Thursday, August 03, 2006

Derivatives shown to increase volatility

Well Fischer Black is right again. Or at least that is the conclusion of a new paper by Bhamra and Uppal. They model a market with and without "non redundant derivatives" and find that derivatives do lead to increased return volatility.

A few look-ins at their largely theoretical paper:

* "Our main result is to show that introducing a new derivative security that improves risk
sharing leads to an increase in the volatility of the stock market of stock returns is higher in the economy with improved risk sharing if the discount rate is countercyclical, because the change in the discount rate magnifies the effect on stock returns of a shock to dividends; this condition is satisfied if the average prudence in the economy is not too large."

* The logic behind their conclusion is that:
"In the economy without the derivative, agents cannot share risk at all, and so the distribution of wealth across agents changes only deterministically. Consequently, the discount rate is deterministic, and so there is no excess volatility over and above fundamental volatility. But with the introduction of a non-redundant derivative risk sharing is possible, and hence, the discount rate is stochastic."
Interesting. And I confess it does make sense. Even though it may take a second reading to convince me of all of it.

Cite: Bhamra, Harjoat Singh and Uppal , Raman, "The Effect of Introducing a Non-Redundant Derivative on the Volatility of Stock-Market Returns" (March 14, 2006). Sauder School of Business Working Paper Available at SSRN:


Eric said...

Hi Jim,
I am not sure I buy it either. Seems to me (at first glance) that the model is way too specific to draw the general conclusion it pretends to draw. I don't like models where agents differ only by their levels of risk aversion: They are unable for obvious reasons to explain the volume of trade we DO observe on real markets. Dumas made the same point in his paper even though he was able to generate a slight volume of trade. Next and more important, we are faced with Hakansson catch 22 paradox: If markets are complete, we know how to price derivatives because we know how to replicate them, hence they are redundant (in that sense CAPM (with the standard assumptions) is a pricing theory without much trading activity!). They cannot increase volatility by definition.

If markets are incomplete, we may need derivatives but we do not know how to price them and which ones we need.

In a nutshell, one the one hand, if we have a Sharpe-Tobin world (stocks + risk-free asset and the whole assumptions shabam), we don't need derivatives, hence they cannot add to aggregate volatility. On the other hand, what I fail to understand is why adding zero net supply leverage (ie the bond) to the economy adds to total risk. The bond being in zero net supply should neither add or substract to total risk the aggregation of the two individual leverages (reflecting risk aversion differentials) should in principle cancel out. Am I missing something here?

Finally I fail to see why prudence and precautionnary savings are truly at work. There is only one Wiener process at work. If my recollection of Kimball's seminal definition of prudence is correct, prudence applies when a background risk is added to an already risky situation. This is by the way, the setting under which Franke et alii and others have shown that risk sharing rules are no longer linear but non linear (hence the case for derivatives).

I'll re-read the paper but things do not seem to add up.

Anonymous said...

When a derivative is used to complete the market, you price it the same way that you price any other just use the stochastic discount factor to value the payoff, so Eric's point seems strange.

In the paper, while there is a risky stock, borrowing and lending are forbidden. Since agents differ in their risk aversion, they would like to borrow and lend. But they cannot, and this is why markets are incomplete. The introduction of the derivative allows agents to circumvent the constraint on borrowing and lending, thus making markets complete.

The interesting thing about the paper is that when markets are complete and risk sharing is better, stock market return volatility is higher. This may have seemed like a strange theoretical result back in 2006, but in 2009, this seems to resemble aspects of the current credit crisis. We have seen huge use of derivatives, making it easier for householders to borrow. But we have also seen an explosion in volatility.