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Session 6: Estimating Hurdle Rates - Equity Risk Premiums - Historical & Survey - YouTube
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- In this, Session Six of a 36 session
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corporate finance class, I'd like to talk
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about a second input into
every risk and return model
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in finance, which is
the equity risk premium.
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After defining what we'd like to measure
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with that estimate, we're going to look at
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two ways in which people
come up with that number.
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Doing a survey and looking at the past.
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In this third session in
estimating hurdle rates,
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I'd like to start talking
about equity risk premiums.
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In the very first session in hurdle rates,
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we talked about what
went into a hurdle rate:
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a risk free rate and a risk premium.
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And we defined risk.
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In the second session, we talked about
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a risk free rate, how you
come up with a risk free rate.
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In this session, I want to start talking
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about equity risk premiums, the premium
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you demand on an average risk investment.
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So let's set the table.
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Here's our objective.
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The equity risk premium is the premium
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you, as an investor, would demand for
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investing in the average risk investment,
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relative to the risk free rate.
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Sounds abstract, right?
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Let's assume you can make three
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percent on something risk free.
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The equity risk premium is what you
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demand over and above that three percent
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to invest in the average risk investment.
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So here's what's going
to go into risk premium.
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The first is, it should
be greater than zero.
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If you're accepting
three percent risk free,
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you would not settle for
less than three percent
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if you're investing in something risky.
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Second, it'll depend on how risk
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averse you are as an individual.
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The more risk averse you are, the
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higher the risk premium should be.
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And if you think about what goes
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into risk aversion,
part of it is your age.
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Younger people are less risk
averse than older people.
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Men are a little less
risk averse than women.
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And over time, your risk aversion
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might change, but you're born with
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some risk aversion you're
never going to change.
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So risk aversion varies
across individuals,
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and how risk averse you are will
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determine your equity risk premium.
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So let's try a little experiment.
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Let's assume that you've saved some money.
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And that you have all of
your money invested in
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something risk free making
three percent guaranteed.
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I come to you with a sales pitch.
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I say, "Look, I know you're
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invested in something guaranteed.
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"Three percent."
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Let's assume you want to invest in
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the 500 largest stocks in the US,
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the S&P 500, the Vanguard 500 Index Fund.
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How much more than three percent
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would I need to offer you to leave
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where you are right now, that perfectly
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safe spot, and invest in stocks?
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Do you see the question I'm asking?
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You can make three percent guaranteed,
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but maybe you'd be induced
to invest in stocks
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if I offered you a little
bit more than three percent.
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So I'm going to go through the choices,
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and if this is the choice
you would make, check it off.
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There's no right answer here.
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There's actually one wrong answer
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that hopefully none of you will pick.
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But there's no right answer.
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It really depends on
how risk averse you are.
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The first choice is
less than three percent.
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Thank God nobody picked it, because
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that's the one wrong answer because
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if you can make three percent guaranteed,
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you should never settle for less
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than three percent on a risky investment.
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Next choice is three to five.
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That's a risk premium
between zero and two percent.
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If you pick that, you're one of
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the least risk averse
people in this crowd.
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And if you're less risk averse, again,
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there's nothing good
or bad, you're going to
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be more invested in risky
acts than anybody else.
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You'll be quicker into stocks than
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everybody else, and that's going to
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be the pattern for the rest of your life.
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The next choice is five to seven.
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Your risk premium is now two to four.
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A little less risk averse
than the previous group,
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but still fairly low risk aversion.
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Seven to nine.
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If you're in that group, you're actually
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in the middle of the distribution,
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because I've done this survey on
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potentially thousands of investors
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and that's where the middle
of the distribution falls.
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A risk premium between
four and six percent.
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Nine to 11, you're
getting more risk averse.
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And if it's more than 11, you're probably
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among the more risk averse
people in this group.
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Now the reason I ask that question is
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if this were the entire
market, here's what I could do.
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I could take the numbers you gave me,
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back out from those numbers
your equity risk premium.
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So if you said seven percent, that's
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a risk premium of four percent.
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And after I had estimated all of your
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risk premiums, I could take a weighted
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average of all of those numbers to come up
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with an equity risk premium
for the entire market.
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Now, what did I weight it by?
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By how much money you have.
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This isn't a democracy.
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If you have no money, what you think
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about the risk premium
matters very little.
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If you have a lot of
money, it matters a lot.
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So that's basically the way to think
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about equity risk premiums, but if you
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decide to go down this route,
here's another problem.
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That number you just gave me is very
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sensitive to what's going
on in the outside world.
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For instance, let's assume
in the three or four minutes
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you've been watching this
session, that the market
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had dropped 25 percent
while you were watching.
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Now I come back to you with the same
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question I had just three minutes ago.
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You've invested safely
making three percent.
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How much more than three percent
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would I need to offer you
to invest in risky stocks?
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I'm sure some of you, after hearing
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the news story, might say,
"I demand a larger premium."
