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Author: dbau One star, 50 posts Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: of 677  
Subject: Riskless Portfolio Example Date: 2/9/2000 2:01 AM
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Bruce writes: ... big arbitragers would steal the improved returns by buying a sure-thing portfolio that diversifies away the unsystemic risk and hedges away the systemic risk...

I think that this is really important, but I am not sure I understand exactly. Care to expand on this?


Yow - this is pretty off-topic again. But, well, it's fun, so here goes...

We'll do an example that just separates two risks (1) next year's favorite hat color (undiversified risk) and (2) the fate of the whole hat industry next year (diversified risk).


THE COLORED HAT INDUSTRY

Among the hundreds of various hat companies, you might find two hatmakers that are average in every way, except that they are making opposing "Big Bets":

New Red Hat Factory (NRHF)
"We Just Sell Red Hats"

Old Colored Hat Group (OCHG)
"Making All Sorts Of Hats That Are Not Red"


FUTURE PROSPECTS OF THE TWO BIG BETS

We don't know ahead of time if consumers will really love or hate Red Hats. We know one company will Win Big, and the other company will Lose Big, and the competition is in delicate balance today. Maybe it's a 50/50 game. Maybe the probability can't be estimated because nothing like Red Hats have ever been seen before. We see these kind of situations in the tech industry all the time. On the other hand, despite this one unknown, suppose everything else about the competition between the two companies was very solid and certain, and all investors agree on the following facts:

(A) If consumers Like Red next year
The value of NRHF will be 20% of the whole hat industry.
The value of OCHG will be 2% of the whole hat industry.

(B) If consumers Hate Red next year
The value of NRHF will be 2% of the whole hat industry.
The value of OCHG will be 20% of the whole hat industry.

The numbers are contrived, of course, so that the value of the two companies together is going to be 22% of the industry next year regardless of the fate of the color Red.


CURRENT PRICES IN A RISK-AVERSE WORLD

So what should be the price of NRHF and OCHG today? It depends on how the market views undiversified risk. If the market were sensitive to undiversified risk, then most investors would shy away from these Big Bets.

Here are some prices you might see today if most investors worry about undiversified risk:

The price of NRHF might be only 4% of the whole hat industry.
The price of OCHG might be only 11% of the whole hat industry.

If you the Risk-Taking Investor see this pricing, you're attracted to these stocks. You figure, "NRHF is a bargain at 4% since the upside is so huge! And I don't care about risk!" And at these prices, how can you be wrong? Even if you bought both NRHF and OCHG by paying for 15% of the hat industry today, it's a cheap way to buy yourself into 22% of the industry's value next year. Of course, there's always the little problem that the whole hat industry could be set to take a dive next year. But then, you always like to say, "No risk, no reward," right?


THE RISKLESS HEDGED PORTFOILIO

But academics believe that you'll never see this kind of situation, where individual companies are undervalued simply because they are taking Big Bets. This is because the Filthy Rich Investor Equity Hedge Fund is always active and fully alert, and they can make money on these prices without any risks at all! Here is what they do:


FRI Equity Hedge Fund Hat Investment Proposal

(1) We buy equal amounts of both NRHF and OCHG. Combining these two companies guarantees us a stake in 22% of the industry next year.

(2) And we short the Whole Hat Industry Index (WHIX) to offset our 22% fraction of the industry next year.


Now, the FRI hedge fund will take on no Hat Industry risk, because their long and short positions will be equal portions of 22% of the industry next year no matter what the value of the whole industry is next year. And they are taking on no color-specific risk, because regardless of how the color Red fares, their combined long position will be worth 22% of the industry next year.

On the other hand, at current prices they only have to pay for 15% of the hat industry today to buy the 22% share for next year, so they get to pocket the remaining 7%-of-the-industry difference (in cash!) for themselves. This is so lucrative that Filthy Rich investors pump billions of dollars through this structure within a few minutes, buying more and more of NRHF and OCHG and forcing the prices of the two companies to rise. They can continue doing this until the numbers are no longer in their favor.


THE MORNING AFTER

By the time you roll out of bed, FRI is through, and you might see prices like this:

The price of NRHF might be 6% of the whole hat industry.
The price of OCHG might be 16% of the whole hat industry.

At this point, FRI has stopped because it costs them 22% of the industry this year to buy 22% of the industry next year. There's no more gap to exploit.

But this means that by the time you have a chance to buy some stock there's no obvious good deals to be had any more. Even though risk-averse investors might be scared away from Big Bet companies, the existence of big hedge funds has eliminated any possible discount due to undiversified risk.

Even if you're not risk-sensitive at all, there's no particular advantage in buying into the Big Bet of either NRHF or OCHG. Neither company - nor any combination of the two companies - is obviously cheap compared to their prospects next year.

Now, FRI has not eliminated a possible discount that might be due to Hat-Industry-Wide risk. So the hat industry itself might be undervalued (or overvalued). FRI's arbitrage scheme doesn't eliminate any possible excess returns from systemic risk.


This is why many academics don't believe that you should be able to find a good discount (a good risk premium) for undiversified risk. If you could, then big investors would diversify and hedge away the risk, and steal the risk-free premium for themselves. If there is any risk premium, they believe it must be due to systemic, diversified risk.

Of course, the real world is not so neat, and the theory is probably not literally true. The market has some inefficiencies, and undiversified risk probably causes some undervaluation. But the reasoning is sensible, and it's a good motivation for avoiding an undiversified investment strategy.
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