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Convertible Bonds and Variance Swaps


Because these bonds are convertible into stock at a certain price, there is an imbedded call option. Through this call option, the manager is long volatility. But because the bond's value is subject to changes in credit and because it is purchased with borrowed money, she is also short volatility.

When option prices are bid up to extremely high levels, these managers will often take advantage of the situation and sell an amount of equity "vega" (the price of volatility) imbedded in the portfolio (this requires either being very comfortable with the short volatility due to credit exposure and ignoring it or hedging it out with default swaps at the same time). Because they do not want to deal with the details and risks of managing actual options, they will accomplish this by selling what is called an equity "variance swap".

A variance swap is just a bet. The fund will call a dealer and agree to sell a certain dollar amount of vega per volatility point. Both parties agree on the current level of implied volatility (see my explanation of the new calculation on VIX for details) based on a certain basket of options in a certain index (like the SP500) and strike the bet there. For example, the fund and the dealer agree to a six month swap struck at 19% on SP500 volatility (the current level for the basket of options) for $250,000 per vega point. If at the end of the term the predetermined basket of options exhibits a lower implied volatility of 18%, the fund will collect $250,000 from the dealer. The dealer hedges this transaction by selling options on that basket of options.

In this way the fund manager profits from an overall decline in volatility through the swap. It is in a sense a hedge since she is probably losing some value from her convertible bond portfolio from this general decline in volatility. But in a sense it is not a hedge since a pick up in volatility could be accompanied by a widening of credit spreads. The main point is that if the manager hedges the long volatility, she must hedge the short volatility (through default swaps) also to really be fully hedged.

Convertible bonds have enjoyed a stellar month as credit spreads have narrowed significantly. We have seen two large hedge funds sell variance swaps today. The curious thing is that we normally have not seen them sell volatility at these levels, using only a slight pick up recently in option prices. This is a source of volatility selling that I normally do not see at this stage. Selling equity vega at these levels probably would not even pay for a credit hedge.

In managing our convertible bond portfolio, which has also done very well this month, we are doing the opposite. We are buying volatility outside of our convertible bonds to hedge a possible reversal of the credit spreads: if this occurred it is most likely that we would see a further pick up in volatility.

The convertible bond managers that are selling the variance swaps must be convinced that credit spreads are not going to widen. Even if volatility were to contract more they would still do very well. So what they are doing at this stage cannot be considered a "hedge", but more like a doubling of the bet they already have on.
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