Welcome to the market risk management project. In this course, we've spent a lot of time talking about different types of market risk. Market risk for equities or stocks, market risks for bonds, and also looked at different types of derivatives that you can use to manage that market risk. We then looked at how you can use probabilistic measures and statistical measures to measure that risk and get an idea of exactly what type of losses that you might face as an investor or as a portfolio manager. Now in this project, we're going to go through a process that you would go through as a risk manager. That process starts with identifying a portfolio that you want to measure risk for, looking at the data set that you have for that portfolio but historical data set, then analyzing that data set and coming up with some statistical measures of risk, also the cortosity of the portfolio and so on. Then finally, what we talked about before in the course, coming up with value at risk numbers. What we learned in the course is that value at risk is the risk that won't be exceeded with a certain level of confidence. What we're going to look at in this project, is different levels of confidence and how that affects the value at risk loss number. Let's get started first, by looking at the data set that we're going to use. Art data set covers two years of trading information of trading prices and it's a data set on four equity indexes. We have a portfolio that is globally diversified and it's composed of equity indexes from the US, Japan, China, and the EU. The indexes that we're going to look at are the S&P 500, the Nikkei 225, the Hang Seng Index, and then the DAX index. Now we're going to look at two years of data from those indexes, and basically look at the value of a portfolio of those indexes for two years starting in February of 2018 and ending in February of 2020. Now I've chosen this time period deliberately in order to look at a period before the COVID epidemic, or not exactly before the COVID epidemic, but before the market really had a good idea of how much volatility and risk and uncertainty was going to come from that epidemic. We're going to look at a two-year period because as you can recall from the course, if you're going to analyze a historical data set, then you should have at least two years of data to do your analysis. Two years of data is roughly 500 trading days. Our data set consists of 500 days of trading in each of the four indices. Now, since some of these indices are not denominated in dollars, we're also going to need information about the exchange rate. The exchange rate in this case for the Hang Seng Index, which is based in Hong Kong. We need the exchange rate from a Hong Kong dollar. For the Nikkei index which is based in Tokyo, we're going to need the Dollar-Yen rate. Then for the DAX index which is based in Frankfurt, we're going to need the Euro-dollar rate. We need that information because in order to measure risk we have to measure it in a single currency. In this case, we're choosing the dollar as our reference currency or reporting currency. Now, you don't have to do this, you could also measure the risk in this portfolio in Hong Kong dollars or in yen or in euros, really in any of the currencies that the indexes are based on. Now, this is true of any kind of risk. I mean, you need to measure the risks from the perspective of your investors or your organization, what is their reporting currency? Anyway, let's look at the data. The data that I have shown here are ordered from day zero all the way down to day 500. I'm not going to show you all the way down there but you can see quite a lot of data here. What I have here is our first date is February 26, 2018, and that's day zero. Actually, I have 501 data points here and that will allow me to get 500 daily returns because you need two days to get a return. We're going to be looking at the daily returns for this portfolio of these four indexes over 500 days up to right before the market started realizing that COVID was going to be important. We want to get an idea of whether the market had any sense of the risk that was coming. Or if the market pretty much had no idea that the risk was coming, and you as a risk manager back in 2020, probably wouldn't have said that there was very much risk in this portfolio. Now, keeping in mind that the second part of this project, we're going to actually look at the same data, same portfolio. But we're going to shift our timeframe forward by six months. We're going to look at six must of new data starting in February of 2020, we're going to drop out the first six months of data that you see here, going roughly from February of 2018 to August of 2018. But anyway, so let's just focus on what we're looking at now. We have 500 days of trading data, and four indexes, and we're going to combine this into a portfolio. Now before we combine it into a portfolio and convert each of the non-dollar indexes into dollars, let's have a look at what's going on in each of those indexes over the two-year period. The best way to look at that is just to look at a graph of the index over that two-year time period. Let's look at that. In the upper left-hand corner you see the S&P 500, and this shows over that time period from February 18 to February of 2020, and you can see that pretty much, not a whole lot of volatility there. You see a little bit of a down move here there, and overall though, the market has gone from a level of roughly 2,700 here up to about, let's see, 3,300 here. Now, that's the S&P 500. That's going to be 40 percent of our portfolio. Now I have chosen the portfolio allocations to more or less mirror the market cap of stocks in that particular country. Next, the 30 percent Hang Seng Index and we're doing 40 percent absentee. Now, Hang Seng Index actually was down a little bit over that time period. It started off in a level of about 30,000 a year, and then went down to about 28,000 by the end of a two-year period. Now the Nikkei started off at about 2,500 and ended up around 23,200. So it went up just a little bit. Then the DAX index, which is based in Frankfurt, started off at a level of about 12,500 and ended up at a level of about 13,800. Now the Nikkei they we're giving a 20 percent allocation, and the DAX we're giving a 10 percent allocation. Now, that's the performance of each of the indexes in their own currency. Then what I have shown below there is the performance of Nikkei and the DAX in dollars. You can see that there's not a whole lot of difference there between the performance of the Nikkei index. You see a very slight upward movement in the index over that period, the shape is more or less the same. Now with the DAX index, actually you see something where in dollar terms, the DAX index started off at about 15,500, and then ended up around 14,000 and say about 700. Actually the DAX went down a little bit, if you looked at it in dollar terms. Now, you know what's going on there. Why is it going up in Euro terms and then down in dollar terms. Obviously, it's because the Euro got weaker or the dollar got stronger, but basically that's the same thing. Anyway, now you have a good look at the data, and you have an idea of overall what the individual indexes have been doing, and then in the next part of our project, we're going to combine them all into a portfolio and then look at some statistical measures of how much risk is there. Looking at things like volatility and kurtosis and so on. For now, you've got an overview of what is going on in your portfolio during the historical time period, and you have a sense that really there hasn't been that much risk there, but now we're going to actually measure that risk and measure it in our portfolio with our allocations.
