I've posted a draft of my brief paper on popping asset bubbles on my other web site. It can be found here. Comments are welcome.
Wait, nobody reads this blog.
Never mind.
Thursday, July 9, 2009
Sunday, July 5, 2009
Bubbles Always Pop!
That's the working title for the paper I'm working on as discussed in the last post. The key is not that the number investing in the risky asset depends on the growth rate of the risky asset but that it depends on the momentum of that asset. That is, how long has the asset been outperforming the risk-free bond? This attracts more investors until it stops outperforming the risk-free bond and then everybody tries to get out and the bubble pops.
Here's the abstract and the intro to the (very short) paper. I'll post the pdf when it's nearer to completion.
Abstract
This brief paper sets up a simple model in which investors can be ruled by “animal spirits” and bid up the price of a risky asset well above its fundamental value. The price of the asset eventually plateaus so that the annual return is less than could be earned in a risk-free bond. This lower return signals the end of the bubble and investors rush to the exit, pushing the price well below its fundamental value in one period. If model parameters remain the same, this cycle continues indefinitely with bubbles inflating and popping over and over again. A change in the parameter values allows the risky price of the asset to hover around its fundamental value. A bubble, at least in terms of this model, can be interpreted as an increase in the weight of irrational “animal spirits” as opposed to the rational value investors in the market. When the bubble pops, the irrational investors diminish in importance and the asset no longer experiences bubbles. There are a number of additional steps that need to be taken int he model in order to make it useful from a macroeconomic point of view.
1 Introduction
When Great Uncle Frank calls on that lazy Sunday morning and tells you he has a guaranteed investment opportunity, what do you do? You ask him some questions, and eventually, you realize that he invested early in a Ponzi scheme. And now you're at an ethical crossroads. After all, Great Uncle Frank earned fifty percent on his money in six months. You could use an extra five thousand dollars. Hell, who couldn't? Of course the ethical course is clear. Getting money in a Ponzi scheme isn't really different then mugging old ladies in the back alley. Either way, you've stollen money that doesn't belong to you. You explain to Great Uncle Frank that you can't invest in his “once in a lifetime” investment opportunity and tell him to give your love to Great Aunt Miriam.
Of course, homo economicus, that near relation of ours who fully developed in our great midwestern town of Chicago, is not familiar with ethical dilemmas. His only concern, when his Uncle Bernie calls with the same investment opportunity, is to figure out the likelihood that he can get in on the Ponzi scheme before it runs out of money and the last round of investors are left holding the bag. If he thinks the scheme will continue for at least another round, he's likely to invest, make some money, and then get out. Homo economicus is entirely rational and doesn't have to worry about Keynesian “animal spirits.” The rest of us are not so perfect and can get carried away with the thought of making a pile of money in an easy investment. If a friend or neighbor just made a bunch of money investing in a Ponzi scheme, we're likely to want to invest as well. If the asset is a stock or a house, then we have no ethical qualms and we can rush into the invesment with a clear conscience.
And an asset bubble is really no different than a Ponzi scheme, even if there's no postal reply coupons at the center of it. If I knowlingly buy an asset for a price above its long-run value and sell it to you for even more before the bubble bursts, then I've taken your money, as sure as if I was an early investor with Bernie Madoff and you were one of the ones holding the bag when the Feds arrived. The fact that it's not illegal may help me sleep better at night, but we're both just gamblers trying to make a buck before the final whistle blows. And when we see an asset that has outperformed others for an extended period of time (whether it's tulips, stocks, or houses) we want in as well. Who wouldn't? Even if we know the asset is overpriced, it's not completely irrational to invest if we don't think the bubble is going to burst anytime soon. As Charles Kindleberger said, “There is nothing so disturbing to one’s well-being and judgment as to see a friend get rich.”
As the bubble expands and the price pushes higher and higher, Cassandras warn that the prices won't keep on going up forever. Eventually they are proved correct and something triggers an exodus. It may be that risk-free bonds outperform the risky asset. It may be a scandal in the financing of the asset comes to life. It may be a panic that spreads through the market. Whatever it is, the bubble has popped and asset values head south much faster than they headed up as everybody wants to divest at once. After the bubble has popped the animal spirits of investors are tempered and are more likely to be replaced by the small voice in the back that was telling us it was all to good to be true in the first place.
This paper has its origin in a number of blog posts by Brad DeLong and Paul Krugman looking for a model that exhibits asset bubbles and also has those bubbles pop. In fact, the main setup for the model presented here comes from DeLong (2009). His model exhibits asset bubbles as investors randomly compare returns between the risky asset and the safe asset and switch to the asset that offers the higher return. In his model, however, there is no way for the bubble to pop. Instead the bubbles deflate slowly as the price of the risky asset passes its fundamental value before starting to inflate again. DeLong shows that his model is fairly sensitive to changes in the main parameter value.