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Because you think that's
changed your risk.
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For others, you might say I'd settle
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for a smaller premium, because if stocks
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were great at 12,000, at
9,000 they're even better.
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But whatever the reason, risk premiums
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are not just difficult to
get, they keep changing.
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The world shifts around you.
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Your equity risk premium
is going to shift.
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What I'm arguing for is an equity
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risk premium that's
dynamic, that's constantly
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changing 'cause the world
is changing around us.
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Since I described the different ways
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in which you can estimate equity
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risk premiums, pass it through that test.
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Is it going to be dynamic?
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Is it going to be forward looking?
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Is it going to change when
the world changes around me?
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Because there are three basic ways
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in which people estimate risk premiums.
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The first is to do surveys, not of
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all investors, but of
subsets of investors.
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I'm going to start with that.
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The second is to look at
the past, historical data.
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To see what kind of premium you'd
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have earned investing in stocks as opposed
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to T-bonds or something
riskless and use that premium.
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The third is to get a forward looking
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premium that reflects
the world we live in.
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I'm not going to get a chance to do
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the third approach in
this particular session,
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but we'll do at least the first two.
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Let's start with the survey approach.
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Clearly, you can't ask all investors,
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because there are just way
too many investors out there.
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So almost every survey I've seen
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looks at a subset of investors.
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For instance, the very first listing there
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which looked at individual investors,
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that survey was done
until 2004 at which point
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the Securities Industries
Association which used
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to do it stopped doing the
survey because they discovered
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it was completely and totally useless.
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Useless in what sense?
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When you ask people what they thought
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stocks would make over the next year
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or the next five years, and that's
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what all these surveys do, they try to get
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a sense of what your
expected return on stocks is,
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they discovered that what they were
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getting were not expectations but hopes.
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The other groups of surveys continue.
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For instance, Merrill Lynch surveys
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portfolio managers around the globe
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every month, and they report a premium.
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That premium ranges
between three and a half
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to five percent depending on
the month you catch it in.
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Campbell Harvey & Graham surveys CFOs.
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CFOs use risk premiums in companies
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to come up with hurdle rates.
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They report that premium once every year.
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That number is about four,
four and a half percent.
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Pablo Fernandez, a friend of mine
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from Spain, does surveys of both academics
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and practitioners and he
reports those premiums.
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They range from five to
six percent depending on
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where you ask the question
and when you ask the question.
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But these are all survey premiums.
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I'll be quite honest, I
don't trust survey premiums.
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They're much too volatile, and they're
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much more a reflection of the past
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than their expectations of the future.
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What I mean by that is after a period
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of when stocks have done well, these
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surveys reflect much higher numbers.
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When the stocks do badly, they go down.
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In other words, they're reactions
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to the past rather than
expectations for the future.
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Which brings me to the second and most
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widely used approach
estimating equity risk premiums
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is to estimate a historical premium.
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Let me set the table.
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Here's what you're trying to do.
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You take a slice of history.
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20 years, 50 years, 80 years.
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You look on average what you'd have made
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investing in stocks over that period.
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Let's say it's eight percent.
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Then you look on average what you'd
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have made investing in
T-bonds over that period.
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Let's say it's three percent.
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Eight minus three is five.
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That's a historical premium.
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Easy, right?
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In fact, I have a table there that reports
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12 different numbers, all of which
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pass muster as historical risk premiums.
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Using 12 different risk premiums?
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How is that possible?
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Here's why.
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I took three slices of history.
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One going all the way back to 1928.
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That's 86 years.
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The second going back 50 years,
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and the third going back 10 years.
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And I got three very different premiums.
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I took the premium over T-bonds,
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which are longer term
government securities,
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and I got a very different premium
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than when I used the premium over T-bills,
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which are short term
government securities.
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I looked at arithmetic average premiums
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or added up 80 numbers and divided by 80
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and then I looked at
the compounded average,
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geometric premium, and I
got very different numbers.
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The equity risk premiums you see
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on this table, and this
is the most updated
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version of this table using data through
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the end of 2013, give you numbers ranging
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from three percent to eight percent,
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all of which technically are
historical risk premiums.
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Now, you might think it's
very convenient to have all
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these different numbers,
because you can use any
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number you want and get away with it.
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But unfortunately, that's a
bad way to think about it.
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I'm going to give you three suggestions
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on historical risk premiums which you
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can abandon if you feel you
have a better way of doing it.
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The first is go back as far as you can.
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Sounds strange, right?
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I want you to go back to 1928,
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before the Great Depression.
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The reason is statistical.
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Every one of these numbers on this table
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is a statistical estimate, and because
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it's a statistical estimate, there's
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a standard error associated
with that number.
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So for instance, if you go all the way
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back to 1928, and you tell me the
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risk premium for stocks over T-bonds
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is 4.62 percent, that's
a geometric premium.
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Before you get too excited, take a look
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at the standard error on that estimate.
