Options, Futures and Structured Products. Jos van Bommel Aalto - Period Class 6a and 6b. Warrants, Convertibles, Death Spirals.

Transcription

1 Options, Futures and Structured Products Jos van Bommel Aalto - Period Class 6a and 6b Warrants, Convertibles, Death Spirals Warrants A U.S.-style warrant gives the holder the right to buy a given number of primary shares at a predetermined price (the Strike Price), on or before a predetermined date (the expiration date), from a company. They thus resemble call options. But, upon exercise there will be dilution. Consider a company with 100 shares outstanding each trading at $4. You own a warrant to buy 20 shares for $2. It expires today. You exercise it, and the firm s value goes up by $40 (your cash!) But the number of shares outstanding goes up by 20.. After exercise, the sharevalue drops to $440/120 = $3.67 due to dilution.. Right? 1

2 Warrants Wrong.. In an efficient market, the price should already reflect the warrant s imminent exercise. Analysts call it a hanging warrant (it considered bad, as it reduces the share s upside potential). (they are also hanging convertibles) To value a warrant, we need to adjust the (Black-Scholes) value for the dilution. You need to multiply it with N/(N+M), where N is the number of shares outstanding before warrant exercise, and M is the number of shares issued due to the warrant. Warrants are part of the firm s equity. To estimate the volatility, it s best to look at the (historical) volatility of warrants+shares. After issuance of warrants: the shares become less volatile as before, because the warrants are more volatile.. Warrants 2

3 Why do firm issue warrants? - To raise money. Potentially twice.. - As a deal sweetener in capital raising (with bonds or equity) - If warrants are non-detachable, Bonds+Warrants = Convertible bond. - As a deal sweetener in M&A - Rights (in rights issues ) are also warrants (deep in the money) - As Employee Stock Options - ESOPs can not be sold - Have a vesting date (at which they become exercisable) - Are often exercised before maturity.. Why? Convertible debt (or preferred stock) Many debt issues are of the convertible kind. That is, they can be converted, at the option of debt-holder, into common stock. Conversion right: Each Bondholder has the right to convert its bonds into fully paid-up ordinary shares of common stock of the issuer at any time during the period from and including October 18, 2010 up to and including The conversion ratio January is the 18, number 2034 (the of Conversion shares into Period ) which the bond Conversion can be converted. Price: The price at which shares will be delivered upon conversion (the Conversion Price ) will be The conversion price = facevalue/conversion ratio. $ per Share. The number of shares to be delivered upon (the Conversion Ratio ) When the stockprice hits the conversion price, conversion becomes will be determined by dividing the nominal amount interesting. per Bond by the Conversion Price. Consequently, shares will be delivered upon conversion of Should the bondholder each Bond. convert when the stockprice reaches the conversion price? Firms can often force conversion? By calling the bond. 3

4 Convertible debt Upon conversion, new primary shares are issued by the firm. Accounting entry: Long term Debt -X Owner s Equity +X How do we price a convertible bond? With option pricing! The value of a convertible bond equals the PV of the bond-payments (coupons + facevalue),..plus the option to exchange these bond payments for a slice of the firm s equity. We can use Black Scholes but should take into account that: (1) The exercise price (the value of the bond) is uncertain.. (2) Upon exercise (conversion) dilution obtains. 4

5 Why do we have convertibles? A disadvantage of convertible debt is that it is hard in the bad states (potential bankruptcy costs) while it is soft in the good states. Then why do we see so much convertible debt? 1) Convertible debt can be issued at a lower interest-rate than straight debt? 2) Convertible debt reduces risk shifting? 3) Convertibles can resolve information asymmetries between lender and borrower about the firm s risk? 4) It s a clever way of back-door equity financing? 5) If conversion price is set higher than current stock-price, convertible debt offers a win-win situation: If there s conversion, you suffer less dilution than if you would issue stock now. If there s no conversion, you get cheap debt (lower coupon)? 6) The increased complexity justifies higher fees for Investment Banks? 7) For behavioral reasons the investors like them (and overvalue them)? Caledonian Cash 400 'Assets in place' 2400 Risky project Debt, Facevalue 2500 O.E. Risk shifting Debt is worth 2500, Equity is worth 300 (k ) (discounted CF) Debt gets Equity gets /2 1/ Expected payoff In highly leveraged firms, Debt dislikes risk, even if project is positive NPV In highly leveraged firms, Equity likes risk, even if project is negative NPV 5

