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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
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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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Filed under: Finance

Political Pitfals of Social Security Privatization

Dynamic Consistency and Social Security

Since the end of impeachment ordeal, Social
Security reform has been threatening to take center stage. As such
– and since economists have spent enormous amounts of time investigating
the economics of the program – I have been expecting to see, hear, and
read from a parade of economists on the relative merits of various proposals.

Wishful thinking, I suppose.

Instead, it seems as though the debate is on the politics of reform
– which policy is more “politically feasible” or “politically stable”.
My reading comes down to this: politically speaking, if there is any other
option available, you can’t substantially cut benefits or raise taxes.
By process of elimination, this leaves privatization — investing a chunk
of money in the stock market — as the only real political alternative.

Besides, if the privatization plan doesn’t work, the failure will be
many years from now, which means that current policy makers will be able
to claim success today.

However, there are political pitfalls with each of the two main privatization
proposals.

1) Investing the Social Security Trust Fund

“I doubt if it would be feasible to insulate, over the long
run, the trust funds from political pressures — direct and indirect —
to allocate capital to less than its most productive use.” Alan Greenspan
Testimony
from 01/28/1999
.

The president’s plan would invest a portion of the current surplus in the
stock market in order to increase the size of the Social Security trust
fund in the future.

Alan Greenspan, among others, have criticized this plan on political
grounds – arguing that the invested funds would represent a pool of money
that would tempt future lawmakers to either spend the money, or to direct
the investments into politically popular companies or investment areas.

The government run investments, even if they were be invested wisely
now, could not be guaranteed to be invested wisely in the future. The system
would, in this sense, be politically unstable.

Proponents of the plan argue that an independent agency could be set
up to insulate the regulation of the funds from the political process.
(The irony of the situation is that the Chairman of the Federal
Reserve
is arguing that it would be politically impossible – or at
least unlikely – that such an institution, with qualities nearly identical
to the Federal Reserve, could be set up and maintain its independence.)

2) Individual Accounts

“Early access to individual accounts and the receipt of benefits
as a lump-sum might not preserve adequate benefits for workers and for
surviving spouses.” From the NASI
– Report of the Panel on Privatization of Social Security

It is argued that individual accounts – which would allow individual investors
to make decisions about where the money is invested – would not suffer
the same political stability problems as the above plan. However, individual
accounts are subject to political stability problems also.

There will be winners and losers in the stock market game – a large
number of losers could form enough of a political will to compensate them
for their misfortunes, then we may wind up with a bailout of the social
security system that would make the S&L bailout look like a drop in
the bucket. The program would then have to be reexamined again in the future.

(This point, of course, depends upon the specific individual account
plan adopted – if retirement accounts required are in addition to a base
level of benefits, there would not be as much instability. However, the
higher the base benefits, the lower the gain from investing in the stock
markets higher returns. Also, if guaranteed benefits are high, there is
the obvious and explicit moral hazard problem – people will become extremely
risky in their investment decisions. Even if there are no explicit guaranteed
minimum benefits, there may actually be an implicit guarantee, hence the
political instability.)

A second source of political instability comes from the fact that people
will have an account with their name explicitly written on it. When people
retire, many will demand the cash up front leading to a loss of the benefits
from real annuities – including the implicit insurance on running out of
money before dying. The political demand for leaving the money in the accounts
as bequests will most likely rise also.

The ultimate political consequences of each of these factors is at best
uncertain.

Next on CNN…

I keep hoping to see more economists
on TV
talking about the reforms (hey, we’re not that ugly!),
but if not us, then maybe they can get some political scientists to talk
about how the program might be reformed the next time we have to address
a Social Security crisis.

I won’t hold my breath for that either.

 

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Filed under: Economics

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