## Portfolio Management

Portfolio ManagementINSTRUCTIONS:
1. This problem set counts for 20% of the final mark for this course.
2. The problem set must be handed in by 6 pm on Monday, 4th April,2016; No
marks will be awarded if it is handed in after this date.
3. All assignments must be placed in the assignment box. This is located under the
student pigeon-holes on the 7th floor (opposite the main lifts). The assignment
box is accessible outside of office hours. Submissions will not be accepted via
email.
4. It is a requirement that you keep a photocopy of your problem set and a copy of
5. Attempt ALL questions.
enable you to edit the document to change box sizes etc. but you must maintain
the general format of the presentation. You may print the document and insert

Q1. This question requires the use of a spreadsheet such as Excel. No values are to be
displayed with more than 2 decimal places. Rates may be displayed as percentages to 2
dec. places.
In this question assume the risk free rate is 0.015 = 1.50%.
Easyjet Plc (EZJ.L) for the period 1-Jan-2010 to 31-Dec-2015. Use the ‘Download to
be presented in csv format. Save your file as an excel file. Then re-open your excel file.
Note: If the Date is in American format: mm/dd/yyyy then click on the top of the date column
to select the whole column; then right-click; select format cells; date and in the date window
select the format, 14-Mar-01. This will change the format of the dates in the whole column.
Ensure there are 72 rows dated from (most recent) 31-Dec-2015 to (oldest) 01-Jan-2010.
Select then delete all the columns except the date and Adjusted Close column. These will be
reversed later. Save your edited file.
https://uk.finance.yahoo.com/q/hp?s=EZJ.L&b=1&a=00&c=2010&e=31&d=11&f=2015&g
=m
of Aviva Plc (AV.L) for the period 1-Jan-2010 to 31-Dec-2015 in a separate tab or
spreadsheet. Ensure there are 72 rows dated from 31-Dec-2015 to 01-Jan-2010.Delete all
https://uk.finance.yahoo.com/q/hp?s=AV.L
of Intertek Group Plc (ITRK.L) for the period 1-Jan-2010 to 31-Dec-2015 in a separate tab
or spreadsheet. Ensure there are 72 rows dated from 31-Dec-2015 to 01-Jan-2010. Delete all
https://uk.finance.yahoo.com/q/hp?s=ITRK.L&b=1&a=00&c=2010&e=31&d=11&f=2015&
g=m
of Croda International Plc (CRDA.L) for the period 1-Jan-2010 to 31-Dec-2015 in a
separate tab or spreadsheet. Ensure there are 72 rows dated from 31-Dec-2015 to 01-Jan-
https://uk.finance.yahoo.com/q/hp?s=CRDA.L
FTSE 100 Index (FTSE) for the period 1-Jan-2010 to 31-Dec-2015 in a separate tab or
spreadsheet. Ensure there are 72 rows dated from 31-Dec-2015 to 01-Jan-2010. Delete all
https://uk.finance.yahoo.com/q/hp?s=%5EFTSE&b=1&a=00&c=2009&e=31&d=11&f=2014
&g=m
Adjusted closing prices of the EZJ, AV, ITRK, CRDA and the FTSE in side by side
columns in that order. Insert a new row just above the first row qith prices if necessary to
name the columns.
Note that the prices are presented in ‘Z Æ A’ order i.e. from 31-Dec-2015 to 01-Jan-2010.
Now reverse the order of the data (date and all prices columns) so they are displayed in ‘A
Æ Z’ (chronological) order from 01-Jan-2010 to 31-12-2015 as follows: Select all six
columns including the date column. Then click on the ‘Data’ Tab of the tool bar at the head
of your spreadsheet. On the sort option click on ‘A Æ Z’. The data will now be presented in
chronological order starting with 01-Jan-2010 and ending at 31-Dec-2015.
Now use Ctrl-A to select the whole spreadsheet; right click; select format cells; number and
then set the display to be number in 2 decimal places. You may also select the whole
spreadsheet, then in the Home Button set the data to be displayed in the middle of the
columns. Periodically use Ctrl-S to save your file.
