Session 4: Defining and Measuring Risk

We're now in session four of a 36 session corporate finance class. And we're starting in the meat and potatoes part of corporate finance. In this session, I want to define risk, a central measure in any financial decision. I want to look at conventional definitions of risk and how financial theory measures risk. In the process, we will set up the estimation questions that'll be coming up in the next few sessions. In this session, we're going to start a discussion of hurdle rates. To put it in perspective, remember we've talked about the objective in corporate finance. It's to maximize firm value. If you accept that objective, the next question becomes picking the right projects, and to pick projects right, you need a hurdle rate for projects. So what we're effectively talking about is that sub box in the big picture. The hurdle rate should be higher for riskier investments and lower for safer investments. And to put that hurdle rate in place, we need to measure risk and convert it into a number, 12%, 15%, 18%. So let me start off by giving you the building blocks for a hurdle rate. I call it a benchmark. And what I mean by a benchmark is when you make an investment, you need to tell me what you need to make on that investment to break even. Not even to be happy, but to break even. And that benchmark becomes the hurdle rate. So let's not make this more complicated than it has to be. If you ask me what the hurdle rate for an investment should be, there are two pieces to it. The first is what I would make on an investment with absolutely no risk. Let's call that the riskless rate for the moment. And then I'm gonna add a risk premium on top to reflect the fact that some investments are riskier than others. And the riskier the investment, the larger that risk premium. So fundamentally, there are two questions I need to answer to put this into practice. The first, I need to measure risk. What do you mean by risk? Second, I need to be able to convert that risk measure into a risk premium. So let's start with the first of those two questions. What is risk? I know if you've taken a finance class, you've been programmed already. You tend to think of risk in terms of statistical terms, variance, volatility, or maybe even Greek alphabets, betas. But my favorite definition of risk is several thousand years old. It's a Chinese symbol for crisis or big risk. The Chinese symbol for crisis or big risk is actually a combination of two symbols, danger and opportunity. Risk is equal to danger plus opportunity. That's the perfect way to think about risk. Risk is neither good nor bad. It's a combination of danger and opportunity. And the reason I like that linkage is we all like opportunity, right? We all want to make 70% returns. And this definition cautions us. It says, look, if you wanna make 70% returns, be willing to live with a lot of danger. You don't like danger? Then don't ask for 70% returns. Think of how many mistakes in investing in corporate finance would be avoided if we remembered that linkage. We tend to fall for fads and scams when we think we can be exposed to opportunity without being exposed to danger. One way to think about what we're gonna try to do in corporate finance is we're measuring the danger in an investment and asking, how much opportunity do I need to compensate me for taking that danger? We're not bungee jumpers in corporate finance. We don't take on risk for the sake of taking on risk. We take on risk because we expect to get rewarded for taking that risk on. So here's what I'm gonna try to do. I'm gonna try to take everything I know about risk and return models in finance and fit it into a single page. Might take some doing, but I don't wanna spend sessions after sessions after sessions talking about theory of risk and return. So here's how I think about risk and return models in finance. In fact, the reason I'm able to compress them into one page is the first two steps in the derivation are exactly the same for every risk and return model in finance. In the first step, we defined risk as the deviation of actual returns around an expected return. What am I talking about? Let me give you a couple of examples. Let's assume you have a one-year time horizon and you buy a one-year US Treasury bond. Let's for the moment assume that the US Treasury has no default risk. If the one-year Treasury bond right now is a yield of half a percent, if at the end of the year of holding period, I came and knocked on your door and asked, how much do you make on your investment? The answer is always gonna be half a percent. That is a truly riskless investment where the actual return is always equal to the expected return. Let's move one step up the ladder. Let's assume you buy a ten-year US Treasury bond and you still have a one-year time horizon. At the end of the year, if I come and knock on your door and ask you what return you made on your bond, part of it is gonna be certain. The coupon is gonna be guaranteed. But the price could have changed, because every time interest rates change, prices change. So a ten-year T bond is not risk-free if you're looking at a one-year time horizon. Now if you bought a stock, let's say Google, and I came to you at the end of the year and asked you what did you make on the stock, you can be almost guaranteed that you will never make what you expected to make at the start of the period. So if you expected to make a 15% return and you got lucky, you might have made an 80 or 100 or 150% return. If you weren't, you might have dropped 30%. That's a very risky investment. Notice that in all three cases, I defined risk by looking at what happens over the next year. And it's a point I wanna emphasize. There is no risk in the past. All risk is in the future. Unfortunately, all our risk measures come from looking backwards. But risk is always in the future. So the first step in every risk and return model in finance is we define risk