Session 5: Estimating Hurdle Rates - The Risk free Rate

In session five of this 36 session corporate finance class, I'd like to talk about a central input into almost everything we do in finance, which is what a risk free rate is. A risk free rate is what you can earn on a guaranteed investment. Should be simple to compute. But as we'll see in this session, you can sometimes run into serious measurement issues in coming up with a risk free rate. In this session five, I'd like to talk about the risk free rate. To get a hurdle rate, you need a starting point, and that starting point is what you can make on a guaranteed investment. This is a number that we used to think very little about 20 years ago, maybe even 10 years ago. It's a number that's becoming increasingly controversial in the markets we're in right now. So let me set up where we are in this process. We started the discussion of hurdle rates in session four. In this session, we're going to look at the risk free rate. In other words, we're moving towards using the CAPM or some risk and return model to come up with an expected return. So let me set up what the expected return in the CAPM should be. The expected return should be a risk free rate, that's a base, plus a beta, which measures the relative risk of your investment times an equity risk rate. Three numbers to get an expected return. And in practice, I think we tend to mangle all three. I see people, for instance, using the current risk free rate. And in particular, they try to think about the six month table rate or government bond rate as a risk free rate. But in particular, we need to start with that risk free rate and what it is. They often will use a regression beta. We'll come back and talk about the right way of measuring relative risk. And they often will look at the past to get a historical risk free rate. This session is going to be focused just on the risk free rate. So let's start with what should go into a risk free rate. Let me go back to my earlier definition of a risk free investment. A risk free investment is one where you know exactly what you're going to make with absolute and complete certainty. In other words, if you think you're going to make half a percent, that's what you're going to make. So for a risk free rate to exist, here are the two conditions that have to be met. The first is the entity issuing the security can have zero default risk, absolutely none. Even a smidgen of default risk will not make it risk free. Second, there can be no reinvestment risk. And let me explain what I mean by this as well. If you have a five-year cash flow, a six-month T-bill is not risk free, even if you think the U.S. Treasury is default free. And here's why. At the end of six months, you've got to reinvest and reinvest again and reinvest again at rates you do not know right now. So for something to be risk free, it's got to be issued by a default free entity. And it's got to match up to when the cash flow comes in, which actually puts us in a bit of a problem. Because when you do investment analysis evaluation, you often have cash flows at different points in time, one year, two years, three years. So let's assume you're doing a U.S. dollar investment analysis, and you're going to see in a minute why currency is going to matter. You have cash flows in year one, two, three, all the way through year 10. If you're a purist and you buy into what we've just said in this page, your risk free rate should actually be different for each cash flow. For the one year cash flow, I should use the one year zero coupon because a coupon throws off my interest rate. On the two year cash flow, I need a two year zero. On the three year cash flow, I need a three year zero all the way through, which means each cash flow will have its own risk free rate. What a pain. So I'll offer you a solution that might make your life a little easier. It comes from what's called duration matching. It's the way the old banks used to be run. And here's how they manage interest rate risk. Rather than take each individual asset and match it up to a liability of equivalent duration, banks used to take the average duration of their assets and set it equal to the average duration of their liabilities. What they were trying to do then was to reduce interest rate risk, if not eliminate it. We're going to do a variant of that. Remember that 10 year analysis I talked about? We have cash flows in years one, two, three, all the way through year 10. Think of the weighted average duration of those cash flows on average. In which year do those cash flows come in? If the cash flows are back-ended, the bigger cash flows are towards the end of the life, that might be seven, seven and a half years. If you can use a risk free rate with roughly the same duration, you're going to be okay. It's not going to be perfect, but you're going to be okay. In fact, I'll make life even simpler for you. In much of corporate finance evaluation, you can assume that a 10 year maturity default free bond will effectively be a pretty good risk free rate. So find me a default free 10 year bond, and I've got a risk free rate for you in that currency. So let's start easy. In November of 2013, I needed a U.S. dollar risk free rate. I assumed, and this was not an easy assumption as it might have been five