Transcription
When you decide to value an asset, you have to start off by answering a fundamental question: What can you make on a guaranteed investment? The answer to that question is the risk-free rate. A number we throw around in valuation constantly, but a number that we often have to grapple with in the real world. How do you estimate a risk-free rate? Most people say, look up a government bond rate, the US Treasury bond rate, for instance. If it were only that simple to get something that's risk-free, you first have to make sure that the entity issuing the security has no default risk. Not always easy to do in some parts of the world.
In this session, we will lay the foundations of how best to estimate a risk-free rate and why those rates may be different in different currencies. So, we're talking about discounted cash flow valuation, right? Discount rate should matter. You're right, they should matter, but they don't matter as much as most people think they do. So, while discount rates are a critical ingredient in discounted cash flow valuation, my view is that most analysts spend far too much time on discount rates and too little time estimating the cash flows. Having said that, though, let me start laying the foundations for discount rates in this particular session.
If you remember, in the last session, we talked about consistency, right? You have cash flows to equity, make sure your discount rate is the cost of equity. We've cash flows to the business, make sure the discount rate used is the cost of capital, the overall cost of financing. I'm going to add two more consistency principles. When you do valuation, you can do valuation either in nominal terms or real terms. You're saying, what are you talking about? When you do things in real terms, you basically ignore inflation. So, when you do cash flows, you forecast out the number of units you will sell and act like the price is not going to go up, even if there's inflation. Those are real cash flows. If your cash flows are real cash flows, your discount rate has to be a real discount rate.
If your cash flows are nominal cash flows, you have a second choice to make. What currency are you going to do the cash flows in? Note that currency becomes an issue only with nominal cash flows. You can estimate the cash flows in dollars, you can estimate them in pesos, you can estimate them in Euros. You're saying, I don't have a choice. Not really. You can value any company in any currency, and once you pick the currency in which you're going to estimate the cash flows, your discount rate has to be in exactly the same currency.
So, let's get started on the ingredients that go into a discount rate. Let's start off with the cost of equity. Again, the basic principle is a very simple one: the cost of equity for riskier investments should be higher than the cost of equity for safer investments, right? That's pretty intuitive. But now we run into the more, more difficult issue: How do we measure risk? What is it?
Now, if you look at finance textbooks, we've had this bad habit of defining risk in terms of statistical measures: standard deviation, volatility. And we tend to use stock prices. There's a reason we do this. We could use accounting earnings, but accountants measure earnings only once every three months for us companies, and perhaps less for non-US companies. So, we don't have a lot of data. Stock prices, on the other hand, we can slice and dice and get as much data as we want. So, much of what we know about risk and return in finance is based upon using stock prices and statistical measures of risk, varying standard deviation, volatility, as our measures of risk. We'll come back and talk about what to do if you don't agree with those measures, but let's, for the moment at least, use those as a starting point.
But here's the bigger principle I'd like you to take out: When you sit down to value a company, your first instinct is going to be, "How risky is this company to me?" But here's what I'd like you to do instead: Ask yourself, "How risky is this company to the marginal investors in this company?" You see, who are these marginal investors that I'm thinking about? They're the investors who are setting the prices for that stock. You and I, maybe I should just talk about me, don't have enough shares to affect the stock price. The marginal investors tend to have two characteristics. One is they own a lot of shares, millions of shares rather than thousands of shares, and they trade those shares. So, when you look at the risk in a company, you're looking at how will those marginal investors perceive the risk in this company. We'll come back and see how that changes how we think about risk, but it does.
Now, if you look at the different risk and return models in finance, they're all based on the premise, at least the traditional models in finance are based, based on the premise that that marginal investor is a diversified investor. Because that marginal investor is diversified, some kind of institutional investor owning tens of stocks, maybe hundreds of stocks, the risk they see in a company or an investment is the risk that it adds to a diversified portfolio.
Now, I don't want to rush you through risk and return models in finance, but I'm going to try to do it anyway. Here are the, the list of potential risk and return models that come out of traditional finance theory. This is the Capital Asset Pricing Model, or CAPM. It's been around a long time, and in the CAPM, the risk of an investment is the risk that it adds to the market portfolio. What's a market portfolio? It's a portfolio that includes every single traded asset out there. That risk is captured with a one number, a beta. And the expected return on a risky investment then becomes a risk-free rate plus a beta for that investment times a risk premium you demand for an average risk investment. Only three inputs.
The Arbitrage Pricing Model and multifactor models, which are of more recent origin, try to do the same thing, but they're a little more creative in measuring market risk. Rather than try to capture it all with one beta, they allow for multiple sources of market risk and allow for a beta against each one. You're saying, what's the difference between the Arbitrage Pricing Model and the multifactor model? Very simply put, the Arbitrage Pricing Model leaves these market risk factors as unnamed factors; they're statistical factors. A multifactor model puts economic names: interest rates, inflation, etc., on those factors.
