KYNEX Bulletin - March 2006

Summary

Over the past two years, dividend protection has grown in popularity among new convertible issuance. In the United States, 94% of the proceeds in 2005 and 87% of new convertible securities have some form of dividend protection, compared to 41% of number of issues and gross proceeds in 2003 and 6% for both in 2001.

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 either at the time the dividends are paid or upon conversion.

Based on our valuation analysis, the ratio-adjustment, as well as pass-thru upon conversion type of dividend protection, completely insulates the convertible holder from future increases in the stock dividend, but for minor administrative and other limits. The pass-thru-as-dividends-occur type of dividend protection tends to over compensate the convertible holder at low parity levels, and completely compensate at higher parity levels, from future increases in the stock dividend.

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 also find a vast majority of prospectuses stating that the dividend protection adjustment is done when the dividend “exceeds” the anchor dividend amount. While this is in the interest of the convertible holder and the market is currently going through a phase of increasing dividends, we believe the issuers are setting themselves up for a rude awakening if they start to cut their dividends in the future and the prospectus language does not permit them to lower the conversion ratios.

The Kynex convertible valuation model has been refined and extended to include various types of dividend protection in the valuation of a convertible security. Our calculator always has and continues to support continuous, discrete and discrete-proportional type of dividend assumptions. The valuation of convertible securities is sensitive to the type of dividend specification, and it is more so if the convertible security has dividend protection features. We recommend our clients favor a discrete dividend stream as far in the future as practically possible to estimate, in order to ensure realistic projected future ratio-adjustments/pass-thru amounts.

Kynex also tracks the dividend payments on stocks that underlie convertible securities with dividend protection and calculates the necessary adjustments on a daily basis, to ensure accurate valuation. We have been doing this for the past several months, and are pleased to report that our automated dividend protection tracker has calculated adjustments within 1/10,000^th of what the companies actually reported. The same engine is used in our valuation model to project future expected conversion ratios/pass-thru amounts and we are confident our methodology is accurate.

You will notice significant differences in valuation of certain convertible securities with our enhanced dividend protection model when compared to our previous versions. We believe the new valuation is more accurate and takes the dividend protection features into account appropriately. We have included the convertible securities with significant differences from previous versions in Appendix A. We corrected a minor flaw in the treatment of screw provision in this version. The convertibles listed in the appendix include securities whose valuation would differ from prior versions due to the change in the screw provision treatment.

A comprehensive list of dividend protection terminology, variations and brief descriptions are provided in Appendix B.

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An illustrative example

We analyze the LFG 3.25% convertibles due March 2034, as an illustrative example. This security was issued in May 2004. At the time of issue, the underlying stock was paying a dividend of 10c a quarter. In July 2004, LFG increased the dividend to 15c a quarter. In July 2005, LFG increased the dividend to 18c a quarter. The convertible security was issued with a ratio adjustment type of dividend protection.

We compare Fair Values on the date of issue in three scenarios: i) assuming the stock did not institute any increase in dividends, ii) applying annual dividend increase of 3c a quarter until 2008 and proportional dividends thereafter and iii) applying the same dividend pattern as mentioned in item ii above but dividend protection feature disabled. 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-proportional dividends.

Overall we find that discrete dividend as far as practically possible to estimate specification, completely compensates the holder of the convertible from future dividend increases. The ratio-adjustment type of dividend protection and pass-thru-on-conversion type of dividend protection are about the same at all parity levels. The pass-thru-as-dividends-occur type of dividend protection over-compensates the convertible holder at low parity levels because the convertible holder is guaranteed to pick up the extra cash (windfall) while the excess dividend on the stock does not affect the embedded option significantly since it is out-of-the-money.

With continuous yield specification, the calculator has to overcome challenges such as computing ratio-adjustments from dividend protection after simulating dividends in small chunks at every time step. This forces adjustment at every time step proportional to the stock price at every grid node. These small adjustments have to be carried forward to future time steps which will create their own adjustments that are proportional to stock prices. If a convertible has four to five years or more of call protection and the stock dividend yield is a non-trivial amount, the small adjustments compound over time. Unfortunately, the calculator has no choice but to simulate ratio adjustments in this fashion for a continuous/proportional dividend specification. It is for this reason that we recommend favoring discrete dividend as far as practically possible to estimate as your dividend specification in valuing convertibles with dividend protection, especially if the stock is currently paying dividends or you expect the company to institute new dividends.