years or 10 years ago, I assumed the U.S. treasury was still default free. And I used a U.S. 10 year T bond as my risk free rate. In November of 2013, that rate was 2.75%. That is going to be my risk free rate in U.S. dollars, no matter where I do my analysis. In other words, if I do an investment analysis in Indonesia, but decide to do my cash flows in U.S. dollars, my risk free rate is going to be in U.S. dollars. A risk free rate is driven by what currency you choose to do the analysis in, not the company doing it or the country in which the analysis is done. So that was easy. The risk free rate in U.S. dollars, if you assume the U.S. treasury is still default free, is 2.75%. Now you're saying, what if I assume there's default risk in the U.S. treasury? We'll come back to that. There's a way to fix that. But I'm going to assume the 2.75% as my risk free rate in dollars. Now let's climb the difficulty ladder. Let's assume I want a risk free rate in euros and I need one to do my Deutsche Bank hurdle rate, right? So to get a risk free rate in euros, I looked up 10 year government bond rates in euros and I ran into a bit of a problem. There were at least 10 governments that had 10 year bonds denominated in euros and the rates were all different. They ranged from 1.75% for Germany to much higher rates for Spain, Portugal, and Greece, which are riskier parts of the EU. Now which of these rates should I use as my risk free rate? The answer, I'm afraid, is surprisingly simple. If you think about it, these are all 10 year euro bond rates, right? They're not drachmas and French francs and Deutsche marks like they were 15, 20 years ago because they're all in euros. There's only one reason why the rates are different, which is the market sees default risk in some countries and more default risk in some countries than others. It sees more default risk in Greece and Spain and Portugal than it does in Germany. So that's the answer. If you want a risk free rate in euros, maybe the risk free rate you should be using should be the 10 year German bond rate, the 1.75% because it's the closest to being default free. If you're a stickler and argue there's default risk even in that rate, you might be right. You could consider using the 10 year bonds issued by the European Central Bank. The rate on that was about 1.73% of the time that I did this analysis. That could be a risk free rate in euros. In fact, if you're looking at a currency where the government issuing the bond is AAA rated, you can get a risk free rate by using the 10 year government bond rate in that currency. So you want a Swiss franc risk free rate, look up the rate on a 10 year Swiss franc bond. In fact, in this graph, I've risk free rates in different currencies where the government at the time that I did this analysis was still viewed as default free. It had a AAA local currency rating and I've risk free rates vary across these developed market currencies. Now that's your easy task. What if I came to you and asked you for a risk free rate in a currency where there is no default free entity? In fact, with my company examples, I have at least three currencies where there is default risk. One is the Indian rupee because Startup Motors is an Indian company and I could get an Indian rupee hurdle rate, an Indian rupee risk free rate. The second is Vale, which is a Brazilian company. And if I choose to do the analysis in nominal REIs, I need a nominal REI risk free rate. And the third is Baidu, which is a Chinese company and I need a risk free rate in Yuan. I'm gonna set up the process for estimating risk free rate in these three currencies or any currency where the issuing entity has default risk. There are three choices you can make. The first is you can stay with the local currency, get a government bond in the local currency and then net out from that government bond rate the portion that you think is due to default risk. Sounds fancy, right? Let me take an example. In November of 2013, the Indian rupee government bond rate was 8.82%. That was an Indian government bond denominated in rupees 10-year maturity, 8.82%. However, the Indian government was not rated default free. How do I know? I visited the Moody's website and I checked under sovereign ratings and the rating for India was not bad. It was B883. But the default spread for that rating was 2.25%. There we'll talk about how to estimate that default spread. But if you can estimate the default spread and you agree with that number, here's what the risk free rate in Indian rupees will become. 