Transcription
So let's say you have all your money invested in something guaranteed making 2%. I come to you with a question: How much more than 2% what I need to offer you for you to take your money out of where it's now guaranteed and invest it in stocks? The answer to that question is the equity risk premium.
Now think of asking that question to every investor in the stock market. The consent answer you will get across all investors is the equity risk premium you use in valuation. That's going to be tough to estimate, I know. And there are two basic ways that you can estimate it. One is to look backwards. It's called a historical risk premium. Essentially, you're looking at how much you'd have made in the past. The other is to look forward, which is a dynamic, forward-looking premium. That's not as difficult as it sounds, and hopefully, by the end of the session, you will have the tools to be able to estimate a reasonable equity risk premium.
Almost everybody who does valuation uses an equity risk premium. Every analyst, every company, every consulting firm uses it. And it surprises me how little thought often goes into estimating this number. So I'd like to spend this session talking about what this number is and how best to estimate it. So let's start off by laying the basics. The equity risk premium is the premium you would demand, you being the investor, would demand over and above the risk-free rate for investing in risky assets, equities as a class. So think about it: if you're making 2% or 3% riskless, the question I'm asking is, how much more than that would I need to offer you to buy stocks collectively? So think about a broad index.
Now, as you start thinking about that, two things are going to drive the number you're going to come up with. One is how risk-averse you are as an individual. What's going to drive that? Some of it you're born with, some of it is a function of your age. But if you're risk-averse, you're probably going to demand a larger premium. Second, it's also going to depend on what you think about the riskiness of equities as a class. Saying, what's going to drive that? That's going to be driven by a perception of macroeconomic risk. So if you've come off a crisis, or you see a lot of uncertainty or volatility in the overall economy, you're going to demand a larger premium. If you're worried about catastrophic risk, the risk that something terrible could happen, you're going to demand a larger premium. But bluntly, the equity risk premium is a number that can and should change over time. So as we look at the different approaches, keep that in mind. Any approach that yields the same number year after year after year is probably not that dependable a number.
Now, the way most people get equity risk premiums is to look backwards. I don't blame them, because that's where the data is. They look at the past and they ask a very simple question: What would I have made investing in stocks over the last 10, 20, 50, 80 years as opposed to investing in something riskless, T-bills or T-bonds? The difference is a historical risk premium. So, as an example, for over the last 50 years, you had thought you'd made 12% investing in stocks each year over those 50 years, but you'd have made only 4% investing in treasury bonds over that same period. 12 - 4 would have yielded an 8% historical risk premium. That should be pretty simple to do, right? Especially in a market like the US, we have a long history.
Take a look at that table at the bottom of this page. You'll see three slices of history I've taken. One goes back to 1928, it's 85 years of history. One goes back 50 years, one goes back 10 years. I get very different estimates of the risk premium depending on how far back in time I go. I get a very different premium with 85 years as opposed to 10. What I use is my risk-free investment, I use T-bills, a short-term government, as opposed to T-bonds, which are long-term. And whether I compute arithmetic averages or geometric averages. You're saying, "What the heck is that? Sounds like inside statistics." But here's the difference: arithmetic averages, I add up 85 numbers and divide by 85. It's a simple average. Geometric averages, I take into account the compounding that happens over time. So depending on the decisions you make on estimation, your equity risk premium could be 7.7 and 1.2% or it could be 11 and a 12%. All these numbers can't be right at the same time.
But here are the two things that I would like you to keep in mind. One is, whenever you estimate a risk premium looking at the past, it's a statistical estimate. It's an average over time. That average comes with a standard error. That again is something we tend to forget after our statistics classes, but those standard errors carry a message. Take that 4.2% that you saw on the previous page as my risk premium over an 85-year time period. That is the geometric average premium for stocks over T-bonds over 85 years. That sounds pretty precise, right? 4.2%. But before you get too excited about that number, take a look at that 2.33% you see in brackets right below that period. That's my standard error. So think about it: when I tell you the historical risk premium is 4.2%, what I'm not telling you is the standard error in that number is 2.33%, which means my true premium could be less than zero, be higher than 9%. And that's with 85 years of history. With 10 years of history, I might as well not look at that number because the standard error is so large. So that's the first problem with historical premiums: is the estimates you get are noisy, which is just a fancy way of saying they're error-prone.
