Financial engineering and corporate applications Flashcards
(34 cards)
what is financial engineering?
Financial engineering is the process of building new instruments from existing building blocks
elaborate on the state pre Modigliani and Miller
Investors found it difficult ot understand how to compare the value of firms that had different financial policies and structures.
Especially, firms with similar operating characeteristics, but different financials. How to compare.
what is the core of the Modigliani and Miller theorem?
Capital structure doesnt matter. The total value of the firm is the value of all claims. The total cash flow payed to all kinds of investor, equity and debt holders, is equal regardless.
The outcome of this is that if we have 2 equal firms, but with different capital structure, it should not be possible to earn arbitrage on them.
elaborate on single payment bonds
basically zero-coupon bonds, but a more general term.
A single payment bond is essentially the same as a prepaid forward contract on the underlying.
what is the value of a single payment bond that pays one share of stock at time T?
We know that single payment bonds are equivalent to prepaid forward contracts.
F^P_{0,T} = S_0 e^(-∂T)
what are “zero coupon equity linked bonds”?
bonds that pay one share (typically) of a stock.
Therefore, its price is equal to what we should pay at time 0 to get one asset later. This is the same as the prepaid forward.
in what cases would a single payment bond on a commodity be worth less than spot price
if lease rate is positive. Because the bond is pre paid forward, which means that we are not gettingthe lease payment. As a result, we do not want to pay equal to, or larger than spot price.
can lease rate be negative?
Yes, if ther eare large storage costs
introduce bonds that include options
written options lower the price of the bond while purchasign the options increase the price of the bond
what is a convertible bond
combination of bond and call option.
what is reversible convertible bond
combining bond with written put option
what is tranched payoff
the payoff is determined by some range that relates to the udnerlying asset. If the price of the asset is below to lower end of the range, we get nothing. Then, inside the range we typically get proportional returns. The payoff of the tranched payoff is capped at the high end of the range ,and pay no more than this upper bound.
what is variable prepaid forward
combination of reversible and regualr convertible
elaborate on convertible bonds
typically have a minimum payoff, and convert into units of underlying if the underlying performs well.
This is done by including call option in the bond. We also have a principal/FACE value, which cause the minimum payoff.
formula for convertible bond
elaborate on equity as as option
Looks liek a call option.
E_t = max (0, Assets_t - Debt_t)
Debt at time t is the strike price. Assets change in value. Therefore, the assets, therefore the firm itself, is the underlying in this option. Therefore ,we can view the equity in the firm as a call option.
value of debt can be written as
B_t = min(A_t, Debt)
elaborate on the option view from the perspective of the bond holders
The bond holders recevie the smallest amount possible.
they get: B_t = min(A_t, Debt)
We can write this as:
B_t = A_t + min(0, Debt - A_t)
why?
because if min is 0, they will acquire all the assets.
If min is debt-A_t, assets outweights the debt, and they are payed the debt.
We can swap this to:
B_t = A_t - max(0, A_t - Debt)
Now we can view this as the following:
The debt that the bond holders receive, is equivalent to all the assets of the firm, but they write a call option to the equity holders.
This is key:
DEBT is assets plus a written call to the equity holders.
The interpretation of this is that if the option expire ITM, the debt holder has to give away the assets. If the assets expire OTM, the debt holders keep the assets. Wit hthis perspective, the moment debt holders enter the case, they own all assets, but will likely give them away.
what do we need to assume to use BS on the debt and eqiotiy options?
Assume that assets of the firm follow log normal distribution.
elaborate on finding yield to maturity
Assuming that the debt is zero coupon, we can do the following:
YTM is the itnerest rate that equates the price of the bond to the face value of the bond.
price = FV/(1+r)^t
since we use continuous time, we should use:
B_t = B e^(-r(T-t))
Meaning, the debt level at time t is equal to the face value level B, discounted accordingly.
B_t/B = e^(-r(T-t)
-r(T-t) = log(B_t/B)
r = log(B/B_t)/(T-t)
Just remember: Yield to maturity on the zero coupon debt is the level of return yearly that we get in continuously compounded return.
what can equity holders do that may affect the debt value?
1) Increase asset volatility. Since equity holders basically hold a call option on the firm’s assets vs debt, where debt is fixed and is given as the strike price, if we increase volaitlity we increase the value of our call.
2) Dividends, share repurchase. Since delta is less than 1, if we pay 1 usd, assets decrease by 1, but the call does not change by 1. Meaning, the value of the equity does not change by 1.
what is a warrant
An option that a firm writes on its own stock
why are warrants special
Warrants are special becasue they dilute equity. this is notthe case for ordinary options, because they are written by third parties and use existing shares. Warrants create new shares.
elaborate on the value of shares that result from a warrant
We pay K strike price for the shares. Let us say the firm has “n” shares outstanding originally, and warrants on “m” shares.
After the warrants are exercised, the firm icnrease in total value: Before it was A total, and A/n per share. After it is (A+km) total, and (A+km)/(n+m) per share. As a result, the shares acquired from the warrants are different from ordinary.
We can re-write this:
= (n/(n+m)) (A/n - K)
The first term can be considered the dilution factor, while the other term is the difference between share value and strike price.
