Financial Modelling 2020-2021 Coursework c1 (50%)

Q1. Bond price, yield and duration exercises
Go to the London Stock Exchange’s bonds’ website
http://www.londonstockexchange.com/exchange/prices-and-markets/retail-bonds/retail-bonds-search.html
Choose 3-4 bonds. Fixed coupon rate bonds only.
(35 marks)
Required:

Work out the yield with the given coupon and price.

Calculate their durations.

Using your cases to support the statements that:
Bonds with the coupon rate < YTM will be priced at a discount; Bonds with the coupon rate > YTM will be priced at a premium;
Bonds with the coupon rate = YTM will be priced at the face value.

Verify that:
Other things being equal, bonds with a higher coupon rate have a shorter duration;
Other things being equal, bonds with a higher YTM have a shorter duration;
Other things being equal, bonds with a longer time to maturity have a longer duration.

Note:
If you have difficulties in finding a pair of two bonds that are equal in maturity and YTM or coupon rate, it is acceptable that one of the bonds is real while the other is hypothetical.

Q2. You are required to construct stock portfolios with returns on two stocks or two stock market indices. You can download stock return data from yahoo finance or other sources. The data can be of any frequencies and from any markets. Additionally, you need to find out a risk-free interest rate appropriate for the market you have chosen.
(40 marks)
Required:

Estimate the expected returns on the two stocks or stock indices.

Estimate the variances and standard deviations of the two returns.

What is the covariance between the two returns?

What is the correlation coefficient between the two returns?

Plot the efficient frontier of the portfolios constructed with these two stocks or stock indices.

Find out the minimum variance portfolio constructed with these two stocks or stock indices, solving for the weights of the two stocks or stock indices in the portfolio.

What are the expected return and risk of this minimum variance portfolio?

Construct an “optimal portfolio” with these two stocks or stock indices and solve for the weights of the two stocks in the portfolio.

What are the expected return and risk of the “optimal portfolio”?

Q3. VaR exercises
Download returns on two or more stocks from yahoo finance or other sources. The data can be from any markets.
(25 marks)

Required:

Estimate their VaR with different criteria and different investment horizons.

Using your cases to verify that:
Higher VaR losses with higher volatilities, other things being equal;
Higher VaR losses with tighter criteria, other things being equal.

Requirements:

Provide all data and workings on excel. Write in word a narrative for each of the questions that summarises your results with pertinent analysis. The guideline for the length of a narrative is 200 words ± 25%. Printing/reporting numbers only without analysis, interpretation and explanation will earn no marks.

Submit both excel and word documents on Moodle.

Coursework c2 (50%)

Q4. What are financial models? Explain the concept of parsimony when building a model.
(15 marks)

Q5. A basic model is shown by the equation: Y = ? + ?*X. Explain what ? and ? are, what happens when ? = 0?
(10 marks)

Q6. What are confidence intervals in statistics? What does it mean if a variable is significant at the 5% level?
(10 marks)

One of the reasons students go to university is in order to earn higher wages in their future career. Questions 7 to 12 are an investigation of the ‘return to education’, the causes of wage differentials in general and the important factors in designing a good financial model. Use the excel file on Moodle called ‘Wages in the USA’; a sample of 534 real people giving details of their hourly wages and other variables.

Q7. Prepare a table of ‘descriptive statistics’. This will include the minimum, maximum, mean and standard deviation of each of the variables.
(10 marks)

Q8. Regression model 1 is:

?Wages?_i= ?+ ?_1 ?Education?_i+ ?_i

Run regression model 1 and prepare a table of the most important results including coefficients, significance and model fit. Prepare a scatter chart showing the line of best fit. How much on average do wages rise for each additional year of education?
(10 marks)

Q9. Regression model 2 is:

?Wages?_i= ?+ ?_1 ?Education?_i+ ?_2 ?Experience?_i+ ?_i
Run regression model 2 and prepare a table of the most important results including the coefficients, significance and model fit. How much on average do wages rise for an additional year of education or experience in this model? Why are these results different to model 1?
(10 marks)

Q10. Regression model 3 is:

?Wages?_i= ?+ ?_1 ?Education?_i+ ?_2 ?Experience?_i+?_3 ?Gender?_i+ ?_i
Run regression model 3 and prepare a table of the most important results including the coefficients, significance and model fit. Gender is a dummy variable; explain dummy variables and discuss the differences in wages between men and women using these results.
(10 marks)

Q11. Prepare a correlation matrix of all of the variables. Use the matrix to discuss the importance of each variable for wages as well as the relationships between the variables.
(10 marks)

Q12. Regression model 4 is:

?Wages?_i= ?+ ?_1 ?Education?_i+ ?_2 ?Experience?_i+?_3 ?Gender?_i+ ?_4 ?Age?_i+ ?_5 ?Married?_i+?_6 ?Union?_i+ ?_i

Run regression model 4 and prepare a table of the most important results including the coefficients, significance and model fit. Discuss these results and possible problems with this model. Suggest ways the model could be improved.

15 marks)

Guidance for coursework part C2

Read each part carefully. Ensure that your answer is focussed on directly answering each question. Number your answers.

Use Arial 12 – point font with 1.5 line spacing. Coursework part 2 is expected to have between 1,400 and 1,800 words.

The section will be marked on the following criteria:
All relevant parts of the question covered
Logically organised
Good presentation that is easily understandable