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(a) What is the no-arbitrage price for a 1-year UK Pound Sterling foreign-exchange forward denominated in US Dollars, if the current exchange rate is $1.65/£, the risk-free interest rate in the UK is 3% per year, and the risk-free interest rate in the US is 2% per year?

(b) Carefully outline the steps a US investor must undertake in order to invest $1000 in UK Gilts (risk-free bonds), assuming his current wealth is in US Dollars, and that he wants to consume his money in US Dollars afterwards. Assume he uses the foreign-exchange forward you priced in the previous part in converting his money back to Dollars at the end of his investment.

(c) When pursuing this strategy, is the investor exposed to any foreign-exchange rate risk? Why or why not?

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Lelia Lubowitz
Lelia LubowitzLv2
28 Sep 2019

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One-year zero coupon treasury bonds are selling for £975.61 in the U.K. and for $963.86 in the U.S. Assume $1,000 face value in dollars for the U.S. bond and £1,000 face value for the U.K bond, and round interest rates to two decimal places, e.g. 2.50%. The current spot ex-rate is $1.5350/£. Use THIS IRP formula: ius ≈ iuk +/- %CHG in £. Use this formula (F – S) / S to calculate the forward discount/premium (or the %CHG function on your calculator). a. Using a time value of money calculation, calculate the one-year yields (YTM) in the U.S. and in the U.K. for T-bills (round to 2 decimal place, e.g. 3.45%). b. If interest rate parity (IRP) is holding, should the British pound be selling at a forward discount or premium? How much and why? Explain in an essay with full sentences. (Use the IRP formula above.) c. Based on your answer in part b, and using the current spot ex-rate, calculate and report the expected one year forward ex-rate if interest rate parity holds. (Note: You don’t need the IRP equation to answer this question.) d. If interest rate parity does not hold and the actual one-year forward rate is $1.5657/£, calculate and report the actual forward discount or premium for the pound (to 2 decimal places). Using that forward discount or premium and the one-year yields from part a, compare an American investor’s rate of return in the U.S. versus the effective dollar return in the U.K. For the U.K. investment, assume the US investor would use a forward contract to cover ex-rate risk, and use the formula: Effective Dollar Return in UK = Interest Rate in UK +/- Forward Discount (%) or Premium (%) for the £. e. Starting with either $1M or £1M, calculate and report the covered interest arbitrage profit you could make (express the arbitrage profit in both pounds and dollars in one year, using the one-year forward ex-rate). Explain each transaction in words. f. Based on your answers to part d and e, explain what would happen to interest rates and bond prices in the U.K. and explain why that would happen in an essay. What would happen to interest rates and bond prices in the U.S. and why would that happen?

Consider the following model of the saving-investment balance. In this model, the following relationship must remain in balance: S + (M-X) = I + (G-T) where,

S is domestic saving by households and businesses

M is U.S. imports of goods and services

X is U.S. exports of goods and services

I is private domestic investment in capital goods

G is total federal, state and local government spending on goods and services, and

T is the net receipt of tax revenues by federal, state and local governments

The presentation: “Lesson 1: The Savings and Investment Balance” in this week’s lesson can help you understand this identity better.

Clearly, as with any high-level model, there are limitations but let’s try to understand how this model functions mechanically.Consider the model of the saving-investment balance only as an algebraic accounting identity (i.e., do not consider any economic repercussions or additional complications (those can come later)), What does the model predict will happen to gross private domestic investment (I) if:

a) Domestic saving by households was to decrease, everything else remaining the same?

b) U.S. net tax receipts were to increase, everything else remaining the same?

c) There was a sudden increase in exports from the U.S., everything else remaining the same?

d) Pre-tax business profits were to increase, everything else remaining the same?

e) Federal grants to state and local governments were to disappear, everything else remaining the same?

2. Examine the note and bond yields presented below for Treasury and Corporate AAA, AA and A-rate bonds. Why do the yields differ across the securities and within securities, across time? Which premiums or market expectations most appropriately explain those differences? In particular, what accounts for the differences in rates across securities types for the same maturities? And speculate on what factor or factors can best explain why the yields rise as maturities lengthen (within particular types of bonds). Finally, do any securities look out of place and, if so, which and why?

Treasuries

2 year 0.33%

5 year 1.39%

10 year 2.64%

20 year 3.42%

Corporate, AAA

2 year 0.40%

5 year 1.77%

10 year 3.52%

20 year 4.93%

(table continues on next page)

Corporate, AA

2 year 0.63%

5 year 1.91%

10 year 3.50%

20 year 4.43%

Corporate, A

2 year 0.84%

5 year 2.15%

10 year 3.67%

20 year 4.75%

3. Suppose that today the one-year Treasury note yields 0.12% (0.0012 in decimal form), the two-year note yields 0.40% (0.0040), the three-year note yields 0.78% (0.0078), the five-year note yields 1.60% (0.0160), the seven-year note yields 2.22% (0.0222) and the ten-year note yields 2.81% (0.0281). Under the pure expectations theory with no maturity risk:

a) What is the expected yield on a one-year note delivered one year from now?

b) What is the expected yield on a one-year note delivered two years from now?

c) What is the expected yield on a three-year note delivered two years from now?

d) What is the expected yield on a two-year note delivered five years from now?

e) What is the expected yield on a five-year note delivered five years from now?

f) What is the expected yield on a seven-year note delivered three years from now?

