Presentation on theme: "Part 5 - Convertible bonds as an asset class"— Presentation transcript:
1Part 5 - Convertible bonds as an asset class Various features in convertible bondsIssuance of convertibles - perspectives of corporate treasurers- conversion into sharescall (hard and soft provisions)- put- reset on conversion number- dilution protectionDelayed call phenomenaDecomposition of convertibles into different componentsValuation of convertibles- interest rate sensitivities (duration analysis)- binomial tree calculations
2Combination of bonds and equities - bond plus a conversion option * Bondholder has the right to convert the bond into common shares atsome contractual price (conversion number may change over time).Conversion value: stock price x conversion numberConversion premium: (bond price – conversion value) / conversion valueBond floor value: sum of present value of coupon and parconvertiblebond priceconversion valueconversionpremiumstraight bond valuestock price
3Perspectives on convertibles •To take advantage of the upside potential growth of the underlying stock (participation into equity).Conversion option that allows the investor to exchange the straight bond for fixed number of shares.Swapping the variable stock dividends in return for fixed coupon payments until the earlier of the maturity date and the conversion date.••Provides the “bond floor” value as downside protection.
4Analytics of convertible bonds stock price $30.00 per sharestock dividend $0.50 per shareconvertible market price $1,000coupon rate %maturity yearsconversion price $36.37Stock dividend yield = annual dividend rate/ current stock price= $0.50 / $30.00 = 1.67%
5Conversion ratio= number of shares for which one bond may be exchanged= par / conversion price= $1,000 / $36.37 = sharesConversion value= equity value or stock value of the convertible= stock price x conversion ratio= $30.00 x = $825.00
6Premium for conversion right • An investor who purchases a convertible bondrather than the underlying stock typically pays apremium over the current market price of the stock.• Why would someone be willing to pay a premiumto buy this stock? The market conversion premiumper share is related to the price of a call option –limit the downside risk of the convertible bond.
8Capture of accrued interest upon conversion Upon conversion to stock, any accrued interest will be lost. This is the infamous screw clause.Trick - sell an equivalent amount of stock short against the convertible bond, hold the short sale until the interest payment date; then convert the bond and deliver the stock against the short sale.
9Break even calculations Break even (years)= conversion premium / (convertible yield – stock yield)= / (7.00 – 1.67) = 3.98 (years)Number of years necessary for the stock investor to recoverthe conversion premium from the convertible’s higherincome relative to an instrument of an equivalent amount inthe stock.After 3.98 years, the convertible has made up, in income alone, the amount of the conversion premium.
10Break-even calculations (cont’d) Dollar maintenanceThe time it takes for the convertible yield advantage to pay for its premium compared to an equivalent dollar amount purchased of the underlying stock.May use conversion ratio instead of marketprice/ stock price.market price – conversion value=market pricecoupon stock dividendstock price
11Weaknesses of break-even analysis It ignores the main advantage of convertible: protection on downside risk on the underlying equity.It ignores the margin of safety offered by the convertible with the payment of principal at maturity.
12Call termsIssuer has the right to call back the bond at a pre-specified call price prior to final maturity, usually with a notice period requirement. Upon call, the holder can either convert the bond or redeem at the call price.Issuer’s perspective on the call rightRefinancingTo have the flexibility to call if they think they can refinance the debtmore cheaply.Managing the debt / equity balanceTo force bondholders to convert debt into equity, which can reduce debtlevels. The issuer has the flexibility to shift debt into equity to reducethe leverage of the firm.
13Investor’s protection Call protectionHard (or absolute):To protect the bond from being called for a certain period of time.Soft (or provisional):The issuer is allowed to call only when certain conditions are satisfied.For example, the closing price of stock has been in excess of 150% of the conversion price on any 20 trading days within 30 consecutive days.Investor’s protectionTo preserve the value of the equity option for the bondholders. While waiting for the stock price to increase, convertibles typically provide more income than the stock. Without the call protection, this income stream could be called away at any time. Hard call protection with the longest possible duration is the most desirable for the investors.
14Background for make-whole provision Provisional call protection give issuers the option to retire the debt early, while the make-whole payment just what would have had to make anyway.2. They are designed to protect investors from sharp premium contraction in a rapidly rising equity market.Make-whole payments should become a price variable at the pointwhere a convertible without a make-whole provision, given a risingcommon stock, would begin to lose premium.
