Introduction
Over the past one year, dividend protection
has grown in popularity among new convertible issuance. In the
We have seen a wide variation in the type of dividend protection as well as conditions under which the dividend protection gets triggered. Primarily we have seen two types of dividend protection, a) Conversion Ratio Adjustment, which is the overwhelming majority (over 99%) promises to change the conversion ratio (conversion price) when the dividend on the underlying common stock is changed and b) Dividend Pass-Thru promises to pass on increases in dividend amount to the holders of the convertible.
One important conclusion from our analysis is the most common ratio-adjustment type of dividend protection does not completely eliminate the risk of dividend increases from the convertible holders’ perspective; it cushions the impact on the valuation to some degree. The pass-thru type of dividend protection does completely eliminate the risk of dividend increases to the convertible holder at high deltas and increases the value of the convertible at low deltas. While it is in the interest of the convertible holders to demand pass-thru type of dividend protection in all situations, the issuers may find that to be not in the best interest of existing equity share holders.
We are unimpressed with the complexity of the language in the prospectus when it comes to dividend protection. The language unfortunately is unnecessarily confusing in our opinion, and we believe an average trader, analyst or a portfolio manager will have a very hard time deciphering when the dividend protection gets triggered and how it is executed. We also believe a legal professional will have a very hard time figuring this out because he/she may not know enough about convertible securities. It is our sincere hope that the legal teams at the investment banks will come up with a simplified and unified language that is easier for an average investor to understand.
We have seen several types of thresholds (conditions) under which the dividend protection gets triggered. These thresholds vary from a simple 1% change in conversion ratio or conversion price which is done for administrative reasons, to very aggressive limits on dividend yield, which in some situations might make dividend protection worthless from a convertible holders’ perspective.
The Kynex convertibles valuation model has been extended to include dividend protection in the valuation of a convertible security. The dividend protection can be via either a cash pass-through or an adjustment to the conversion ratio. As of the date of this publication the Kynex valuation model has provision for only one threshold, while the prospectus in some situations could specify multiple thresholds that have to be met for the dividend protection to become effective. Our data team used their best judgment to specify the most dominant threshold. Depending on market conditions there might be situations when our choice of dominant threshold may not be correct. While the number of convertible securities in the market today that come under this category is very few, we cannot predict the nature of future issuance. We plan to incorporate multiple thresholds in future versions of our convertible valuation model. A comprehensive list of known thresholds with a brief description is presented in appendix A.
We analyze the HMT 3.25% convertibles due March 2024, as an illustrative example. This security was issued in March 2004. At the time of issue, the underlying stock was not paying any dividends. In September 2004, HMT instituted an annual dividend of 20 cents. The convertible security was issued with a ratio adjustment type of dividend protection.
We compare Fair Values in three scenarios i) assuming the stock did not institute any dividends, ii) applying the new dividends with dividend protection and iii) applying the new dividends with no dividend protection. For illustration, we ran these comparisons applying ratio-adjustment type of dividend protection as well as pass-thru type of dividend protection. We also ran the comparisons applying continuous yield as well as discrete dividends for life (arguably not correct for long periods of time, but is useful for illustration).
Overall, we find that dividend protection via a cash pass-through offers better protection than a ratio adjustment against future dividend payouts. The compensation from ratio-adjustment is inadequate especially at mid-deltas (high gamma) and gets better at the tails. This is because, the ratio-adjustment is done when the dividend is increased once, and is not recurring once the cumulative dividend over a twelve-month period is unchanged. Therefore, if a convertible has five years of call protection and a dividend increase is instituted in the first year, the ratio adjustment is done until the cumulative dividend over a twelve month period becomes unchanged (typically four quarters). Also, most ratio-adjustment type of dividend protection gets applied in both directions, i.e. if the dividend is decreased the ratio adjusts downward in the same proportion as the upward adjustment in the ratio if the dividend is increased (GATX convertibles had the ratios adjusted downward). Hence the ratio adjustment compensates the convertible holder for the drop in the stock price when the dividend is instituted and not for the entire penalty imposed on the valuation of the embedded option from the new dividend. A cash pass-through on the other hand is recurring every time a dividend is paid and hence compensates the holder completely.
At low deltas however, the dividend pass-thru type of protection tends to increase the valuation (see Fig 3 and Fig 4 below) of the convertible because, i) the extra dividend on the stock does not penalize the value of the embedded option since it is out-of-the-money, ii) the convertible is trading close to bond floor and iii) dividend pass-thru is bringing in new cash flow that was not existent before (a windfall).
Since market conditions are unpredictable, there is no certainty that holders of convertibles today are future equity share holders, because the convertible may very well get put back to the issuer or redeem for cash at maturity. However the dividend pass-thru will take a bite out of the earnings of the issuer and hence may not be fair to the existing equity share holders. If the convertible holders are certainly future equity share holders, not giving dividend pass-thru would differentiate existing equity share holders from future equity share holders. Therefore, it is not an easy decision for the issuers when it comes to the type of dividend protection to offer the convertible holders at issue.
