Managment Engineer - Investment banking

3 - Options, warrants and special bonds

Divided by topic

Contenido 1. Options ................................ ................................ ................................ ....................... 2 2. Warrants ................................ ................................ ................................ ..................... 4 3. Convertible bonds ................................ ................................ ................................ ....... 5 4. Reverse convertible bonds ................................ ................................ ........................... 6 5. Structured bonds ................................ ................................ ................................ ......... 7 1. Reverse floater ................................ ................................ ................................ ......... 7 2. Linked bonds ................................ ................................ ................................ ............ 7 3. Step -down and step -up bonds ................................ ................................ .................. 8 4. Callab le bonds ................................ ................................ ................................ .......... 8 1. Options Options can be used both to obtain a profit ( speculation ), or to minimize risk . Some variations of “regular” options are futures and forwards , in which both parts are forced to make the transaction at the signed price (there is not exercise right for anyone) ; and swaps , which are a combination of futures/forwards and regular options . With American options, the holder can exercise the option whenever he wants. With European options, they can only be exercised on the exercise date. Call options give the exercise right to the buyer of the underlying, while put options give said right to the seller. The one with the exercise right is said to have the long position , while the one without it has the short position . The holder of the long position has to pay a premium for it An option is said to be in-the -money when it gives a benefit to the one with the long position, and thus it will most likely be exercised, out -of -the -money when it likely won’t be exercised, and as -the -money when it is neutral. Given the following terminology: • S0 = spot price of the underlying (“real” price) • X = strike price (“exercise” price) • N() = cumulative standard normal distribution function • T = maturity • r = risk free rate of return (continuously compound ed! ) • σ = volatility of returns We have to take into account that: • N( -x) = 1 - N(x); N-1(x) = N -1(1-x) • A continuously compound discount rate and a “normal” discount rate are not the same!!! ������ (������+ ������������)������= ������−������������������∗������ Which means that: ������������������ = ������������ (������+ ������������) 1 2 3 2. Warrants They are usually sold together with a regular bond (forming a “ bond cum warrant ”), but the bond and the warrant can be detached at any time, so we can just focus on the warrant. The warrant gives the holder the right to purchase a fixed number of shares (or bonds or any other financial security) for a fixed price once maturity is reached . That is, it acts as a call option in which the holder has the long position and the issuer has the short one. Theoretically the buyer of the warrant should pay a premium, but companies might give them away for free in some situations (given th at, if the warrant is exercised, the company gets a cash -in) . When a warrant is exercised new shares are issued by the company, which causes share dilution. The calculation of fully diluted shares must take into account the number of warrants in circulatio n. Warrants can be used in different situations: • In relation to a capital increase . • To creditors willing to cancel their debt in order to significantly increase the value of a stressed company. • In relation to M&As and LBOs (to “save” capital, to align the management’s interests with the company’s,…). In order to valuate a warrant, there are 2 possible methods: • No new shares are issued: first we have to value the call option of a single share, and multiply it by the number of shares per warrant . • New shares a re issued: once again we have to calculate the value of the call option of a single share, and then we have to apply the following formula in order to take into account share dilution: � = � � + � ∗ γ ∗ γ ∗ �������������� With: - n = nº of outstanding shares. - m = nº of issued warrants. - γ = nº of shares per warrant. The formula indicates the value of a long call option on a single share (1), times the number of shares per warrant (2), taking into account dilution (3). It is important to notic e that n + m* γ is the number of outstanding shares after all the warrants have been executed, so this formula might be a reasonable assumption if the share price at maturity is highe r than the strike price (in -the -money shares). 