15Make-whole provision Premium make-whole provision First issuance of Amazon.com 4.75% convertible note in January 1999Assures that holders will recover the amount of original premium paid at issuance, less any interest already paid.Soft (or provisional):The issuer is allowed to call only when certain conditions are satisfied.For example, the closing price of stock has been in excess of 150% of the conversion price on any 20 trading days within 30 consecutive days.
16Put featureAllows the holder to sell back the bond to the issuer in return for a fixed sum. Usually, the put right lasts for a much shorter time period than the maturity date of the bond.The holder is compensated for the lesser amount of couponsreceived in case the equity portion of the convertible has lowvalue.It protects the holder against rising interest rates by effectively reducing the year to maturity. The convertible’s price then becomes less sensitive to interest rate.The put feature may shorten the maturity of the bond (par paid earlier) and thus effectively raises its investment value and lower the sensitivity to interest rate fluctuation.••
17Reset feature in convertible bonds In most cases, the reset on conversion price is downward and this makesthe bond more valuable. For example, the conversion number is resetby dividing the par by the prevailing stock price.Floor limitThe extent of downward reset cannot be below a certain multiplier ofthe first conversion price.
18Why reset convertible bonds are popular in Japan in mid-1990’s? •Japanese banks were considered quite risky as they had largereal estates exposures.To raise capitalequity issuance was out of the question since the stockmarkets were depressed;straight bond issues would have required a high coupon yield.•Reset feature was included in convertible bonds to give investors somesort of insurance against bank’s stock decline.
19Pricing difficultiesThere are many possible conversion prices since they depend on the past history of the stock price.Impact on bond priceAt high stock price (not likely to reset) or low stock price (low equity value) regions, the reset premium is low. The reset premium is significant only at intermediate stock price level.Nightmare for the issuersThe feature is too sweet for the investors and harmful to the issuer.When the stock price drops, the investors are compensated.When the stock price rises, the conversion premium becomes moreexpensive.These structures have fallen from popularity in recent years.
20Takeover clausesAn unexpected takeover bid can have the effect of eliminating any conversion premium if the takeover price is below the conversion price.Poison put is added as protection in the change-of-control clause:triggered as a result of a hostile takeover and would allow the bondholder to put the bonds back to the company at par.Alternatively, the issuer can prevent the conversion premium from evaporating by increasing the conversion ratio to restore the premium to the average level seen before the takeover announcement.
21Dilution protection (extraordinary dividends) Convertible investors are not compensated for normal dividend payment. However, if a company makes an extraordinary payment, resembling a return of capital, convertible holders want to be compensated.Dilution protection clause may be added:If the dividend payment yields more than a specified amount, any amount over the threshold will be compensated.
22Convertible bond issued by the Bank of East Asia US$250,000,0002.00 percent Convertible Bonds due 2003Issue date July 19, 1996Issue price 100 percent of the principal amount of the Bonds, plus accrued interest, if any, from July 19, 1996(in denominations of US$1,000 each)Conversion period From and including September 19, 1996 up to and including July 7, 2003
23Conversion featureConversion price HK$31.40 per Share and with a fixed rate of exchange on conversion of HK$ = US$1.00.Dilution protection The Conversion Price will be subject to adjustment clause for, among other things, subdivision or consolidation of the Shares, bonus issues, right issues and other dilutive events.
24Call featureRedemption at the On or after July 19, 1998, the Issuer may redeem option of the the Bonds at any time in whole or in part at the bondholders principal amount of each Bond, together with accrued interest, if for each of 30 consecutive Trading Days, the last of which Trading Days is not less than five nor more than 30 days prior to the day upon which the notice of redemption is first published, the closing price of the Shares as quoted on the Hong Kong Stock Exchange shall have at least 130 percent of the Conversion Price in effect on such Trading Day.
25Soft call protection Parisian feature The closing price has to be above 130 percent of the conversion price on consecutive 30 trading days.On the date of issuance of the notice of redemption (treated as day 0),the Issuer looks back 5 to 30 days (corresponds to [-30,-5] timeinterval) to check whether the history of the stock price pathsatisfies the Parisian constraint. That is, the last of the 30 trading daysfalls in [-30,-5] time interval.From Issuer’s perspective, when the Parisian constraint has beensatisfied, the Issuer has 5 to 30 days to make the decision onredemption or not.
26Put featureRedemption at the On July 19, 2001, the Bonds may be redeemed at option of the the option of the Bondholders in US dollars at the bondholders redemption price equal to percent of the principal amount of the Bonds, together with accrued interest.The investors are protected to have 27.25% returns on the bond investment upon early redemption by the issuer.