We present the graphical representation of the comparisons below. Each chart contains three Fair Value lines; pink – assumes dividend was never instituted, blue – assumes new dividend and applies appropriate dividend protection, and green – assumes new dividend and does not apply dividend protection. In addition each chart contains two lines; red – represents the difference between base case with no dividend (pink) and dividend protection (blue); purple – represents the difference between base case (pink) and no dividend protection (green) as a percentage. If the red line is at zero, the convertible holders are fully compensated, if the red line is less than zero, the convertible holders are not fully compensated, and if the red line is greater than zero, the convertible holders are more than compensated potentially at the expense of current equity share holders. The relative distance between the zero, the red line and the purple line is a measure of the degree to which the dividend protection is compensating the convertible holders for increases in stock dividends.
We have labeled the various fair value lines on the chart in addition to consistent color coding for easy identification as follows:
C1 – Assumes dividend was never instituted (shown in all charts as pink line)
C2 – Assumes new dividend as a continuous yield and applies ratio-adjustment type of dividend protection (shown in Fig. 1)
C3 – Assumes new dividend as a continuous yield and applies pass-thru type of dividend protection (shown in Fig. 2)
C4 – Assumes new dividend as a continuous yield and does not apply any form of dividend protection (shown in Fig. 1 and Fig. 2)
C5 – Assumes new dividend as discrete dividends for life and applies ratio-adjustment type of dividend protection (shown in Fig. 3)
C6 – Assumes new dividend as discrete dividends for life and applies pass-thru type of dividend protection (shown in Fig. 4)
C7 – Assumes new dividend as discrete dividends for life and does not apply any form of dividend protection (shown in Fig. 3 and Fig. 4)
Fig.1 HMT 3.25% convertible bonds valued
using a proportional dividend yield model. The curves show the fair value vs. parity.
The dividend protection is via a ratio adjustment.
Fig. 2 HMT 3.25% convertible bonds valued using a proportional dividend
yield model. The curves show the fair value vs. parity. The dividend protection
is via a cash pass-thru.
Fig. 3 HMT 3.25% convertible bonds valued using a discrete dividend
model. The curves show the fair value vs. parity. The dividend protection is
via ratio adjustment.
Fig. 4 HMT 3.25% convertible bonds valued using a discrete dividend
model. The curves show the fair value vs. parity. The dividend protection is
via cash pass-thru.
Mathematics
We present the financial engineering details below.
Recall (December 2003 Bulletin) that the basic valuation pde is
(1) 
The notation was explained in the Dec 2003
Kynex Bulletin, e.g. 
is the value of the
convertible, 
is the stock price,
and 
denotes the coupons.
For clarity, it is sufficient here to ignore the modeling of bankruptcy
(default). The above pde implements a continuous proportional dividend model,
with a dividend yield of
. If the current stock spot price is 
and the stock currently pays dividends with an IAD (indicated
annual dividend)
, then
.
There are two models of dividend protection, viz. cash pass-through or a conversion ratio adjustment. We treat them separately below. We begin with the cash pass-through.
Dividend Cash
Pass-Through
Suppose now that the company (issuer)
announces a new dividend
. The new dividend yield is
. Let the conversion ratio be 
. Holders are protected against the excess dividend payouts.
We model this situation by modifying the pde to
(2) 
Where the notation means
(3) 
Obviously, the dividend yield in the
original pde is changed from to 
, because the stock now pays a dividend yield . In addition there is an extra term, effectively an increase
in the coupon, given by
. The rationale behind this term is that, in a time interval
, the stock pays (continuous proportional) dividends
, which is to be compared against the “baseline” value of
. The excess dividend payout per share is therefore
, multiplied by the conversion ratio.
Note that most issuers also impose
constraints as to when the dividend protection will be applied. For example, it
may be necessary for the annualized payout to exceed a threshold value
. In that case the excess payout will only be applied at
nodes 
in the
finite-difference grid where the stock price 
is such that
. Another common constraint is that the excess yield must
exceed a threshold
, e.g. 1%. In that case the excess payout is applied at the
nodes where
.
Conversion Ratio Adjustment
The more common technique of dividend
protection is to adjust the conversion ratio. Once again the new dividend is, and the new dividend yield is . The pde in this case is modified
to incorporate the new yield of
(4) 
However, there is no additional term of
“excess payouts.” Instead, the boundary
conditions on the solution are modified. When deciding whether or not the
convertible should be (voluntarily or forcibly) converted into stock, the
conversion ratio at the grid node is changed, according
to
(5) 
Note that at the low nodes in the grid,
where the value of is small, the above
adjustment implies a decrease in the
conversion ratio. (In fact the conversion ratio of the GATX 5% 2023 bonds was reduced because of a cut in the
dividend.) Hence a ratio adjustment does not
imply an increase in the value of the convertible.
As with the case of cash pass through,
there are usually constraints as to when the dividend protection will actually
be applied. The two constraints given above (in the cash pass-through case)
also apply here. In addition, another criterion is that the change in the
conversion ratio must exceed some threshold
, e.g. 1%. In that case, we require, at the grid node, that
.