We present the graphical representation of the comparisons below. Each chart contains three Fair Value lines; pink – assumes future dividends are increasing and dividend protection feature is turned on, blue – assumes dividends are not changing from the initial amounts and dividend protection is turned off, and yellow – assumes future dividends are increasing and dividend protection is turned off. In addition each chart contains two lines; red – represents the difference between increasing future dividends (pink) and no change in dividends and no dividend protection (blue) as a percentage; purple – represents the difference between increasing dividends with dividend protection (pink) and with no dividend protection (yellow) 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 future dividends are increasing and dividend protection feature is turned on (pink on all charts)

C2 – Assumes no change in dividends from the initial amount, dividend protection is turned off (shown in Fig. 1 and Fig. 2 and Fig. 3 and Fig. 4)

C3 – Assumes future dividends are increasing and dividend protection feature is turned off (shown in Fig. 1 and Fig. 2 and Fig. 3 and Fig. 4)

C4 – Assumes future dividends are increasing and pass-thru is only on conversion (shown in Fig. 3 and Fig. 5)

Fig.1 LFG 3.25% convertible bonds valued using a discrete-proportional dividend yield model. The curves show the fair value vs. parity. The dividend protection is via a ratio adjustment.

Fig. 2 LFG 3.25% convertible bonds valued using a continuous dividend yield model. The curves show the fair value vs. parity. The dividend protection is via a ratio adjustment.

Fig. 3 LFG 3.25% convertible bonds valued using a discrete-proportional dividend model. The curves show the fair value vs. parity. The dividend protection is via cash pass-thru.

Fig. 4 LFG 3.25% convertible bonds valued using a continuous dividend yield model. The curves show the fair value vs. parity. The dividend protection is via cash pas-thru.

Fig. 5 LFG 3.25% convertible bonds valued using a discrete-proportional dividend yield model. The curves show the fair value vs. parity.

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Mathematics

We present the financial engineering details below.

For simplicity, we describe only the continuous proportional dividend model below (discrete dividends merely make the formulas more cumbersome).

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. It is sufficient here to ignore the modeling of bankruptcy (default). The above PDE implements a continuous proportional dividend yield of. If the current stock spot price is and the stock currently pays dividends with an IAD (indicated annual dividend), then.

In the more common case of a ratio adjustment, there is no change to the basic valuation PDE. (This also includes formulas based on a conversion price adjustment.) Instead there is a change in the boundary conditions which are applied to the solution of the PDE. At each time step in the valuation grid, the value of the bond on conversion (voluntary or forced) is calculated using the relevant conversion ratio at that time step.
In the (less common) case of a cash pass-through, a modification to the PDE is required. The modified PDE is
(2)

There is an extra term on the right-hand side (extra cash flow). In a time interval, the cash flow amount is. For a discrete dividend model, the cash flow would be the dividend amount multiplied by the conversion ratio, but applied at only one point in time: where is the ex-dividend date. Note that some issuers only pass on a fraction (e.g. 85%) of the dividends to the investors. The above equation assumes that all the dividends are passed through.

There may also be a variety of thresholds on the dividend protection boundary conditions. For example, in many cases there is a dividend anchor: adjustments are only made based on the dividends in excess of the anchor. Most issuers do not adjust the conversion ratio unless the change is at least 1% of the ratio then in force. All such constraints are implemented in the boundary conditions.

Appendix – A.

Convertible Securities expected to show meaningful difference from previous versions of our calculator.

