Session 6: Estimating Hurdle Rates - Equity Risk Premiums - Historical & Survey

In this session six of a 36 session corporate finance class, I'd like to talk about a second input into every risk and return model in finance, which is the equity risk premium. After defining what we'd like to measure with that estimate, we're gonna look at two ways in which people come up with that number, doing a survey and looking at the past. In this third session in estimating hurdle rates, I'd like to start talking about equity risk premiums. In the very first session on hurdle rates, we talked about what went into a hurdle rate, a risk-free rate and a risk premium, and we defined risk. In the second session, we talked about a risk-free rate. How do you come up with a risk-free rate? In this session, I want to start talking about equity risk premiums, the premium you demand on an average risk investment. So let's set the table. Here's our objective. The equity risk premium is the premium you as an investor would demand for investing in the average risk investment relative to the risk-free rate. Sounds abstract, right? Let's assume you can make 3% on something risk-free. The equity risk premium is what you demand over and above that 3% to invest in the average risk investment. So here's what's going to go into a risk premium. The first is it should be greater than zero. If you're accepting 3% risk-free, you would not settle for less than 3% if you're investing in something risky. Second, it'll depend on how risk-averse you are as an individual. The more risk-averse you are, the higher the risk premium should be. And if you think about what goes into risk aversion, part of it is your age. Younger people are less risk-averse than older people. Men are a little less risk-averse than women. And over time, your risk aversion might change, but you're born with some risk aversion and they're never going to change. So risk aversion varies across individuals, and how risk-averse you are will determine your equity risk premium. So let's try a little experiment. Let's assume that you've saved some money and that all your money invested in something risk-free, making 3% guaranteed. I come to you with a sales pitch. I say, look, I know you're invested in something guaranteed 3%. Let's assume you want to invest in the 500 largest stocks in the US, the S&P 500, the Vanguard 500 index fund. How much more than 3% would I need to offer you to leave where you are right now, that perfectly safe spot, and invest in stocks? Do you see the question I'm asking? You can make 3% guaranteed, but maybe you'd be induced to invest in stocks if I offered you a little bit more than 3%. So I'm going to go through the choices, and if this is the choice you would make, check it off. There's no right answer here. There's actually one wrong answer that hopefully none of you will pick, but there's no right answer. It really depends on how risk-averse you are. The first choice is less than 3%. Thank God nobody picked it, because that's the one wrong answer, because if you can make 3% guaranteed, you should never settle for less than 3% on a risky investment. Next choice is three to five. That's a risk premium between zero and 2%. If you pick that, you're one of the least risk-averse people in this crowd, and if you're less risk-averse, again, there's nothing good or bad. You're going to be more invested in risky assets than anybody else. You'll be quicker into stocks than everybody else, and that's going to be the pattern for the rest of your life. The next choice is five to seven. Your risk premium is now two to four, a little less risk-averse than the previous group, but still fairly low risk-aversion. Seven to nine, if you're in that group, you're actually in the middle of the distribution, because I've done this survey on potentially thousands of investors, and that's where the middle of the distribution falls, a risk premium between four and 6%. Nine to 11, you're getting more risk-averse, and if it's more than 11, you're probably among the more risk-averse people in this group. Now, the reason I ask that question is this were the entire market. Here's what I could do. I could take the numbers you gave me, back out from those numbers your equity risk premium. So if you said 7%, that's a risk premium of 4%, and after I had estimated all of your risk premiums, I could take a weighted average of all of those numbers to come up with an equity risk premium for the entire market. Now, what did I weight it by? By how much money you have. This isn't a democracy. If you have no money, what you think about the risk premium matters very little. If you have a lot of money, it matters a lot. So that's basically the way to think about equity risk premiums, but if you decide to go down this route, here's another problem. That number you just gave me is very sensitive to what's going on in the outside world. For instance, let's assume in the three or four minutes you've been watching this session that the market had dropped 25% while you were watching. Now I come back to you with the same question I had just three minutes ago. You've invested safely, making 3%. How much more than 3% would I need to offer you to invest in risky stocks? I'm sure some of you, after hearing the news story, might say I demand a larger premium because you think that's changed your risk. For others, you