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Gordon Growth Model - Financial Markets by Yale University #22 - YouTube
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So, Professor,
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if I was hoping we can go through
the idea of the Gordon Growth Model?
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>> Mm-hm.
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>> And kind of how that relates
to what we've learned in CAPM?
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>> Myron Gordon, a half century ago,
nearly told what,
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he gave a formula for
the present value of a growing quantity.
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Suppose we have an asset,
let's call it land,
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that is producing revenue for
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you every year, and
the revenue is growing in value.
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So it produces x the first year, then
it produces x times 1 + a growth rate,
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the next year, and
then it produces x times 1 + the growth
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rate squared the next year,
and then it does that forever.
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So this is year, now it's times 0,
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and then we have time 1, time 2, times 3,
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time 4, it would be 1 + g cubed etc.
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I say this might be land, because land,
assuming that it's managed properly and
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doesn't get depleted,
will yield a crop every year.
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And as time goes on,
the crop will be worth more.
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Partly because demand for it probably
goes up in a growing economy and
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probably because of technical progress.
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And we're going to assume this land
goes on growing like this forever.
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So the question is what do you pay for
this land at time 0?
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Okay, so Myron Gordon, he's famous for
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this formula principally,
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is that the present value = x/r- g,
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where r is the rate of discount.
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What he's saying is that,
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the present value is x/1 + r,
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that's this first term here,+ x (1
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+ g)/1 + r squared + x (1+g)
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squared/1 + r cubed, okay.
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And if you calculate,
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you can show that infinite sum
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reduces to this simple formula,
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as long as g is less than r.
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If g is less than r, then each term
is smaller than the one before it.
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And it sums to a finite number.
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If g equals r,
then every term here is x/1 + r,
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they are all the same, and so
the sum would be infinite.
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So as long as g is less than r this
is a formula for pricing the value of
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a asset that actually yields
an infinite amount, but
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in the future It's
actually growing forever.
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[LAUGH] Right, so
actually g can be negative also.
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It doesn't matter whether it's positive or
negative.
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>> So that would be like you're losing
some proportion every [CROSSTALK]
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>> Yeah-
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>> Every decade or something.
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>> It could be that
the land is being depleted.
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>> Okay.
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>> And so
the growth rate of the value is negative.
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So then this becomes r plus
something because g is negative.
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You still have a present value, and
this is an important thing to recognize,
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that even assets whose payments
are running down to zero,
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there still is a price for them today.
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That's really important to recognize.
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So some people think that businesses that
are growing are the only ones I should
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invest in.
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That's bad investing.
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You can make a fortune investing
in businesses that are declining.
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You can fill up your portfolio
with declining industries.
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It doesn't matter, it's the question,
can you buy them for
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less than the present value?
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And if you're buying them for less than
the present value, it's a good investment.
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>> I see.
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And so, here, just to clarify, g is given?
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>> Yes, I'm taking that as given, the
growth rate, it might be like 2% a year.
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>> Right
>> And the interest, r might be 5% a year.
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>> Okay.
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>> The value would be x divided by
5% minus 2% or x divided by 0.03.
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>> Okay.
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>> And this is a very useful
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formula because a lot of possible
investments have a growth rate.
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In fact they usually do.
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Usually you don't expect the earnings
of a company, for example,
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to stay exactly where they are today.
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Some companies are expected
to grow through time and
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some are expected to decline through time.
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So you end up using this
formula all the time to judge.
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You look at their earnings today and
you think, well what is it worth?
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What is the stream of
future earnings worth?
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And you can plug it into this formula.
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>> I see, and r is that also given or
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is that-
>> Now, okay.
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>> Being determined?
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>> Now I haven't talked
about risk in this equation.
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I was saying the land is going to do this,
we just know this for certain.
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>> Right, that's just given.
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>> But we don't in fact, often,
we don't know the future with certainty.
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So there's an amount of risk.
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So if this growth rate is more
uncertain than you thought,
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that should lower the price.
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Right, so if the assets is riskless,
if there's is no risk,
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if we actually know all the future
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payouts from the asset, then this r
would be the riskless interest rate.
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But if it's greater, if there is risk.
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And that would be measured by beta
in the capital asset pricing model.
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Then r would be increased
reflecting that risk.
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You still use the same Gordon formula,
but you have a higher r.
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R is no longer the riskless rate.
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>> Okay.
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And I also found that to be a very
fascinating statement you made that even
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if most people I think
typically think that if
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there's a industry that's declining,
I don't want to have that in my portfolio.
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>> Right.
>> But in this case we're kind of bringing
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out the idea that even stocks of declining
industries, those should be in your
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portfolio if you kind of followed the-
>> Right.
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>> The standard traditional [CROSSTALK]
>> I like to bring up the example of
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railroads.
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When the first railroads came in,
well it was in the 1830s, but
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by the 1840s,
there was a big bubble in railroad stocks.
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Lots of people thought wow,
railroads are growing.
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They were right.
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Railroads were growing.
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But people paid too much.
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Even though they're growing,
you can pay more than the present value.
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So lots of famous people in the very
beginning of the railroad era,
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lost fortune, even including
Charles Darwin, the great biologist.
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He couldn't figure out present value.
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He was a smart guy, but
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he couldn't figure out what the real
value of these railroad stocks were.
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But then as time went on, railroads
stopped being glamorous and exciting.
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And they became old hat.
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And then we got airplanes, and trucks,
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and cars, and
all these other alternatives to railroads.
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So railroad stocks then became
underpriced relative to this formula.
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So one of the best investments
to make in 1929 was railroads,
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already people were thinking about Charles
Lindbergh flew across the Atlantic Ocean,
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everything is moving fast for airlines,
and they just got overpriced.
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The same thing happened in the year 2000.
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In 2000,
that was the peak of the dot-com bubble.
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Everybody was investing in computer or
software, or social media stocks.
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And because they saw the growth rate.
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But they made a mistake.
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You have to use this formula.
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They made a mistake in thinking that
they're worth more than they really were,
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and the whole dot-com bubble collapsed.
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The good thing to invest in, if you
could go back in a time machine to 2000,
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was railroads,
[LAUGH] everyone was ignoring them.
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But they're still chugging along,
doing all this work.
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And now, even being declining industry,
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it wasn't living up to
expectations initially,
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in terms of earnings growth,
but they made good investments.
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Sometimes, not every time,
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depending on how the price compares to
the present value of their earnings.
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