There's a final variation on these models that's taken off in the last 20 years, especially as we have access to more data, and these are proxy models. In proxy models, you basically give up on measuring risk; you let something else stand in for it. I'll give you two very widely used proxies over the last 30 or 40 years in finance. We've discovered that small companies seem to earn higher returns than large companies, small and large defined in terms of market cap. You're saying, so what? If we assume that markets are right over very long time periods, here's the next leap of faith we can make: We can assume then that size, in this case, a market cap, measures the risk of a company, that small companies are riskier than larger companies. Low price-to-book stocks, stocks with the market value of equities well below the book value of equity, tend to earn higher returns than companies with high price-to-book ratios. Again, we could use that as a proxy.
Over the last two decades, these proxy models have either developed on their own or as add-ons to traditional models. What do I mean by that? You'll often see composite models where you use beta to measure risk, that's a CAPM, and you'll see a proxy thrown into the model, a small-cap premium. But almost every traditional risk and return model you see out there will be an offshoot or an extension of one of these four models.
But take a look at all four models. Every single one of these models starts with an input that we need, which is a risk-free rate, right? In fact, if you take the CAPM, which is the simplest of these models, it's easy to see what role the risk-free rate plays in your expected return. It's a base from which you build off. So, to get any expected return with any of these models, you first need a risk-free rate. For the rest of this session, I want to talk a little bit about how we come up with that risk-free rate.
Now, before we embark on that search, here are the characteristics you need for something to be risk-free. First, for something to be risk-free, the entity issuing the security cannot have any default risk. Even an inkling or an iota of default risk will make that investment risky. Second, for something to be risk-free, there can be no reinvestment risk. What do we mean by reinvestment risk? Let's assume you have a one-year time horizon and you invest for one year in a T-bill. That investment is risk-free to you right now. Let's say you have a five-year time horizon and you invest in a one-year government security. Even if there's no default risk, you have reinvestment risk. Reinvestment risk in what sense? At the end of year one, you've got to reinvest again and again and again at rates you don't know today.
So, when you're looking for something risk-free, you're looking for something default-free, and you're looking for something matched up to the cash flows that you're trying to discount. If your cash flows are long-term, your risk-free rate has to be long-term, and that long-term rate has to be default-free. That should be easy to do, right? It used to be. Because here's what we used to use for a risk-free rate: We would take the government bond rate, preferably a long-term government bond rate, in the currency of our interest. We'd use that rate as a risk-free rate. Note, though, implicitly, what we're assuming is that governments are default-free.
In fact, here are the two basic propositions I'd like you to take away about risk-free rates: First, you cannot give me a risk-free rate in a vacuum. I need to specify over what time horizon. Risk-free over a year can be very different than risk-free over five years or ten years. Second, not all governments are default-free.
So, let's do a few exercises in getting risk-free rates. Let's start easy. Let's start with trying to estimate a US dollar risk-free rate. Okay, here's a simple way to do it, right? Look up a 10-year government bond rate. But remember, you have choices. The US Treasury issues 3-month T-bills, 6-month T-bills, one-year, two-year, five-year, 10-year, all the way up to 30-year. How do you decide which one to use as your risk-free rate? The answer, I think, lies in what you're trying to do. If you're trying to do valuation, your cash flows in a sense extend forever. Even if you stop at the end of year five or year 10, that N number that you leave, that terminal value, often assumes your cash flows keep going after your five or 10. So, you would like to have a long-term, default-free rate. So, you want to go with the longest-term rate you can find. In this case, that sounds like the 30-year bond rate.
I actually prefer to use the 10-year bond rate, and let me explain why. The risk-free rate is just the start of the process. I need to get default spreads, I need to get equity risk premiums. Now, in other words, I need other inputs to get the rest of the model going, and those inputs are easier to get with a 10-year T-bond rate than with a 30-year bond rate. For instance, to get a default spread for a corporate bond, I need to find other corporate bonds of equivalent maturity. It's easy to find 10-year corporates; it's very difficult to find 30-year corporates.
One final point. You're saying, what about the TIPS rate? When can I use it as my risk-free rate? The TIPS rate, if you're not familiar with it, is an inflation-protected Treasury bond. It's a real interest rate. If your valuation were being done in real terms, remember we talked about estimating cash flows without inflation, real cash flows, that would be your risk-free rate. If you're doing a nominal US dollar valuation, the TIPS rate should not even be a choice.
So, if you're looking at US dollars, you could use the 10-year US T-bond rate as a risk-free rate. But one final point: we are implicitly assuming when we do this that the US Treasury is default-free. Is it? We used to think that was a given. It no longer is something to think about, right?