might say I'd settle for a smaller premium because if stocks were great at 12,000, at 9,000, they're even better. But whatever the reason, risk premiums are not just difficult to get, they keep changing. The world shifts around you, your equity risk premium is going to shift. What I'm arguing for is an equity risk premium that's dynamic, that's constantly changing because the world is changing around us. So as I describe the different ways in which you can estimate equity risk premiums, pass it through that test. Is it going to be dynamic? Is it going to be forward-looking? Is it going to change when the world changes around you? Because there are three basic ways in which people estimate risk premiums. The first is to do surveys, not of all investors, but of subsets of investors. I'm going to start with that. The second is to look at the past, historical data, to see what kind of premium you'd have earned investing in stocks as opposed to T-bonds or something riskless, and use that premium. The third is to get a forward-looking premium that reflects the world we live in. I'm not going to get a chance to do the third approach in this particular session, but we'll do at least the first two. Let's start with the survey approach. Clearly, you can't ask all investors because there are just way too many investors out there. So almost every survey I've seen looks at a subset of investors. For instance, the very first listing there which looked at individual investors, that survey was done until 2004, at which point the Securities Industries Association, which used to do it, stopped doing the survey because they discovered it was completely and totally useless. Useless in what sense? When you ask people what they thought stocks would make over the next year, the next five years, and that's what all these surveys do, they try to get a sense of what your expected return on stocks is. They discovered that what they were getting were not expectations, but hopes. The other groups of surveys continue. For instance, Maryland surveys portfolio managers around the globe every month, and they report a premium. That premium ranges between 3 1⁄2 to 5%, depending on the month you catch it in. Campbell Harvey and Graham survey CFOs. CFOs use risk premiums in companies to come up with hurdle rates. They report that premium once every year. That number is about 4, 4 1⁄2%. Pablo Fernandez, a friend of mine from Spain, does surveys of both academics and practitioners, and he reports those premiums. They range from 5% to 6%, depending on where you ask the question and when you ask the question. But these are all survey premiums. I'll be quite honest. I don't trust survey premiums. They're much too volatile, and they're much more a reflection of the past than they're expectations of the future. What I mean by that is, after a period when stocks have done well, these surveys reflect much higher numbers. When stocks do badly, they go down. In other words, they're reactions to the past rather than expectations for the future. Which brings me to the second and most widely used approach to estimating equity risk premiums. It's to estimate a historical premium. Let me set the table. Here's what you're trying to do. You take a slice of history, 20 years, 50 years, 80 years. You look on average what you'd have made investing in stocks over that period. Let's say it's 8%. Then you look on average what you'd have made investing in T bonds over that period. Let's say it's 3%. Eight minus three is five. That's a historical premium. Easy, right? In fact, I have a table there that reports 12 different numbers, all of which pass muster as historical risk premiums. You're saying 12 different risk premiums? How is that possible? Here's why. I took three slices of history, one going all the way back to 1928. That's 86 years. The second going back 50 years, and the third going back 10 years, and I got three very different premiums. I took the premium over T bonds, which are longer-term government securities, and I got a very different premium than when I used the premium over T bills, which are short-term government securities. I looked at arithmetic average premiums, or I added up 80 numbers and divided by 80, and then I looked at the compounded average, a geometric premium, and I got very different numbers. The equity risk premiums you see on this table, and this is the most updated version of this table, using data through the end of 2013, give you numbers ranging from 3% to 8%, all of which technically are historical risk premiums. Now, you might think it's very convenient to have all these different numbers because you can use any number you want and get away with it, but unfortunately, that's a bad way to think about it. I'm gonna give you three suggestions on historical risk premiums, which you can abandon if you feel you have a better way of doing it. The first is go back as far as you can. Sounds strange, right? I want you to go back to 1928, before the Great Depression. The reason is statistical. Every one of these numbers on this table is a statistical estimate, and because it's a statistical estimate, there's a standard error associated with that number. So, for instance, if you go all the way back to 1928, and you tell me the risk premium for stocks over T bonds is 4.62%, that's a geometric premium. Before you get too excited, take a look at the standard