The second problem, and especially when you use the US data, you face this problem, is you have a survivorship bias. What am I talking about? The most successful equity market of the 20th century was the US market. Using that market to estimate a forward-looking premium assumes that I will know what the most successful equity market is for the next century, and I don't. So a better measure of historical premium might average out the premiums across multiple markets, and there are databases that do that. Having said all of that, though, a historical premium is a flawed way of thinking about equity risk. It's backward-looking. It assumes that everything reverts back to historic norms. That might have been okay in the old days, 2005, 1995, 1985, but I think the crisis of 2008 should have shaken your faith in things reverting back to normal.
What I'd really like is an equity risk premium looking forward, and I think there's a way to do it to get a sense of what I'm going to do next. Let me give you a sense of what the calculations involve. You know how to compute the yield to maturity on a bond. You take the price of the bond, you take the coupons as the cash flows, you include the face value, and the yield to maturity is that discount rate that makes the present value of your cash flows equal to the price of the bond. We do this with fixed income all the time. But let's assume that we can do this with equities. Instead of buying a bond, let's assume you bought the S&P 500 at the start of 2013. You know what that have cost you? $1,426.19. So instead of buying a bond, you bought the entire index, 500 largest market cap stocks, right? Instead of coupons, what do you hope and pray you get? Hope and pray you'll get some cash flows, right? Those cash flows will take the form of either dividends and with US companies, some buybacks. I can't tell you what they will be in the future, but I can tell you what they would have been last year. That's easy enough to do. I just count up the dividends and buybacks across all US companies. So I know what you paid for stocks, I know what the cash flows were last year. I bring one final piece into the puzzle: analysts in the US often estimate growth in earnings for the S&P 500. I collect those growth numbers, and based on those growth numbers, I project out an expected growth in cash flows for the next 5 years of 5.27%. I'm almost home.
I take the cash flow from last year, I grow it at that 5.27%, at some point in time, I assume that that growth rate will revert back to the growth rate of the economy, and I use the risk-free rate as my proxy for that. And we'll come back and talk about why. And I'm pretty much set on computing an equivalent to the to the yield to maturity. I have the price for stocks, what you paid, $14.26.19. I have the expected cash flows. I solve for that discount rate that'll make the present value of my cash flows equal to the level of the index today. It's a little messy, but I can get there. And when I get there, I have an expected return on stocks. At the start of 2013, that number was 7.54%. You say, "How, how are you going to use that?" Remember the risk-free rate, the T-bond rate at that time was 1.76%. The difference of 5.78% is my estimate of a forward-looking equity risk premium at the start of 2013. You know what's neat about this? You can recompute this number the next day, and you get a different number. It's forward-looking and it's dynamic.
To give you a sense of how this number shifted over time, take a look at this graph. So if you look at this graph, then you have the implied premiums over time. Now, you might wonder, why do we care about implied premiums? Implied premiums carry a message that we ignore at our own peril. Let's take an example. Let's suppose at the start of 2013, and you work at an investment bank or an equity research house. Everybody in the bank uses 4.2% that historical risk premium to value companies. But the implied premium is 5.8%. You know what's going to happen, right? Use a 4.2% premium, everything is going to look cheap to you. Why? Because you used too low of a premium, not because this company is a great investment, but because you think the market is cheap. So even if you decide not to use implied premiums, I think it behooves you to at least know what it is at any point in time.
So all of this talk we've had so far is about estimating equity risk to the US, where you have a luxury of data. You have historical data going back 100, 150 years. You have all the data you need for implied premiums. You're saying, "What do I do though if I have an Indian company, an Indonesian company, a Chinese company, a Brazilian company? In other words, an emerging market where you don't have a lot of data?" Let me suggest a couple of things you can do to estimate risk premiums in these markets. One is to build off a measure we used in a previous session to get to a risk-free rate. Remember how we did that? We started with the government bond rate, we came up with a default spread for the country, we netted that default spread from the government bond rate to come up with a risk-free rate. Now I'm going to use that default spread again to get to an equity risk premium. And here's what I'm going to do: I'm going to start with that default spread. In the case of Brazil, it's 1.75%. Then I'm going to look up two more numbers: one is the standard deviation in the Brazilian equity index. In this case, I used the Bovespa, it came up at 21%. The other is the standard deviation in that Brazilian dollar-denominated bond that I used to look up the default spread, and that number was 14%. He's saying, "Where are you going with this?" If you look at the 21% and the 14%, it looks like the Brazilian equity index is about 1.5 times more volatile than a Brazilian bond. That's 21 divided by 14. If I scale up the default spread of 1.75% for that additional risk, I come up with about 2.63%. I add that 2.63% to my base premium for the US, which let's assume is 5.8% based on my implied premium. I have an equity risk premium for Brazil.