27Put above par value or premium redemption at maturity Renong Berhad (a Malaysian company) issued a 5-year bond with a 2.5 percent coupon with yield-to-put at 7.5 percent and a put price of This is above the par of 100 used in the calculation of conversion into stock. Also, this results in increased downside protection in case the equity portion has low value.Investors’ perspectiveEven if the conversion turns out to be unprofitable, they are guaranteed a 7.5 percent return to the time of the put.
28Examples of reset convertibles •United Artists Communications (1987) issued convertibles that aftera fixed period of time, the bonds were evaluated by an independentinvestment banker. This is to determine the coupon rate that wouldallow the bonds to trade at 101 plus accrued interest.Mitsuibishi Bank issued (Oct., 1995) $2 billion of 7-year bond withannual reset of the conversion ratio. It offers investors more shares ifthe stock price declines, with the goal of keeping the bond’s equityvalue at par.•
29Casino operator brings ringgit convertible Malaysia's only casino operator, Resorts World, has raised M$1.1 billion ($300 million) from a convertible bond that was well received despite offering a negative yield.Desire to see bonds convert prompts Resorts World to use rare negative yield structure – less bond characteristics.Reset feature added to prompt higher propensity of conversion.
30Bond indentureNegative yieldIssuing the zero-coupon bonds at par and setting the redemption price at 99%, which results in a yield to maturity of -0.5%.Lower conversion priceThe conversion price was fixed at launch at 10% over yesterday's (September 7, 2006) volume weighted average price of M$11.593, giving an initial conversion price of M$12.75.
31Forced conversionThere is an issuer call after one year, subject to a 120% hurdle, to force conversion in case investors drag their feet.The reset mechanism has a floor at 90.9% of the original conversion price, which is high compared with the typical reset floor at 80-85%.The bonds were priced assuming a credit spread of 40 basis points over the Malaysian interest rate curve, a dividend yield of 2.2% or 120% of the previous year's, and a stock borrow cost of 5%.
32Issuer’s perspectives While common a few years back when interest rates were much lower, negative yields are rarely seen on CBs nowadays but highlights the issuer's desire to have the bonds convert in order to get equity on its balance sheet.The bonds have a short maturity of only two years, a conversion premium of only 10% and two conversion price resets - after the first year and 60 days before maturity - making it all but inevitable that the bonds will convert.
33Investor’s perspectives The bond floor was set at 90.7%, which one observer says is "reasonably attractive" given the strong focus on conversion and the implied volatility is 24%.Market backgroundThe share price is up a modest 4.5% this year to Thursday's closing price of M$11.70, which compares with a 6.2% gain in the Kuala Lumpur Composite Index.The expected appreciation of the ringgit makes the bonds a reasonable proposition.Of the 19 analysts that cover the company, according to Bloomberg data, 16 have a "buy" or "overweight“ recommendation.
34Types of companies as convertible issuers Companies that are characterized by strong performing, high-visibility, sub-investment grade, high-growth potential havecomparative advantage in the convertible market versus thefixed income market.They lack a long-term track record and have volatile capital structures – high coupon must be offered.They can transform the high volatility into a benefit since the warrant is more expensive.When the company grows, they may call the bonds. This in turn will strengthen the company’s equity base at the moment when it is most needed.
35Convertibles as backdoor equity financing Delayed equityConvertibles provide a way of selling common stock at a price above the existing market.They are employed as deferred common stock financing.The call feature is important since it gives thecompany the means to shift debt to equity.Convertibles offer a means to control thedebt/equity ratio.
37Reasons for offering (cont’d) By order of importance, please rank the following factors on a scale of1 to 6 on the extent to which it influenced your firm’s decision to issueconvertible; 1 = most influential, 2 = next most influential, etc.)
38Environment in which issuance occurred 1. In retrospect, my firm’s stock was _____ valued around the timeof the convertible debt offering.2. Around the time of the convertible debt offering, my firm’smanagement expected future earning to be _____ the market wasexpecting.3. At the time of the convertible debt offering, prospects for myfirm’s short-term (1-2 years) performance relative to its industrywere:
39Delayed call phenomena • Firms wait until the value of the bond value is muchhigher that the call price times the conversion numberbefore issuing the call. In Ingersoll’s study of179 convertibles, the percentage amount exceeded hada median of 43.9%.• How to explain such delayed call phenomena?• Several possible theories are proposed for the rationalesof delayed call.
