[MUSIC] Hello, I'm Ines and today we're going to talk about Currency Risk. Whenever you go and invest globally, you face all the currencies. So, it is important to understand what is the contribution of fluctuation and exchange rate to the return and risk of your portfolio. Before starting, bear with me, we need to introduce some mutation that is going to be useful for the rest of this presentation. I denote by PFCt for the value of a foreign investment measured in foreign currency. So, the superscript FC is for the currency and the subscript t is from the time t. So, that's the value of my portfolio measured in foreign currency at time t. To make things easy, I'll assume that the domestic currency is the dollar. Okay? So, we take the perspective of a US investor and we measure everything in dollars. We define the spot rate by St, and that's the dollar value of one unit of foreign currency. How much it cost me to buy one unit of foreign currency. So if you see that the spot rate increases, it means that the foreign currency appreciated vis-a-vis the dollar. And then I can define the dollar price of the foreign investment. I denote it by P$t. Again, the superscript is for the currency now denominated in dollars and the subscript is for the time "t". So, that's the dollar value of the foreign investment. And is simply the foreign currency value multiplied by the spot rate. And then I can define the return on my foreign investment. And that's the capitol gain or loss which is the price at 20 in foreign currency minus the price times zero. When I part the stock for the portfolio, divided by this original price P0 and that gives me the return in foreign currency, FC. I can also compute the return of this foreign investment in dollar terms. So, now I'm computing the capital gain or loss in dollar terms. That's the dollar price time t minus the dollar price at time 0 divided by the original price of the dollar price at time 0. And finally, I define the percentage change in exchange rate by denoted by s, so that the st minus s0 divided by s0. Now, let's see what is the relationship between the dollar return and the foreign return, so that I can see the contribution of exchange rate changes. Remember that dollar return is what? Is simply the dollar value at time t minus the dollar value at time 0 divided by the dollar value at time 0. But the dollar value simply the foreign currency value times the exchange rate, that's what I'm substituting here in this equation that you see in front of you. And then I can manipulate a little bit this equation to get to the following. The dollar return is the foreign currency return plus the change in exchange rate plus this cross product term, the exchange rate changes, multiplied by the foreign currency return. Why does cross product term? Simply because the change exchange rate is not only applied on the original price, but also on the capital gain or loss. So, from here we can compute the currency contribution to the return of this foreign investment. And that's simply, the dollar return minus the foreign currency return, which we can write as the change and exchange rate plus this cross product term ES times the foreign currency return. So, let's now take an example. On February 2015, Maria an American investor bought a portfolio of Brazilian stocks that worth 1000 Brazilian Real. And the exchange rate at the time was at $0.3 per Real. One year later, she sold that 1,200 and exchange rate drop at 0.25. So, what is the dollar return of her portfolio? And what's the currency contribution to this return? You see it here from the table, let's first compute the foreign currency return. So, she bought at 1,000, that's February 2015, let's call it time 0. And one year later, period 1, he sold that 1,200. So, the return is simply 1,200 minus the 1,000, that's 200 capital gain divided by the original price of 1,000 so that's 20% return. Now, in dollar terms, we need first to convert each of these prices in dollar terms. So at time 0, that's the 1000x0.3 dollar per Real exchange rate at the time, and that gives us $300. At time 1, is the 1, 200 times the exchange rate a year later which was at 0.25 but that gives us again $300. So her return in dollar terms is what? Is 0%. She made 20% Because of the appreciation of the Brazilian market, but she lost all of this gain because of the exchange rate that moved against her. So, the brial depreciated against the dollar. The percentage exchange rate was 16.67, so that's the 0.25 minus the 0.3 divided by 0.3, so that's -16.67%. So, what is the currency contribution? Take simply the dollar return minus the foreign currency return, so here it's the 0% minus the 20%, that's -20%. Why it's not just equal to this changing exchange rate of 16.67%? Remember, you need also to take into account the cross product. So, if you take the 16.67% x 20%, that's around 3.3% add it to the 16.67, that gives you the total 20% less. [MUSIC]
