
c.) Suppose that the four stocks are equally weighted, find the annualised portfolio expected returns and portfolio variance. [2 marks]
d.) Find the efficient portfolio with the maximum Sharpe ratio. What is the corresponding Sharpe ratio?
[2 marks]
e.) Plot the efficient frontier (Without the use of the Plotly library in Python). [3 mark]
f.) Based on the concept of diversification, comment on the current portfolio. How can this portfolio be improved? (Answers should be no longer than 200 words) [4 marks]
Question 5 [14 marks]
A high-profile client Pam, whom you’ve built a great business relationship with over the years has asked you to quickly double-check some figures for life insurance he has received. You decide to apply the 2015 VBT Unismoke ANB/ALB, the Valuation Basic Table (VBT) to using the Age Nearest Birthday (ANB) method, with a valuation interest rate of 5.1% you submit your calculated figures to aid Pam's decision.
Today is 11 November 2022, and the type of life insurance Pam was viewing was permanent life insurance. Pam was born on 25 March 1979, with the health condition standard for her cohort of the same age and gender (Female).
a.) Calculate Pam’s annual unconditional survival rates npx from now to age 54. [4 marks]
b.) Calculate Pam’s life expectancy in years (to one decimal place). [3 marks]
c.) Calculate the probability that Pam dies exactly between 6 and 9 years from now (to five decimal places). [3 marks]
d.) Calculate the minimum annual premium rate (premium as a fraction of death benefit) that your company should charge for Pam’s cohort (to five decimal places). [4 marks]
Question 6 [8 marks]
The conglomerate you are working for, Accretion, decided to digitalize the financial analysis in order to optimize their operations. Since you have expertise in a multitude of financial instruments, you have been tasked to perform the innovation.
Firstly, you are asked to design a tool for computing the zero spot rates using the bootstrap method, and then verify its validity by applying it to Exhibit 6 below.
Exhibit 6: Spot Rate Table
SA: Semi-annual coupon A: Annual coupon
99.8 0.5 (SA) 0
101.2 1 (A) 0
102.4 0.5 (SA) 0
Principal Maturity Coupon (per Price Coupon Zero Rate (Years) Year) Frequency (Continuous)
a.) Design a function that take in the required parameters for the bootstrap method in form of a Pandas DataFrame and returns the same DataFrame but with a new column called "Zero Rates". Then, check that your function gives the correct spot rates in the table above. [4 mark]
It is often that in real world investors encounter friction costs such as fees, commissions and other types of expenses. Currently, NPV is used to measure the value of an investment opportunity:
NP V = C0 + P V .
Your task is to design a tool for evaluating net value of a bond, which takes into consideration accrued interest, commission fees on entrance and exit (assume there is commission for settling the return of the principal), and administrative fees, which are monthly fees associated with the exchange that keeps track of asset ownership.
b.) Define a python function for calculating the net value of a bond subject to accrued interest, entry and exit fees and administrative fees (assume the administrative fees are paid out at the same frequency as the coupons). The accrued interest MUST be computed from the coupon value. [3 marks]
c.) Using the values from Exhibit 7 compute the net value of the investment. Is this a good investment considering all the expenses? [1 mark]
Exhibit 7: Information for an Investment
Principal
Coupon
Price
Interest Rate
Maturity
Administrative Fee
Entry Fee
Exit Fee
Days from Last Coupon
$100
$4 (Yearly)
$101.5
2%
3 years
$1 (Yearly)
$5
$5
Parameter Value
Section C: Assessment of This Coursework
Within each section of this coursework, you may be assessed on the following aspects, as applicable and appropriate to this particular assessment, and should thus consider these aspects when fulfilling the requirements of each section:
The accuracy of any calculations;
The strengths and quality of your overall analysis and evaluation;
Appropriate use of relevant theoretical models, concepts and frameworks;
The rationale and evidence that you provide in support of your arguments;
The credibility and viability of the evidenced conclusions/recommendations/plans of action you put forward;
Structure and coherence of your considerations and reports;
Appropriate and relevant use of, as and where relevant and appropriate, real world examples, academic materials and referenced sources. Any references should use either the Harvard OR Vancouver referencing system (see References, Citations and Avoiding Plagiarism);
Academic judgement regarding the blend of scope, thrust and communication of ideas, contentions, evidence, knowledge, arguments, conclusions;
Each part has requirements with allocated marks, maximum word count limits/page limits and where applicable, templates that are required to be used.
You are advised to refer to the UCL Assessment Criteria Guidelines.