error on that estimate. It's about 2.3%, which effectively means you can't rule out the possibility that the true risk premium is about zero or as high as 9%. In fact, as you go to 50-year and 10-year numbers, look at how big the standard errors become. In fact, with a 10-year estimate, you might as well not tell me what the number is because the standard error is so large. Second, be consistent about what you call risk-free. I use the premium over T bonds, not T bills, because to me, the T bond rate is my risk-free rate. So because I use it as my risk-free rate, it's the only premium I care about. Third, use the geometric average because this premium gets built into your discount rate and compounds over time. So if you forced me to pick a number on this table, I'd pick the 4.62%, but I'd add the caveat that I feel very uncertain about what it's telling me about future risk premiums. And that's with the U.S., where you have a lot of history. Remember, there are markets that we're going to be dealing with, India, China, Brazil, where you don't have 10 years, let alone 80 years of history, 20 years of history. Historical risk premiums outside the U.S. are often close to useless because the historical data is just not there. There is actually a study that comes out of Credit Suisse every year, and it's run by the London Business School that looks at equity risk premiums over the last 100 years in about 20 different markets. It's a very good historical risk premium study, but even that study points to the shortcomings of historical data because even in that historical data with 100 years of data across multiple markets, the standard error remains at about 2%. So let's think about ways of estimating risk premiums in markets outside the U.S. where you don't have historical data. There are a couple of ways you can do it. One very simplistic way borrows on an approach we already used to get to a risk-free rate in multiple currencies. We said if you're looking at estimating a risk-free rate in a currency where there's no default free entity, you can use the sovereign default spread to come up with a risk-free rate, right? If you used a sovereign default spread to come up with a risk-free rate, that same sovereign default spread can do double duty, and here's how it helps you with your equity risk premium. Let's say you have an equity risk premium for the U.S. Let's say at the start of 2013, that equity risk premium was 4.20%. Incidentally, that's a number we've updated to 4.62% through the end of 2013. But in November of 2013, the historical premium is, let's say, 4.2%. Let's say I want a risk premium for India. Remember that default spread we came up with for India, 2.25%? That's a spread I subtracted out of the government bond rate to come up with a risk-free rate in Indian rupees. I'm gonna add that 2.25% to the U.S. risk premium of 4.2% to come up with an equity risk premium for India. I use the same approach with China and Brazil. I add the default spreads for those countries, 0.5% for China and 2% for Brazil, to my equity risk premium for the U.S. to come up with an equity risk premium for India, China, and Brazil. And I could extend this to any country for which I either have a sovereign CDS spread or a sovereign rating. I take the default spreads, add them to the U.S. risk premium to come up with a total risk premium for that country. That's the state-of-the-art, if you can even call it that, of estimating country risk premiums that most practitioners use. I use one tweak on this approach, and it's built on a very simple principle. Those default spreads were the spreads you charge for buying a government bond issued in rupees or riyas or yuan, right? That was a default spread for buying a government bond. You're not interested in buying a government bond. You're interested in buying equities issued by these countries. I would assume that equities are riskier than bonds, and to measure the relative risk of equity, I'm going to look at two numbers. One is the standard deviation of the equity index in that country. The other is the standard deviation of the government bond. So as an example, if you had a standard deviation of 21% in the equity index and 15% in the government bond, equities are about 1.3 times more risky or 1.4 times more risky than the government bond. You multiply the default spread by that ratio. That's effectively what I did for my three countries. I took India, Brazil, and China. I took the default spreads that I got from their ratings, and I scaled up the default spread for the additional risk of equities in each of these countries, and this is how I defined the equities. In India, I looked up the standard deviation in the SENSEX, which is the Indian Equity Index, and the standard deviation in the Indian government bond. In Brazil, I looked at the standard deviation in the Bovespa and the standard deviation in the Brazilian government bond. In China, I used the standard deviation in the Hang Seng or the Shenzhen Chinese Equity Index and scaled it to the standard deviation of the Chinese government bond. In each of these, I'm scaling up the default spread for the additional risk of equities, adding it to my equity risk premium for the U.S. to come up with a total equity risk premium for that country. As we go through, we will talk more about country risk premiums. Thank you very much for listening.