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ASSIGNMENT: due at Tuesday March 10th 1545 hours (2015)

Please hand in the assignment to the lecturer Ludger Buijs at the beginning of the lecture on March 10th or hand in the assignment in the box close to the secretarial office of the Economics Department (T. v. A. 5.01.74). This assignments is meant to be group work (max. 4 students[1])
Some questions are taken from Hull’s book. In this case I refer to the book: John Hull, Fundamentals of futures and option markets, 7th edition, 2011.

Problems related to riskless securities and the term structure of interest rates

On January 1 of the year 2011 a number of Dutch government bonds had the following quotation. The bonds are quoted as a percentage of their nominal value of €. 1,000.00
The examples below explain the pattern of the quotations.

“nl 9.00 92-08": nl Dutch classical government bond 9.00 interest rate; annual (not continuous) compounding 92-08 term begins in 1992 and ends at December 31, 2008 Maturity: 31st of December 2008

“nl 0cpn 06": nl Dutch zero coupon government bonds 0cpn 06 zero-coupon bond, maturity end December 2006

Al coupon payments and redemptions will take place on December 31st.
Explain your answers carefully and show which government bonds are used to make your calculations.

“nl 0cpn 11” 97.56 “nl 0cpn 12” 93.35 “nl 0cpn 13” 87.63
“nl 9.00 92-14” 118.24 “nl 0cpn 14” 85.48
“nl 9.00 90-15” 122.35 “nl 0cpn 15” 82.19

1) Calculate the one-year, the two-year and the three-year spot rates on the basis of Dutch zero coupon government bonds

Om de spotrate uit te rekenen gebruik je de volgende formule: Pt = Mt / (1 + st)t.

“nl 0cpn 11” 97.56
975.60 = 1,000.00 / (1 + s1)1
S1= 0.025, dus 2.5%

“nl 0cpn 12” 93.35
933.50 = 1,000.00 /(1 + s2)2 s2 = 0.035, dus 3.5%

“nl 0cpn 13” 87.63
876.30 = 1,000.00/(1 + s3)3 s3 = 0.045, dus 4,5%

2) a) Calculate the forward rate between January 2014 (beginning) and December 2014 (end)

“nl 0cpn 13” 87.63
“nl 0cpn 14” 85.48
Rf = R4 + (R4 – R3)*(T3/(T4-T3))
R3 = 0.045
854.80= 1,000.00 /(1 + s4)4
S4 = 0.040 = R4

Formule invullen geeft:
Rf = 0.04 + (0.04-0.045) * ( 3/(4-3)) = 0.025
Dus forward rate tussen januari 2014 en december 2014 is dus 2,5%. Gezien R4 kleiner is dan R3, zal Rf ook kleiner zijn dan R4.

b) Suppose that the liquidity premium L3,4 for this type of bond is equal to 0.50 %. What is the value of the expected spot rate es3,4 in this case?

De liquidity premium is het deel van de forward interest rate dat groter is dan de expected future spot interest rate.

Bij 2a hebben we een forward rate tussen jaar 3 en 4 berekend van 2.5%. Als de liquidity premium 0.5% is, zal de expected spot rate es3,4= 2.5-0.5= 2 %

3) a) Explain carefully what is meant by the unbiased expectations theory.

De unbiased expectations theory stelt dat Es1,2= de forward rate = f1,2

In woorden: forward rates zijn unbiased verwachtingen van de toekomstige spot rates. De unbiased expectations theory stelt dat de

b) Calculate the market expectation for the two year spot rate between January 2013 (beginning) and December 2014 (end) on the basis of the unbiased expectations theory (use proper government bonds)

Volgens de unbiased expectations theory is es1,2 = f1,2

“nl 0cpn 13” 87.63
876.30 = 1,000.00/(1 + s3)3
S3 = 3√(1000/876.30) -1 = 0.045

“nl 0cpn 14” 85.48
854.80= 1,000.00 /(1 + s4)4
S4= 4√(1000/854.80-1) = 0.04

S1 =4.5% (2013)
S2 = 4.0% (2014)

Volgens unbiased expectations theorie moet de roll-over strategie gelijk zijn aan de maturity strategy.
Roll-over strategy = maturity strategy
1.045 * (1 + es1,2) = 1 * (1.040)2
1.045 * (1+es1,2) = 1 * 1.0816
1+es1,2 = 1.03502, dus es1,2 = 3.502%

Gezien de expected spotrate gelijk is aan de future spot rate, is dus de future spot rate 3.502 %

4) Explain why the Dutch government bond “nl 9.00 92-15” is more expensive than the government bond “nl 9.00 92 – 14”

We verwachten dat de bond “nl 9.00 92-15” minder duur zal zijn dan de “nl 9.00 92 – 14”, gezien de rente voor beide bonds gelijk is maar de maturity van de eerst genoemde een jaar langer is. Hierdoor zou de face value van de eerstgenoemde bond dus lager zijn.