?After the EZJ column insert a new column Headed REZ (Return on Easyjet Prices) and
calculate the annualised returns on Easyjet Prices using the formula: -1 *12
P
P
R =
t-1
t
t ¸
¸
¹
·
¨
¨
§ (note
this will give 71 values of annualised returns from the 72 prices, starting from February 2010
and to Dec 2015)
?In the same manner create a new column headed RAV (Return on Aviva Prices) and
calculate the 71 corresponding annualised returns from the 72 Aviva Prices after the AV
column.
?In the same manner create a new column Headed RITRK (Return on ITRK Prices) to
calculate the 71 corresponding annualised returns from the 72 Intertek Prices.
? In the same manner create a new column Headed RCRDA (Return on CRDA Prices) to
calculate the 71 corresponding annualised returns from the 72 Croda Prices.
? In the same manner create a new column Headed RMKT (Return on FTSE 100 Index
Prices) to calculate the corresponding 71 returns on the FTSE100 Prices.
Q1(a)
At the end of each column (REZJ, RAV, RITRK, RCDA and RMKT) calculate the average
annualised return,R as a decimal using the Excel function =Average(). The row label of R
can be placed under the EZJ price column.
Below the Average Returns value at the of end of each column (REZJ, RAV, RITRK,
RCRDA and RMKT) insert the variance of returns, s
2 using the Excel function = VARP().
Use the label s2 for this row.
Below the s
2 values at the of end of each column (REZJ, RAV, RITRK, RCRDA and
RMKT) insert the annualised Standard Deviation, s of returns as a decimal using the Excel
function = STDEVP(). Check that the Std. Dev. is the square root of the variance. Use the
label s for this row.
Below the s values at the of end of each column (REZJ, RAV, RITRK, RCRDA and RMKT)
calculate the beta, ß. Use the label ß for this row.
(Hint: the covariance function in excel is =Covar(), the correlation coefficient function in
excel is =Correl())
Below the beta column calculate the alpha of each share including the Market. (Take the risk
free rate as 0.15 = 1.5%. Caution:In your spreadsheet insert 0.015 or 1.5%. Do not use 1.5)
Use the label, a for this row.
Below the a row insert the ERB (excess return to beta) of each share including the market.
Use the label ERB for this row.
Below the ERB row calculate the values of Specific risk, ?2 of each share including the
market. Use the label, ?2 for this row.
Select the following rows individually and display them as percentages to 2 dec. places. (In
excel Select values in the row; right click; select format cells; percentage to 2 dec places):
R , s, and a.
In your answer booklet copy the following values in the format shown.
REZJ RAV RITRK RCRDA RMKT
R
s2
s
ß
a
ERB
?2
Formula used
Rßa
ERB?2
Q1(b)
(i)
Use Excel’s formula =CORREL() to calculate the correlation coefficients of each pair of
returns in the table format shown below.
Copy the table into your Answer Booklet in the square array as shown below (display to 2
decimal places):
Correlation Coefficients
REZJ RAV RITRK RCRDA RMKT
REZJ
RAV –
RITRK – –
RCRDA – – –
RMKT – – – –
Populate only the diagonal and the upper triangle, leaving the lower triangle blank.
(ii) An investor holds a portfolio of Easyjet shares. She is risk averse and wants to combine
her portfolio with one other share (from these 4 shares) to make her portfolio less risky.
Which share should she choose? Provide a brief explanation.
Q1(c) You are given the following financial information on the four FTSE companies. All
prices are in pence.
price (7-03-16)
EPS P/E PEG Div R
ITRK 3126 141.9 19.6 2.9 52.3 0.12
EZJ 1529 139.1 12.8 1.3 55.2 0.15
AV 461.9 39.45 10.7 -0.6 20.66 0.10
CRODA 2919 135 22.5 2.9 69 0.12
Div = Annual Dividend. r = required rate of return.
(i) In your spreadsheet, use the information to complete the following Table.
dy g
Ret.
ratio ROE
No
Growth
Price
(NGP)
DDM
Price
PVGO
(Market)
PVGO
(DDM)
ITRK
EZJ
AV
CRODA
dy = dividend yield;
g = growth rate implied by the PEG ratio.
Ret. Ratio = Retention ratio.
ROE = Return on Equity.
NGP = Intrinsic Price based on the no growth model.
DDM Price = Price derived from the Constant Growth Dividend Discount Model.