40Safety premium• Since convertible bond covenants typically require 30-daynotice before the bonds are redeemed, and during thatperiod, the stock price may fall (likely to fall given thenormal negative reaction to the call announcement),forcing the firm to redeem for cash.• There would be a higher cost to raise funds shortly so thatthe calling firms require a safety premium on the risk thatthe stock price may drop significantly over the noticeperiod causing the bond to become out-of-the-money.
41Tax advantage Some firms enjoy an advantage of paying less in after-tax interest than they would pay in dividendswere the bond converted.Therefore, firms have the incentive to keep thebond alive even if the net present value of couponsto be paid somewhat exceeds the net present valueof the dividends that would be paid to the formerbondholder following conversion.
42Stripping different components of convertible bondsA convertible bond consists of 3 components• bond component – interest rate risk• equity component – equity risk (long volatility)• credit quality component - credit riskcoupon paymentperiodicpaymentDefault riskprotectionproviderFixed incomeinvestorFinancialinstitutionprincipalpaymentcontingentupon defaultholding aconvertible bond
43Contingent claims approach Wide spread use of the option pricing theory for pricingconvertibles.The underlying state variable is the issuer’s firm value process. The firm value is not the total value of assets owned by the firm. It is the takeover value when the firm is sold.Overall assessment of the price impact of different features in a convertible.
44Dominant factors in structural models for risky convertibles 1. Issuer’s firm value process - volatility.2. Issuer’s capital structure – debt/equity ratio.3. Loss given default.4. Terms and conditions of the debt issue.5. Interest rate process.6. Correlation between the interest rate and asset value.• Difficult to estimate the parameter values when implementingthe models.
45Structural models for pricing convertible bonds AssumptionsNon-callable and can be converted only at maturity.No transaction costs and no bankruptcy costs.Capital structure consists of common shares and non-callable convertibles.
46N = number of common shares M = number of convertiblesf = face value per convertibleF = face value of the convertible issue = Mfr = conversion ratioUpon conversion, the convertible holders will possessl fraction of equity, whereThe parameter l is called the dilution factor of theconvertible issue.
47Let VT denote the value of the firm at maturity after the last coupon has been paid.The holder will convert if and only ifValue of the convertible bond at maturityl VT > F
48payoff toconvertiblestraight bondwarrantVTF F/lDecomposition into a straight bondplus l units of call with strike F/land short a put to issuer
49Intrinsic value of convertibles The intrinsic value of a convertible bond is the greater ofConversion valueBond investment value – value as a corporate bondwithout the conversion option (based on the convertiblebond’s cash flow if not converted).• To estimate the bond investment value, one has todetermine the required yield on a non-convertible bondwith the same quality rating and similar investmentcharacteristics.• If the convertible bond does not sell for the greater ofthese two values, arbitrage profits could be realized.
50Convertible = bond + warrant Factors that affect the bond componentInterest ratesCredit rating/spreadsCouponDurationFactors that affect the warrant componentStock performanceEmbedded strike priceCommon dividend yield and dividend growth rateStock volatilityLife of warrant / call protection
51Put plus stock plus yield advantage Applying the put-call parity:call + bond = put + stock.Here, put is the right to sell the stock for bondOne may treat a convertible bond as yield-enhanced stockplus a put option.• The put option represents the bond floor protection.The strike price is the bond investment value.
52Bond investment valuePresent value of the interest and principal payments discounted at the straight (non-convertible) bond interest ratebond interest value =where P = par value, r = discount rate, C = coupon rate,n = number of periods to maturity.take r = 10%
53Estimation of the discount rate Use the yield-to-maturity of a similar non-convertible bond as a proxy.The apparent deterioration of the creditworthinessof an issue will not be reflected in the convertibleprice because the value of the conversion optionmay be rising due to higher share price volatility.
55DurationDuration is the weighted average of the times that the principal and interest payments are made.where t is the time of paymentCt is the coupon and/or principal paymenti is the market yield.Duration analysis provides a measure how bond values change with changing interest rates.duration =
56Duration analysis applied to convertibles The approximation for the convertible bond’s interest rate sensitivitywhere C = conversion value and I = investment value.The equity component of the convertible bond maydampen the convertible’s interest rate sensitivity,depending on the bond’s equity participation.Hence, convertibles trading high above theirinvestment value will be less sensitive to interestrates.