3. Convertible bonds A convertible bond acts like a regular bond but, once maturity is reached, the holder has the option to be paid in shares instead of receiving the face value . The amount of shares is fixed apr iori and it can be more valuable than the face value, so it acts like a call option in which the bond holder has the long position. The holder will have to pay a premium (somehow), so a convertible bond will always be more expensive than its regular counte rpart. Convertible bonds are used by companies to raise cash : if the holder decides to get paid in shares the company doesn’t have to pay the principal, and if he doesn’t, he still paid more for the bond than he would have for an equivalent regular bond. If the bond holder decides to get paid in shares these new shares have to be issued by the company, so the effect of dilution must be taken into account to value the bond . Given: - F = face value paid at maturity - Nb = number of bonds issued - D = total debt iss ued = Nb * F - n = value of outstanding shares - Cr = conversion ratio = nº of s hares per bond - m = Nb * Cr= number of new shares - γ = stake in the hands of bond holders = m/(m+n) = value of the issued debt relative to the total value of the company, being n the number of outstanding shares, and m the number of issued bonds time the number of shares per bond - X = strike price of the company = D/ γ - S0 = current value of the company - Ct = coupon paid on time t We have to calculate the value of the call using the t otal value of the company ( S0) and its strike price ( X). Once that is done, the value of each convertible bond is calculated as: ���������� .���� = ∑ ������������ (1+ �������)������ ������ + ������ (1+ �������)������+ γ ������� ∗�������������� The coupons and face value can also be discounted using exponentials, as long as we are using the continuously compounded rate and not the “normal” one. 4. Reverse convertible bonds They have some characteristics in common with regular convertible bonds: the holder receives a coupon, and, once maturity is reached, he can either receive the face value or a fixed number of shares. The difference is that, in this case, the issuer is the one with the right to decide whether to pay the princi pal with cash or shares , not the bond holder, so it behaves like a put option instead of a call, and the bond holder has the short position. In exchange for that the issuer will pay the holder a premium, which will take the form of high coupons . Reverse co nvertible bonds can not be admitted to official listing in the Stock Exchange. We will calculate the value of a reverse convertible bond as: �������������� .��������� .���� = ∑ ������������ (1+ �������)������ ������ + ������ (1+ �������)������+ ������� (������)∗(−�������� ) • We are calculating the value of a short put option, which is why the negative sign is there. • X is the angle formed by the line in the graph of the put option (x axis = share price, y axis = profit). If x=45º we are in the “normal” case, and tg(45 o)=1 Share price (X) vs profit (Y), for regular convertible bonds (left) and reverse convertible bonds (right) 5. Structured bonds • Structured bonds are mainly issued by banks, and they can have a large variety of complexities and working mechanisms. • Their offering to the public is not preceded by the publication of an information prospectus preventatively sent to the Authority. • They can be listed in the Stock Exchange, in which case they are required to publish a listing prospectus explaining in detail how they work. • They are not always listed on regulated markets, and if they are liquidity is low, which leads to potential bond holder s having trouble selling them to third buyers. 1. R ev erse floater The coupons of these bonds depend on a floating rate : they are usually the difference between a fixed rate and a market rate (Euribor, Libor,…). This means that, if the markets worsen their performance the coupons will increase, but, if the markets go up, the coupons decrease. This would also decrease the v alue of the bond, forcing the holder to either sell it for a low price or keep receiving low coupons and thus, in a way, losing money. 2. Lin ked bonds There are bonds in which, at maturity, the holder receives a premium linked to the performance of a spec ific financial or real product (shares, commodities, exchange rates,…). This makes them act like a combination of a regular bond and a call option in which the bond holder has the long position, and the holder will pay for said long position by receiving smaller coupons than usual . Some variations of these bonds include receiving a single coupon upon maturity, or guaranteeing a minimum yield to reduce the risk. 3. S t ep -down a nd step -up bonds These bonds’ coupons are fixed, in the sense that they do not dep end on any other product, but they change over time . Step -up bonds have coupons that increase as they get closer to maturity, while step -down bonds’ coupons decrease. 4. C a llable bonds They are fixed rate bonds with a clause that allow the issuer to reimb urse the investor prior to maturity . This will be beneficial for the issuer if market rates are lower than usual, allowing him to mitigate the risk. In exchange for that, the bond holder will receive higher coupons than usual.