Ticker	Issuer	% Coupon	Maturity	Ticker	Issuer	% Coupon	Maturity
*North America*				*North America*
AFR	American Financial Realty Trust	4.375	15-Jul-24	SPG	Simon Property Grp	6.000
AHL	Aspen Insurance Holdings	5.625		TEVA	Teva Pharmaceuticals - D	1.750	1-Feb-26
AIN	Albany International	2.250	15-Mar-26	TWX	UBS / Time Warner	21.218	15-Aug-07
ARC	Affordable Residential Cmtys	7.500	15-Aug-25	TXU	TXU Corp	6.100	15-Jul-33
ARM	ArvinMeritor Inc	4.625	1-Mar-26	UAG	United Auto Group Inc	3.500	1-Apr-26

ATU	Actuant Corp	2.000	15-Nov-23	UDR	United Dominion Realty	4.000	15-Dec-35
B	Barnes Group Inc	3.750	1-Aug-25	UIC	United Indl Corp	3.750	15-Sep-24
BDC	Cable Design Technologies	4.000	15-Jul-23	UNS	Unisource Energy Corp	4.500	1-Mar-35
BLK	Blackrock Inc	2.625	15-Feb-35	VGR	Vector Group	5.000	15-Nov-11
BPFH	Boston Private Finl Hldgs	4.875	1-Oct-34	WLT	Walter Industries	3.750	1-May-24

CARS	Capital Automotive Reit	6.000	15-May-24	*Europe*
CDL	Citadel Broadcasting	1.875	15-Feb-11	ABBN VX	ABB Ltd	4.625	16-May-07
CKR	CKE Restaurants Inc	4.000	1-Oct-23	ADEN VX	Sonata Securities/Adecco	1.500	9-Dec-10
CLF	Cleveland-Cliffs Inc	3.250		AEM IM	Comune di Milano	2.250	22-Dec-09
CSE	CapitalSource Inc	1.250	15-Mar-34	ALV GR	JP Morgan Bank/Allianz	4.500	15-Feb-08
CSE	CapitalSource Inc	3.500	15-Jul-34	ASML NA	ASM Lithography	5.500	15-May-10

CTCO	Commonwealth Telephone Enter.	3.250	15-Jul-23	BIO SW	BB Biotech AG	3.500	6-Jan-09
DRL	Doral Financial Corp	4.750		BSY LN	News Corp / BSY LN	0.750	15-Mar-23
EK	Eastman Kodak	3.375	15-Oct-33	CON GR	Continental AG	1.625	19-May-11
EP	El Paso Energy	4.990		DCX GR	UBS/DaimlerChrysler	4.350	18-Feb-10
ESS	Essex Ppty Tr Inc	3.625	1-Nov-25	DPW GR	KFW/Deutsche Post	0.875	8-Jan-07

FCE-U CN	Fort Chicago Energy Patners	7.500	30-Jun-08	ELE SM	Caixa/Endesa	0.250	3-Jul-06
FCX	FreeportMcmoran	5.500		ESFA LX	Espirito Santo Fin Group SA	3.550	15-Nov-25
FIF	Financial Federal Corp	2.000	15-Apr-34	FP/ LN	Friends Provident Plc	5.250	11-Dec-07
GM	General Motors	6.250	15-Jul-33	FTE FP	France Telecom SA	1.600	1-Jan-09
GMT	GATX Corp	5.000	15-Aug-23	HDD GR	Heidelberger Druckmaschinen	0.875	9-Feb-12

GNW	Citigroup Funding/Genworth Financial Inc	4.583	27-Sep-08	MOL HB	Magnolia Finance Ltd. (Pending)	3.750
GY	GenCorp Inc	5.750	15-Apr-07	NUM NA	Royal Numico	3.000	11-Jul-10
HAL	Halliburton	3.125	15-Jul-23	PUB LN	Punch Taverns Plc	5.000	14-Dec-10
HCR	Manor Care Inc.	2.125	1-Aug-35	REP SM	Repcon Lux/Repsol YPF SA	4.500	26-Jan-11
HET	Caesars Entertainment	4.600	15-Apr-24	RNK LN	Rank Group Plc	3.875	1-Jan-09

