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Exchange rate risk is the uncertainty of returns to an investor who acquires securities denominated in a currency different from his or her own. The likelihood of incurring this risk is becoming greater as investors buy and sell assets around the world, as opposed to only assets within their own countries. A U.S. investor who buys Japanese stock denominated in yen must consider not only the uncertainty of the return in yen but also any change in the exchange value of the yen relative to the U.S. dollar. That is, in addition to the foreign firm’s business and financial risk and the security’s liquidity risk, the investor must consider the additional uncertainty of the return on this Japanese stock when it is converted from yen to U.S. dollars.
As an example of exchange rate risk, assume that you buy 100 shares of Mitsubishi Electric at 1,050 yen when the exchange rate is 115 yen to the dollar. The dollar cost of this investment would be about $9.13 per share (1,050/115). A year later you sell the 100 shares at 1,200 yen when the exchange rate is 130 yen to the dollar. When you calculate the HPY in yen, you find the stock has increased in value by about 14 percent (1,200/1,050), but this is the HPY for a Japanese investor. A U.S. investor receives a much lower rate of return, because during this period the yen has weakened relative to the dollar by about 13 percent (that is, it requires more yen to buy a dollar—130 versus 115). At the new exchange rate, the stock is worth $9.23 per share (1,200/130). Therefore, the return to you as a U.S. investor would be only about 1 percent ($9.23/$9.13) versus 14 percent for the Japanese investor. The difference in return for the Japanese investor and U.S. investor is caused by the decline in the value of the yen relative to the dollar. Clearly, the exchange rate could have gone in the other direction, the dollar weakening against the yen. In this case, as a U.S. investor, you would have experienced the 14 percent return measured in yen, as well as a gain from the exchange rate change.
The more volatile the exchange rate between two countries, the less certain you would be regarding the exchange rate, the greater the exchange rate risk, and the larger the exchange rate risk premium you would require.
There can also be exchange rate risk for a U.S. firm that is extensively multinational in terms of sales and components (costs). In this case, the firm’s foreign earnings can be affected by changes in the exchange rate. As will be discussed, this risk can generally be hedged at a cost.

Pricing an interest rate swap means finding the fixed rate that equates the present value of the fixed payments to the present value of the floating payments, a process that sets the market value of the swap to zero at the start. Using the time line illustrated earlier, the swap cash flows will occur on days hl, h2,…,hn-l, and h,, so there are n cash flows in the swap. Day h, is the expiration date of the swap. The time interval between payments is m days. We can thus think of the swap as being on an m-day interest rate, which will be LIBOR in our examples.
As previously mentioned, the payments in an interest rate swap are a series of fixed and floating interest payments. They do not include an initial and final exchange of notional principals. As we already observed, such payments would be only an exchange of the same money. But if we introduce the notional principal payments as though they were actually made, we have not done any harm. The cash flows on the swap are still the same. The advantage of introducing the notional principal payments is that we can now treat the fixed and floating sides of the swap as though they were fixed- and floating-rate bonds.
So we introduce a hypothetical final notional principal payment of $1 on a swap starting at day 0 and ending on day h,, in which the underlying is an m-day rate. The fixed swap interest payment rate, FS(O,n,m), gives the fixed payment amount corresponding to the $1 notional principal.

Finally, we note that swaps can be equated to combinations of options. Buying a call and selling a put would force the transacting party to make a net payment if the underlying is below the exercise rate at expiration, and would result in receipt of a payment if the underlying is above the exercise rate at expiration. This payment will be equivalent to a swap payment if the exercise rate is set at the fixed rate on the swap. Therefore, a swap is equivalent to a combination of options with expirations at the swap payment dates. The connection between swaps and options is relatively straightforward for interest rate instruments, but less so for currency and equity instruments. Nonetheless, we can generally consider swaps as equivalent to combinations of options.
In this series of posts, we have learned that swaps can be shown to be equivalent to combinations of assets, combinations of forward contracts, combinations of futures contracts, and combinations of options. Thus, to price and value swaps we can choose any of these approaches. We choose the simplest: swaps and assets.