Portfolio Management
INSTRUCTIONS:
1. The problem set counts for 10% of the final mark for this course.
2. The problem set must be handed in by 6 pm on Tuesday the 21st April, 2015; No marks will be awarded if it is handed in after this date.
3. All assignments must be submitted into the assignment box, this is located under the student pigeonholes 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 any spreadsheets used.
5. Answer ALL questions showing all your working.
6. Provide your answers in the Answer Booklet provided. This is in Word format to enable you to edit the document to change box sizes etc. You may change the format to suit your answers but attempt to maintain the general format of the presentation. You may print the document and insert your answers by hand but handwriting must be clear and legible.
Q1. This question requires the use of a spreadsheet such as Excel. All rates must be
displayed as percentages to 2 decimal places.
In this question assume the risk free rate is 1.50%.
Use the following link to download the monthly Share Prices of the Euromoney Institutional
Investor Plc (ERM.L) for the period 1Jan2009 to 31Dec2014. Use the ‘Download to
Spreadsheet’ button below the Table of Prices (72 Items) to save your data to a spreadsheet.
https://uk.finance.yahoo.com/q/hp?s=ERM.L&b=1&a=00&c=2009&e=31&d=11&f=2014&
g=m
Repeat these steps to obtain the corresponding data set for the prices of the Amlin PLC
(AML.L)LSE. (link given below) in a separate spreadsheet.
https://uk.finance.yahoo.com/q/hp?s=AML.L
Repeat these steps to obtain the corresponding data set for the prices of the Catlin Group Ltd
(CGL.L) LSE (link given below) in a separate spreadsheet.
https://uk.finance.yahoo.com/q/hp?s=CGL.L
Repeat these steps to obtain the corresponding data set for the prices of the National Grid
PLC (NG.L) LSE Prices (link given below) in a separate spreadsheet.
https://uk.finance.yahoo.com/q/hp?s=NG.L
Repeat these steps to obtain the corresponding data set for the prices of the FTSE 100 Prices
(link given below) in a separate spreadsheet.
https://uk.finance.yahoo.com/q/hp?s=%5EFTSE&b=1&a=00&c=2009&e=31&d=11&f=2014
&g=m
Using the downloaded data above create a new, separate spreadsheet containing only the
Date, the Close (Not Adj. Close) Prices of the ERM.L, AML.L, CGL.L, NG.L and FTSE
100 Index in 5 contiguous columns.
?Use the ‘Sort AZ Downarrow’ key in the DATA tab to ensure the date and prices are
ordered from oldest to latest values. (Jan 2009 to Dec 2014).
?Create a new column Headed RERM (Return on ERM Prices) to calculate the monthly
return on ERM Prices using the formula: 1
P
P
R =
t1
t
t (note this will give 71 values of
monthly returns from the 72 prices, starting from February 2009 and to Dec 2014)
?Create a new column Headed RAML (Return on AML Prices) to calculate the monthly
return on AML Prices.
?Create a new column Headed RCGL (Return on CGL Prices) to calculate the monthly
return on CGL Prices.
?Create a new column Headed RNG (Return on NG Prices) to calculate the monthly return
on NG Prices.
? Create a new column Headed RMKT (Return on FTSE 100 Index Prices) to calculate the
monthly return on the market.
Q1(a)
At the end of each column (RERM, RAML, RCGL, NG and RMKT) calculate the average
annualised return,R as a percentage using the Excel function =Average()*12*100.
Below the Returns values at the of end of each column (RERM, RAML, RCGL, RNG and
RMKT) calculate the annualised Standard Deviation, s of returns as a percentage using the
Excel function = STDEV()*12*100.
In your Answer Booklet tabulate these values as percentages to 2 decimal places as follows:
RERM RAML RCGL RNG RMKT
R (%)
s (%)
Q1(b)
Use Excel’s formula =CORREL() to calculate the correlation coefficients of each pair of
returns.
In your Answer Booklet tabulate these values in a square array as shown below (display to 2
decimal places):
Correlation Coefficients
RERM RAML RCGL RNG RMKT
RERM
RAML
RCGL
RNG
RMKT
Q1(c)
Write down the equation for the Total risk, s2 in terms of the market risk and the specific risk,
?2.
Use the statistics calculated in 1(a) and 1(b) and the equation given above to calculate the
beta ß (Beta), alpha a (Alpha), Excessreturntobeta (ERB), the Total Risk s2 and the
Specific Risk ?2 and of each stock and of the market portfolio. Give your answers to 2
decimal places.