6 Risk shifting Debt dislikes risk, because its payoff is concave in firm value. Equity likes risk, because its payoff is convex. Equity Payoff Debt firm value Equity is in control.. They prefer the yellow probability distribution over the green one.. They like risk because heads I win, tails, you lose Solution: add a warrant Offer debt a (non-detachable) warrant to buy 20% of the equity for 60 Caledonian Cash 400 'Assets in place' 2400 Debt, Facevalue 2500 O.E (discounted CF) 1/ /2 50 Debt gets Expected payoff 2516 Equity gets = ( )*20% - 60 Debt 20% of Equity X Thanks to the equity kicker, incentives are better aligned. Debt is a bit less concave, equity a bit less convex Equity does not gamble.. 6

7 The Assymetric Information problem: The undervalued ( good ) firm cannot issue equity Assets in Place: 600 Firm A Debt: 100 Eq: 100 shrs t=0 t=1 Project: A s problem: Issue 33.3 shares and invest in project: Next year s shrprice: ( )/133.3 = $4.88 Don t issue shares, don t invest: Next year s shareprice: ( )/100 = $5 Firm B Assets in Debt: 100 Place: 200 Eq: 100 shrs t=0 t=1 Project: B s problem: Issue 33.3 shares and invest in project: Next year s shrprice: ( )/133.3 = $1.13 Don t issue shares, don t invest: Next year s shareprice: ( )/100 = $1 Problem: Market can not distinguish between firm A and B Hence, both stocks are trading at $3 per share Assumption: At time t=1, true value is revealed So: if market sees an equity issue, shareprice will drop dramatically, making A s problem even worse!! The solution: Floating-Priced Convertible Preferred Stock that becomes convertible after the revelation of type. Firm A Assets in Debt: 100 Place: 600 Eq: 100 shrs t=0 t=1 Project: A s problem: Don t issue shares, don t invest: Next year s shareprice: ( )/100 = $5 Issue a FPC with F = $90, d = 10%, and invest: Next year s shrprice: ( )/118.2 = $5.50 If S - = $5.00, then the conversion price is $4.50 and the FPC converts into 20 shares, S + = 650/120 = $5.42 If S - = $5.50, then the c.p. is $4.95 and the FPC converts into 90/4.95 = 18.2 shares. S + = 650/118.2 = $5.50 If S - = $6.00, then the c.p. is $5.40 and the FPC converts into 90/5.40 = 16.7 shares, S + = 650/116.7 = $5.57 Firm B Assets in Debt: 100 Place: 200 Eq: 100 shrs t=0 t=1 Project: B s problem: Don t issue shares, don t invest: Next year s shareprice: ( )/100 = $1 Issue a FPC with F = $90, d = 10%, and invest: Next year s shrprice? Owner is allowed to convert $F of face value into newly issued stock at a conversion price which is set at a discount d of the preceding day s shareprice. (assume r f = 0%) If F at $90 and d = 10%, the fair value of the security is $100, whatever S will be.. Assume S = $5, conversion price is $4.50, investor obtains 90/4.5 = 20 shares (worth $100) Assume S = $1, conversion price is $0.90, investor obtains 90/0.90 = 100 shrs (worth $100!) Assume S = $10, conversion price is $9, investor gets 90/9 = 10 shares (worth $100!!) 7