De huidige interest rate is relatief laag en gezien we verwachten dat deze ook laag zal zijn in 2014 en 2015, zal men tevreden zijn met een 9% uitbetaling van de bond. Door te kiezen voor de 2015 bond is de extra return hoger, dan dat we kunnen krijgen van de (verwachte lage) interest rate. Men zal dus bereidt zijn om meer te betalen voor een 2015 bond en daarom is de prijs van deze bond ook hoger dan van een 2014 bond.

Forwards and Futures
Q1. The two-month-interest rates in Switzerland and the United States are 2% and 1 % per annum respectively with continuous compounding. The spot price in Swiss franc is $0.9500. The futures price for a contract deliverable in two months is $0.9450. What arbitrage opportunities does this create?
De future value na twee maanden is F0=S0*ert = 0.95*e0.01*(2/12)= $??. De future price van het contract is te laag. Men zal future contracts moeten kopen zodat hij Swiss francs kan kopen voor $?? na twee maanden.
Bij de bank leent men 1000 Swiss francs. Na twee maanden moet men de lening terugbetalen inclusief de rente wat 1000*e0.01*(2/12)=??. Men kan het geleende geld gebruiken om dollars mee te kopen, hierbij ontvangt men $950. Dit geld zet men op een rekening en na twee maanden heeft men 950*e0.02*(2/12)=??. En na twee maanden gebruikt men de future contracts om de Swiss francs weer te kopen. Dan ontvangt men

Q2. The current USD / euro exchange rate is 1.150 dollar per euro. The six – month forward exchange rate is 1.145. The six – months euro interest rate is 0.8% per annum continuously compounding. Estimate the six – month USD interest rate.

USD/Euro: So=$1.150/€
F0= 1.145/€

0=0*(−) rf = 0.008 (euro)


1.145 *0.008*1/2 = 1.150 *1/2r
1.145/1.150 *0.004 = 1/2r ln (1/2r) = ln (1.145/1.150 *0.004)
0.5r = ln (1.145/1.150 *0.004) r = 2 ln (1.145/1.150 *0.004) = r = …. Dit is de six-month USD interest rate

Properties of Stock Options
The price of a European call that expires in six months and has a strike price of $30 is $2.50. The underlying price is $29, and a dividend of $0.75 is expected in one month and again in three months. The term structure is flat, with all interest rates being 6%. What is the price of a European put option that expires in six months and has a strike price of $30?

Put call parity: c+ D + Ke−rT = p+S0




p = 4.10

Company A and B have been offered the following rates per annum on a $2 million 8-year loan
| |Fixed Rate |Floating Rate |
|Company A |3.4% |LIBOR +0.2% |
|Company B |4.2% |LIBOR +0.5% |

Company A requires a floating – rate loan; company B requires affixed rate loan. Design a swap that will net a bank, acting as an intermediary, 0.1% per annum and that will appear equally attractive to both parties.

Bedrijf A wil een floating rate voor hun lening, terwijl bedrijf B juist een vaste rate willen voor hun lening. Omdat A een comperatief voordeel heeft in fixed rate leningen en B een comperatief voordeel heeft in floating rate leningen zal een swap het perfecte instrument zijn voor beide bedrijven om te krijgen wat ze willen. De financiële institutie ontvangt 0.1% per jaar.


Questions taken from Hull’s book:
Chapter 7 See: Assignment question 7.22 (7e edition, 2011)
OR: Chapter 7 See: Assignment question 7.25 (8e edition, 2014)
Company A wishes to borrow US dollars at a fixed rate of interest. Company B wishes to borrow sterling at a fixed rate of interest. They have been quoted the following rates per annum
| |Pound Sterling |US dollar |
|Company A (UK) |11% |7% |
|Company B (US) |10.6% |6.2% |

Answer this question in two ways!
First: Design a swap that will net a bank, acting as an intermediary, 10 basis points and produce a gain of 15 basis points for each of the two companies. The bank is exposed to exchange rate risk in the swap!

