There is a lot of talk in the financial media about there being a "Bernanke Put" for the stock market. Indeed, some authors even believe there is a global central bank "put." This is the belief that the Fed Chairman will do whatever is necessary to keep the stock market and economy from going down. The notion was popularized in the 1990s under former chairman Alan Greenspan.
The rest of this article will, for the sake of argument, take the premise of Ben Bernanke providing puts to the stock market to be true. Let me be clear, I am not claiming this is in fact true, but only using it as a reasoning device. With that said, what are the consequences of Bernanke selling puts to the market?
First, let's look at the equation for put-call parity for a European Option:
Call + Cash (Present Value [P.V.]) = Put + Stock
Source: Options, Futures, & Other Derivatives by Hull page 174 (5th ed.)
We can rearrange the formula to find out the position of those "investors" holding the puts sold to them:
Call + Cash (P.V.) - Stock = Put
Hence, "investors" of the puts are long a call, long cash, and short stocks. Now, let's look at the seller of the put position:
-Call - Cash (P.V.) + Stock = - Put
If Bernanke is indeed selling a stock market put, then this would make him short a call, short cash, and long stock.
From this put-call parity analysis, we can see that "investors'" gains are capped from being short stock, even though they own the call. There are only three forms of profit they could hope to achieve. First, the put was purchased at a price below fair value, and they arbitrage the other side of the equation. Second, that interest rates would rise, unexpectedly, and the interest received would be greater than originally expected. Third, the stock could fall in price.
Now let's look at Bernanke's short put position. The long stock position is capped by being short a call, but a minimal profit could be made from the initial premium received. It would actually gain by a reduction in interest rates. The lower the present value of cash, the better for this position. The position would also gain if volatility fell. Less volatility means a lower option price if all else is held equal. The position would be hurt by a fall in the stock price. There would be a need for hedging. Finally, the position would decrease in value by a rise in interest rates.
Hence, Bernanke has a vested interest in not having rates rise, but it would even help if they fell further. Then there is the problem of the long stock position. There would be a problem if stocks fell and there was no hedging of the position.
So what to make of this?
What if the "Bernanke Put" was sold below "fair value" and made an arbitrage play possible? If the put was sold below fair value, then the put "buyers" would then look to take the opposite position.
A put buyers position is long the put ( "Put" ), and they then want to sell the put ( "- Put" ) to lock in the arbitrage. "- Put" is the same theoretical position as Bernanke -- short a call, short cash, and long stock. The financial intermediaries would be buying an undervalued put from Bernanke, and then selling that position to another party, who would most likely be hedging long stock portfolios.
This would then seem to align interests of three parties: central banks, financial intermediaries, and long stock investors. The central banks can control interest rates and do not have to worry about being short cash. The financial intermediaries do not worry about the short cash position, since it is aligned with the central bank. They only care that "underpriced" puts are sold to them, which can then be arbitraged to other investors. These other investors are long stock and do not want the stock market to go down, but only to pay a "fair" price for the hedge. Entities that might receive the underpriced put, and then try to push down the stock, would have to be excluded.
The holders of cash would have the central bank and financial intermediaries positioned against them. Those long volatility would be in the same boat as well.
This line of theoretical reasoning could be a possible reason why interest rates are expected to remain very low for a considerable time, and for the drop in the VIX in mid August to its lowest level since June of 2007.
(click images to enlarge)
Source: Yahoo Finance