8 The solution: Floating-priced Convertibles In theory: A way a risky firm can issue a riskfree security. A wonderful instrument that allows good firms to signal their type. The FPC have no cash-obligations. No bankruptcy cost! Only good companies with +NPV projects will issue them! Hence, in theory: If a firm issues a Floating-Priced Convertible, its price increases! In practice: Not quite. They re known as Death Spirals. Empirical evidence: price drops on announcement.. and much more so, thereafter.. So what s the problem? Consider a FPC investor who owns 1,000 FPCs with Face value $1,000. Discount is 10%, stock is trading at $ He expects to get 100,000 shares. Selling 100,000 shares is difficult. Risk is that stock drops while selling.. Hence, investor hedges, by shorting, say, 80,000 shares before conversion. Assume that, due to the shorting, stock drops so that the proceeds are $800,000 (average price of $10) and that after the operation the stock stands at $9.26. Now the conversion price is $8.33, so that he stands to receive 120,000 shares. Hence he hedges a bit more, by shorting another 24,000 shares. Additional proceeds $180,000 (shorted at average price of $7.50). He s still 16,000 long. No, wait a minute, he s 46,000 shares long (because stock fell further, to $6.67..) Speculators wake up, and short some stock too. Stock drops to $5.55, and FPC investor now stands to get 200,000 shares (he sold only 104,000) Hence he hedges some more 8

9 The Death Spiral Speculators are happy (stock went down), they short some more. FPC investors don t mind (price went down but they stand to get more shares), they hedge some more. Speculators short some more. FPC investors hedge some more. Etc., etc. Does all this shorting change the fundamental enterprise value of the company? No!!?? Yes! A tanking stockprice is bad publicity for their product market activity.. Still, even if the dropping shareprice does not affect the fundamental equity value, it does affect the fundamental share price! This is why the FPC, in theory a great security for small and risky firms, may suffer from a serious design fault.. The empirical evidence 9

10 Is there a free lunch for shorters? We should just look for firms who issue FPC convertibles and start shorting If the fundamentals are (and stay) sound, death-spirals should be broken! Consider a firm with Enterprise Value $1,000. It has 100 shares outstanding each trading at $10. It issues a FPC with F = $500 and d = 10%. Proceeds are only $500 (even though FPC s value is 500/0.9 = $555.55). (r f = 0%) Proceeds are invested in project that returns $525 (positive NPV) Stockprice after full revelation S=$9.69, FPC converts into 500/( ) = shrs S* =1,525/ =$9.69 If speculators drive stock price to $9, fundamental value goes down to $9.43: S=$9.00, FPC converts into 500/(.9 9) = shrs S* =1,525/ =$9.43 S=$8.00, FPC converts into 500/(.9 8) = shrs S* =1,525/ =$9.00 S=$5.00, FPC converts into 500/(.9 5) = shrs S* =1,525/ =$7.22 S=$3.00, FPC converts into 500/(.9 3) = shrs S* =1,525/ =$5.35 Selling pressure does affect the fundamental price per share negatively. But if fundamentals are not affected, the mispricing (and buy-opportunity!!!) increases. Does the stockprice affect asset-value? Null- Hypothesis: the stock-price goes down, but the enterprise value does not. (Then there is only a wealth transfer from long term shareholders to FPC-holders and arbitrageurs.) Hypothesis rejected enterprise value goes down, on average, by 12% 10

11 1) Does stock price affect asset (enterprise) value? Or 2) Were assets - on average - overvalued at the time of the issue? Hillion and Vermaelen favour argument 2): They say that FPC-issuers were overvalued in the market, yet did not issue equity because: - (over optimistic) managers thought the company to be undervalued. I personally believe that also argument 1) holds water. What about Log On America? They went public on April 21 st They raised $22 Mio (only!) by selling 35% of their equity. It was about two months after the bursting of the dot.com bubble. The issue was lead-underwritten by Dirks & Co. The offering price was $10 per share. Two days after the IPO the price reached $30.. Six months later, they again needed money!! How would the market react if they would announce a follow up offering? Instead of issuing equity, they issued a convertible that would convert for sure. The buyers of the convertible would receive > $1000 in shares, for every $1000 they d contribute to the firm. 11

12 Q1: Debt, Equity, Convertibles, or FPCs, for LOA? 1) FPC vs. Debt: Straight debt would be hard to get.. No cashflows on horizon, no collateral? 2) FPC vs. Equity: We just went public. Another equity issue would cause stockprice to tank. Stock Price is too low, definitely below what it s worth. Severe dilution. 3) FPC vs. Straight convertible. Straight convertible would still be difficult to sell. No cash for coupon payments. Straight convertible may lead to financial distress and bankruptcy... There s not really an alternative. The Floating Price Convertible seems a last resort financing option.. Q1: What security would you sell? 12

