Title 2.8 Exchange Rate Calculations.pdf ✅

1. An analyst gathers the following information related to the New Zealand dollar (NZD) and the Australian dollar (AUD): Selected Exchange Rate Information Spot exchange rate (NZD/AUD) 1.1800 Arbitrage-free one-year forward exchange rate (NZD/AUD) 1.1974 Dealer offered one-year forward exchange rate (NZD/AUD) 1.1700 New Zealand one-year interest rate 3.0% Australian one-year interest rate 1.5% Based on this information, the maximum arbitrage profits (in AUD) are closest to: A. 0.0120  B. 0.0238 C. 0.0276 Explanation When the risk-free interest rates of two countries are different, the forward rates of their currencies must be priced to prevent arbitrage profit in an efficient market. The forward rate calculation is based on the spot rate, the interest rates, and the length of the forward period. In this scenario, since a dealer is offering a rate of 1.1700 NZD/AUD, which differs from the arbitrage-free rate, arbitrage profits are possible. According to the arbitrage-free rate, AUD 1.000 should purchase NZD 1.1974. However, using the dealer quote, AUD 1.000 only purchases NZD 1.1700. Therefore, in the market, the AUD is underpriced and the NZD is overpriced. Arbitrage profits can be earned by committing today to sell (ie, deliver) the overpriced NZD and to buy (ie, take delivery of) the underpriced AUD through a forward exchange rate contract. One of the key elements of arbitrage is that investors do not risk their own funds, but instead borrow to initiate the transaction. In this scenario, the first step is to borrow AUD to obtain the NZD, which will be invested and eventually delivered under the forward contract. The complete steps to exploit this opportunity are as follows:

2. If spot exchange rate quotes are 0.1427 CAD/SEK and 0.1366 CAD/NOK, the no-arbitrage SEK/NOK spot rate is closest to: A. 0.0195  B. 0.9573 C. 1.0447 Explanation A cross exchange rate can be derived by cross multiplying two other rates. Cross rates are commonly used to derive an exchange rate for a seldom-quoted currency pair, but they can also be used to determine whether a quoted rate is fairly priced. One currency must be common to both cross-multiplied rates. In this scenario, the SEK/NOK cross rate is calculated by cross multiplying the CAD/SEK and CAD/NOK exchange rates. Since both quotes have CAD in the numerator, the steps to calculate the cross rate are as follows: This cross rate is referred to as the no-arbitrage rate since it is calculated from observed market rates. Here, any SEK/NOK exchange rate other than 0.9573 would allow an investor to earn arbitrage profits by selling the relatively overvalued currency and buying the relatively undervalued currency. (Choice A) 0.0195 results from failing to invert the CAD/SEK quote before multiplying it by the CAD/NOK rate. (Choice C) 1.0447 results from incorrectly inverting the CAD/NOK quote rather than the CAD/SEK rate. Doing so results in the NOK/SEK cross rate instead of the SEK/NOK rate. Things to remember: Cross rates result from multiplying two separate exchange rates to derive a third rate. They can be used to provide an exchange rate between two currencies that are not commonly traded or to determine whether a quoted rate is priced fairly. Calculate and interpret currency cross-rates LOS Copyright © UWorld. Copyright CFA Institute. All rights reserved.
3. A GBP/USD forward exchange rate quoted at positive forward points most likely indicates that GBP: A. is expected to appreciate against USD.  B. is trading at a forward discount relative to USD. C. has an interest rate that is lower than the USD interest rate. Explanation A forward exchange rate is the amount of one currency that can be exchanged for one unit of another currency in the future; this rate can be quoted by forward points. The forward exchange rate is determined by adding the quoted number of positive or negative forward points, also known as pips, to the price currency in the spot rate quote. If there are: Positive forward points, then the specified number of pips is added to the spot rate to determine the forward exchange rate. In this scenario, it takes more GBP (ie, price currency) to buy USD 1 at the forward rate than at the spot rate. This means each GBP is worth less relative to the USD in the forward market, so the GBP is trading at a forward discount. Negative forward points, then the specified number of pips is subtracted from the spot rate to determine the forward exchange rate. In that case, it takes fewer GBP to buy USD 1 at the forward rate than at the spot rate. This means each GBP is worth more relative to the USD in the forward market, so the GBP is trading at a forward premium. (Choice A) The positive points signal that it will take a greater amount of GBP to buy USD 1 at the forward rate than at the spot rate and that market participants expect the GBP to depreciate against the USD. (Choice C) A forward exchange rate greater than the spot rate indicates that the price currency interest rate is greater than the base currency interest rate. Things to remember: Forward discounts or premiums refer to the value of a currency at the forward versus the spot exchange rate. Positive forward points indicate it takes more of the price currency to buy one unit of the base currency at the forward rate (ie, in the future) and the price currency is trading at a forward discount. Explain the arbitrage relationship between spot and forward exchange rates and interest rates, calculate a forward rate using points or in percentage terms, and interpret a forward discount or premium LOS Copyright © UWorld. Copyright CFA Institute. All rights reserved.