Bryan Caplan  

How Are Stocks Like Bonds?

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From John Cochrane:

The standard portfolio rule says that your stock percentage should rise with the expected return (stocks and bonds) divided by squared return volatility. So, if you were happy with a 50/50 portfolio with an expected return of 7% and 15% volatility (standard numbers), 50% volatility means you should hold only 4.5% of your portfolio in stocks!

...Many sophisticated investors and hedge funds who use this standard formula are getting out, waiting for at least a return of lower volatility before getting back in.

The answer to this paradox is that the standard formula is wrong. It assumes that stocks are a random walk, and the chart tells us otherwise. Stocks act a lot like long-term bonds -- when prices decline and dividend yields rise, subsequent returns rise as well.

Good bond investors know this. If you have a 10-year Treasury indexed bond, and a 10-year liability (say, you want to retire in 10 years), and you desire complete safety, you can ignore quarterly statements. If you see interest rates rise, bond prices tank, and bond volatility go through the roof, you would be foolish to call your broker and cry, "We've got to sell! I can't take any more losses." ...Stocks are much riskier, of course. But the same logic explains why you can ignore "short-run" volatility in stock markets.


HT: Mankiw

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COMMENTS (6 to date)
Troy Camplin writes:

Apparently I'm missing something, so perhaps you can help me here. Paulson is now talking about using the $700 billion to inject money into companies by buying stocks. Now, unless the companies issue more stocks, the treasury buying stocks isn't going to affect how much money the companies have at all, since they will be buying stocks that have been sold by people like me, unless they in turn sell the stocks they hold once the stock prices go up. You neither lose nor make money on a stock until you sell that stock, after all. Or am I misunderstanding what goes on in the stock market? And who holds the stocks once they are sold? In a typical market, if you have a seller, you have a buyer. Do the sold stocks revert back to the companies that issued them?

NickK writes:

@Troy -

I believe they will be making direct purchases in the companies themselves, not buying stock on the secondary market from you or I. By purchasing this equity stake directly from the company, they get ownership while infusing the company with cash.

Mike writes:

I'm glad this post was written. I read the same article in the WSJ and the first paragraph quoted above didn't make sense to me. Is there someone brighter or more educated than me that can explain how he got a 50/50 and 4.5/95.5 stock/bond portfolio from his assumptions?

Thanks in advance

nicholas shackel writes:

Stock% = constant x expected return/ variability^2

solve for constant given S = 50 ER = 7 and V=15

gives C= 225x50/7

then solve for S given that C= 225x50/7, ER= 7 and V=50

Phil writes:

The difference is that with the bond, the return is fixed, even if the price of the bond fluctuates. With the stock, the return varies with the success of the company. So it's possible that when the stock price drops (say) 30%, it's because the rational expectation of the future return has dropped 30%.

If you believe the markets are reasonably efficient, then the volatility in stock prices is actually volatility in economic expectations.

So you can ignore quarterly statements on the bond, but not on the stock.

Philippe writes:

Could someone elaborate on the following:

50% volatility means you should hold only 4.5% of your portfolio in stocks!

The formula:Stock% = constant x expected return/ variability^2 is not clear to me at all.

I'm trying to figure out how the author got to 4.5% but I'm unable to get it with Nicolas formula.....

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