Hi, welcome back. I know today has been, depending on what today means to you, you have been taking breaks, hopefully. This week has been a little bit of a tangent, but on a topic that requires you to go on a tangent. I remind you again that we just did statistics, and we've done that part of statistics that's completely necessary for us to move forward. However, I guarantee you that if you do these statistics and if only you practice with the assignments I've given you, then what will happen is the same skill set will translate into other disciplines. If you remember what we did in each with the distribution, with means, with variances, with covariances, with regression, we basically said that we could use any data or any example. I purposely, following my general practice, I just pull out examples while I'm talking, those that could relate to you and that's the beauty of statistics. As I said, I almost think sometimes like statistics got an edge over finance, almost. Let's get back to why did we do statistics? The beginning was about risk and return, and we know why we're doing risk and return because we want to figure out the cost of capital. But as always, in spite of the fact that we have statistics now in our little toolkit, I'm not going to use formulas. I'm going to go back to why are we doing this? Why risk and return? We all know we are risk-averse, and experiments have been conducted to show that that's the case. But we like return, and turns out that if you look at data, which I'll reveal in a second, and that'll be some really cool data today will be the wrap-up of this week to give you a sense of how reality and the concepts match up so well together. But we like return, and most of us are prepared to take on some risk. If we were so risk-averse that we didn't take on any risk, I think it would be a sad situation, but then things would be very different. Now, we are thinking about taking on risk, however, we don't like it. The good news is we like the return piece of it. But how do we take the risk given that we're risk-averse? We are taking the risk with what in mind? You'll see. In some kind of benefit or return in mind, otherwise, we wouldn't do so, and that's the punchline. But how do we take risk given that we are risk-averse? We hold large, diversified portfolios. I emphasize again, before I even talk about this, that a lot of this part requires individual investment and a thought process that lets you do so. There are a lot of people in the world who can barely consume enough to survive for the next day. I always feel like we have to keep that in mind. That till the world is such a place where all of us can think like this at our individual levels and not have stocks and bonds in every portfolio, but think about the fact that we can save for the future would be a wonderful world to be in. It's not. However, there's a lot of activity in markets, and the hope is more and more families can take advantage of the marketplace and hold portfolios that are large and diversified. Why am I saying large and diversified? Why don't I just say large? You'll see in a second, and we'll do this next week, is that large alone doesn't mean anything. Imagine if you are really fascinated by technology but you are risk-averse, you could hold a very large technology portfolio. In fact, Fidelity and other Vanguard and other companies create such portfolios within industries too. You could hold a very large technology portfolio, but it wouldn't be diversified. It may be diversified within technology, but it's not diversified across all aspects of life. In some sense, the diversification is more important than large and we'll see explicitly next week why that's the case. Now, why are we talking about this? Because the process of holding a diversified portfolio is an attempt to deal with your queasiness in your stomach when you see risk. But what that leads to is the following phenomena, the queasiness will make you hold large portfolios and take risk only if there is some kind of a positive relationship between return and risk. Here's another reason why I like this and anything that I have talked about in finance, is that it's not shockingly counter-intuitive. It took a lot of effort to boil down a lot of thinking and work to simple things. But it's the simplicity of the eventual outcome that's the awesomeness of finance. That's why I like it. It's extremely intuitive. Everybody would agree that if you're risk-averse, you like return, we'll take risk only through spreading our wealth or whatever across multiple assets and diversify our portfolio. But even then, we'll do that only if you benefit from it, otherwise, what's the point taking risk. I hope everybody gets this. I'm going to spend now two significant chunks of time on something that will be on the slide on available for you to look at, and I'll go back and forth talking about these numbers. The good news is all these numbers are real. The bad news is there are a ton of numbers as we go along, just bear with me. Does US data, for example, reinforce the intuition? That is, the intuition being that is there a relationship between taking on risk and the return we get? This data is very famous data. Almost every textbook reports American data. There is a bias towards American data simply because in about 1926, I know the University of Chicago started going back and collecting data, which is very clean data. Then with the development of technology, more data has been available. But this is clean data, very well measured, and so on, and not just randomly selected data. This data I will talk about does not preclude you from looking at data in different countries. But I guarantee you, the pattern that we'll see here will emerge in any country, any context that you're thinking of. One more thought, all the data I'm showing you has to do with things that trade easily, stocks and bonds. I want to caution you that that is not the entire investment of even the American people or outside people in America. Why? Because there are other assets out there, one of which is what? You, human capital. The belief is, as a country progresses economically, more and more of