[MUSIC] Hello, I'm Ines, and today we're going to talk about how you can hedge currency risk. If you're concerned about how fluctuation and exchange rate can affect the return and risk of your portfolio. You should still invest abroad, but just properly hedge your currency risk exposure. How do you do that? Well, simply, all you need to do if you're in a hedge with forwards is to sell the foreign currency Forward. We can also say that you're short the forward contract. Let me denote by F T with a subscript t, the forward rate which is known at time 0 today, with maturity t. Now, the subscript here indicates the maturity of the forward contract. Now, if you decide to hedge, you don't know the future value of the foreign portfolio. All you know is that market value today of this portfolio. So that's the amount that you would hedge. And now, we want to compute the headed return and compare this to the unhedged return. How do we do that? We start by computing the capital gain or loss in. Our domestic currency, we still keep the dollar as our domestic currency. So we want to compute the capital gain or loss in dollar amount. And that's the dollar price at time T minus the dollar price at time 0 which is again simply the value in foreign currency multiplied by the spot rate at time t minus the value of the foreign currency at time zero times the spot rate. We also have this forward contract and at expiration what we're going to do is we buy at the spot rate as the because the value of the forward rate at that time will just be conversation to the spot rate and we sell the currency at the forward rate, so the gain and loss we make on the forward position is FT-ST. And that's multiplied by the foreign currency value that we decided to hedge. So the P zero FC. The initial amount of our foreign investment. Now, the net profit hedged is just the set of this too. So the change in the dollar value plus the dollar profit or loss on this forward position and that gives us what you read here. In that computer return, all I need to do is just divide by the dollar value initial value of the foreign investment that is the paid UFC times to zero. And if you divide by this what you get is the end hedged dollar return, that's the first part, the end hedged dollar return plus the return on this forward position which is actually the difference between the forward rate and the spot rate divided by the spot rate at time zero. If you still remember the case of Maria, she was bullish about the Brazilian market and she bought on February 2015 a portfolio of Brazilian stocks for 1000 Real. But then, she was concerned about the political state in Brazil and that could maybe affect exchange rates. The real could depreciate against the dollar. So she decided to hedge her current position, to sell forward the 1000 real at the forward rate and the forward rate. At that, time was at 0.3. So the dollar per Real, 0.3. And the spot rate on February 2015 was also at 0.3. A year later, the portfolio of Brazilian stocks went up 1,200 but then the exchange rate indeed move against Maria. The Real depreciated and it was at 0.25. So let's now see how we can compute the hedged return and how that compares to the unhedged return? This is the same example we looked at before but now we're assuming that Maria is hatching her currency risk. Let's compute again this unhatched return. First of all, let's compute the dollar return in foreign Kara season real. So, that's the 1200 minus 1000 divided by the 1000, that's 200 capital gain divided by 1000, that's 20% return. The change in exchange rate is -16.67%. Now if you add up the Real return plus the change in exchange rate plus the cross product, the change in exchange rate times the real return, you will get the 0% or we could have also computed this an hedged dollar return as simply the 1,200 multiplied by the exchange rate at 0.25. So that's 300 minus the initial dollar value which is 1000 X 0.3, that's 300 divided by 300. So that's 0 divided by 300 at 0% return. Now, let's see what would be the hedged return for Maria for the investment. The dollar profit on the stock market is what? Is does change in dollar value which is $300 minus $300, 0. But her possession on the forward contract Is now positive. She's selling at 0.3, but then at time t she can buy the currency at just 0.25. So she made this gain of 0.3 minus 0.25 per foreign currency and since she's hedging that 1000 A Real position, so this applies on this 1000. We're multiplying this gain by 1000 and that give us $15 gain. If we sum up two, we get the 0 + 50. So that's the hatchet return $50. If you want to express in terms of return, we divide this 50 by the 300 original dollar value of the foreign investment and that give us 16.7%. So that's the hedged return. That we could also have computed simp using our formula. The hedged return is equal to the end hedged return, 0% plus the fold rate, at time t minus portrayed at time t divided by this portrayed at zero. And this difference, this gain in this forward position divided by this pot-rate is the 16.7 % plus the zero that gives us 16.7%. So you see here that Maria is not perfectly hedged. The real return on her portfolio is 20% but now the dollar return is 16.7%. The difference is simply because is hedging only the original amount, the 1,000 Real but not the typical gain or loss in the Brazilian market. And this difference is exactly the cross product that change in exchange rate times the foreign return 16.67% times the 20% the 3.3%. Alternatively, she could have that of hedging the expected value of the portfolio, but that's still risky, because the realized value could end up higher or lower than her expectation. So now, you should be able to know how to hedge currency risk using forwards and to compute hedged returns and compare that to the unhedged returns. [MUSIC]