Session 3: The Risk Free Rate

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 the business make sure the discount rate use 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 ninal 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 it on on the ingredients 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 3 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 ask 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 and finance they're all based on the premise at least the traditional models and 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 stand the capital asset pricing model of the capam it's been around a long time and in the capam 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 price ing model and multifactor model 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 bait they allow for multiple sources of Market risk and allow for a bait against each one you saying what's the difference between the Arbitrage pricing model and the multiactor 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 in 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 in 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 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 capam 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 a 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 and in fact if you take the cap app 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 iote of Def 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 table that investment is risk-free to you right now let's say you have a 5year 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 your one you 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 longterm 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 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 5 years or 10 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 3mon ebles 6mon ebles one year 2 year 5 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 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 10e corporates it's very difficult to find 30-year corporates one final point you 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 10year 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 European company it could be us company you want a Euro risk re rate right that should be easy let's go find some government bonds nomin Euros I tried and I found too many say what do you mean too many I found a dozen European governments all issuing 10year bonds all denominated 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 Frank bonds and the German government at deark 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 you is 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 the lowest of those 10year 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 reiz so first step is the same you find a 10-year Government Bond denominated in reiz 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 to proxy know whether you're familiar with Moody 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% he 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's 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 reiz of 7 and a/4 per. 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 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 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 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 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.