So let me recap: start with the mature market premium, look up the default spread for the country you're interested in, scale that spread up if you can. If you can't, just use the default spread and just add it on to the mature market premium. You have an equity risk premium for a country. Now, I could also use an implied premium. It's a little trickier when I use an implied premium because I have to get those same inputs for Brazil that I got for the US, which is the cash flows from the most recent year, which is not a problem. The index level from the most recent time period, which is not a problem. And an expected growth rate, which might be a bit of a problem. But if I can get an implied premium for a market, I can bypass this process and tell you what the equity risk premium going forward is for a country.
So in this graph, for instance, I've tried to map out the implied equity risk premium for Brazil versus the implied risk premium for the US. And note something interesting: note how much the additional premium charging for Brazil has dropped over the last decade. Brazil today is a lot less risky, at least in the eyes of investors, than it used to be. So use either the rating-based, default spread-based approach, or an implied premium to come up with risk premiums by country. At the start of every year, I actually develop a table of equity risk premiums by country. There's no magic to this table. I start with the base premium. So this is the table from the start of 2013. I use the 5.78% I estimated as my implied premium for the US as my base. I rounded up to 5.8%. That is the premium I use for every mature market. What's mature? I use any country with a AAA rating as a mature market. I know it's cheating, it's probably sloppy, but it's easy to do. Every other country, I add an additional premium based on the rating and the default spread and adjusting that default spread for additional risk. This table gives you the entire picture of equity risk premiums by country.
Why would you need this? Well, it's not just to value companies within a country. In fact, if you think about equity risk premiums, here are the three ways you can use those country risk premiums you come up with. In the first approach, you come up, you you start off with a risk-free rate and a mature market premium, and then you add the country risk premium onto that number to come up with the cost of equity for a company. In the second approach, you bring the country risk premium to the brackets and multiply by your beta. You see what's the difference? Well, if a beta is close to one, you're going to get pretty close to the same number with approach one and approach two. But if you have a beta greater than one, the second approach will give you a higher number. And there's a third approach where you break the country risk premium separate from the mature market premium, and you estimate how exposed your company is to that country risk.
So let me very quickly at least lay the table for how you can come up with these numbers. When you think about country risk, there are two ways you can think about country risk. One is the lazy way, where if you tell me where you're incorporated, I assume your country risk comes from where you're incorporated. So if you're a Brazilian company, I assume you're exposed to Brazilian country risk. I think that's sloppy because it basically assumes that emerging market companies are exposed to country risk and developed market companies are not. What I think makes more sense is for you to think about country risk from the perspective of where you do business. So if you're Coca-Cola, you're exposed to country risk because you operate in a lot of emerging markets. So when you think about the country risk premium, I think the second approach is a more sensible way of thinking about country risk premiums.
So let's try this out. I have two companies on this table. The first is Embraer in 2004. And Embraer in 2004 got 3% of its revenues in Brazil. It's a Brazilian company, but got only 3% of its revenues in Brazil, got 97% of its revenues in developed markets with no country risk. If you look at my estimation of country risk premium for Embraer, it reflects the fact that only 3% comes from Brazil, and that 3% means that their risk premium, or the risk premium for Embraer, is not going to be as high as the typical Brazilian companies. MBV, on the other hand, and this is from a more recent valuation, has exposure to lots of Latin American countries as well as exposure in Canada. So if you look at my estimation of country risk for MBV, it's a revenue-weighted average of the country risk premiums of all of the different countries that they operate in. You know what I'm trying to say, right? Just because you're valuing a US company doesn't mean you can ignore country risk. Here, for instance, my estimation of country risk premium and the total risk premium for Coca-Cola. Coca-Cola is a US company, but it gets a dramatic amount of its exposure from emerging markets with a substantial amount of risk, and my risk premium has to reflect that exposure.
Now, you're saying, "What about that lambda approach you talked about?" I'll at least give you an insight into how you can start thinking about this. Lambda, you're basically saying, "Let me separate our country risk from everything else." A company's exposure to country risk can be very different from its exposure to everything else. You can base your lambda entirely on revenues, like I did for MBV, or look at or Embraer, or you can go for something richer, where your production facilities, what kind of risk management tools you use. But I want you to start at least thinking about ways of separating country risk from all other risk and measuring your company's exposure to that country risk.
So in summary, equity risk premiums can be simple, they can be messy. You can get them by looking backwards, you can get them by looking forwards. But whatever you do, remember they play a big role in your evaluation, and that number that you use has to tell a story.