(1) Use the exchange rate table below to answer the questions. All rates are against USD.
USD is CCY2 for GBP and EUR but is CCY1 for all other currencies.
a. What are the closing bid and offer rates for USD/NOK?
b. Did USD appreciate or depreciate against EUR on October 10?
c. As a customer, which rate would you get if you were to convert CHF to USD?
d. What is the 3-month forward USD/TRL rate?
(2) Suppose the 6-month (annualized) interest rates are 0.50% for USD and 1.50% for EUR. The current spot rate is USD 1.3000/ EUR. For simplicity, assume that for 6 months, you earn half of the annualized interest rates.
a. What is the arbitrage-free 6-month forward EUR/USD?
b. If the 6-month forward rate is 1.3000 as opposed to the rate in (a), describe briefly the transactions you need to make to earn arbitrage profits?
(3) The USD/BRL spot rate is 2.40. The gasoline prices (per gallon) are BRL 9.00 in Brazil and USD 3.00 in the U.S.
a. According to PPP, is BRL overvalued or undervalued relative to USD? Recall that the same good is more (less) expensive in the country with overvalued (undervalued) currency.
b. Speculate: Why might this deviation from PPP (based on gasoline prices) persist?
Note: Use the data and setups in the excel file: "Problem Set 1.xlsx" to answer questions (4) - (6). Each sheet in the file corresponds to the question of the same number.
(4) UIRP is overwhelmingly rejected in the data. On average, high-interest rate currencies do not depreciate as much against lower-interest rate currencies as predicted by UIRP. In the long exercise below, we will try to take advantage of this violation.
Go to sheet "Question 4". Here, I am asking you to implement "carry trades", borrowing low-yielding currencies and depositing high-yielding currencies (uncovered). We are going to use the data for 6 currencies from 5/31/1990 to 6/30/2010. Columns B to D
contain the time series of 1-month annualized interest rates, and columns I to N contain the corresponding exchange rates, expressed in terms of USD per 1 unit of foreign currency. In columns P to U, I have calculated for you the currency returns measured against USD.
These returns include both the change in exchange rate and the money market return. That is, the return of Currency A from time t to t +1(from the perspective of a USD investor) is given by
where MR(A,t)is the money market rate (or interest rate) of Currency A at time t and S(USD / A,t) is the (textbook convention) exchange rate expressed in terms of the number of USD per unit of Currency A. You can use the same formula for USD return by treating the exchange rate as always equal to 1. Check my formula to make sure you understand what I did.
Next, we need to rank these currencies based on the level of interest rates-- 1 for the currency with the highest interest rate (and 6 the lowest). The formulas again have been entered for you in row 5; you just need to study the formulas and if you agree, please
copy these formulas down to rows 6 through 246.
Now, go long the first and second ranked currencies (two highest interest-rate currencies) and go short the fifth and sixth ranked currencies (two lowest interest-rate currencies). Note that when there are ties, you will go long or short more than two currencies. This is fine, since we are going to equally weight them. I have entered the formulas for you that generate "1" for the currencies you need to go long, -1 for the currencies you need to go short. These formulas are in row 5 from columns AD to AI. Check my formulas and if
you agree, please copy them down to rows 6 through 246. Columns AK to AL just count the number of currencies you go long and the number of currencies you go short, respectively.
To have "zero" net investment, you must start with equal amount of long and short positions (that is you borrow in low interest-rate currencies and lend all the proceeds in high interest-rate currencies). For simplicity, you may assume that the total long and short amounts are both USD 1. Therefore, if you start by going long 2 currencies (each with equal weight) and short 2 currencies (each with equal weight), then your excess return from time t to t +1 is given by
These formulas again have been entered for you in row 6 of columns AN to AP. Column AN calculates the average return of the two currencies you are long, and column AO calculates the average return of the two currencies you are short. Column AP gives you
the net excess return, given in the above formula. Note that these returns are one row below the positions, in order to reflect the fact that the positions you put in on 5/31/1990 yield returns on 6/29/1990. Check these formulas again. If you feel that you understand
them, then again copy them down to rows 7 through 246. (These calculations are equivalent to calculating the returns, assuming you rebalance your portfolio every month based on the new ranking but you always keep the notional amount at USD 1.) In the end, you should obtain a time series of excess returns from carry trade in column AP.
Use these net excess returns to answer the following questions.
a. What is the average monthly return per USD 1 notional amount from the carry trade described above?
b. What is the standard deviation of monthly return from the carry trade?
c. What is the lowest monthly return (i.e. maximum loss during 6/29/1990 and 6/30/2010)) from the carry trade?
d. How many months do you observe positive returns from carry trade? How many months do you observe negative returns from the carry trade?
e. Based on the evidence above, is carry trade risk-free?
f. Instead of the trades we implement in this exercise (borrow, sell/buy currencies at spot, and lend), you can achieve the same payoff, using just FX forward transactions.
Would you buy or sell the high-interest rate currencies forward?
(5) Go to sheet "Question 5." Take the period from 1/4/2005 to 1/31/2012 as your estimation period, in measuring the risk of USD/INR exchange rate (questions (a) to (d)). Then, you will be asked to check your number against the actual realizations in the period from
2/1/2012 to 9/30/2014 (questions (e) to (f)).
a. What is the average daily rate of appreciation of INR relative to USD?
b. What is the standard deviation of INR's daily appreciation rate?
c. What is the Z-score that corresponds to the 1st percentile of the standard normal distribution? That is, if you randomly draw a standard normal variable, the chance that the number you draw will be above (below) this Z-score is 99% (1%).
d. Assume that the INR's rate of appreciation is normally distributed. Using your answers in (a), (b), and (c) above, find the rate of appreciation of INR relative to USD, below which the probability of realization is 1%. This is just a 99% daily Value-at-Risk (VaR) of INR with positive/negative signs denoting gains/losses.
(Hint: This should be a negative number.)
e. During the period from 2/1/2012 to 9/30/2014, what is the percentage of days on which INR appreciated against USD by less than your answer in (d)? Or, in other words, what is the percentage of days on which INR lost in value against USD by more than the (unsigned) 99% daily VaR?
(6) Go to sheet "Question 6." Your task is to find the payoffs of the 6-month receivable of EUR 1,000 and the 6-month EUR/USD forward contract as a function of the future EUR/USD realizations. The forward rate is 1.28. You need to enter calculation formulas in cells B17:D53 and F17:G53. The graphs on the right should change automatically to reflect your results. Once you're done with the calculation, you should be ready to answer the following questions.
a. If you sell EUR 1,000 forward today and, in 6 months, the EUR/USD rate turns out to be 1.15, what will be your net USD payoff (including the original receivable plus a derivative position)? What if the rate is 1.40?
b. If you buy EUR 1,000 forward today and, in 6 months, the EUR/USD rate turns out to be 1.15, what will be your net USD payoff (including the original receivable plus a derivative position)? What if the rate is 1.40?
c. Which of the above strategies is considered hedging in the sense that it establishes the floor (minimum) on the net USD payoff?
Table and formulas used for answer the questions are in attached problem set. pdf file.
Attachment:- Problem-Set-.rar
Attachment:- Problem-Set-.rar