PVGO (Market) = Market’s estimate of the PVGO based on the Intrinsic price of the
No growth Model. Calculate it as the excess of the market price over the NGP.
PVGO (DDM) = defined as the excess of the DDM Price over the NGP.
In your spreadsheet display the Dividend Yield as a percentage to 2 dec. places.
table below and copy the table into Answer Booklet:
Formula
dy
g
Ret. Ratio
ROE
NGP
DDM Price
PVGO (Market)
PVGO (DDM)
(ii) Explain why in 2 cases the No growth price (NGP) is higher than the DDM Price.
No growth price (NGP) is higher than the DDM Price in the cases of
Reason:
Q1 (d)
In your spreadsheet apply the Elton and Gruber operational procedure to construct an equity
portfolio using the 4 stocks given. This involves calculating the cut-off rate, Cj up to and
including the unique cut-off rate c
*
as shown below.
SHARE R ß ?2 ERB Cj
Your answer must show which stocks are in the portfolio and their relative proportions.
Q1 (e)
Apply the Treynor-Black (TB) procedure to construct the active portfolio using the stocks
that have been included in the Elton-Gruber Portfolio constructed Q1(c). In the Answer
in the active portfolio,
(ii) the alpha of the active portfolio, the beta of the active portfolio, the specific risk of the
active portfolio and
(iii) the proportion of the active portfolio and the proportion of the market portfolio in the
Treynor-Black portfolio.
Comment on the weights of the active portfolio and the market portfolio in the final TB
portfolio.
Q1(f)
Suppose a market is comprised with only the four shares used above namely ESJ, AV, ITRK
and CRDA. Using the beginning of year share prices (given below) of the four shares
construct the following beginning of the year values of the following Market Indices:
PWAI, VWAI, EWARI, EWGRI where
PWAI is the Price Weighted Arithmetic Index,
VWAI is the Value Weighted Arithmetic Index,
EWGRI is the Equal weighted Geometric Relative Index
EWARI is the Equal Weighted Arithmetic Relative Index,
Use the 1st Jan, 2010 as the base date with an index value of 100.
You are given the following beginning of year prices and the number of shares issued:
EZJ AV ITRK CRDA
1-Jan-10 374.06 265.70 1095.37 641.24
4-Jan-11 362.21 321.92 1977.31 1743.73
2-Jan-12 426.62 274.45 2954.50 2245.60
1-Jan-13 835.11 312.49 2730.65 2292.32
1-Jan-14 1510.86 395.38 2248.34 2594.60
No of shares issued (m) 3952.10 4048.76 4990.08 135.94
tabulated format:
Market Indices
Date PWAI VWAI EWGRI EWARI
1-Jan-2010 100 100 100 100
4-Jan-2011
2-Jan-2012
1-Jan-2013
1-Jan-2014
Q2. Answer ALL parts of this question.
(a) Use the LSE ORB web site (link below)
http://www.londonstockexchange.com/exchange/prices-and-markets/retail-bonds/companysummary/XS0181816652ZZGBPUKCP.html
to download the specification of the VO25 Vodafone Group Plc 5.625% NTS Bond.
Include a copy of the specification (Bond Information) in your Answer Booklet specifying
(ii) What was the value and date of the most recent (2015) coupon?
(iii) Calculate the dirty price on your quote date of (i).
(iv) Find the current yield on the date of (i).
(v) Use the ‘Interactive chart’ tab at the top of the web page to obtain the clean
price on the most recent (2015) coupon date.
(vi) Write down the equation for the yield to maturity, rm of the bond on the last
(2015) coupon day. Assume the coupon has been paid so that the next cash
flow is the coupon on the 2016 coupon payment day. The equation must
equate the price of (v) above to the sum of the present value of the cash flows
of the next 10 years, using rm as the discount rate. Your equation must be
specific to this bond and must have only rm as the variable.
(vii) In a spreadsheet solve your equation of (vi) to find rm, the yield to maturity
using the price obtained in (v). Insert your answer to 2 dec. places in the
This question continues on the next page.
