SUGGESTED READINGS
3.6 SUMMARY
of conditional volatility as a black line. RiskMetrics conditional volatility rises in periods of high absolute monthly changes in the value of the dollar, such as when the dollar depreciated by 15 percent in October 1998. Conditional volatility falls during less volatile periods, such as in the early years of the 21st century. Conditional volatility estimates are sensitive to market conditions, and that is a useful attribute for a volatility measure that is used to manage exposures to currency risk.
−20 percent in the value of the yen. If the dollar in the denominator appreciates by 25 percent, then the yen must depreciate by 20 percent. This can be verified with Equation 3.5.
s$/¥ =1/(1+s¥/$)−1=1/(1.25)−1= −0.20, or−20 percent
–1.95% 98.05 +1.99%
100 100
Let’s try the example from the text in which the Swiss franc changes from
$0.5839/SFr to $0.5725/SFr. The percentage change in the dollar-per-franc spot rate is
[($0.5725/SFr−$0.5839/SFr)]/($0.5839/SFr)≈ −0.0195
or−1.95 percent. If the franc in the denominator falls to (100.00−1.95)= 98.05 percent of its beginning value, then the dollar in the numerator must go up accordingly.
A dollar appreciation from 98.05 to 100 results in (100.00−98.05) / 98.05≈ +0.0199, or+1.99 percent. Although this yields the same result as Equation 3.5, you may find it easier to remember this method than the equation.
KEY TERMS
allocational, informational, operational efficiency Basel Accords
basis points
bid and offer (ask) rates and the bid-ask spread
capital vs money markets correlated default
currency of reference (referent currency)
dealers (market makers) vs brokers direct vs indirect terms
Euro Interbank Offered Rate (Euribor) Eurocurrency markets
Eurodollars, Eurosterling, and Euroyen markets
European vs American terms
external vs internal markets financial markets
financial price risk
foreign exchange (currency) market foreign exchange (currency) risk forward premium or discount GARCH
liquidity
London Interbank Bid and Offer Rates (LIBID and LIBOR)
outright forwards vs currency swaps random walk
spot and forward market SWIFT
term premium value-at-risk (VaR)
CONCEPTUAL QUESTIONS
3.1 Define liquidity.
3.2 What is the difference between a money market and a capital market?
3.3 What is the difference between an internal and an external market?
3.4 What is the Eurocurrency market and what is its function?
3.5 In what way is the Eurocurrency market different from an internal credit market?
3.6 What is the LIBOR?
3.7 What are the Basel Accords? What effects have they had on international banks?
3.8 What is the difference between spot and forward markets for foreign exchange?
3.9 What is Rule #1 when dealing with foreign exchange? Why is it important?
3.10 What is Rule #2 when dealing with foreign exchange? Why is it important?
3.11 What are the functions of the foreign exchange market?
3.12 Define operational, informational, and allocational efficiency.
3.13 What is a forward premium? What is a forward discount?
3.14 Describe the empirical behavior of exchange rates.
PROBLEMS
3.1 Citigroup quotes Danish kroner as ‘‘DKK5.62/$ Bid and DKK5.87/$ Ask.’’
a. Which currency is Citigroup buying at the DKK5.62/$ bid rate, and which currency is Citigroup selling at the DKK5.87/$ offer rate?
b. What are the bid and ask prices in American terms? Which currency is Citigroup buying at these prices and which currency is Citigroup selling?
c. With the foreign currency in the numerator, the ‘‘DKK5.62/$ Bid and DKK5.87/$ Ask’’ quotes are indirect quotes for a U.S. resident. What are the bid and ask prices in direct terms for a U.S. resident? At these prices, which currency is Citigroup buying and which currency is it selling?
d. If you sell $1 million to Citigroup at a bid price of DKK5.62/$ and simultaneously buy $1 million at their offer price of DKK5.87/$, how many Danish krona (‘‘krona’’ is the plural of kroner) will you make or lose? What is Citigroup’s kroner profit or loss on the transaction?
3.2 You want to buy Swedish krona (SKr). Your bank quotes ‘‘SKr7.5050/$
Bid and SKr7.5150/$ Ask.’’ What would you pay in dollars if you bought SKr10,000,000 at the current spot rate?
3.3 The Canadian-U.S. spot rate SC$0 /$ is quoted as ‘‘C$1.2340/$ Bid and C$1.2350/$ Ak.’’ The 6-month forward rate FC$1 /$is quoted as ‘‘C$1.2382/$
Bid and C$1.2397/$ Ask.’’ Assume you reside in the United States. Calculate forward quotes for the Canadian dollar as an annual percentage premium or discount. Would a FX trader in Canada get a different answer if asked to calculate the annual percentage premium or discount on the U.S. dollar for each forward rate? Why?