13 Q2: Why can the contract-design encourage FPC holders to short the stock? Why are others encouraged to short? The FPC holders are large relative to the market s depth. If a FPC holder gives a conversion notice, it may take a day or two until he has the stock in his account. Hence it makes sense to hedge by selling before conversion, i.e. before they own the stock. This is short-selling. It is also specifically allowed, as long as the holder delivers a conversion notice within two days of the short-sale. The selling pressure lowers the price, triggering more selling because the holder receives more shares upon conversion.. (see where s the catch? slide). Other investors realise this feedback cycle and also start shorting to drive the price down. Q3: You are the judge. What are the arguments against/in favour of the FPC-holders LOA says: the FPC and its holders ruined our company! Yes, the FPC invites its holders to short the stock in order to hedge their return on investment. However, if the fundamentals (the true firm value) were sound, the market price should reflect this, as sufficient buyers would buy and bid the price to its fundamental value. What do the fundamentals look like? poor! How do LOA s industry peers do they go down too.. Do the FPC holders benefit from a tanking stockprice? No, their upside comes from increasing stockprice.. Possibly the negative fundamentals are due to the tanking stockprice. I.e. there is a second negative feedback loop, of negative publicity. But that s not the fault of the FPC holders 13

14 How does LOA s operating performance compare? Check out table 4a and 4b).. It seems that LOA performed even worse than its peers.. 5% 0% -5% -10% EBITDA/Assets 99Q1 99Q2 99Q3 99Q4 00Q1 00Q2 00Q3 00Q4-15% -20% Average competitors LOA 0% -5% Return on Assets 99Q1 99Q2 99Q3 99Q4 00Q1 00Q2 00Q3 00Q4-10% -15% -20% -25% Median competitors LOA What about LOA s peers? Was the drop in its market value due to the Series A convertible? check out Fig 3A and 3B.. Not only LOA went down the drain. All dot.coms tanked...and Fig 4A and 4B LOA s did only slightly worse than peer average....and Fig 5A and 5B LOA-stock very similar to small competitors 14

15 Is a falling stockprice in the interest of the FPC-investors? Conversion price Shares per FPC payoff Stockprice : $ 10 $ 20 $ 30 $ 40 Face value $ 1,260 $ 1,260 $ 1,260 $ 1,260 conversion price $ 9 $ 18 $ $ Conversion ratio Payoff $ 1,400 $ 1,400 $ 1,566 $ 2,088 Valuing LOA s Floating Priced Convertibles (Q4) Step 1 (Question 4a): No cap on conversion price, no default. Because the dividend yield (8%, Pay In Kind ) > r f (=6%), investors should wait with conversion until maturity. In 3 years the face value will be $ = $1260. At that time, the value of the convertible will be equal to: 1260/(0.9 S) S = 1260/0.9 = $1400 Number This value of shares is independent of the shareprice!! per convertible shareprice True, the payoff comes in shares. And shares may be hard to sell,..but the FPC investors are allowed to (short-) sell the shares before conversion! So the payoff is pretty much guaranteed. Hence we discount the payoff at the riskfree rate and find that the present value is 1400/( ) = $1,175 15