(viii) Set up and complete the following table in your spreadsheet to calculate the
duration of the bond on the 2015 coupon payment date of the bond. Assume
the coupon has been paid so that there are 10 future cash flows the first being
the coupon of 2016. Use your answer to rm from (vii) as the discount rate to
calculate the Present Value of the future cash flows. Calculate the Duration as
the weighted sum of the times in years. Each weight is the PVof a future cash
flow calculated as a proportion of the price paid on the last coupon date.
Complete the table in your spreadsheet. Display the PVs and weights and the
Time (y)
Cash
Flows (£) PV weights
1
2
3
4
5
6
7
8
9
10
rm =
Price (£) =
Duration (y) =
Use the following link to read the announcement by Vodafone to raise £2.88 billion through
the issuance of mandatory convertible bonds.
http://www.vodafone.com/content/index/media/vodafone-group-releases/2016/mandatoryconvertible-bonds.html#
Answer the questions that follow. Relevant parts of the publication are provided below.
Vodafone Group Plc (“Vodafone”) announces the placement of £2.88 billion of
mandatory convertible bonds, to be issued in two tranches, one with an 18 month
maturity and the other with a three year maturity (together, the “Bonds”).
The Bonds will be physically settled on mandatory conversion in accordance with
their terms.
(i) What is a ‘Convertible Bond’?
(ii) What is a ‘Mandatory Convertible’ Bond?
(iii)What does ‘physically settled’ mean?
The initial Conversion Price will be determined on the basis of the higher of (i)
GBP2.1730 (being Vodafone’s closing share price on the London Stock Exchange
(the “LSE”) on Wednesday, 17 February 2016, the “initial Share Price”) and (ii) the
arithmetic average of the daily volume-weighted average prices of an Ordinary Share
on the LSE over a period of three consecutive scheduled trading days starting on 19
February 2016.
(iv)What does the Conversion Price represent?
(v) The following are the volumes and average prices of the 3 consecutive days starting
on the 19th February, 2016. Use this information to calculate the arithmetic
average of the daily volume-weighted average prices.
Day Volume Price
Day3 52,978,100 213.90
Day 2 48,586,500 215.65
Day 1(19th Feb,2016 59,956,600 212.95
(vi)What is the Initial Conversion Price as determined by the rule above?
Vodafone intends to hedge its exposure under the Bonds to any future movements in
its share price by an option strategy comprising (i) the purchase of cash-settled call
options from, and (ii) the sale of cash settled put options to, J.P. Morgan Securities
plc and Morgan Stanley & Co. International plc (or their respective affiliates). The
option strategy is designed to hedge the economic impact of share price movements
during the term of the Bonds. Should Vodafone decide to buy back Ordinary Shares
to mitigate the dilution resulting from conversion of the Bonds, the hedging strategy
is intended to provide a hedge for the repurchase price.
(vii) Why are these options considered to be OTC (Over The Counter) traded?
(viii) What does cash-settled (options contract) mean?
(ix) Is Vodafone’s hedge against falling share prices or rising share prices?
(x) How does buying the calls provide a hedge?
(xi)How does selling the Puts provide a hedge?
(xii) Identify the ‘speculators’ that have enabled Vodafone to hedge and what positions
have they taken?
(xiii) In order to execute a near perfect hedge which options should be used?
Out of the money/At the money/In the money. Explain.
The Bonds will be issued at par. The coupon has been fixed at 1.50% per annum (in
respect of the Bonds with an 18 month maturity) and 2.00% per annum (in respect of
the Bonds with a three year maturity). The Bonds (less an amount equal to the
present value of all future coupons payable under the Bonds) are expected to be
accounted for as equity.
(xiv) What is the bond price per £100 nominal?
(xv) What is the coupon stream of the 18 month bond?
(xvi) What is the yield to maturity of the 3 year bond? State your reasoning.
(xvii) Why are the bonds to be accounted for as equity and not debt?
Day 0 Day 1 Day 2 Day 3 Day 4 Day 5
Sept Price 96.34 96.42 96.53 96.67 96.42 96.51
June Price 96.24 96.31 96.37 96.43 96.12 96.44
Long June – – – – – – –
Initial Margin 500
Variation Margin –
Maintenance Mar 400
Accumulated Gain 0
Short Spread – – – – – – –
Initial Margin 225
Variation Margin –
Maintenance Mar 150
Accumulated Gain 0
The table above shows the daily market to market for a trader A who buys one June ST3