Hi. My name is David Hsieh. I'm a finance professor at Duke University's, Fuqua School of Business. I have a PhD from the Economics Department at MIT, and I have been doing research on financial markets for 40 years. Much of this research is useful in understanding and managing financial risk. In this course, I will give you an introduction to financial risk management with some numerical examples using R. The main goal of financial risk management is to quantify the risk of a portfolio. This is of interest to banks, hedge funds, insurance companies, university endowments, and pension funds. They have portfolios of assets and liabilities. The values of assets and liabilities change over time because of movements in financial markets. One of their main concerns is to make sure that the value of assets do not fall below the value of liabilities. In this course, we will analyze real-world data using the program R. We will assume that students have some basic knowledge of R, finance, and statistics. At the level say of an introductory course in each one. We are not going to write a lot of code in R. We will provide some sample R in the lectures. Short exercises will be used to reinforce learning. The key concepts in risk management is to understand risk factors. The value of assets and liabilities depend on many risk factors which are common sources of risk that are not diversifiable. From your basic finance course, you have learned about diversification, that is, not putting all your eggs in one basket. For example, you do not want to invest all your money in just one or two stocks, you want to spread your investments into many stocks so that if any one of the stocks drops in value, it will not greatly hurt the overall portfolio. Now in your basic finance course, you also learned that stocks tend to move up and down together in response to economic conditions such as business conditions, monetary policy. We refer to these common sources of risk using the term risk factors. Here are some examples of risk factors: equity indices, interest rates, foreign exchange or FX rates, commodity prices, and inflation. We will not be concerned with idiosyncratic risk, which is the risk that is unique to a stock but not to other stocks because idiosyncratic risk is diversifiable. The main tools of our analysis will be something called value at risk or VaR, unexpected shortfall of our portfolios. To give you a real-world example of risk management, let me start with the 10K filing from JP Morgan in 2016. The 10K is an annual document filed by all US public companies with the Securities and Exchange Commission or the SEC. It contains detailed financial information about the firm. The table on this slide is a simplified balance sheet of JP Morgan. Now on the left-hand side of the table are the assets held by the bank. You can see that JP Morgan has about $2.5 trillion worth of assets. On the right-hand side are the banks liabilities, which comes to about two and a quarter trillion dollars. The difference is about $250 billion of shareholder equity. Now when a bank makes money, that is, when earnings on the assets on the left-hand side of the balance sheet exceeds the cost from the liabilities on the right-hand side of the balance sheet, the shareholders would gain. However, when the assets suffer losses which happens say, when a borrower defaults on a loan, then the losses come out of shareholder equity. If the value of assets fall below the value of liabilities, then the bank becomes bankrupt. So the shareholders and managers of JP Morgan are very interested to understand how the value of their assets are related to the risk factors that we just talked about. Now in JP Morgan's 10K filings, there is a long discussion about risk management. I have listed some of them on this slide. In this course, we will be focusing on what is called market risk management which is highlighted in red on this slide. JP Morgan uses a graph to show their market risk. Each bar on this graph represents gains and losses of the assets that are related to market risk in a given day in 2016. The gains are bars above the horizontal axis and the losses are bars below the horizontal axis. The dark line represents the banks value at risk measure on each of those days. In this chart, JP Morgan is showing a one day VaR at the 95 percent confidence level. This is always a negative number. The losses for that day should be no worse than the VaR with 95 percent probability. Now if JP Morgan's risk management VaR is correct, the actual losses in the vertical boss should not go below the blue dark line more than five percent of the time. As you can see from the chart, the actual daily losses in the vertical bars are mostly above that dark VaR line. So in 2016, JP Morgan's risk management VaR did a good job. In this course, I will show you how to produce a similar chart for a portfolio of stocks. By now, you must be guessing that value at risk has a lot to do with probability and statistics and you are absolutely right. Risk management in general and Value at Risk in particular, uses a lot of statistical analysis. So we need a good statistical tool kit. First, we need to know and we need to have an understanding of which risk factors are important in our portfolio. If we are not sure which are the important risk factors, there are statistical methods to help us answer this question. But for the purpose of this course, we assume that we already know the answer to this question. Now once we know which risk factor is important, we need to understand the distribution of the returns of the risk factor. We are mostly concerned with the shape of the return distribution, is it normally distributed or not? If we find that the distribution is not normally distributed, we would want to know if the tails of the return distribution is heavier than the normal distribution. Now beyond the shape of the distribution, we also want to know how predictable are the returns of the risk factors. Are they serially correlated? Do they exhibit volatility clustering? If either answer is yes, then there is information in the history of the risk factor returns that can help us to predict their future distribution. In this course, we will apply our statistical toolkit to a very simplistic setting using real-world data. This will help us understand the key ideas in value at risk and expected loss calculations, which are applicable to much more complicated settings. We will need a statistical program called R to perform these calculations. We recommend using Microsoft's open R version along with the free edition of RStudio. Now please go to exercise one, which will show you how to setup R.