The model here has investors in the risky asset pulled by two opposing forces. One, meant to represent irrational animal spirits, attracts more investors the longer the risky asset has outperformed the risk-free bond. The second, meant to capture the small voice that tells you the asset is overpriced, repels investors as its price gets farther from its fundamental value. The bubble pops when the risk-free asset outperforms the risky asset and nobody wants to hold the risky asset anymore.
Here's the abstract and the intro to the (very short) paper. I'll post the pdf when it's nearer to completion.
Abstract
This brief paper sets up a simple model in which investors can be ruled by “animal spirits” and bid up the price of a risky asset well above its fundamental value. The price of the asset eventually plateaus so that the annual return is less than could be earned in a risk-free bond. This lower return signals the end of the bubble and investors rush to the exit, pushing the price well below its fundamental value in one period. If model parameters remain the same, this cycle continues indefinitely with bubbles inflating and popping over and over again. A change in the parameter values allows the risky price of the asset to hover around its fundamental value. A bubble, at least in terms of this model, can be interpreted as an increase in the weight of irrational “animal spirits” as opposed to the rational value investors in the market. When the bubble pops, the irrational investors diminish in importance and the asset no longer experiences bubbles. There are a number of additional steps that need to be taken int he model in order to make it useful from a macroeconomic point of view.
1 Introduction
When Great Uncle Frank calls on that lazy Sunday morning and tells you he has a guaranteed investment opportunity, what do you do? You ask him some questions, and eventually, you realize that he invested early in a Ponzi scheme. And now you're at an ethical crossroads. After all, Great Uncle Frank earned fifty percent on his money in six months. You could use an extra five thousand dollars. Hell, who couldn't? Of course the ethical course is clear. Getting money in a Ponzi scheme isn't really different then mugging old ladies in the back alley. Either way, you've stollen money that doesn't belong to you. You explain to Great Uncle Frank that you can't invest in his “once in a lifetime” investment opportunity and tell him to give your love to Great Aunt Miriam.
Of course, homo economicus, that near relation of ours who fully developed in our great midwestern town of Chicago, is not familiar with ethical dilemmas. His only concern, when his Uncle Bernie calls with the same investment opportunity, is to figure out the likelihood that he can get in on the Ponzi scheme before it runs out of money and the last round of investors are left holding the bag. If he thinks the scheme will continue for at least another round, he's likely to invest, make some money, and then get out. Homo economicus is entirely rational and doesn't have to worry about Keynesian “animal spirits.” The rest of us are not so perfect and can get carried away with the thought of making a pile of money in an easy investment. If a friend or neighbor just made a bunch of money investing in a Ponzi scheme, we're likely to want to invest as well. If the asset is a stock or a house, then we have no ethical qualms and we can rush into the invesment with a clear conscience.
And an asset bubble is really no different than a Ponzi scheme, even if there's no postal reply coupons at the center of it. If I knowlingly buy an asset for a price above its long-run value and sell it to you for even more before the bubble bursts, then I've taken your money, as sure as if I was an early investor with Bernie Madoff and you were one of the ones holding the bag when the Feds arrived. The fact that it's not illegal may help me sleep better at night, but we're both just gamblers trying to make a buck before the final whistle blows. And when we see an asset that has outperformed others for an extended period of time (whether it's tulips, stocks, or houses) we want in as well. Who wouldn't? Even if we know the asset is overpriced, it's not completely irrational to invest if we don't think the bubble is going to burst anytime soon. As Charles Kindleberger said, “There is nothing so disturbing to one’s well-being and judgment as to see a friend get rich.”
As the bubble expands and the price pushes higher and higher, Cassandras warn that the prices won't keep on going up forever. Eventually they are proved correct and something triggers an exodus. It may be that risk-free bonds outperform the risky asset. It may be a scandal in the financing of the asset comes to life. It may be a panic that spreads through the market. Whatever it is, the bubble has popped and asset values head south much faster than they headed up as everybody wants to divest at once. After the bubble has popped the animal spirits of investors are tempered and are more likely to be replaced by the small voice in the back that was telling us it was all to good to be true in the first place.
This paper has its origin in a number of blog posts by Brad DeLong and Paul Krugman looking for a model that exhibits asset bubbles and also has those bubbles pop. In fact, the main setup for the model presented here comes from DeLong (2009). His model exhibits asset bubbles as investors randomly compare returns between the risky asset and the safe asset and switch to the asset that offers the higher return. In his model, however, there is no way for the bubble to pop. Instead the bubbles deflate slowly as the price of the risky asset passes its fundamental value before starting to inflate again. DeLong shows that his model is fairly sensitive to changes in the main parameter value.
The model here has investors in the risky asset pulled by two opposing forces. One, meant to represent irrational animal spirits, attracts more investors the longer the risky asset has outperformed the risk-free bond. The second, meant to capture the small voice that tells you the asset is overpriced, repels investors as its price gets farther from its fundamental value. The bubble pops when the risk-free asset outperforms the risky asset and nobody wants to hold the risky asset anymore.
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