HMT	Host Marriott	3.250	15-Mar-24	RUKN VX	Swiss Re	6.125	23-Jul-07
INN-U CN	InnVest REIT	9.750	30-Jun-07	SOI FP	Silicon On Insulator Tech	5.500	27-Nov-06
INTC	Intel Corp	2.950	15-Dec-35	SOO1 GR	Solon AG	4.500	29-Jun-10
IPL-U CN	Inter Pipeline Fund	10.000	31-Dec-07	SPW LN	Scottish Power (Perp)	4.000	29-Jul-49
KTO	K2 Inc.	5.000	15-Jun-10	XTA LN	Glencore/Xstrata	4.125	6-Oct-10

LAD	Lithia Motors Inc	2.875	1-May-14	*Japan*
LFG	Landamerica Financial	3.125	15-Nov-33	2337 JP	Asset Managers Co	-	18-Mar-11
LFG	Landamerica Financial	3.250	15-May-34	6423 JP	Abilit Corp	-	24-Sep-10
LGND	Ligand Pharmacy	6.000	16-Nov-07	7203 JP	Toyota Motor Corp	-	30-Jun-08
LLL	L-3 Communications Holdings	3.000	1-Aug-35	CAHB MK	Commerce Asset-Holding	-	22-Sep-09
				UNI MK	Unisem Berhad	3.000	12-Feb-09
LMT	Lockheed Martin Corp	4.499	15-Aug-33
LXP	Lexington Corp	6.500		*Asia/Pac Rim*
LYO	Millenium Chemical Inc	4.000	15-Nov-23	066570 KS	LG Electronics	-	11-Aug-06
MECA	Magna Entertainment Corp	7.250	15-Dec-09	175 HK	Geely Auto Holdings	-	10-Apr-11
MECA	Magna Entertainmemt Corp	8.550	15-Jun-10	2314 HK	Lee & Man Paper Manufacturing	-	13-Jan-11
				2382 TT	Quanta Computer Inc	-	26-Jul-10
MLS	Mills Corp	6.750		2890 TT	SinoPac Holdings	-	12-Jul-07
NAFC	Nash Finch Co	1.631	15-Mar-35
NCOC	National Coal Corp (Unit)	10.500	15-Dec-10	2891 TT	Chinatrust Financial	-	8-Jul-07
NHP	Nationwide Health Properties	7.750		363 HK	Shanghai Industrial Hldg Ltd.	-	16-Mar-09
OMM	Omi Corp	2.875	1-Dec-24	450 HK	Hung Hing Printing Group	-	29-Mar-11
				5371 TT	Coretronic Corporation	-	18-May-10
ORH	Odyssey Re	4.375	15-Jun-22	5387 TT	PromosTechnologies	-	20-Jun-10
PIR	Pier 1 Imports	6.375	15-Feb-36
PRV	Province Healthcare	4.250	10-Oct-08	HDFC IN	Housing Development Finance	-	27-Sep-10
PTA	Penn Treaty American	6.250	15-Oct-08	HKL SP	Hongkong Land Holdings	2.750	21-Dec-12
PTA	Penn Treaty American	6.250	15-Oct-08	TEL PM	First Pacific/Philippine Long Distance	-	18-Jan-10
				VCLF IN	Videocon Industries	5.000	7-Mar-11
RA	Reckson Associates	4.000	15-Jun-25
RGC	Regal Entertainment Group	3.750	15-May-08
SAH	Sonic Automotive Inc	4.250	30-Nov-15
SEE	Sealed Air	3.000	30-Jun-33
SOV	Sovereign Bancorp	4.375	1-Mar-34

Appendix - B.

Dividend Protection: Why? An increase in the dividends on the stock underlying a convertible security adversely affects the value of the convertible. This is because, the increased dividends lower the value of the option embedded in the convertible.

For an outright investor, the reward-risk tradeoff between owning the convertible versus owning the underlying stock moves away from the convertible. While, an increase in the dividend tends to cause the stock price and hence the parity of the convertible to go up, the outright investor is still affected because the increase in the value of the convertible is less than the increase in the value of the stock due to the delta of the convertible which in fact goes down in response to an increase in stock dividends.

