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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.

In this section, we explore how to price and value three types o f equity swaps: ( I ) a swap to pay a fixed rate and receive the return on the equity, (2) a swap to pay a floating rate and receive the return on the equity, and ( 3 )a swap to pay the return on one equity and receive the return on another.
To price or value an equity swap, we must determine a combination of stock and bonds that replicates the cash flows on the swap. As we saw with interest rate and currency swaps, such a replication is not difficult to create. W e issue a bond and sell a bond, with one being a fixed-rate bond and the other being a floating-rate bond. I f we are dealing with a currency swap, we require that one o f the bonds be denominated in one currency and the other be denominated in the other currency. With an equity swap, it would appear that a replicating strategy would involve issuing a bond and buying the stock or vice versa, but this is not exactly how to replicate an equity swap. Remember that in an equity swap, we receive cash payments representing the return on the stock, and that is somewhat different from payments based on the price.
Pricing a Swap to Pay a Fixed Rate and Receive the Return on the Equity: By example, we will demonstrate how to price an n-payment m-day rate swap to pay a fixed rate and receive the return on equity. Suppose the notional principal is $1, the swap involves annual settlements and lasts for two years (n = 2),and the returns on the stock for each o f the two years are 10 percent for the first year and 15 percent for the second year. The equity payment on the swap would be $0.10 the first year and $0.15 the second. I f ,    however, we purchased the stock instead o f doing the equity swap, we would have to sell the stock at the end o f the first year or we would not generate any cash. Suppose at the end o f the first year, the stock is at $1.10. W e sell the stock, withdraw $0.10, and reinvest $1.OO in the stock. At the end o f the second year the stock would be at $1.15. W e then \ell the stock, taking cash of $0.15. But we have $1.OO left over. To get rid of,or offset,this cash flow, suppose that when we purchased the stock we borrowed the present value of $1.00 for two years. Then two years later, we would pay back $1.00 on that loan. This procedure would offset the $1.00 in cash we have from the stock. The fixed payments on the swap can be easily replicated. I f the fixed payment is denoted as FS(O,n,m),we simply borrow the present value o f FS(O,n,m) for one year and also borrow the present value of FS(O,n,m)for two years. When we pay those loans back, we will have replicated the fixed payments on the swap.Equity

Recall the four types of currency swaps: (1) pay one currency fixed, receive the other fixed, (2) pay one currency fixed, receive the other floating, (3) pay one currency floating, receive the other fixed, and (4) pay one currency floating, receive the other floating. In determining the fixed rate on a swap, we must keep in mind one major point: The fixed rate is the rate that makes the present value of the payments made equal the present value of the payments received. In the fourth type of currency swap mentioned here, both sides pay floating so there is no need to find a fixed rate. But all currency swaps have two notional principals, one in each currency. We can arbitrarily set the notional principal in the domestic currency at one unit. We then must determine the equivalent notional principal in the other currency. This task is straightforward: We simply convert the one unit of domestic currency to the equivalent amount of foreign currency, dividing 1.0 by the exchange rate.
Consider the first type of currency swap, in which we pay the foreign currency at a fixed rate and receive the domestic currency at a fixed rate. What are the two fixed rates? We will see that they are the fixed rates on plain vanilla interest rate swaps in the respective countries.
Because we know that the value of a floating-rate security with $1 face value is $1, we know that the fixed rate on a plain vanilla interest rate swap is the rate on a $1 par bond in the domestic currency. That rate results in the present value of the interest payments and the hypothetical notional principal being equal to 1.0 unit of the domestic currency. Moreover, for a currency swap, the notional principal is typically paid, so we do not even have to call it hypothetical. We know that the fixed rate on the domestic leg of an interest rate swap is the appropriate domestic fixed rate for a currency swap in which the domestic notional principal is 1.0 unit of the domestic currency.
What about the fixed rate for the foreign payments on the currency swap? To answer that question, let us assume the point of view of a resident of the foreign country. Given the term structure in the foreign country, we might be interested in first pricing plain vanilla interest rate swaps in that country. So, we know that the fixed rate on interest rate swaps in that country would make the present value of the interest and principal payments equal 1.0 unit of that currency.
Now let us return to our domestic setting. We know that the fixed rate on interest rate swaps in the foreign currency makes the present value of the foreign interest and principal payments equal to 1.0 unit of the foreign currency. We multiply by the spot rate, So, to obtain the value of those payments in our domestic currency: 1.0 times So equals So, which is now in terms of the domestic currency. This amount does not equal the present value of the domestic payments, but if we set the notional principal on the foreign side of the swap equal to l/So, then the present value of the foreign payments will be So(l/So) = 1.0 unit of our domestic currency, which is what we want.