## Friday, February 3, 2012

### SLCG Research: Reverse Convertibles and Stochastic Volatility

We've talked a lot about structured products -- and reverse convertibles in particular -- on this blog.  In this blog post we discuss reverse convertibles in more detail and present some results found in a new research paper my colleagues and I have just completed.

Reverse convertible notes -- or simply "reverse convertibles" -- are structured products whose payoff at maturity is dependent upon the return of an underlying asset or security during the tenor of the note.   If the underlying asset price falls below a trigger price during the term of the note, the note pays the face-value times the fraction of the maturity date asset price to the issue date asset price (with the proviso that the note never pays more than the face-value).   If the note pays less than the face-value at maturity, the investor is usually delivered the appropriate amount of the underlying asset.

To get a feeling for reverse convertibles, let's consider the following example: $1,000 face-value reverse convertible (issued today and maturing in six months) linked to the common stock of Ford Motor Company (F), let the initial asset price be$12 and the trigger price be $10. There are three possibilities for the payoff at maturity: 1. Ford never trades below$10: note pays the face-value at maturity ($1,000). 2. Ford trades below$10 at least once during the term of the note, but the asset price at maturity is $15: note pays the face-value at maturity ($1,000).
3. Ford trades below $10 at least once during the term of the note and the asset price at maturity is$9: note pays the fraction ($9/$12 = 0.75) of the face-value at maturity  (\$750).
Because reverse convertibles expose investors to significant downside risk and therefore loss of principal, these notes generically pay higher coupon payments than similar short-term debt issued by corporations.

By studying a set of reverse convertibles issued in 2008 and 2009, SLCG showed in a previous paper that reverse convertibles are issued well above their fair market value.  In other words, investors were not being appropriately compensated for the downside risk of the notes.

In that paper, SLCG researchers made the approximation that the volatility of asset returns is non-dynamical.  While this is a common assumption, market prices of traded options indicate that the implied volatility is lower for at-the-money options than for out-of-the-money and in-the-money options for the same underlying asset. In addition, there is a wealth of evidence that the volatility of a generic asset's returns varies over time.  Neither of these phenomena can be explained within the model used to value reverse convertibles in this first paper.

In our new paper, we relax this simplifying assumption about the dynamics of asset returns.  We considered a simple model of stochastic volatility to value a set of reverse convertible notes issued in 2010 and 2011.  We show that when the volatility of asset returns is incorporated, reverse convertibles are worth even less than previously considered.  Even using sophisticated valuation models, reverse convertibles again and again prove to be systematically overpriced.