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Economic News, Data and Analysis

D10K A Bubble or not a Bubble

That is the question!

So the Dow has finally hit 10,000. I know my life (if not my poor, empty,
graduate student wallet) is fundamentally richer for it.

I’ve been waiting for CNBC to give
me a call to ask my opinions on Dow 10,000, but, alas, sitting patiently
by the phone has not paid off. Instead, I thought I would ask myself about
the market and bubbles.

Q: What’s a stock bubble?

A: A bubble is used to describe a stock that is trading at a price above
its fundamental value.

Q: So then, wise guy, what is a stock’s fundamental value?

Typically, the fundamental value of a stock is equal to the present
discounted value
of the stream of dividends paid by the stock. Basically,
it’s the amount of money that you can expect to get back from the stock
if you hold it into the distant future – taking into account the fact that
1$ is worth more today than tomorrow. Things like a healthy
economy
, growing profit margins, a growing consumer base, etc., lead
to better fundamentals and a higher stock price.

It’s getting harder to sell this story to my students since a growing
number of stocks – especially the new hot internet issues which typical
MIT students follow – do not pay regular (or any) dividends. The best way
to think about the fundamental value of a stock for these cases is to think
of the value of the company as the price it would receive should it be
sold to another company at some point in time – the equivalent of a zero
coupon bond with an uncertain maturity and face value!

Q: So why do prices get above the fundamental value?

A: Well, that’s the hard question. The easy — well, easier — question
to answer is why the price stays above the fundamental value once it’s
there. Below is a simple numerical example of how
a bubble might work.

The basic story is that if there is a bubble that has some chance of
“bursting” – or have its price drop significantly – people will not be
willing to hold the stock unless there is a high rate of return. As the
price rises, the loss of money due to a fall becomes even greater, causing
the price to rise even faster. The price rise will continue to accelerate
until the price falls back to its fundamental level.

Why the price is initially too high is a much murkier question. It could
simply arise from valuation mistakes, “irrational exuberance”, “animal
spirits”, or other idiosyncratic shocks.

Q: How can you tell if there’s a bubble?

A: You can’t. Not until it has already burst.

Anyone claiming to know that a current stock price is a bubble (or not)
is either fooling
themselves, selling something, or both.

A quickly rising price reflects either a legitimate increase in the
future earnings of the company, or a stock bubble – which case it is cannot
be told from current information. Remember that the fundamental price of
a stock should depend only on the future performance of the company.
We can only observe the price, but not the future – at least not without
a crystal ball.

People are wrong about their bubble predictions all the time. See below
for an extreme example.

Even after the fact, a large fall in the price could be either due to
a bubble bursting, or due to bad news which reduced the estimates of future
performance and lowered the fundamental price. Hindsight is not always
20/20.

Q: Is there any difference between “irrational
exuberance
” and a bubble?

A: Well, I shouldn’t put words into Alan Greenspan’s mouth, but I think
there is a fundamental difference between the two.

A bubble can be perfectly rational in the sense that everyone is making
informed and reasonable decisions. The investors simply demand a higher
rate of return on stocks that face a risk of bursting. Bubbles are not
necessarily irrational.

On the other side, a stock that follows “irrational exuberance” may
be priced exactly according to fundamentals – e.g. perceived future dividends;
but may be completely irrational in the sense that the perceptions are
too high. In this case the prices are too high – not because of a bubble,
but because of mistaken expectations of the future.

Q: So what’s the bottom line?

A: A stock is worth what everyone else thinks it’s worth. If everyone
thinks eBay is worth 200$ a share, then it is worth that.

Does this price – does Dow 10,000 – represent a bubble?

Only if it pops.

 

Comment via the Bulletin
Board
.

See also:

People who were wrong:

PDV

The formula for the PDV of a (real) stream of payments given a real
interest rate, r, and payments {x(t), x(t+1), x(t+2), ...} is

V = x(t)/(1+r) +  x(t+1)/(1+r)^2 + x(t+2)/(1+r)^3 + ...

 

 

Simple Example of a Bubble.

Let’s say that Amazon.com, according to its fundamentals, is really
worth 100$ a share.

The price of Amazon, however, is 10$ overvalued and currently trading
at 110$ a share. Lets say that there is a 40% probability that the share
will drop down to the 100$ (plus interest) level in the next year.

price = 100 (1 + r) + b  with prob .60

      = 100 (1 + r)     
with prob .40

In order to induce people to hold amazon shares we must have that the
return to holding amazon shares be the same as a safe investment in T-bills,
so

100 (1 + r) .60 + [100 (1 + r) + b ] 0.40 = 110 (1 + r).

Some simple algebra shows that

b = 10 ( 1 + r ) / 0.60

so if the interest rate is 5%, then b = 17.5 and the price of Amazon
will be 122 1/2 tomorrow.

Over time, the amount of the overvaluation will be:

b(t+1) = b(t) (1+r)/(1-q)

where q is the probability of a crash.

This gives the price of Amazon.com over the next several years (assuming
the stock does not burst) as

 

Year Price Rate of Return 
1 110  
2 122 11%
3 149 22%
4 202 35%
5 301 49%
6 479 59%
7 798 66%
8 1362 71%
9 2357 73%
10 4105 74%

So, in order to induce people to hold Amazon.com stock, the rate of
return must be higher than the 5% safe return; and this rate of growth
increases over time.

Note that there is nothing “irrational” about this, people are perfectly
happy to accept the high risk, so long as they are compensated by the high
returns.

 

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