as the deviation of actual returns around an expected return. And the greater the deviation, the riskier the investment. So far, so good, right? It's the second step that gives people trouble. The second step, I say that when you're exposed to the risk in investment, don't expect to get rewarded for all that risk. You say, why not? Let's take an example. Let's assume you invest in Disney. Think of all the risks you're exposed to. You're exposed to the risk that the next movie they come up with might not make as much money as they thought it would and might even lose the money. Remember the Lone Ranger. The other example is maybe that California Adventure theme park they've invested a billion dollars in over the last few years might not pay off. Those are risks that affect Disney and just Disney, right? Disney is also part of the broadcasting business. Any loss that affect the broadcasting business will affect Disney and maybe 5, 10, 15 other companies in that business. That's risk that affects a few companies. But let's assume interest rates go up a lot in the next few months. That's risk that affects not just Disney, but almost every company. The reason I'm separating risk that affects a few companies from risk that affects most companies is here's where we make a distinction. If you're an investor who's diversified and in corporate finance, all risk and return models make the assumption that the marginal investor looking at a company, and we'll come back and define marginal investor in a moment, is a diversified investor. You're saying, so what? If you're diversified, you own stock in Disney and maybe 50 other companies. Risk that affects one or a few firms will tend to average out. Average out in what sense? For every company where something better than expected happens, in another company, something worse than expected will happen. Things will average out across your portfolio. It's a law of large numbers in action. However, risk that affects most or all companies, you cannot diversify away. So in finance, we assume that because the marginal investor is diversified, he or she does not care about risk that affects a few companies. That's called firm-specific risk, but does care about risk that affects most or all companies. And that's called market risk, it's macro risk. And what we try to measure and bring into a hurdle rate is only the latter, market risk or macroeconomic risk. And that's where the different risk and return models in finance part ways. The oldest risk and return model in finance is called the capital asset pricing model or the CAPM. Makes the assumption that there are no transactions cost and that nobody knows which stocks are cheap or expensive. If you make those assumptions, you will diversify and keep diversifying till you have every single traded asset in the world in your portfolio. That's called the market portfolio. And since all of us hold that portfolio, the risk of an investment becomes a risk added to that market portfolio. That's captured with a single number. It's called the beta. The next time you use beta, remember all the baggage you're carrying with you when you use a beta. But in the CAPM, the risk that cannot be diversified away is captured in a single beta. For a few years, perhaps as long as 14 or 15 years, that was the only model in town. In 1978, Steve Ross at Yale said, this is crazy. Why are we trying to measure all of that market risk in one beta? Why don't we allow for multiple sources of market risk and measure the beta against each one separately? Nice idea, right? When he first came up with it, people said, well, how will we know how many measures of market risk there are and what those betas are? He said, no problem. Give me some stock price data and I'll tell you. And he did. He took a long period of stock price history and he let the computer go on a search mission looking for common patterns or factors. The computer came back and said, we found five factors, and here are the betas for each company against each factor. That's called an arbitrage pricing model, where you have multiple unnamed economic factors and betas against each one. You can come up with a hurdle rate using that model, but unfortunately, it doesn't have much intuitive feel to it, because those factors remain unspecified. Now in the decade following the arbitrage pricing model, people tried to attach macroeconomic names, interest rates, term structure, inflation, GDP growth to those factors. And when you do that, you've gone from an arbitrage pricing model to a multi-factor model. That's much better, right? Multi-factor models actually do much better in explaining the past, but the factors themselves are very unstable. What I mean by that is the macroeconomic factors that drove stock prices in the last decade might not be the factors that drive them in the next decade. As a consequence, neither the arbitrage pricing model nor multi-factor models caught on. Now to complete the story, in the early 1990s, Gene Farmer and Ken French, two professors at the University of Chicago, decided that rather than try to measure risk, they'd let the market tell us what risk was. What I mean by that is they went back and looked at a long period of stock price history to see what kinds of companies had earned higher returns. They found, for instance, that small companies had earned higher returns than large market cap companies. Small price-to-book companies had earned much higher returns than high price-to-book companies. So what does that mean? They made a leap of faith. They said, that must mean that small market cap companies are riskier than large market cap companies. Low price-to-book companies are riskier than high price-to-book companies. Didn't ask why, and they did not care. Those models are called proxy models. And effectively, you've given up on measuring risk, you let something else stand in. Every risk and return model you will see out there is either going to be one of