A Myriad Of Protection Features
Different types of dividend protection features will likely require their own modelling methodologies. For example, Pemex's exchangeable bond into Repsol YPF due January 2011 (issued December 2003) offers a starkly different type and degree of protection. Here, holders are compensated for full-year dividends in excess of USD0.489 per share. At the time of issuance, this translated into EUR0.40 per share, which was exactly Repsol's FY 03 dividend. Hence, bondholders were effectively short dividends and long a slightly in-the-money compo call option on the dividend amounts declared in future years. The compo, or foreign-currency payoff, of this dividend option is interesting, and has benefited bondholders over the past year. The dollar has weakened to approximately USD1.30 versus the euro, which implies Repsol's dividend in dollar terms rose to USD0.52, or USD0.04 excess above the protection threshold. Assuming the company's payout and the euro/dollar rate remain unchanged next year, exchangeable bond holders will receive a small (around 0.21%) increase to the exchange ratio to compensate for this excess. If dividends rise further or the dollar continues to fall versus the euro then bondholders are neutral, thanks to the protection. If Repsol's dividends fall or the dollar rises, however, then bondholders may reap a positive valuation impact (Figure 3)
As with the France Telecom convertible discussed last week, quantifying the value of the dividend option embedded in the Pemex-Repsol exchangeable bond is tricky. As a back-of-the-envelope calculation, let's assume the annual standard deviation of dividend yields is 0.5%. Then the average standard deviation over the remaining six years of the bond is approximately 1.2% (0.5% *(check)6), assuming a Brownian-type dividend process, in which case the average annual option value is approximately 0.5%. If we lower our base-case modelling assumption of a 2% dividend yield to 1.5% to account for holders' dividend optionality, then the valuation of the bond would rise by roughly 1.5 points.
We caution such examples are illustrative only. Firstly, techniques for valuing embedded dividend options are not readily available and secondly the benefit to holders depends on the market's agreement on and willingness to pay for this dividend option value.
Estimating The Dividend Hedge Ratio
As mentioned above, convertibles with higher equity delta () should generally have higher µ. But, the greater the dividend protection or the further in the money investors' embedded dividend option due to this protection, the lower the µ. Therefore, the hedge ratio must be adjusted for the delta of the call option on the dividends that the convertible investor is long. Taken together, we intuit that:
Hedge ratio, or µ ~ ∆CB * (1 - ∆divs),
where ∆CB is the sensitivity of the convertible bond value with respect to a change in the underlying share price and ∆divs is the sensitivity of the bondholder's embedded call option on dividends (resulting from the dividend protection feature) with respect to a change in dividend levels.
For the Pemex-Repsol exchangeable bond, the embedded dividend option is now in-the-money, but if we assume its delta (∆divs) is roughly 50%, then this logic implies bondholders wishing to hedge their dividend exposure should assume roughly half of the hedge ratio implied by a model that ignores the dividend protection feature.
Dividend Swaps
Dividend swaps are over-the-counter derivatives that allow investors to take or hedge dividend risk in isolation or on a relative value basis. Equity index dividend swaps have been used for several years now, but the use of single stock dividend swaps is increasing. As such, for some of the more liquid stocks, they can provide a flexible solution for convertible investors to hedge their dividend risk.
A dividend swap is a contract between two counterparties in which one receives a fixed dividend level over the term of the contract and the other receives the actual or realised dividends. This is analogous to fixed and floating legs of interest rate swaps. Contract specifications include the underlying equity, valuation period, fixed level (at inception) and notional amount.
What Next?
We recommend convertible portfolio managers scan their portfolio to locate and then quantify their dividend risk, whether to actively take dividend views or to hedge dividend risk. We expect both single stock and basket/index dividend swaps will have an increasing role to play for either activity.
Lastly, we remark the choice between single stock dividend swaps and index dividend swaps involves a trade-off between the required precision of the hedge versus cost (ie, index dividend swaps tend to trade at discounted levels relative to analysts' consensus dividend expectations, but only provide a macro hedge for dividend risk).
This week's Learning Curve was written by Luke Olsen, head of convertible bond research at Barclays Capital in London.
