[MUSIC] Let's now look at some real data and see to what extent the currency will contribute to the return of your foreign investment. A typical benchmark used to assess the performance of foreign equity, non-US Equity is the EAFE index that stands for Europe, Australasia, Far East index provided by MCI. And here in this plot in gold, you see the foreign currency return and in green, you see the currency return contribution. And the sum of the gold and green will give you the dollar return. Look at 2003. Almost half of your dollar return is due to this favorable move of the foreign currency. So depreciation of the foreign currency is [INAUDIBLE] a dollar, or likewise the depreciation of the dollar is [INAUDIBLE] other currencies. But in '97 it was the other way around. You almost lost all of the gain you made in the foreign equity because of the depreciation of the foreign currency against the dollar. So, when you see this you might say wow, I should not go and invest in foreign markets because I can get a lot of exposure to currency. This is wrong. Remember you can gain a lot by investing abroad and you can manage this risk if you don't like it. In next video we'll see how you can manage currency risk. Now let's move on and see how this currency now contributes to the risk of your portfolio. So far we have been seeing the contribution to the return. Now we move to the risk. The variance of the dollar return is equal to the variance of the foreign currency return. Plus the variance of the change in exchange rate plus twice the correlation between the foreign currency return and the exchange rate changes. And times the standard deviations for foreign currency and of the exchange rate. So see here that dollar return volatility is not just the sum of the foreign currency volatility and the exchange rate volatility. The risk is not additive which is good for us because of the less than perfect correlation between that exchange rate and the foreign currency return. The currency risk contribution is simply the difference between the volatility of the dollar return and the volatility of the foreign currency return. Let's take an example. A foreign investment has a volatility of 20%, let's assume that the exchange rate changes volatility is 10%. The correlation between the exchange rate changes. And the foreign currency return is at 0. So what would be the risk in domestic currency and the contribution of currency risk. Is it A, the risk in domestic currency is 30% and currency risk contribution is 10%. Or is it B, the risk in domestic currency is 22.4% and currency risk contribution is 2.4%. If you answered A, you didn't get it right. You thought that you can simply add up the two risks, the 20% and the 10% and forgot about the correlation. So if you compute the variance of the dollar return, that's the 20% squared plus the 10% squared, and twice the correlation times the standard deviation, but the correlation here is zero. So you end up with the 20% squared plus a 10% squared, and you take the square root of this sum and you end up with a volatility of simply 22.4%. And a risk contribution then of 22.4 minus the 20 which means 2.4%. So the right answer is b. Let's see now with some real data what is the currency risk contribution to your portfolio. And here we'll distinguish between equity and bonds, specifically sovereign bonds. What you see here is the first column shows you the foreign return risk, so the percentage of the risk that is due to the changes in foreign returns. And the second column shows you the currency risk. Better the same calculation that we did but this is expressing percentage of the total risk, okay? So you see that for all of these markets, whether developed or emerging, the contribution of currency risk is rather small over this period that lies from 1990 to 2013. And that's in general the case. It is a little bit higher notice for emerging markets because of the higher volatility of that currencies. But you see that the large part of the variation is due to the variation in the foreign returns. For sovereign bonds it's different. A large part of the variation is due to the fluctuation of exchange rates. So you're now able to calculate the return and volatility of a foreign asset in your domestic currency and to measure how changes in exchange rates could affect return and risk of your foreign investment. If you dislike currency risks, don't think I'm not investing globally, just remember that you can hatch this risk and that's what we'll see in the next video. [MUSIC]