Well, now that we've got a risk-free rate in US dollars, let's move one step up the difficulty ladder. Let's suppose you're valuing a company in Euros. Could be a European company, could be a US company. You want a Euro risk-free rate, right? That should be easy. Let's go find some government bonds denominated in Euros. I tried, and I found too many. Say, what do you mean, too many? I found a dozen European governments all issuing 10-year bonds, all denominated in Euros, and the rates are all different. Now, remember, these are all Euro-denominated bonds. These are not the 1990s with the French government at franc bonds and the German government at deutsche mark bonds. These are all Euro bonds. The only reason these rates are different is because the market perceives some of these governments as having default risk. And there, in lies your answer.
If you want to do a valuation in Euros and you want a Euro risk-free rate, even if the company is a Greek company or a Spanish company, you know what you should use as a risk-free rate? I would use a German 10-year government bond rate as my risk-free rate. Not because it's German, but because it's the lowest of those 10-year government bond rates. I'm trying to get as close as I can to a default-free rate, and that probably is as close as I can get.
So, let's assume that you've got a Euro risk-free rate now, and you want to try an even more difficult task: you want to get a risk-free rate in nominal Reais. So, first step is the same: you find a 10-year government bond denominated in Reais. The Brazilian government has those bonds. At the time that I did this analysis, that rate was 9%. Is that my risk-free rate? Well, before I use it as my risk-free rate, I have a check to make, right? Is that a default-free rate? Now, that's a tough question to answer.
So, I used a proxy. You know whether you're familiar with Moody's and S&P, but these are ratings agencies that usually rate corporations for default risk. They also happen to rate sovereigns. Basically, they tell you how much default risk they see in sovereigns. So, I went to the Moody's website, I looked up the rating for Brazil, and guess what? Brazil is not a AAA-rated country. There is default risk in the country. Based on its rating, I looked up a measure of how much default spread I would charge for investing in a Brazilian bond. Now, this requires an assumption, so we'll talk about how to estimate this default spread. But in the case of Brazil, the default spread I estimated for the government was 1.75%.
You're saying, where are you going with this? Remember, the government bond rate was 9%. That was a rate that incorporated the default risk that investors see in Brazil. By my estimates, that spread should be 1.75%. I'm going to subtract out the 1.75% from the 9% to come up with a risk-free rate in nominal Reais of 7 and a quarter percent. It's not rocket science, but it does add a layer to the risk-free estimation process.
Now, the key number you need to convert a government bond rate into a risk-free rate is a default spread for the government. You're saying, where do I get that? There are actually three ways you can do it. The first two are actually pretty straightforward, and I'll use Brazil to illustrate the process. Brazil has dollar-denominated bonds. If I take the interest rate on those dollar-denominated bonds and look at the US bond rate on that same day, that difference gives me a measure of default risk. So, as an example, if the Brazilian dollar-denominated bond has a rate of 3% and the USD bond rate is 1.8%, that difference of 1.2% is a default spread for Brazil.
The second choice is you can go to what's called the CDS market, the credit default swap market. It's an insurance market. It's a market that you can go to to buy insurance against default risk. If you bought a Brazilian bond. And the nice thing about the CDS market is it's constantly updated, and it gives you a measure, at least as the market sees it, of the default spread for this country. Right now, in January 2013, for instance, the CDS spread for Brazil was 1.42%. How would I read that? If you believe the CDS market, 1.4% is the default spread for Brazil based on its sovereign risk right now.
So, these two approaches work if you have a dollar-denominated bond or you have a CDS spread. You're saying, what do I do if I don't have either? Take an example: India does not have a CDS spread, it does not have a dollar-denominated bond. So, let me give you a third approach if the first two don't work. If your country has a sovereign rating, and Moody's rates about 115 countries, so my guess is your country should have a sovereign rating, and it doesn't have a CDS spread and it doesn't have a dollar-denominated bond, you can use this lookup table. Saying, where does this lookup table come from? It's a table that I update at the start of every year, and what I do is I try to find as many CDS spreads and dollar-denominated bonds within each ratings class, and I come up with an average spread for each rating. You give me your sovereign rating as a country, and I'll give you the default spread that best matches that rating. So, for instance, if you have a country with a sovereign rating of Baa2, my default spread given that rating is 1.75%. So, it allows you to convert a sovereign rating into a default spread.
There's one final scenario I haven't looked at. What if your country does not have a rating, a CDS spread, or a dollar-denominated bond? There are a few countries still left out there. Well, then you're in real trouble. One solution maybe is to find a country risk score. There's an outfit called PRS, which is Europe-based, that actually provides a country risk score, which is numerical. So, as an example, let's suppose you're trying to get a country default spread for Rwanda. You might be able to find a country, a number for Rwanda, a numerical score. Try to find a rated country with that same score and try to find a default spread based on that. I know it's desperation time, but what else can you do?
So, summing up again, in this session, we looked at the first building block to get to an expected return or a discount rate, which is a risk-free rate. In some currencies, it's easier to get than others, but in every currency you do a valuation in, you have to try to come up with this number before you do anything more ambitious.