8.82% is the government bond rate. Some of that is for default risk and based on my estimate, it should be 2.25% for default risk. You net that out. My risk free rate in Indian rupees is 6.57%, 8.82 minus 2.25%. So if you want a risk free rate in any local currency, that's all you can do. Take the government bond rate, net out the default spread for that government in the local currency, you get a risk free rate in that currency. So that's your first choice, is stick with the local currency, try to back out from the government bond a risk free rate. Now there are other ways in which you can try to tweak out a risk free rate in the local currency. Here are a couple of choices. You could take the expected inflation in the local currency and add an expected real interest rate to try to come up with what I call a synthetic risk free rate in local currency. You're building one assumption on top of the other, but sometimes you have no choice. There are some cases where you might decide getting a local currency risk free rate is just way too much work. You have an alternative. You can do everything in a different currency. In fact, until very recently in Latin America, that's what most analysts and companies did. Rather than try to do an investment analysis in nominal reais or nominal pesos, they will do them in U.S. dollars. You're not avoiding the problem, you're just shifting it somewhere else because now your cost of capital and hurdle rate will be estimated in U.S. dollars, but all your cash flows will have to get converted into U.S. dollars as well, which means you replace the estimation problem from the discount rate to getting an expected exchange rate. But if you feel that's an easier problem to deal with, that's a second choice is switch to a different currency and do your entire analysis in a different currency. There's a third choice. You can try to avoid currencies altogether. In other words, rather than do things in nominal dollars and nominal pesos, you can do everything in real terms. What I mean by that is you take inflation out of your cash flows, in which case your discount rate has to be built off a real risk-free rate. One choice you have for the real risk-free rate is the TIPS rate. That's a U.S. Treasury Inflation Index Bond. At the time of this assessment, for instance, it was about 1%. That would be a real risk-free rate. But the key is to make your choice early about what currency or real analysis you're doing and get a risk-free rate in that currency. So let's see what the different ways of getting that default spread out, because especially if you decide to go that first route of netting out a sovereign default spread from the government bond rate, you need to get that number. There are three ways you can get a default spread. Some cases, you might get lucky and be able to use all three. Some cases, you might be able to use only one. And some cases, none of them will work. One is to look at market-based measures. There are two market-based measures. One is if you have a government bond, and this is from the local government that's been issued in U.S. dollars. The Brazilian government, for instance, has 10-year bonds denominated in U.S. dollars. You subtract out the T bond rate from that, you get a measure of the default spread for Brazil, because they're both dollar-based bonds, and the difference in rates has to be because the market assesses default risk in Brazil. That's one market-based number. The other is to go to the market called the CDS market, the credit default swap market. There you will see sovereign CDS spreads. The sovereign CDS spread for Brazil at the time of this assessment was 2.53%. That's a measure of how much default risk the CDS market sees in Brazil. So those are both market-based numbers. One is the CDS market. The other is a government bond denominated in dollars or euros. But what if you can't find either? In November of 2013, for instance, India did not have a CDS spread. India did not issue dollar-denominated bonds, but India did have a sovereign rating. The third approach what you do is you use the sovereign rating for the country, and you look up a typical default spread based on the sovereign rating. You're saying, how do I know what that typical default spread is? I create a lookup table at the start of every year where I take all sovereign countries, I take their ratings, and I estimate the average spreads for each ratings class. So if you tell me what your rating is, I can assess what the typical default spread is given that rating. Each of these three ways ultimately will give you a spread. If you can use all three, you have to make a judgment as to which one you want to hang your hat on. If you can get only one, go ahead and use it. If you can get none, maybe it's time to switch to a different currency. So in closing, let me show you what the risk-free rates look like in different currencies in January 2014. They range the spectrum from less than 1% for the Japanese yen and Swiss franc to more than 10% for the Brazilian riyal. And you're saying, that's strange. Why don't I just pick the lowest risk-free rate currency and do everything in that currency? It'll give me a lower hurdle rate. You're right, but there's a reason why risk-free rates vary across currencies. And there's only one reason, which is differences in inflation. High-inflation currencies have high risk-free rates. Low-inflation currencies have low risk-free rates. If you pick a low-inflation currency to do your discount rate, then your cash flows have to be in that same low-inflation currency. What one hand gives you, the other hand will take away. So there should really be no benefit or cost from going from a low-inflation currency to a high-inflation currency on the same project. That's tough to believe, I know. But we will come back and in the context of investment analysis, hopefully show that if you do a good analysis, it should be currency invariant. Currencies matter because of their expected inflation rates, and that's good to keep in mind. Thank you very much for listening.