Note: This concept is discussed in Chapter 3 of the text and in “Lesson 2: More On Yield Curves and Forward Rate Determination” in this week’s online materials.

4. Assume that interest rate parity holds so that future or forward exchange rates adjust to eliminate investor arbitrage profits. If interest rates in Britain are higher than corresponding interest rates in Japan, would you expect an appreciating pound or a depreciating pound in the futures (forward) market relative to the current spot market rate? In terms of the supply and demand for pounds in the spot and forward currency markets, what is implicitly occurring in each as a result of interest rate parity? Is the pound selling forward at a premium or at a discount relative to the yen? (The presentation “Lesson 3: On Exchange Rates” from this week’s materials can help shed light on this subject. The portion on interest rate parity later in the presentation, so stick with it. It’s also discussed in Chapter 16.)

5. The spot market rate for the euro is 1.4059 Canadian dollars per euro. The 3-month futures (forward) rate on the euro is 1.4147 Canadian dollars per euro. The yield on a 3-month Canadian government security is 1.16 percent (0.0116 decimal), annual percentage rate (APR). The yield on a 3-month euro area security is 0.24 percent (0.0024 decimal), annual percentage rate (APR). Show that interest rate parity (IRP) does not hold by solving for the forward rate that ensures IRP. How would you take advantage of the arbitrage opportunity arising from the actual data (i.e., borrow 1,000,000 euros, convert to Canadian dollars, invest in Canada, sell the proceeds forward and then repay your loan or borrow 1,000,000 Canadian dollars, convert to euros, invest in Europe, sell the proceeds forward and then repay your loan)?

Derivative

Vanguard High Yield Corporate Fund
Materials
• Website information (23/05/2016)
https://personal.vanguard.com/us/funds/snapshot?FundId=0029&FundIntExt=INT
• Summary Prospectus (27/05/2015)
• Prospectus (27/05/2015)
Anakin’s Job
In May 2016, Anakin leaves his job in Hollywood and returned to the finance industry. It is his
first love after all and the industry appears to be picking up again after the credit crunch of
2007-2008. He applies to be the risk analyst to the fund manager of the Vanguard High Yield
Corporate Fund as his quantitative training positions him well for a job that requires ever more
numerical and computational skills over the years. His solid background in applied analytics
in business management and humble demeanour help him clinch the post without much
difficulty.
The Vanguard Group is an American investment company that has approximately USD 3
trillion in asset-under-management. It is founded in 1975 by John Bogle who created the first
index fund (tied to the S&P 500 index) in the process. After an initial lull, the index grew
rapidly along with the bull market of the 1980s. The Group has since added various financial
services and products to its core business, particularly the ETFs.
Anakin is tasked by the fund manager to become thoroughly familiar with the structure of the
fund as is documented by files provided under “Materials”. After that, he is to assess the
exposure of the High Yield Corporate Fund to risks in the market. He seeks the opinion of
Darth who is a veteran market analyst with the Vanguard Guard group for over 20 years.
Outlook
Darth has this to say about the economy and fixed income market:
" The US economy is improving steadily. It will not be long before the Fed decides to raise
interest rates. Once the Fed restarts the regime of rising rates, it will about 2 years for the yield
curve to rise by 100 basis points.
Consequently, in the more stringent economic environment, companies of lower credit
qualities, namely those of Caa and below, are expected to have their credit standing further
eroded. There is a 25% chance that a Caa-rated issuer may go into default and another 25%
chance that it may be downgraded to C.
The Greek debt problem, though much stabilized than before, is still a matter of grave concern
for the Eurozone. Expect the euro to depreciate against the dollar over the course of the next 6
months. A fall of 500 pips will not be a surprise. "
Assume Anakins’ role and answer the following questions. Questions 1 and 2 concern the
Financial Environment. The Environment at large provides the context and sets the constraints
within which financial decisions are weighed and taken. Questions 3 and 4 pertain to the task
that Anakin needs to complete.

Question 4
The fund is affected by changes in the financial markets. When interest rates rise, the value of
the portfolio falls. Occurrences that are flagged by the rating agency to be credit events can
result in the downgrading of credit rating of bond issuers. Bonds that denominated in foreign
currency are affected by fluctuations in the foreign exchange market.
(a) Analyse generally the need for hedging the various market risks for the fund.

Take into account Darth’s outlook. Address some of these risk concerns by answering the
following question:
(b) Suppose that in the coming 2 years, the prevailing interest rates are expected to go up
by 100 basis points and you are concerned. Show how you could hedge away the
interest rate risk by using an interest rate swap, assuming that the fund by may
represented by a single 5-year par bond on the $18.4 billion net assets with semi-annual
5% coupon payments starting from the current date.
In your explanation, you may assume a scenario in which a flat yield curve increases
uniformly across all terms by 25 basis points per half-a-year.
(c) Credit default swaps may be used to ameliorate credit risk. Appraise the use of such
option-like derivative instruments in managing the risk of the portfolio by explaining
how such instruments function.

https://institutional.vanguard.com/VGApp/iip/site/institutional/investments/productoverview?fundId=0029

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