its investments happen in the human capital development. Education and service industries develop faster as you go. There is controversy about that that should America be only a service industry based country and somebody else should do all manufacturing. I would recommend to you sometimes reading Economist because they have some very cool back and forth by leading experts on issues like that. I just wanted to caution you about the fact that this does not measure everything. However, the fact is, it measures a ton, and for a bunch of years. Another point, right up, if you see the slide up there, it's 1926 to 2008 US experience. Everything I'm showing you is portfolios. Why am I showing you portfolios? Because although later in the next slide, I will show you individual securities, I want you to recognize that when you say risk aversion, you almost automatically have to talk about portfolios. Otherwise, what happens is if you say risk aversion and talk only individual securities, there's a mismatch. Your behavior has to match your instincts, and your instincts all of us is to spread our wealth around if we have some. Okay, let's get started. The first column and stare at it, is different types of assets. The first asset is a portfolio of small stocks. It's not stocks that are small but companies that are small. The reason they are separated out is initially, small stocks are more risky, research shows they're early in their stage of development. There's a separate category paid here. S&P 500 is Standard and Poor's 500 stocks, and they are collected in such a fashion that the hope is that they measure all sectors of the economy. As you'll see later, it'll play an important role in how we measure risk. The next category is corporate bonds. Remember, we talked about corporate bonds largely being a US phenomenon. But corporate bonds are the next category within, say, the riskiness dimension. After it is government bonds. What are government bonds? These are bonds that are coupon-paying and typically long-term. Finally, T-Bills, which are treasury bills, are the most traded asset, probably, in the entire world. These are up to one year maturity, zero coupon bonds. Now turns out there are zero coupon bonds that are of longer maturity but they are called strips and I will talk about that. It's not that important to this discussion. But strips are simply more than one year maturity zero coupon bonds. What is on the next column heading? Average returns and you know how to calculate them, that's why I did some data statistics with you. What is 21 percent? 21 percent is the annual return on a large set of small stocks. There's averaging going on twice. One is over time, the second is across a lot of stocks. So this number doesn't have too much error in terms of saying it's just one stock, it's a large portfolio. Hopefully, this measures something that has happened in the past pretty accurately. That's, what would you get? Average rate of return, and what is returned? Let's just go back to our fundamentals, our return has two components, almost always. In the case of bonds, it's coupon and when you sell a bond, what do you get? In the case of a stock, the coupon part is called dividend. It's not promised or anything. That's, in fact, the beauty of stocks. The second component is capital gain or loss during the year, change in prices. You calculate the return, it's 21 percent. Look what the next number is, 12 percent. The difference is nine percent. That's a huge difference. I will encourage you at the end of this to take 100 bucks and make investments in 1926. Remember we did this and see the future value today of these investments. So suppose you put a $100 in small stocks, 100 in S&P 500, 100 in corporate, you'll see what will happen. There will be a dramatic drop as you go down or increase as you go up. S&P 500 12 percent, corporate bonds seven percent, government bonds six percent, and T-Bills four percent. Let's pause there for a second and ask the following question. Suppose you didn't know much about finance but you knew what a return was and you had some sense of what riskiness is, doesn't a pattern emerge? I think a pattern already emerges. That risky things tend to give a much higher return. In the next column is the average risk premium. Let me define what that means, that is the difference between the portfolio that's risky and something that's not risky and we know that if you believe the government is going to pay up, the not risky thing is the treasury bill. So the 21 percent becomes a 17 percent average risk premium because I've just subtracted four percent from it. As we go along, I'm going to just start. First, I want to show you all the numbers and then I'm going to start drawing a little bit on this. Not much, just a little bit. What's the average risk premium on the S&P 500? Eight percent. Three percent on corporate bonds and two percent and government bonds. The reasons for corporate and government bond difference is pretty obvious. It's something that you believe could default versus something that can't or wouldn't, most probably. Till now we are okay. There's a dropping pattern of returns, which is significant. A 17-percent difference ain't that small. In fact, this is per year. In fact, I would say the eight percent difference on the S&P 500, captures the market more in a representative way than small stocks. Because large stocks dominate the marketplace because they're big in size as in market cap and so on. Let's now look at the last column and this is the punchline. Look at the standard deviation. Remember we calculated it? It's the variance's square root. The mean is 21 percent. The standard deviation of small stocks is twice the size of the mean. This tells you that return comes with risk and maybe a lot of risk even though it's a portfolio, and that's life. But let's go to S&P 500, what happens? The return drops substantially to 12 percent and the standard deviation is half of that of small stocks. Go down one more, return drops some more. What happens to standard deviation for government bonds? Drops drastically. Go to government bonds, and this is the only slight anomaly where the