In your Answer Booklet tabulate these values as follows:
Beta, ß
Alpha,a
(%)
ERB
(%)
s2(%2)
?2(%2)
ERM
AML
CGL
NG
MKT
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 cutoff rate, Cj up to and
including the unique cutoff rate c*
j . In your Answer Booklet provide the Table with columns
as shown below.
SHARE
R (%) ?
?2
(%2)
ERB
(%)
Cj
Your answer must show which stocks are in the portfolio and their relative proportions.
Q1 (e)
Apply the TreynorBlack procedure to construct the active portfolio using the stocks that
have been included in the EltonGruber Portfolio constructed Q1(d). In the Answer
Booklet include calculations for the unadjusted (unnormalised) weights, adjusted
(normalised weights), the alpha of active portfolio, the beta of active portfolio, the specific
risk of the active portfolio and the proportion of the active portfolio in the TreynorBlack
portfolio.
Q2. Answer ALL parts of this question.
(a) Use the LSE ORB web site (link below)
http://www.londonstockexchange.com/exchange/pricesandmarkets/stocks/pricessearch/stockpricessearch.html?nameCode=xs0141704725&page=1#
to download the specification of the National Grid 6% Bond. Include a copy of the specification in your Answer Booklet specifying the date you downloaded the specification. Using your specification where necessary, answer the following questions in your Answer Booklet: (i) Quote the Bond price on this date. (ii) What was the value and date of the latest coupon? (iii) Using the price on the latest coupon date 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 page to obtain the clean price on the latest coupon date. (vi) Write down the equation for the yield to maturity, rm that equates the price of the bond on the latest coupon date to the present value of future cash flows.
(vii) In a spreadsheet solve the equation of (vi) to find rm, the yield to maturity using the price obtained in (v). (viii) Write down the equation for the Duration of your Bond on the last coupon payment date using the yield to maturity of (vii) as the discount rate.
(ix) In your spreadsheet find the duration (to 2 dec. places) of the Bond on the last coupon date.
(b) Answer this part of the question in you Answer Booklet.
You are given the following Annual Coupon Bonds:
Bond
Coupon
Maturity
Price
Duration
STRIPS PRICE
AAA
5%
1y
101.94
BBB
4%
2y
100
CCC
5%
3y
105.66
(i) The durations are 2.86y, 1y and 1.9y nonrespectively. Insert these values in the Duration column in their correct cells (No calculations are required).
(ii) Without any calculation state the yield to maturity of the 2y 4% bond. Explain your reasoning.
(iii)Using the two appropriate bonds construct a bullet immunised portfolio with a duration of 1.5 years. Give the weights of the two bonds to 2 decimal places.
(iv) Use these bonds to construct a cashflow matching portfolio to meet the following liabilities:
End of Year
1y
2y
3y
Liability (£)
122,800
1,380,300
£1,522,500
(v) What is the cost of your portfolio of (iv)?
(vi) By first calculating the implied spot rates given by the prices calculate the Price of 1y, 2y and 3y zero coupon bonds and hence complete the STRIPS PRICE column.
(vii) Construct a cashflow matching portfolio using these STRIPS.
(viii) What is the cost of your portfolio of (vii)?
(ix) Using Z1, Z2 and Z3 to represent the 1y, 2y and 3y zero coupon bond prices, express each bond price as a linear combination of Z1, Z2 and Z3. Solve these equations to find Z1, Z2 and Z3.
(x) Use the prices of (ix) to find the price of the cash flow matching bond portfolio constructed using the zero coupon bonds in (vii).
(xi) Compare the cost prices of the cash flow matching portfolio of (v), (viii) and (x) and comment.
(xii) How many of each of the original bonds would you buy and strip to construct your cash flow matching portfolio made of STRIPS. Comment.
Q3. This question requires the use of the Internet.
(a) Copy and complete the following Table:
Future
Exchange
Clearing House
Face Value
Tick Size
Underlying
Tick Value
FTSE 100
Sterling Currency
Priced as $p£.
ST3 Sterling Deposit
S&P 500
In the following parts state which futures contract are used. Indicate what the opening position is stating the rationale. State number of contracts where appropriate.
(b) A speculator believes that the Bank of England is about to announce a fall in base rates from 0.5% to 0.25%. Briefly indicate with a brief reason how the fall in interest rates will affect the price of each of the above futures (if at all). Design an open trade the speculator can carry out using one of the futures above to profit from the fall.