these models or a combination of these models. Keep in mind, though, that they're all built on the presumption that the marginal investor is a diversified investor. Now, given the fact that many of these models post-date the CAPM, they've come in the last 10, 20, 30 years, you'd think that the CAPM would be a dead model. But you'd be wrong. A lot of people still use the CAPM, including me. And when I use the CAPM, there are a lot of people who pick apart that assumption. They say, why do you continue to use a model that is the oldest model out there and might, in fact, be a flawed model? In fact, there are three critiques I hear about the CAPM, and I'll list all three. The first is that it makes unrealistic assumptions. Does it? Absolutely. But that doesn't bother me. Because I used to be an econ major in a previous lifetime, and I remember those models that made realistic assumptions that nobody could use. I'd much rather have a model with unrealistic assumptions that I can use, rather than one that makes realistic assumptions that nobody can use. The second critique I hear is my parameters might be wrong. My data might be wrong. My risk-free rate might be wrong. My risk premium might be wrong. Absolutely true. But any time you're estimating the future, you are going to be wrong. If you let that be the dividing line, you will never use a model. The third critique, though, cuts to the bone. And that is that the model doesn't work very well. It is true that if the CAPM were the right model, beta should explain most of the differences in returns across talks of very long time periods. Beta doesn't. In fact, that was the basis for the former French proxy model critique, where they said, hey, beta doesn't work very well. Let's look for something that does better. That, again, is something you've got to factor in. It is true that betas don't explain past returns very well. Part of the reason for that, I think, is people are not very good about estimating betas. And we can improve the proportion of return variance that can be explained by betas if we do a better job. I still believe, though, that even if you do a better job, the bulk of the variation of returns will never be explained. There's too much irrationality, too much noise, so to speak, in markets for us ever to build a great model. The CAPM is a flawed model. But it's going to hang around for a very simple reason. The alternatives are just as flawed. In fact, if you think about replacing the CAPM with an arbitrage pricing model or a multi-factor model or even a proxy model, here's what I'd like you to think about. These models might do better at explaining the past. And they do. But they're not that much better at explaining the future. In other words, if your hurdle rate is coming from an arbitrage pricing model or a multi-factor model, I'm not sure it's any more precise than the expected return and hurdle rate that I'm getting from the CAPM. And given a choice between getting a flawed hurdle rate with one beta or one parameter or five betas, I'm going to take the one beta every single time. So it is true the CAPM is flawed. But all of the models I'm picking among are flawed. Here's how I'll end this session, though. To me, the CAPM is a tool. For the moment, it does at least as good a job as any other model out there. But if tomorrow you are able to come up with a more pragmatic, a better model for measuring risk and coming up with hurdle rates, I'd drop the CAPM in a minute. I'm not stuck on betas. I don't want to carry the baggage of modern portfolio theory with me every time I do corporate finance. To me, the CAPM is a means to an end, a way to get to a hurdle rate. And if you don't like the CAPM, come up with a different way of estimating hurdle rates. But don't throw the baby out with the bathwater. What I mean by that is don't abandon estimating hurdle rates just because you don't like betas and the CAPM. A final point, before you use any of these models, remember what you have to determine. You have to determine whether the marginal investor in your company is well-diversified, right? Here's a very simple test. I went back to the list of top 17 stockholders in Disney. And what did I see? I see a lot of institutional investors. I see Steve Jobs. But remember, Steve Jobs cannot be the marginal investor, and here's why. For an investor to be the marginal investor, he or she has to own a lot of stock and trade that stock. So Steve Jobs owns a lot of stock but doesn't trade that stock. Larry Ellison might own 23% of the shares in Oracle, but he doesn't trade those shares. If you look at the kinds of investors who can own a lot of stock and trade shares in these companies, it's almost always going to be institutional investors. And odds are, those investors are diversified. The case of Disney, I feel I'm on pretty safe ground assuming the marginal investor is diversified. Am I always that secure? No. There will be companies where you get to this stage and you feel doubtful about whether the marginal investor is well-diversified. What that effectively means is none of the models we talked about are very effective. We have to come back and deal with that later. But for the moment, at least with Disney, I feel on pretty secure ground that the marginal investor is diversified. In fact, looking across all my companies, I look at the institutional investments in these companies. These are all large market companies around the globe with a lot of trading volume, and much of the trading is done by institutions. I think I'm OK. Perhaps not as secure as I was with Disney, even with the other companies, the Baidu, Tata Motors, and Vale, and Deutsche Bank, assuming the marginal investor is diversified. And the reason, again, that matters, it allows me to focus in only on that risk that cannot be diversified away and bring it into my hurdle rate. That's a first step, and I hope we can continue with this discussion. Thank you very much for listening.