Capital Markets Are Efficient, If We Assume Pi Equals 3

Every time I read about economics, I get annoyed. For a bunch of people who use a lot of math and use a lot of science-ish language, they’re awfully imprecise with their assumptions.

I’m reading Principles of Corporate Finance, by Richard A. Brealey and Stewart C. Myers. To be more precise, I’m reading the third edition, published in 1988. That’s a scant year after the Black Monday stock market crash of 1989, which some of my older readers may recall. This was one of my father’s textbooks for his MBA, and it looks like I’ve reached the right point in my life to be reading it and understanding it. Mostly.

You see, it has lots of exciting mathematical formulas and breathless prose about how modern capital markets (like the one in 1987. Oh, and the one we have right now!) are almost perfectly efficient, and how the price of any stock on the stock exchange must be the right one at any given moment. In other words, whenever you buy a stock, it can’t be overvalued, or undervalued.


For example, there’s a short discussion on ‘money machines’ in chapter 3. Here’s how it works: Assume you can borrow money at, say, 7% p.a. for 2 years, and you can get a return of 20% p.a. by investing money in the next year. So, you can lend $1000 to get $1200 next year. But you could also borrow the present value equivalent of this $1200, which is $1048. You’ve just made $48. And now you can do it again with $1048, and then again, and so on. Do this 147 times and you’ve got a million bucks. This complicated example in the book obfuscates what’s going on. They mean: a bank will give you 20% on your savings, and a personal loan rate of 7%. They’re idiots, because they’re giving you back more money than you give them.

Yes, they are idiots, but there are some assumptions here that are not examined. Firstly, who’s to say that the 20% return isn’t because the bank is investing your savings in AAA rated Mortgage Backed Securities? Or a Ponzi scheme? 20% on savings is amazingly high, so the catch is that the downside risk is probably enormous. Secondly, what sort of risk are you? In the example, you’re not providing any sort of collateral for the loan. The bank is only charging you 7% on an unsecured loan? Are you nuts?

The book says this situation doesn’t exist because all the other investors in the market will see this opportunity and rush to take advantage of it, and the bank will implode. Until I read this book, I certainly wouldn’t have been able to spot an obvious opportunity like the one above, let alone a more subtle one that is more likely to exist in real life. But if I did, do you think I’d be telling anyone? I know that they’d all pile on to take advantage of it, ruining it for everyone, so I wouldn’t tell anyone.

Here in the real world, this is what is called information assymetry. This is a fancy way of saying “I know more than you do, and I’m not telling.” Modern capital markets are not efficient, because there are large information assymetries. A professional securities analyst will know more than a casual day-trader. The advent of cheap Internet brokerages has made things worse, because now you have millions of undertrained people with some spare cash who are free to buy whatever they want. They don’t know anything about net present value theory, nor do they act purely out of rational self interest. Someone who knows more than they do can take advantage of it, and they often do.

This is why the price of a stock is not necessarily equivalent to the value represented by that stock. Stocks can be under- or over-priced.

Outright stock manipulation, such as pump-and-dump schemes and insider trading are, rightly, illegal. And people are allowed to spend their money on stocks if they want to. Yet the more I learn, the more I admire Warren Buffet’s strategy of discouraging those kinds of people from buying Berkshire Hathaway stock, because he wants well informed, emotionally stable investors, not traders, to be part-owners of his company.

All these economic theories are nice and all, but I worry when the people espousing them seem to forget that they only work properly when dealing with toy problems. People are handling large amounts of other people’s money according to the rules dictated by these theories, and we’ve recently seen another example of what happens when the model doesn’t match reality. The math is easier if you ignore the messiness of real life. It’d be much simpler if people were rational all the time, too.

Pi isn’t rational, so why do economists assume people are?

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  1. Read Benoit Mandelbrot’s (of the Mandelbrot Set fame), “The (mis)Behaviour of markets” & you’ll see a massive amount of economic theory is based on the incorrect assumption that market fluctuation is normally distributed & that all the extrapolated math is rubbish due to it’s basis on that false premise.

    I also find it interesting that the media making speculations about an upcoming recession alone can be a self-fulfilling prophecy without any real basis for the original speculation.

    I try not to think about these things too much though, much like I try not to dwell on the fact that prime number factorisation with quantum computing has already been done & only needs to be scaled out (albeit significantly) before the security of almost every electronic financial transaction on the planet becomes moot.

  2. Thanks, John. I’ll have to check out that book. This is my major problem with economics: math doesn’t work if your initial assumptions are wrong. Real mathematicians spend ages ensuring their proofs don’t have flaws. Economists deal with models, not proofs, nor really theories in the strictly scientific sense.

    The thing with models is they break catastrophically if things diverge too far outside the parameters of the model. This happens regularly.

    The fact that the media reporting a likely recession can help to bring one on is just further evidence people are irrational.

    New security mechanisms will be put in place as the old ones become unsuitable. It happens now as flaws are found in older algorithms, like single-DES.

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