Main Examination Period 2020 – January - Semester A
ECOM053 Quantitative Methods for Finance Duration: 2 hours
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EXAM PAPERS MUST NOT BE REMOVED FROM THE EXAM ROOM







Examiner: Dr Panagiotis Koutroumpis

© Queen Mary, University of London, 2020
Page 2 ECOM053 (2020)

Question 1

Let us consider a sample ሼ, … , ሽ with observations on a random variable .
a) Define the sample mean, sample variance, and sample standard deviation for a sample
with size of n observations on a random variable ሼ, … , ሽ.
[8 marks]
b) Define the concept of skewness and kurtosis.
[7 marks]
c) Are hypotheses about testing the actual values of the coefficients (i.e. ) or their
estimated values (i.e. መ) and why?
[6 marks]

Question 2
a) Consider two stock prices for Apple and Samsung from 1st of June 2007 to 1st of June
2012. The spreadsheet below displays these price and return data:

ECOM053 (2020) Page 3
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i) Write the Excel formula on how to estimate the return series of both Apple and Samsung
in Cell E13 (for Apple) and F13 (for Samsung), respectively.
[4 marks]

ii) Write down the Excel formula on how the monthly mean, monthly variance, and monthly
standard deviation of the return series are estimated for both Apple and Samsung in Cells
B3:C5.
[6 marks]

iii) Estimate the annual mean, annual variance, and annual standard deviation for both
Apple and Samsung in Cells B7:C9. Show in detail your calculations
[6 marks]













Page 4 ECOM053 (2020)

b) Let us consider four risky assets, which have the following expected returns E(r) (Cells
F3:F6) and variance-covariance matrix (S) (Cells A3:D6), and two portfolios x and y (see
the Excel spreadsheet below):


i) Write down the Excel formula on how we estimated the mean and variance of portfolio x
(in Cells B12 and B13) and y (in Cells E12 and E13), respectively.
[4 marks]
ii) Estimate the correlation coefficient of portfolios x and y in Cell B15. Show your
calculations.
[5 marks]
iii) Calculate the mean portfolio return, portfolio variance, and portfolio standard deviation in
Cells B19, B20 and B21, respectively. Show your calculations.
[4 marks]







ECOM053 (2020) Page 5
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Question 3
a) Consider four risky assets having the following expected returns E(r) and variance-
covariance matrix (S), where c is a constant:


i) Write down the Excel formula on how we estimated the values in Cells G3:G6 below:

[3 marks]












Page 6 ECOM053 (2020)
ii) Let us compute an envelope portfolio with constant c=0, where the vector z solves the
system of simultaneous linear equations ሺሻ െ ൌ . Then, this solution produces a
portfolio x on the envelope of the feasible set. Write down the Excel formula on how we
estimated the values in Cells A12, F12 and F16, in the Excel spreadsheet below, and
explain the rational behing these calculations:


[6 marks]









ECOM053 (2020) Page 7
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iii) Let us now compute an envelope portfolio with constant c= 4%. Write down and explain
the Excel formula on how we estimated the values in Cells A20, F20, F24, F26:F28, and
B30:B31, in the Excel spreadsheet below:


[12 marks]

Page 8 ECOM053 (2020)
iv) Let us now conduct a single portfolio calculation with a proportion of portfolio equal to
0.3. Estimate the expected return, variance, and standard deviation of the portfolio in
Cells B36:B38, in the Excel spreadsheet below:

[4 marks]








ECOM053 (2020) Page 9
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Question 4
a) Consider two bonds A and B with payments , where ൌ , , … , . Bond A has just been issued. Its face value is $1,000, it bears coupon rate of 7%, and it will mature in 10
years. Bond B was issued 5 years ago, when interest rates were higher.This bond has
$1,000 face value and bears a 13% coupon rate. When issued, this bond had a 15-year
maturity, so its remaining maturity is 10 years. The yield to maturity is 7% (see Cell B2).
i) Using the Excel spreadsheet below write down and explain the Excel formula on how we
estimated the bond A and bond B price in Cells B17 and E17, respectively:

[4 marks]








Page 10 ECOM053 (2020)
ii) Columns C and F in the Excel spreadsheet below report the time-weighted average
maturity of the payments received from the Bond A and B, respectively. Write down and
explain the Excel formula on how we estimated the values in Cells C5:C6 and F5:F6,
respectively. Interpret those numbers.

[6 marks]











ECOM053 (2020) Page 11
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iii) Using the Excel spreadsheet below, estimate the duration of each of the two bonds A
(Cell B20) and B (Cell E20), using the Macaulay duration measure. Which bond has the
longest duration? Show your calculations and interpret your results.


[10 marks]








Page 12 ECOM053 (2020)
iv) Using the Excel spreadsheet below, write and explain the Excel formula on how we
estimated the duration value of bond A and bond B in Cells B22 and B24, respectively, by
assuming that the two bonds' settlement date is 3 December 1996, and the maturity date is
3 December 2006.

[5 marks]




End of Paper