(c) A corporate treasurer of a firm that is to receive a £2m payment in a month’s time fears that short term interest rates are about to fall. Design a futures exposure that the treasurer could use to hedge against this.
(d) An equity portfolio manager with a portfolio of £1.5m with a beta of 0.75 wishes to increase the beta to match the market beta. How can she use one of the above futures to achieve this?
(e) In no more than 100 words outline the corporate history of LIFFE from inception to the present in terms of mergers and acquisitions.
Portfolio Management 2015 Answer Sheet
First Name: Second Name:__________________
Course:___________________________________________________
Q1(a)
ERM AML CGL NG MKT
(%)
s (%)
Q1(b)
Correlation Coefficients
RERM RAML RCGL RNG RMKT
RERM
RAML
RCGL
RNG
RMKT
Q1(c)
Write down the equation for the Total risk, s2 in terms of the market risk and the specific risk, ?2.
Equation is:
ß a(%) ERB (%) s2
(%2) ?2
(%2)
RERM
RAML
RCGL
RNG
RMKT
Q1(d) Elton and Gruber Procedure
Share Number SHARE (%)
ß ?2 (%2) ERB (%) Cj
1
2
3
4
The unique cutoff rate c* =
Calculation of weights in EltonGruber Portfolio:
Elton Gruber Portfolio:
Share Name Proportion (%)
Q1(e) TreynorBlack Active Portfolio:
Calculation of weights of Active portfolio:
Alpha, a of Active Portfolio (%)
= Working
Beta, of Active Portfolio
= Working
Specific Risk of Active Portfolio (as %2)
= Working
TreynorBlack Active Portfolio
Share Proportion (%)
Proportion of Active portfolio in the TreynorBlack Portfolio
Q2 a).
Copy of Specification Of Nation Grid Bond:
(i) Download Date:
Price :
(ii) Latest Coupon Date:
Value of Coupon:
(iii) Dirty Price
= Working:
(iv) Current yield
= Working:
(v) Price on latest coupon date =
(vi) Equation for yield to maturity on last coupon date:
(vii) Yield to maturity, rm =
(viii) Equation for Duration on last coupon date:
(ix) Duration =
Q2b)
(i) Complete Durations Column:
Bond Coupon Maturity Price Duration
AAA 5% 1y 101.94
BBB 4% 2y 100
CCC 5% 3y 105.66
(ii) Yield to maturity of BBB = Reason:
(iii) Two Bonds Required are: Weights of Bonds in Immunised Bonds:
Working:
(iv) Cash Flow matching Portfolio:
Bond Coupon Maturity No. Of Bonds
AAA 5% 1y
BBB 4% 2y
CCC 5% 3y
Working:
(v) Cost of Cash Flow Matching Portfolio, including working:
(vi) Complete STRIPS Price column:
Bond Coupon Maturity Implied Spot Rates STRIPS Price
AAA 5% 1y
BBB 4% 2y
CCC 5% 3y
Working:
(vii) Cash Flow matching Portfolio using STRIPS:
Maturity of STRIPS No. Of STRIPS
1y
2y
3y
Working:
(viii) Cost of Cash Flow Matching Portfolio using STRIPS, including working:
(ix) Calculation of Z1, Z2 and Z3 including Working:
(x) Cost of Cash Flow matching portfolio using STRIPS:
(xi) Comparison of costs:
(xii)
Stripping of Original (AAA, BBB, CCC) Bonds:
Q3(a)
Future Exchange Clearing House Face Value Tick Size Underlying Tick Value
FTSE 100
Sterling Currency
Priced as $p£.
ST3 Sterling Deposit
S&P 500
Q3(b)
Future Effect:(Fall/Rise/No effect) Reason
FTSE 100
Sterling Currency
Priced as $p£.
ST3 Sterling Deposit
S&P 500
Future Selected for open trade:
Open Position Taken (Buy/Sell):
Expectation:
Q3c)
Future Selected for Hedge:
Open Position Taken (Buy/Sell):
No of Contracts:
Q3d)
Future Selected for increasing beta:
Open Position Taken (Buy/Sell):
No of Contracts:
Q3e)
History of LIFFE:
Insert Appendices Here (e.g. excel outputs):
As a result of feedback the following two mods are required:
1. Q2a) iii) Please remove the leading words ‘Using the price on the latest coupon date’.
2. Q2a) v) If the last coupon date is on a non trading day (e.g. Saturday) please use the nearest trading prior to that date (Friday).
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