For an arbitrageur, the impact is more severe. An arbitrageur who is long the convertible and short the stock is automatically short the dividends. An increase in stock dividends adversely affects the arbitrageur in multiple ways. i) The arbitrageur loses money from the short dividend position, ii) The increased dividends cause the stock price in the market to go up and forces the arbitrageur to suffer a loss from the short stock position, iii) the valuation of the convertible suffers from the adverse affect of stock dividends on the embedded option, causing the convertible to trade down in the market on a dollar-neutral basis, and iv) the decrease in delta of the convertible forces an arbitrageur to cover the short stock position as the stock is increasing to stay delta neutral.

The magnitude of the adverse impact is proportional to the amount of dividend increase as well as the time-to-maturity (expected life) of the embedded option in the convertible. As the market absorbed a lot of new issuance in the past few years with five to seven years or more of call protection on stocks which started raising dividends in response to the tax relief passed by the Congress, the demand for protection from stock dividends increased in the convertible securities market. The companies issuing the convertible securities responded by providing dividend protection features as part of the indentures to keep the coupon and premium in a range they could live with.

Dividend Protection: What? The convertible holders are protected from increasing dividends in one of two ways. (i) The issuing company agrees to increase the number of shares into which the holder can convert into (conversion ratio) if the stock dividend is increased above a pre-determined level. (ii) The issuing company agrees to pass on the dividend increases to holders of the convertible either when the dividends are paid out to the share holders or accumulated until conversion.

Dividend Protection: How? Conceptually, the issuing company agrees to compare the dividend paid out to the level of dividends when the convertible was issued and make adjustments to the conversion ratio or pass the dividend increases to the convertible holder. In practice however, a single simple methodology does not exist. The prospectus stipulates conditions (thresholds, anchors) that would force the issuer to perform a calculation (adjustment formulas) and compare the new conversion ratio to the old conversion ratio and if the difference exceeds a stipulated level (administrative limits) then the adjustment is instituted. We would advise you to read the fine print because in some extreme situations, the dividend protection feature may not provide the desired protection against increasing dividends due to very high thresholds. The various terms and formulae used in providing dividend protection are provided below.

Dividend Protection Terminology:

Adjustment Type: Ratio adjustment or Cash pass-thru

Adjustment Formula: If the protection is ratio adjustment, the formula used to calculate the adjustment. We provide the various known formulae at the bottom of this list.

Adjustment Direction: Up-Only – the adjustment is only done if the dividend increases, Up-Down – the adjustment is done for dividend increases as well as dividend cuts.

Dividend Anchor: This is usually the reference dividend amount or dividend yield when the convertible is issued. Prospectuses tend to call this the “dividend threshold amount”. This reference is used in the adjustment formulae.

Anchor Compounding Rate: Some issuers will stipulate that the anchor will increase as time goes by. This is the rate at which the anchor is increasing as a function of time.

Administrative Limit: The difference between the new calculation and old calculation that will cause a revision in the conversion ratio, usually expressed in percentage. 1% limit is a very typical limit we have seen.

Averaging Days: The number of trading days used in calculating the stock price used in the adjustment formulae.

Catch up on conversion: If the dividends have increased from the anchor but no revisions were made due to administrative limits, whether there will be a one-time adjustment upon forced conversion or not.

Auto catch-up years: The interval at which the issuer agrees to synchronize the adjustments if dividends increased and revisions were not done due to administrative limits.

Annualized: Specifies whether the comparison is between quarterly dividends or dividends over a 12 month period in deciding if a revision should be considered.

Ratio Cap: Some issuers will stipulate a maximum conversion ratio above which no revisions will be done even if the stock dividends increase.

Adjustment Formulae:

Ratio Denom: CR * (Average / (Average - (New Div - Anchor))) Ex ROP

Ratio Num: CR * ((Average + (New –Anchor)) / Average) Ex RPT

Ratio NumDenom: CR* ((Average –Anchor) / ( Average – New)) Ex WLT

Ratio CP Denom: CR * ( CP / (CP-(New - Anchor)) ) Ex SOV

CP Num: CP * ((Average – (New- Anchor)) / Average) Ex RGC

CP Denom: CP * (Average / (Average + (New – Anchor))) Ex BGC

Cash Pass Thru: (Divamt) * (Conv Ratio) * (Pct Factor) Ex AIZ, S, DCX GR

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