16 Valuing LOA s Floating Priced Convertibles (Q4) Perhaps FPC-holders convert immediately after 6 months. The face-value has then increased to $ /365 = $1,039, so that the payoff is 1039/(0.9 S) S = $1,155, discounted $1,121 More likely still is that they convert gradually over time: Payoff1 = (1/ 3 $ / S) S = $360 Payoff2 = (1/ 3 $ / S) S = $389 Payoff3 = (1/ 3 $ / S) S = $420 With present value of $1,138 FPC investors seem to get an excellent deal (the FPCs were issued at par) And there s more.. Question 4B: Conversion price capped at $24.13, no default. The cap on the conversion price is a floor on the conversion ratio. Or, the FPC investors are guaranteed a given number of shares, even if the stockprice goes through the roof. The cap thus increases the value of the FPC. If the price increases above 24.13/0.9 = $26.81, the cap becomes valuable The investors are now guaranteed 1260/$24.13 = shares, even if S > $26.81 It turns out that the cap is equivalent to year Call options with X = $26.81 To see this: If S > 26.81, with cap: payoff = S If S > without cap: payoff = S 1260/(S 0.9) = 1260/0.9 = 1,400 Difference = S ,400 = max(s 26.81), which is the payoff of Call options I use Black Scholes with S=$17.56, X = $26.81, r f = 6%, t = 3 yrs, =87%, and find that that the value of one option is $8.44, so that the cap is worth $454! And the total value of the FPC is: $1,629 (!!!!) Figure 2 shows a weekly volatility of 12% (for the year preceding the FPC floatation); Hence annual = 12% 50 = 87% 16

17 Binomial tree method Construct a binomial tree, using quarterly steps. To be consistent with = 87%, I use u = 1.55, d = This results in a risk neutral probability (of an upward movement) of p = Q Q Q Q Q Q Q Q Q Q Q Q Q Payoff r.n. prob 2, , , Stock price Multiply the payoffs with the r.n. probabilities, discount at the risk-free rate. I find that the FPC is worth $1, , ,192 72,651 30,301 12,638 5,271 2,198 1,400 1,400 1,400 1,400 1,400 1,400 1, % 0.04% 0.30% 1.45% 4.71% 10.90% 18.40% 22.82% 20.64% 13.28% 5.76% 1.52% 0.18% Step 3 (Question 4c): Conversion priced capped at $24.13, if price falls below $1, company defaults, making the FPC worthless. In this scenario FPC holders may convert before maturity. They will do so if the danger of default outweighs the value of the dividends and the option value due to the cap. It turns out that investors will convert when the stockprice drops to approximately $2 Q Q Q Q Q Q Q Q Q Q Q Q Q , ,447 Question 4C: Cap = $24.13, default if S<$1, no reset 72,588 72,651 46,858 46,898 30,248 30,274 30,301 19,526 19,543 19,560 12,624 12,616 12,627 12,638 8,213 8,176 8,151 8,158 5,429 5,375 5,317 5,266 5,271 3,699 3,644 3,577 3,495 3,402 2,642 2,598 2,541 2,465 2,360 2,198 2,005 1,978 1,942 1,890 1,817 1,700 $ 1,625 1,616 1,601 1,577 1,541 1,488 1,400 1,403 1,407 1,406 1,401 1,390 1,379 1,292 1,309 1,324 1,339 1,358 1,400 1,246 1,275 1,305 1,338 1,379 1,235 1,273 1,314 1,358 1,400 1,239 1,284 1,331 1,379 1,247 1,296 1,347 1,