Further remarks
- Discrete
Dividends
All of the above can easily be extended to cover the case of discrete dividends or a case where discrete dividends are paid for a few years (1 or 2 years) with a continuous dividend yield there after. The Kynex valuation model in fact handles the mixed discrete-dividends and continuous yield case.
- Term
Structure Dividend Protection
GATX 5% is callable and puttable on
- Embedded
Warrants (aka Variable Conversion Ratio)
For example, American Express AXP 1.85% 2033 offers additional warrants upon conversion and a ratio adjustment (dividend protection). Our reading of the AXP prospectus is that the ratio adjustment changes the base conversion ratio of the convertible, before calculation of the additional warrants. Note that the AXP 1.85% prospectus also imposes a fixed cap of 22.7635 on the final conversion ratio. Our reading of the prospectus is that dividend protection does not change this cap.
Remarks on the
Valuation Example
Recall the HMT 3.25% bond which was used as
a valuation example above. Here we shall briefly
discuss a few mathematical details. The underlying stock used to pay no
dividends; recently an annualized dividend of 0.2 was announced, i.e. 
and
. Consider the structure of the valuation pde (eq. (2)) in
this case. Omitting unnecessary terms, it reduces to
(6) 
At very high parity, the Delta (hedge
ratio) approaches 100%, i.e.
, and so the two terms cancel exactly. This is the
mathematical statement that, at high parity, a cash pass-through policy completely
compensates the convertible holder.
An alternative way to understand this cancellation, from a trading perspective, is as follows. At high parity, one needs to be hedged 100% (for a delta-neutral position). All the cash received from the pass-through (long convertible position) is paid out in the short stock position, hence the two cash flows net to zero.
At low parity, the delta-neutral hedge is nearly zero. Hence no cash payouts are made, but cash inflows are nevertheless received from the dividend pass-through. This increases the fair value of the convertible. Such an increase in the fair value clearly does not occur in the case of a conversion ratio adjustment.
We
have seen many different types of dividend protection thresholds in the
market. There are three main types of
thresholds which could be combined to make it harder for dividend protection to
take place. We have also seen caps put
on the Conversion ratio and a minimum amount that the Conversion price will be
adjusted to.
Percent of conversion ratio/price: If the new dividend prompts a ratio adjustment which
results in the conversion price changing less than the specified threshold, the
ratio is not adjusted. The most common threshold is a 1% change in the
conversion price. The main reason for
this threshold seems to be ease of administration. This threshold is usually
carried forward until the percentage is reached. Some issuers use a percentage
change in the conversion ratio instead of the conversion price. CapitalSource Inc (CSE) 1.25% dividend protection
states that the conversion ratio needs to be adjusted at least 1%. In GATX Corp (GMT) 5% the prospectus states
that the conversion price needs to be adjusted at least 1%.
Stock dividend yield: This threshold seems to be the most difficult to pass because it is reliant on the price of the stock. For example, the New Century Financial (NCEN) 3.5% has increased its dividend three times from .40 per year to .92 per year without triggering the dividend threshold. This is because the stock price for NCEN has increased with the dividend amount, which keeps the dividend yield below the percentage trigger.
Stock dividend amount: The dividend needs to surpass a given dividend amount which is outlined in the prospectus. Usually, the language is interpreted that the dividend needs to exceed this dividend amount for the dividend adjustment to be made. However, in GATX Corp (GMT) 5%, the language in the prospectus reads that the dividend needs to be anything other then the dividend amount given in the prospectus. For GATX Corp the dividend protection can increase or decrease the conversion price. Again, some companies use the conversion ratio instead of the conversion price.
Also, when calculating these changes some companies use only the quarterly dividend and will change it every quarter until the full annual dividend is compensated for. Some companies will adjust the conversion price/ratio once based on the new yearly dividend. These thresholds can be combined in the dividend protection language. Most companies have the 1% change in the conversion price/ratio and will combine it with another threshold. Both thresholds need to be triggered in order to change the conversion price/ratio.
Some companies, in their dividend protection language, put a cap on the conversion ratio or give a minimum conversion price. GATX gives a minimum value that the conversion price can never go below. This minimum number is usually the reference stock price on the convertible bond at issue. Cooper Cameron 1.5% gives a maximum conversion ratio. If you back out the conversion price using the maximum conversation ratio you will get the reference stock price at issue.
Note also the case of convertibles with embedded warrants (Aka variable conversion ratio), e.g. the AXP 1.85% mentioned earlier, or the Wells Fargo 1.45%. In both cases the convertibles have a cap on the maximum value of the total conversion ratio. Note that for embedded warrants, we interpret the dividend protection to apply to the base conversion ratio.
Another nuance in the dividend protection structure is that there are different thresholds for different time periods. An example of this is the Advanced Medical Optics (AVO) 2.5% where after January 2010 the dividends need to exceed a percentage of the stock price. There is also a minimum conversion price through out the bond’s life. Such a “term structure” in the threshold is distinct, from a term structure in the dividend protection policy itself, e.g. the GATX 5% mentioned above.