Het verschil in de interest rate tussen bedrijf A en bedrijf B voor de Pound Sterling is 11%-10.6%= 0.4%, dus 40 basispunten. Het verschil in de interest rate tussen bedrijf A en bedrijf B voor de US Dollar is 7%-6.2%=0.8%, dus 80 basispunten. Het totale voordeel voor alle partijen is dan dus 80-40=40 basispunten. Door deze 40 basispunten heeft de bank de mogelijkheid om 10 basispunten te verdienen en winst te maken van 15 basispunten voor beide bedrijven.
Bedrijf A wil US Dollars lenen, dit kan bedrijf A lenen van de bank tegen een rente van 7.0%-0.15%=6.85%.
Bedrijf B wil Pound Sterling lenen, dit kan bedrijf B lenen van de bank tegen een renten van 10.6%-0.15%=10.45%.
Door deze leningen zal de bank door de US Dollars 6.85%-6.2%=0.65% winst maken en door de Pound Sterling 10.45%-11%=-0.55% verlies maknen. Dus de totale winst van de bank is 0.65%-0.55%=0.1% winst.

Second: Design a swap that will net a bank, acting as an intermediary, 10 basis points and produce a gain of 15 basis points for each of the two companies. The bank is NOT exposed to exchange rate risk in the swap!

Wanneer de bank gebruik maakt van forward contracts wordt de exchange rate risk omzeild. Bij een forward contract wordt de exchange rate van de Pound Sterling en de US Dollar vastgezet. Wanneer de bank met beide partijen forward contracts afsluit dan lopen beide geen exchange rate risico bij de swap.

Chapter 9: Assignment question 9.23 (7e edition, 2011)
OR: Chapter 9: Assignment question 9.26 (8e edition, 2014)
The price of a stock is $40. The price of a one-year European put option on the stock with a strike price of $30 is quoted as $7 and the price of a one-year European call option on the stock with a strike price of $50 is $5. Suppose that an investor buys 100 shares, shorts 100 call options and buys 100 put options. Draw a diagram illustrating how the investor’s profits or loss varies with the stock prices over the next year.
You don’t have to answer the last question: (How does your answer change if the investor buys 100 shares, shorts 200 call options and buys 200 put options?)

Chapter 11: Practice Questions: 11.10 (7e edition, 2011 and 8e edition, 2014)
Suppose that put options on a stock with strike prices of $30 and $35 cost $4 and $7, respectively. How can the options be used to create (a) a bull spread and (b) a bear spread? Construct a table that shows the profit and payoff for both spreads.

Men kan een bull spread maken door een put voor een hogere prijs te verkopen dan waartegen men een put heeft gekocht. Bijvoorbeeld een bull spread ontstaat als men een put koopt voor een prijs van 30 dollar en een put verkoopt tegen een prijs van 35 dollar. Dit zorgt ervoor dat de initial cash flow wordt verhoogd met 3 dollar.

|Stock Price |Payoff |Profit |
|[pic] |0 |3 |
|[pic] |[pic] |[pic] |
|[pic] |[pic] |[pic] |

Men kan een bear spread maken door een put voor een hogere prijs te kopen dan waartegen men een put heeft verkocht. Bijvoorbeeld een bear spread ontstaat als men een put voor een prijs van 35 dollar koopt en de put met een prijs van 30 dollar verkoopt. Deze aanpak kost men 3 dollar.

|Stock Price |Payoff |Profit |
|[pic] |0 |[pic] |
|[pic] |[pic] |[pic] |
|[pic] |5 |2 |

Options (chapter 11): A call option with a strike price of $60 costs $2.50 and a put option with a strike price of $55 costs $1.50. Explain how a strangle can be created from these two options. What is the pattern of profits (and losses) from this strategy?

Een strangle kan gemaakt worden door het kopen van een call- en put-option met dezelfde expiration date, maar wel verschillende strike prices.
[1] You are requested to form mixed groups of students of Economics and students of Business Administration…...

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...Project Kick-Off Meeting Dwayne A. Blanchette BUS 611: Project Planning and Management Dr.: Donald McKay April 25, 2016 Recently the project charter for transitioning the Quick Drop 100 (QD100) from New York to Florida received final authorization. I was awarded the project and assigned as project manager (PM) to lead a team of qualified individuals and complete the task of relocating the QD100 program to the state of Florida. The next step in the preparation phase is to hold a project kickoff meeting. This meeting will be used to acclimate team members, clients, and other attendants to ensure everyone understands the key players and their respective roles. As the PM I plan to generate enthusiasm, motivation, and excitement while maintaining a guided discussion regarding the content, schedule, and duration of the project from start to finish. To prepare for the meeting I will accomplish several preliminary tasks. The most important areas to consider during preparation include identifying stakeholders, communication methods, team building, accountability and code of conduct. Once the tone has been set and key points discussed the meeting will conclude by first reiterating member expectations and responsibilities followed by a summary of all pertinent information. The bottom line is this kickoff meeting will be presented as such to ensure all relevant attendants and stakeholders are provided a transparent achievable list of goals. Stakeholders A......

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