Lecture 1.2: Corporate Claims
The capital structure is the total sum of all claims on the assets of the firm.
Corporate claims have:
1. Cash flow rights → how firm-generated cash will be allocated
2. Control rights → allows the claim owners to enforce their cash flow rights
Bond holders have seniority over the stockholders (residual claimants) → stockholders only
get paid when the firm value exceeds the value of outstanding debt. However bond holders
have a maximum payout (= value of outstanding debt), the upside for shareholders is
unlimited.
Lecture 1.3: Law of One Price
Arbitrage = buying and selling ‘equivalent’ (generating same payoffs) goods to take
advantage of price differences
An arbitrage opportunity is then a situation in which it is possible to make a profit without
taking any risk. Sell more expensive security and buy the cheaper one.
Assumption: arbitrage opportunities don’t exist in the long run because somebody will
immediately take advantage of it and trade accordingly → opportunity disappears
When the highest bid price is lower than the lowest ask price, there is no arbitrage
opportunity.
You can set up a portfolio, C, that replicates S stocks and B bonds
Boom: s * 15 + b * 10 = 10
Bust: s * 5 + b * 10 = 0
S = 1 and B = -0.5 → sell 0.5 bonds or borrow 0.5 * 9 = 4.5
Buy 1 share = 10, sell 0.5 bonds = -4.5
C = 10 - 4.5 = 5.5 (no-arbitrage price for C)
We get 0.5eu today and don’t face any risks later on (payoff) = arbitrage opportunity
,Alternative: portfolio that costs zero today and has non-negative payoff in ALL states →
Lecture 1.4: Options
Option: a contract that gives its owner the right (but not the obligation) to purchase or sell an
asset (the underlying) at a fixed price at some future date.
Strike price (exercise price): price at which an option holder buys or sells the underlying
when the option is exercised.
Expiration (maturity) date: The deadline for exercising the option (USA) or the single date
at which the option can be exercised (Europe).
Payoff call option: max (S - K, 0) → value above strike price → exercise
Payoff put option: max (K - S, 0) → value below strike price → exercise
Combinations of options, stocks & bonds (check the book)
Payoff of portfolio with a stock + put = payoff of portfolio with a riskless bond + call
Both portfolios have the same payoffs at maturity at t=T
S(t) + P(t) = C (t) + K
S(t) + P(t) = C(t) + PV(K) → Put - Call Parity
, Basically equity investors hold a call option on the total assets of the firm where the strike
price equals the level of debt of the firm.
Lecture 2.1: Stylized facts
1. Firms finance themselves through retained earnings (internal financing) and selling
securities in the market (external financing; debt/equity)
a. Between 1995-2000’s equity financing was negative → firms buy back shares
b. Net external funds = Debt + Equity
c. Capex - net external funds = net internal funds
2. Sources of financing vary over time and over business cycle
a. Equity issues (SEO/IPO) increase when stock market returns have been high
for some period of time
b. debt/borrowing issues less cyclical
3. Capital structures vary across different industries
a. High leverage industries: utilities, transportation, real estate
b. Low leverage industries: biotech, software/internet hardware
i. Net debt = debt - excess cash
ii. Excess cash is negative debt
Capital structure ratio: Net debt / (debt + MV of equity)
Lecture 2.2: Modigliani - Miller
The capital structure is the total sum of all claims on the assets of the firm.
Corporate claims have:
1. Cash flow rights → how firm-generated cash will be allocated
2. Control rights → allows the claim owners to enforce their cash flow rights
Bond holders have seniority over the stockholders (residual claimants) → stockholders only
get paid when the firm value exceeds the value of outstanding debt. However bond holders
have a maximum payout (= value of outstanding debt), the upside for shareholders is
unlimited.
Lecture 1.3: Law of One Price
Arbitrage = buying and selling ‘equivalent’ (generating same payoffs) goods to take
advantage of price differences
An arbitrage opportunity is then a situation in which it is possible to make a profit without
taking any risk. Sell more expensive security and buy the cheaper one.
Assumption: arbitrage opportunities don’t exist in the long run because somebody will
immediately take advantage of it and trade accordingly → opportunity disappears
When the highest bid price is lower than the lowest ask price, there is no arbitrage
opportunity.
You can set up a portfolio, C, that replicates S stocks and B bonds
Boom: s * 15 + b * 10 = 10
Bust: s * 5 + b * 10 = 0
S = 1 and B = -0.5 → sell 0.5 bonds or borrow 0.5 * 9 = 4.5
Buy 1 share = 10, sell 0.5 bonds = -4.5
C = 10 - 4.5 = 5.5 (no-arbitrage price for C)
We get 0.5eu today and don’t face any risks later on (payoff) = arbitrage opportunity
,Alternative: portfolio that costs zero today and has non-negative payoff in ALL states →
Lecture 1.4: Options
Option: a contract that gives its owner the right (but not the obligation) to purchase or sell an
asset (the underlying) at a fixed price at some future date.
Strike price (exercise price): price at which an option holder buys or sells the underlying
when the option is exercised.
Expiration (maturity) date: The deadline for exercising the option (USA) or the single date
at which the option can be exercised (Europe).
Payoff call option: max (S - K, 0) → value above strike price → exercise
Payoff put option: max (K - S, 0) → value below strike price → exercise
Combinations of options, stocks & bonds (check the book)
Payoff of portfolio with a stock + put = payoff of portfolio with a riskless bond + call
Both portfolios have the same payoffs at maturity at t=T
S(t) + P(t) = C (t) + K
S(t) + P(t) = C(t) + PV(K) → Put - Call Parity
, Basically equity investors hold a call option on the total assets of the firm where the strike
price equals the level of debt of the firm.
Lecture 2.1: Stylized facts
1. Firms finance themselves through retained earnings (internal financing) and selling
securities in the market (external financing; debt/equity)
a. Between 1995-2000’s equity financing was negative → firms buy back shares
b. Net external funds = Debt + Equity
c. Capex - net external funds = net internal funds
2. Sources of financing vary over time and over business cycle
a. Equity issues (SEO/IPO) increase when stock market returns have been high
for some period of time
b. debt/borrowing issues less cyclical
3. Capital structures vary across different industries
a. High leverage industries: utilities, transportation, real estate
b. Low leverage industries: biotech, software/internet hardware
i. Net debt = debt - excess cash
ii. Excess cash is negative debt
Capital structure ratio: Net debt / (debt + MV of equity)
Lecture 2.2: Modigliani - Miller