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It's about 2.3 percent, which effectively
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means you can't rule out the possibility
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that the true rusk premium is about zero
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or as high as nine percent.
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In fact, as you go to 50 year and 10 year
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numbers, look at how big
the standard errors become.
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In fact, with the 10 year estimate,
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you might as well not tell me what
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the number is, because the
standard error is so large.
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Second, be consistent about
what you call risk free.
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I use the premium over
T-bonds, not T-bills,
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because to me, the T-bond
rate is my risk free rate.
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So because I use it as my risk free rate,
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it's the only premium I care about.
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Third, use the geometric average,
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because this premium gets built into
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your discount rate and
compounds over time.
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So if you force me to pick a number
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on this table, I'd pick the 4.62 percent.
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But I'd add the caveat that I feel
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very uncertain about what it's
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telling me about future risk premiums.
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And that's with the US.
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We have a lot of history.
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Remember there are markets that
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we're going to be dealing with, India,
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China, Brazil, where
you don't have 10 years,
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let alone 80 years of
history, 20 years of history.
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Historical risk premiums outside
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the US are often close to useless,
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because the historical
data is just not there.
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There is actually a study that comes
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out of Credit Suisse every year,
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and it's run by the
London Business School,
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that looks at equity risk premium
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over the last hundred years
in about 20 different markets.
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It's a very good historical
risk premium study,
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but even that study points to the
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shortcomings of historical data.
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Because even in that historical
data with a hundred years
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of data across multiple markets,
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the standard error remains
at about two percent.
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So let's think about ways of estimating
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risk premiums in markets outside
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the US where you don't
have historical data.
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There are a couple of ways you can do it.
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One very simplistic way borrows on
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an approach we already used to get
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to a risk free rate in
multiple currencies.
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We said if you're looking at estimating
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a risk free rate in a currency where
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there's no default free entity,
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you can use the sovereign default spread
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to come up with a risk free rate, right?
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If you used the sovereign default spread
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to come up with a risk free rate,
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that same sovereign default
spread can do double duty.
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And here's how it helps you
with your equity risk premium.
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Let's say you have an equity
risk premium for the US.
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Let's say at the start of 2013,
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that equity risk premium was 4.20 percent.
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Incidentally, that's a number we've
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updated to 4.62 percent
through the end of 2013.
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But in November of 2013, the historical
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premium was let's say 4.2 percent.
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Let's say I want a risk premium for India.
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Remember that default spread
we came up with for India?
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2.25 percent.
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That's a spread I subtracted out
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of the government bond rate to come
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up with a risk free rate in Indian rupees.
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I'm going to add that 2.25 percent
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to the US risk premium of 4.2 percent
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to come up with an equity
risk premium for India.
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I use the same approach
with China and Brazil.
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I add the default spreads
for those countries,
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.5 percent for China and
two percent for Brazil,
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to my equity risk premium
for the US to come up with
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an equity risk premium for
India, China and Brazil.
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And I could extend this to any
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country for which I either have a
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sovereign CDS spread
or a sovereign rating.
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I take the default spreads, add them
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to the US risk premium to come up
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with a total risk
premium for that country.
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That's the state of the art, if you can
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even call it that, of estimating
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country risk premiums that
most practitioners use.
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I use one tweak on this approach,
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and it's built on a very simple principle.
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Those default spreads were the spreads
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you charge for buying a government bond
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issued in rupees or reals or yuan, right?
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That was a default spread
for buying a government bond.
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You're not interested in
buying a government bond.
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You're interested in buying equities
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issued by these countries.
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I would assume that equities are riskier
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than bonds, and to measure the relative
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risk of equity, I'm going
to look at two numbers.
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One is the standard deviation of the
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equity index in that country.
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The other is the standard
deviation of the government bond.
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So as an example, if you had a standard
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deviation of 21 percent
in the equity index
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and 15 percent in the government bond,
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equities are about 1.3 times more risky,
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or 1.4 times more risky
than the government bond.
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You multiply the default
spread by that ratio.
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That's effectively what I
did for my three countries.
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I took India, Brazil and China.
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I took the default spreads that I
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got from their ratings, and I scaled
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up the default spread for the additional
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risk of equities in
each of these countries.
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And this is how I defined the equities.
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In India, I looked up the standard
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deviation in the SENSEX, which is
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the Indian equity index, and the standard
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deviation in the Indian government bond.
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In Brazil, I looked at the standard
[904]
deviation of BOVESPA and the standard
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deviation in the
Brazilian government bond.
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In China, I used the standard deviation
[911]
in the Hang Seng or the Shenzhen,
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Chinese equity index, and scaled
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it to the standard deviation
of the Chinese government bond.
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In each of these, I'm
scaling up the default
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spread for the additional
risk of equities,
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adding it to my equity risk
premium for the US to come up
[927]
with a total equity risk
premium for that country.
[930]
As we go through, we will talk
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more about country risk premiums.
[935]
Thank you very much for listening.
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