standard deviation is slightly off, but this is data and remember, the standard deviation estimates are measured with a lot of error. Finally, Treasury bills. The reason standard deviation is there in Treasury bills is we are looking at a rate of return. Stare at all these numbers, one pattern jumps at you, which is the following. Our gut tells us that if we are risk-averse, we will only take on risk if there is commensurate return in response. Turns out the data supports that and I would say pretty strongly on a broad level. I'm not going to write a paper based on this. If I would, even I would laugh at the paper because this is very simplistic data analysis, but it's pretty powerful too, that on average, large portfolios support the notion that we are risk-averse. I'm trained in always using data to test my thinking, and I think that's an awesome thing that happened with me. That's how I did my research and I think like that, I think that's the thinking that you need to carry with you, is that if you make a statement, you better be willing to support it with data. It's not a personal statement, all of it is because life would be miserable. I told someone, you know I love you. He said, "Show me the data". That's going to be a little miserable way of living. But you know what I mean. This is one set of data and I want to move on to the next one. But before I do, I promised you I would just draw one line. As I'm looking at it, I want to make sure you get what I'm saying. Return goes up. What happens at the same time? Risk goes up. Return and risk are joined at the hip. You know what I mean? They're literally joined at the hip. Let me ask you one question before we go on. Suppose you observe that somebody is holding a portfolio with low risk versus somebody else is holding a portfolio with a high risk, does that mean anything about judgment? What can you say that about that? Remember one thing about return and risk, which the real world always forgets and you will too and I do too, we start focusing on one of it. All the newspapers only talk about this. They never talk about this, almost never, and that to me is a tragedy. For example, open up a newspaper, even the best newspapers of the world will say portfolio X has done better than the S&P 500, nine out of the last 10 years. That doesn't mean anything to me. To me, that's useless information. Unless you say that the risk of S&P 500 was higher than this portfolio in every year. You're not telling me anything. Why? Because whenever you see you return, it comes with risk. Here again, markets are very important. In a market that has gone on for so long, for 80 years, 82 years. That hopefully over time, it has become more efficient in reflecting risk and return opportunities as matching each other. Talking about the last eight years, one final thought. If you look at the risk premium on the S&P 500 of 8 percent, what you'll notice is that it's a very, very large number. I hope you notice that. This number has been around 7 percent in most data when you compare it to other large portfolios and so on, and that's the number we carry in our head. Turns out, if you look historically at all stock markets of the world and they have existed and gone and disappeared. Data shows this number is much lower. The American experience of the last 80-90 years is an aberration. To give you an example, it has a survival bias in it. I think though there's no proof of this, there is enough data pointing to that and intuition suggests that too, that we are not suddenly more risk averse in the US. People are people all over the world. What could be the reason for this huge rate of return difference compared to other stock markets or even the US before 1926? There could be several reasons, as many as you can think of. But I want to point out that survival is one of the reasons, is because it's very tough to come up with other explanations that make as much sense. Just keep that at the back of your mind. Why is it important? Because we're going to use this risk premium and all these numbers to think of our future as we are to be very careful when you're using the past to predict the future. Let's go on to one last thing and then we'll take a break today. I'm going slow in this part because this data is very intuitive and useful and it's not hopefully too painful for you. I'm going to start and show you this and start with this next time. What is this? This is one portfolio right at the end, S&P 500 for 1989-2008 period, different from the period we saw before. In this I am showing you largely what? I'm showing you stocks: Disney, AT&T, Pfizer, General Motors, Alcoa, Home Depot, General Electric, Exxon, Intel, Citibank, Proctor & Gamble. I'll just pick some stocks and their approximate standard deviations. Because I'm not putting decimals and so on, so I'm not going nuts. I want you to just think of one thing and we'll raise issues today and pick up next time. Next time this will be most of our recap context. Stare at these numbers. Think about the one thing that jumps out at you. Just stare at it. Think about the one thing that jumps out at you. Write it down. This is over and above all your assessments and home works, which are largely what? Statistics, that's financial applications. The homework is not that intense by the way, which we're doing statistics so that you get familiar, so please do that. But this is your next homework. Tell me what is the one thing that stares out at you? Once you've identified that one thing, please write it down. Then think about the second point. Why does that one thing happen? What's going on? How do you come up with an explanation of that one thing? The next slide ends with what the heck is going on. At this point, I'm going to leave you with this data and I'm going to leave it up there. What I will also do is I will put both data pieces in a little note for you to look at. Like your assignments are on the web, this will be on the web. I want you to think very carefully about the one thing, don't give me three, the one thing that stands out about this data. Then try to write down what the heck is going on. I don't think that's asking for too much.