57Duration and couponFor non-convertible bonds, the duration decreases as their coupon increases. This is because higher coupon bonds deliver more cash flows near the start of bond’s life.With convertible feature, the higher coupon rate may lead to lower propensity to convert. The CB then has a longer life, so this leads to higher duration.These two effects are counteracting.
58Interest rate sensitivity 1. The exercise price is a function of the investment value. An increase in interest rates will lower the investment value.2. However, the exercise price of the embedded call is reduced. A lower exercise price will increase the value of the warrant.
59Interest rate sensitivity (cont’d) Basic Int rate Change Int rate Changeprice + 1% -1%_______________________________________________________Investment value $ $ $ $36.90Warrant value $ $ $ $24.94Total $ $ $10.17 $ $11.92Percent change % 1.19%
60Correlation with interest rates Consider the impact of an increase on interest rateThe future share price is expected to be higher because of higher drift rate.Due to negative correlation between interest rate and share price (say, the S&P 500-stock index has a correlation of about minus 0.5), the share price drops first.Negative correlations normally lower CB value;positive correlations make the CB worth more.In some situation, CBs may have price differences in the rangeof 10-15% when correlation moves from 1.0 to –1.0.
61Pricing of risky convertible bonds One-factor binomial modelstock price process follows binomial random walk*interest rates to be deterministic*Two discount rates1.If the convertible is certain to remain a bond, it is appropriateto use a discount rate corresponding to the creditworthinessof the issuer - risky rate.2.Suppose the bond is certain to be converted, it is thenappropriate to use the riskfree rate.At maturity, the holder will choose the maximum betweenthe par value and the value of stocks received uponconversion.
62How to account for the creditworthiness of the issuer? The discount rate to be used when we roll back is given bypwu + (1 - p)wd.Here, p is the probability to a node where the discount rate iswu and (1 - p) is probability to a node with wd. The appropriatediscount rate is the weighted average of the discounted ratesat the nodes in the next time step.
63conv = value of stocks received if conversion takes place call = call priceroll = value given by the rollback(neither converted nor recalled)At each node, the optimal strategy of the holder is exemplifiedby taking the maximum of min(roll, call) and conv.The maximum reflects the conversion right, which persistswith or without recall by the issuer.min(roll, call) means the bond value can never shoot beyondthe call price.Dynamic programming procedure:max(min(roll, call), conv)
64Alternative dynamic programming procedure: min(max(roll, conv), max(call, conv))The term max(roll, conv) represents the optimal strategy ofthe holder.Upon recall, the holder chooses to accept the call price orconvert into shares. This can be represented bymax(call, conv).The issuer chooses to recall or to abstain from recalling inorder to minimize the option value.
65ExampleA 9-month discount bond issued XYZ company with a facevalue of $100. Assume that it can be exchanged for 2 sharesof company’s stock at any time during the 9 months.It is callable for $115 at any time.Initial stock price = $50, s = 30% per annum and nodividend; risk-free yield curve to be flat at 10% per annum.Yield curve corresponding to bonds issued by the companyto be flat at 15%.Tree parameters are: u = , d = , p = ,R = e0.1Dt =At maturity, the convertible is worth max (100, 2ST).*****
66Binomial tree for pricing a risky convertible bond equity78.4210%156.8467.4910%D58.0911.03%134.9858.0910%116.18equityB116.1850.0012.27%50.0011.59%104.85AE43.0413.51%105.5643.0415%100.00bondC98.0037.0415%F96.32upper figure: stock pricemiddle figure: discount ratelower figure: value of convertible31.8815%100.00bond
67At node DRoll back gives the bond value( )e-0.1 0.25 =The bondholder is indifferent to conversion or hold, also theissuer is also indifferent as to whether the bond is called;the correct discount rate at node D is 10%.At node FThe correct discount rate is 15% since the convertible iscontain not to be converted if node E is reached.At node EThe correct discount rate is 10% 15% = 12.27%.The value of convertible at E( 100)e 0.25 =The bond should be neither converted nor called.
68At node BThe discount rate is 10% 12.27% = 11.03%and value of convertible is( )e 0.25 =It is optimal to call the bond at node B so that it causesimmediate conversion and leads to $ The discountrate at node B should be taken to be 10%, since conversiontakes place at this node.At node AThe discount rate is 10% 13.51% = 11.59%.The convertible value at node A is( 98.00)e 0.25 =If the bond has no conversion option, its value ise-0.75 0.15 =The value of conversion option = =