You are in charge of Dozier at the FX desk of their bank. Advise Rothschild on the following additional hedging schemes.

1. Delta Hedge

Download the Excel file from eClass (in the same folder as this exercise under the “Assignments” folder). It contains the data in Exhibit 5 of Dozier Case A. Since forward and futures prices are (almost) identical in theory, assume that the 3-month forward rates shown there are the 3-month futures prices (assume CME—the contract size is ₤62,500. Also recall the limited maturities of CME futures contracts). Advise Rothschild on delta hedge as follows:

a) Compute the time series of simple returns (the ratio of the current to last price minus 1) on the spot rate (Δst$/£) and on the futures prices (Δfutt$/£). Show the first several observations of your calculated series. Regress Δst$/£ on Δfutt$/£ and report the result in the following format (for β, show at least three digits below the decimal point):

Δstd/f = α + β ⋅ Δfuttd/f + εt, Adjusted R2=0.xxx

(t-stat) (t-stat)

If you are unfamiliar with running regressions, the last page of this document describes how to do so using Excel.

b) How can Dozier delta-hedge its exposure from the transaction described in the case on January 14? Specify the number of futures contracts it should buy or sell. Show your calculation.

c) Briefly explain why your hedging scheme might be imperfect, mentioning two mismatches; do not question the accuracy of the regression estimates.

(Continued)

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2. Money-market Hedge

It turns out that Dozier has also sought suppliers from foreign markets including Canada, and that the US$847,061 materials cost in the bid preparation (see Exhibit 3 in Dozier Part A) is really a translation of Canadian materials cost, CA$1,178,431.26. Dozier used the spot exchange rate on the bid preparation date, December 3, to arrive at the US dollar materials cost. In fact, on January 14 following bid acceptance, Dozier has placed a purchase order with a Canadian supplier as planned, resulting in a Canadian dollar payment due on April 14 in the above amount. The market rates on January 14 are as follows (based on actual historical rates):

CA$ exchange rate: CA$1.4030/US$

CA$ prime lending rate: 11.00%

CA$ three-month deposit rate: 10.70%

John Gunn of the bank’s International Division suggests that Dozier will be able to borrow in Canadian dollars at 1.00% over the Canadian prime lending rate. Robert Leigh, who is responsible for Dozier’s business with the bank, assures that Dozier can borrow in US dollars at the US prime lending rate flat (see Exhibit 4) given its relationship with the bank. Dozier can make a deposit in either currency at its respective deposit rate; there is no additional spread because a deposit does not concern the depositor’s credit.

a) Construct a money market hedge to fix the amount of US dollars necessary to pay for the Canadian materials cost. Specify the details of the three necessary transactions, i.e., how much of what currency you are borrowing, exchanging, and depositing at what rate. In particular, make sure to choose the correct borrowing and deposit rates.

b) What is the effective forward rate of your money-market hedge? Show at least four digits below the decimal point. Is the Canadian dollar in forward discount or premium in your effective forward contract?

c) In a perfect world in which all parity conditions hold ex post (i.e., without the expectations—see the Big Diamond), was Dozier’s choice to convert the Canadian materials cost by the spot rate as of bid submission conservative, assuming that Canadian interest rates were expected to remain higher than their US counterpart for the relevant future (as they are on January 14—compare the above rates to Exhibit 4)? Support your argument stating which parity condition(s) you are invoking on December 3 and January 14.

Note: It is more conservative to overestimate the cost than underestimate it.

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Running a Regression Using Excel

1) Use the “Example Data” in the accompanying Excel file. The data are generated using the relation

yt = 1 + 2xt + εt.

We are expecting that the intercept and slope estimates will be close to 1 and 2, respectively.

2) In Excel 2016/2013/2010/2007, follow Data > Data Analysis > Regression. If you do not see such a menu, you need to first install the Analysis ToolPak. Consult the Excel Help.

3) Specify the “Input Y Range” and the “Input X Range” and click the “OK” button. If you get the tables below, you are doing it right!

4) Report the result as:

yt = 0.963 + 1.849 xt + εt, Adjusted R2 = 0.797

(3.51) (8.70)

SUMMARY OUTPUT

Regression Statistics

Multiple R 0.898883

R Square 0.807991

Adjusted R

Square 0.797324

Standard Error 1.217209

Observations 20

ANOVA

Significance

df SS MS F F

Regression 1 112.2248 112.2248 75.74578 7.23E-08 Residual 18 26.66876 1.481598

Total 19 138.8936

Standard

Upper

Lower

Upper

Coefficients

Error t Stat P-value Lower 95%

95%

95.0%

95.0%

Intercept 0.962879 0.27424 3.511086 0.002495 0.386723 1.539036 0.386723 1.539036 X Variable 1 1.848811 0.212429 8.703205 7.23E-08 1.402515 2.295107 1.402515 2.295107

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