18 Problem with this analysis is that it assumes to be constant. In the bad states, dilution depends on price, stock s will explode. In the good states, the convertible will dampen the stock s volatility. Solution: construct a binomial tree with the asset-value as underlying Q1-00 Q2-00 Q3-00 Q4-00 Q1-01 Q2-01 Q3-01 Q4-01 Q1-02 Q2-02 Q3-02 Q4-02 Q1-03 Payoff r.n. prob 27,657 17,861 11,535 11,535 Asset (or "Enterprise") Value (millions) 7,449 7,449 FPCs get a 4,811 fixed %-age 4,811 of the assets 4,811 3,107 3,107 3,107 (1260/24.13)/(8.29M+15K 1260/24.13) 2,007 2,007 2,007 2,007 1,296 1,296 1,296 1, Here 94 they get 94 $1400 in shares (1260/0.9S) 61 shares, 61 each worth $S Multiply the payoffs with the r.n. probabilities, discount at r f Gives me $1,422 Here the dilution explodes (#shrs ) so that FPC-holders get all assets (each FPC gets 1/15,000 of assets) ,135 66,371 27,682 11,545 4,815 2,008 1,400 1,400 1, % 0.04% 0.30% 1.45% 4.71% 10.90% 18.40% 22.82% 20.64% 13.28% 5.76% 1.52% 0.18% Step 4 (Q4e): Conversion price cap is reset to 1.2 the price in 180 days. Clearly the lower the conversion price, the more shares the FPC holders get if the stock goes up. Hence the reset provision is valuable!! With a double binomial tree I find that it is worth an additional $224 (per $1000 face value), bringing the total value of the FPC to $1,646!! 86,811 56,039 36,175 36,206 23,352 23,372 82,333 Q Q Q Q Q ,075 15,088 53,149 15,101 Q ,752 9,740 34,309 9,748 34,339 6,368 6,322 22,148 6,293 22,167 6,298 2,450 4,256 cap No reset, stays at: $ ,192 14,297 4,122 14,309 4,066 14,322 1,938 2,956 2,905 9,253 2,828 9,237 2,728 9,245 2,627 2,152 2,134 6,054 2,090 6,004 2,005 5,968 1,873 5,973 1,646 1,633 UD, Cap 1,651 is reset 4,047 to 1.2* ,655 = $ ,998 1,633 3,924 1,557 3,856 1,400 1,487 1,316 2,784 1,359 2,763 1,398 2,713 1,418 2,612 1,379 2,491 1,970 1,118 1,982 1,189 1,980 1,270 1,946 1,358 1,818 1,400 1,425 DD, Cap 1,459 is reset 980 to 1.2*7.51 1,493 = $6.60 1,076 1,524 1,201 1,535 1,379 1,400 1,084 1, , ,272 1,122 1,379 1, , ,

19 On top of that, the FPC holders also received 594,204 5-year warrants with exercise price $ Also these can be valued with Black-Scholes. Take S = $17.56, X = $17.23, r f = 6%, t = 3 yrs, =87%, and find: C = $10.43, Multiply by dilution factor 8.29/( ) Multiply by 594,204 Divide by 15,000 Warrant-value per $1000 FPC face value = $388, which brings to total value of the package to $2,034 However, also warrant is subject to path-dependent volatility. Better to construct binomial tree and calculate payoff to the total package. I find (see spreadsheet) that it s worth $2,011 They paid only $1,000.. Summarizing.. If they believed that LOA was fairly priced at $17.57 per share, the investors received, for every $1000, a package worth $2,011 per certificate of Series Convertible Preferred stock Most of this value comes from the upside potential!! So, the FPC investors were not hoping on a downward spiral.!!! Perhaps they did not believe $17.57 was the true value and valued the warrants and the cap on the conversion price not nearly as high as I did. Perhaps they thought LOA stock to be worth much less, perhaps as little as $5. Then still they stood to get a PV of at least $1,175 per $1000 invested. Probably more because they could short-sell above the eventual fundamental value per share. Clearly the FPC investors (friends of CSFB) got an excellent deal! 19

20 What happened? Although there was no conclusive evidence that LOA s shareprice drop was due only to the Series Convertible Preferred, CSFB settled out of court, agreeing to pay LOA $3.2M and to restructure the FPC into a convertible with fixed conversion price $ Floating-priced convertibles are still widely used. Their popularity increased again after the real estate crises, in Private Issue of Public Equity (PIPE deals). They have different names and are often hard to detect. (Obviously, they re not marketed as death-spirals!!) Slightly more benign versions are forced convertible bonds with conversion discounts of 0%. These tend to have a low cash-coupon and come with warrant or conversion caps. They are sometimes called equity linked bonds Floating-Price Convertibles do not always lead to bankruptcy. But they are a clever way of last resort financing. Contintent Convertibles CoCos CoCos are convertible bonds that convert into equity (a given number of shares), not at the option of the CoCo-holder (in the good state), but when a pre-described condition is triggered, in the bad state. The typical condition would be: If the market value of equity falls below a certain threshold (e.g. 5% of assets). i.e. when the firm is in trouble. CoCos have higher/lower coupons than regular convertibles? Advantages: A Coco is debt when the firm is healty, and comes with interest tax shields, and reduces agency costs of free cashflows. A Coco because equity when the firm falls on hard times, and thus avoids costs of financial distress. They also reduce risk shifting and debt-overhang. Cocos are popular among banks. We saw many coco-offerings during the European sovereign debt crisis of