Currency Risk Problem[1]
It is July 1, 2002, and international entrepreneurs Clifford & Kearns (C&K) are concerned about volatility in the exchange rates between U.S. dollars and certain European currencies.
C&K have incurred costs in dollars to develop, produce, and distribute merchandise to Norway, Switzerland, and Great Britain, for which they expect to realize revenues in 12 months. Specifically, they expect to earn 1 million units each of British pounds, Swiss francs, and Norwegian kroner. Based on current exchange rates, this should result in $2,337,700 in revenue (see current rates, Exhibit 1).
POUNDS/$US / FRANCS/US$ / KRONER/US$0.6533 / 1.4845 / 7.4940
Exhibit 1 — Current Exchange Rates, July 1 2002
Revenue /Unfortunately, it is possible that one or more of these currencies could devalue against the dollar in that one year, causing C&K to realize a smaller total revenue (in dollars) than expected. C&K has turned to their investment bank, Nuccio, Noto, and Rizzi (NNR) for advice. NNR has recommended buying 1.3 million 1-year Euro put options with a strike price of $0.98, for $0.0432 each. NNR claims that this hedging strategy will substantially decrease the risk of a large loss due to exchange rate fluctuations.
(a) Create a simulation model to study the “unhedged” distribution of revenue for C&K, using the historical exchange rate data in Exhibit 2. Make a histogram and report summary statistics. What is the 5% value at risk (VAR) for C&K’s revenue from these three countries over the next 12 months?[2] What is the probability that C&K’s revenue will be less than $2,087,700 (i.e., a $250,000 loss or worse)?
(b) Create a simulation model to study the “hedged” distribution of revenue for C&K. Make a histogram and report summary statistics with the policy recommended by NNR. What is the 5% VAR for C&K’s revenue from these three countries over the next 12 months? What is the probability that C&K’s revenue will be less than $2,087,700?
POUNDS/$US / FRANCS/US$ / KRONER/US$ / EURO/US$3-Jan-00 / 0.6146 / 1.5808 / 7.9640 / 0.9847
1-Feb-00 / 0.6192 / 1.6540 / 8.2770 / 1.0276
1-Mar-00 / 0.6310 / 1.6568 / 8.3115 / 1.0309
3-Apr-00 / 0.6258 / 1.6587 / 8.4640 / 1.0460
1-May-00 / 0.6428 / 1.7135 / 8.9050 / 1.0965
1-Jun-00 / 0.6705 / 1.6878 / 8.9400 / 1.0745
3-Jul-00 / 0.6607 / 1.6323 / 8.5880 / 1.0498
1-Aug-00 / 0.6670 / 1.6758 / 8.8850 / 1.0837
1-Sep-00 / 0.6847 / 1.7230 / 9.0108 / 1.1120
2-Oct-00 / 0.6814 / 1.7322 / 9.1269 / 1.1356
1-Nov-00 / 0.6919 / 1.7765 / 9.2020 / 1.1650
1-Dec-00 / 0.6957 / 1.7285 / 9.2475 / 1.1409
2-Jan-01 / 0.6677 / 1.6075 / 8.7600 / 1.0565
1-Feb-01 / 0.6768 / 1.6330 / 8.7550 / 1.0656
1-Mar-01 / 0.6871 / 1.6557 / 8.8650 / 1.0763
2-Apr-01 / 0.7042 / 1.7317 / 9.1610 / 1.1333
1-May-01 / 0.6974 / 1.7255 / 9.0540 / 1.1189
1-Jun-01 / 0.7062 / 1.7992 / 9.4538 / 1.1832
2-Jul-01 / 0.7058 / 1.8003 / 9.4030 / 1.1827
1-Aug-01 / 0.6978 / 1.7158 / 9.0980 / 1.1373
4-Sep-01 / 0.6923 / 1.7075 / 8.9380 / 1.1276
1-Oct-01 / 0.6764 / 1.6196 / 8.8244 / 1.0918
1-Nov-01 / 0.6840 / 1.6295 / 8.8200 / 1.1057
3-Dec-01 / 0.7034 / 1.6550 / 8.9790 / 1.1240
2-Jan-02 / 0.6920 / 1.6424 / 8.8775 / 1.1073
1-Feb-02 / 0.7063 / 1.7179 / 9.1050 / 1.1610
1-Mar-02 / 0.7047 / 1.7060 / 8.8875 / 1.1558
1-Apr-02 / 0.6941 / 1.6607 / 8.7450 / 1.1356
1-May-02 / 0.6839 / 1.6010 / 8.3500 / 1.1035
1-Jun-02 / 0.6705 / 1.6878 / 8.9400 / 1.0745
1-Jul-02 / 0.6533 / 1.4845 / 7.4940 / 1.0108
Exhibit 2 — Historical Exchange Rates
B60.2350 2 Prof. Juran
[1] David Juran, 2002.
[2] The term “value at risk” refers to a widely used measure of risk. The value that defines the lower 5% tail of the distribution of profit/loss over some specified period of time is called the “5% value at risk”.