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 going to 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 in 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 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 three percent on something risk free. The equity risk premium is what you demand over and above that three percent to invest in the average risk investment. So here’s what’s going
to go into risk premium. The first is, it should
be greater than zero. If you’re accepting
three percent risk free, you would not settle for
less than three percent 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 you’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 you have all of
your money invested in something risk free making
three percent guaranteed. I come to you with a sales pitch. I say, “Look, I know you’re invested in something guaranteed. “Three percent.” 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 three percent 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 three percent guaranteed, but maybe you’d be induced
to invest in stocks if I offered you a little
bit more than three percent. 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 three percent. Thank God nobody picked it, because that’s the one wrong answer because if you can make three percent guaranteed, you should never settle for less than three percent on a risky investment. Next choice is three to five. That’s a risk premium
between zero and two percent. 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
acts 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 six percent. 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 if 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 seven percent, that’s a risk premium of four percent. 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 percent
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 three percent. How much more than three percent 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 ’cause the world
is changing around us. Since I described 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 me? 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 or 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, Merrill Lynch surveys portfolio managers around the globe every month, and they report a premium. That premium ranges
between three and a half to five percent depending on
the month you catch it in. Campbell Harvey & Graham surveys CFOs. CFOs use risk premiums in companies to come up with hurdle rates. They report that premium once every year. That number is about four,
four and a half percent. Pablo Fernandez, a friend of mine from Spain, does surveys of both academics and practitioners and he
reports those premiums. They range from five to
six percent 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 their expectations of the future. What I mean by that is after a period of when stocks have done well, these surveys reflect much higher numbers. When the 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
estimating equity risk premiums is 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 eight percent. Then you look on average what you’d have made investing in
T-bonds over that period. Let’s say it’s three percent. 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. Using 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 added up 80 numbers and divided by 80 and then I looked at
the compounded average, 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 three percent to eight percent, 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 going to 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 percent, 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 percent, which effectively means you can’t rule out the possibility that the true rusk premium is about zero or as high as nine percent. In fact, as you go to 50 year and 10 year numbers, look at how big
the standard errors become. In fact, with the 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 force me to pick a number on this table, I’d pick the 4.62 percent. 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 US. We 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 US 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 premium over the last hundred 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 a hundred years of data across multiple markets, the standard error remains
at about two percent. So let’s think about ways of estimating risk premiums in markets outside the US 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 the 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 US. Let’s say at the start of 2013, that equity risk premium was 4.20 percent. Incidentally, that’s a number we’ve updated to 4.62 percent
through the end of 2013. But in November of 2013, the historical premium was let’s say 4.2 percent. Let’s say I want a risk premium for India. Remember that default spread
we came up with for India? 2.25 percent. 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 going to add that 2.25 percent to the US risk premium of 4.2 percent 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, .5 percent for China and
two percent for Brazil, to my equity risk premium
for the US 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 US 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 reals 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 percent
in the equity index and 15 percent 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 of 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 US 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.

Paul Whisler


  1. I noticed on slide 18 that the formula says (std deviation equity)/(std deviation country bond).
    Just want to verify the top line should really be (std deviation country equity) to match the bottom.

    And I really want to extend my gratitude to you for all the information you post. It is much appreciated.

  2. It is interesting that surveys show a higher risk premium following equity rallies and lower ones following sell-offs. Intuitively, wouldn't we expect risk-aversion to increase following equity sell-offs, resulting in higher risk premiums?

  3. Sir please do make notes for the people who can't really hear your voice my friend has hearing problem so please do give the recitation notes

Leave a Reply

Your email address will not be published. Required fields are marked *