3.4 Today’s spot rate is S$0/¥ =$0.009057355/¥. The 90-day forward rate is F$/¥1 =$0.008772945/¥.
a. Calculate the forward premium on Japanese yen in basis points and as a percentage premium or discount over the 90-day period.
b. Calculate the forward premium on Japanese yen as an annualized percent- age premium following the U.S. convention.
c. Calculate the forward premium on Japanese yen as an effective annual percentage rate (APR).
3.5 In 1984, the number of German marks required to buy one U.S. dollar was 1.80. In 1987, the U.S. dollar was worth 2.00 marks. In 1992, the dollar was worth 1.50 marks. In 1997, the dollar was again worth 1.80 marks.
a. What was the percentage appreciation or depreciation of the dollar between 1984 and 1987? Between 1987 and 1992? Between 1992 and 1997?
b. What was the percentage appreciation of the mark between 1984 and 1987? Between 1987 and 1992? Between 1992 and 1997? (Hint: Follow Rule #2 and convert SDM/$ to S$/DM.)
3.6 A foreign exchange dealer in Warsaw provides quotes for spot and 3-month forward rates for the Polish zloty against the dollar.
Bid (PZ/$) Ask (PZ/$)
Spot 4.0040 4.0200
3-month forward 3.9690 3.9888
a. What would you receive in dollars if you sold PZ 5 million at the spot rate?
b. What would it cost in dollars to purchase PZ 20 million forward three months. When would you make payment?
3.7 You have sold ¥104 million at a spot price of ¥104/$. One year later, you pay dollars to buy back ¥104 million at the prevailing spot rate of ¥100/$. How much have you gained or lost in dollars?
3.8 Euro bid and ask prices on the Japanese yen are quoted direct in Paris at 0.007634/¥ Bid and 0.007643/¥ Ask. What are the corresponding indirect quotes for euros?
3.9 Calculate appreciation or depreciation in each of the following:
a. If the dollar depreciates 10 percent against the yen, by what percent does the yen appreciate against the dollar?
b. If the dollar appreciates 1000 percent against the ruble, by what percent does the ruble depreciate against the dollar?
3.10 Dollars are trading at S0SFr/$ =SFr0.7465/$ in the spot market. The 90-day forward rate is F1SFr/$=SFr0.7432/$. What is the forward premium on the dollar in basis point terms? What is the forward premium as an annualized percentage rate?
3.11 In what way are these quotes equivalent?
a. ‘‘$0.5841/SFr Bid and $0.5852/SFr Ask’’
b. ‘‘$0.5852/SFr Bid and $0.5841/SFr Ask’’
3.12 The Danish kroner is quoted in New York at $0.18536/DKK spot,
$0.18519/DKK 30 days forward, $0.18500/DKK 90 days forward, and
$0.18488/DKK 180 days forward. Calculate the forward discounts or premiums on the kroner.
3.13 At time t =0 the dollar-per-yen spot rate S0$/¥ is $0.0100/¥. The yen then appreciates 25.86 percent.
a. What is the closing spot rate in dollars per yen S1$/¥?
b. By what percentage does the dollar depreciate against the yen?
3.14 Find a formula like Equation 3.1 for calculating a forward premium with currency d in the numerator. [Hint: Substitute S0d/f =1/(S0f/d) and Ftd/f= 1/(Ftf/d) into Equation 3.1 to get currency d in the denominator, and then rearrange and simplify.]
3.15 Suppose you estimate a GARCH(1,1) model of monthly volatility in the value of the dollar and arrive at the following estimates:
σt
2=0.0034+(0.40)σt−12+(0.20)s
t−1
2 (3.8)
where the conditional variance (σt−1
2) and the square of the percentage change in the spot exchange rate (st
−1
2) are from the previous period. Ifσt−1=0.05 and s
t−1=0.10, what is the GARCH estimate of conditional volatility?
SUGGESTED READINGS
The function and operation of foreign exchange dealers are examined in
Richard K. Lyons, ‘‘Profits and Position Control: A Week of FX Dealing,’’ Journal of International Money and Finance17 (February 1998), 97 – 115.
Accounting disclosure of value-at-risk estimates is assessed in
Philippe Jorion, ‘‘How Informative Are Value-at-Risk Disclosures?’’Accounting Review77 (October 2002), 911 – 931.
The GARCH conditional volatility model is developed in
Timothy Bollerslev, ‘‘Generalized Autoregressive Conditional Heteroskedasticity,’’Journal of Econometrics31 (April 1986), 307 – 328.
4
The International Parity Conditions and Their Consequences
Though this be madness, yet there is method in it.
— William Shakespeare