Derivatives, Alternative Investments & Portfolio Management Flashcards
Derivative
a security that derives its value from the value or return of another asset or security
Over-the-counter market
A dealer market with no central location
- Unregulated markets
- Each contract is with a counterparty
- Exposes derivative owner to default risk
- Bond options trade on the over-the-counter market along with forwards and swaps
Forward Commitment
Legally binding promise to perform some action in the future
- Forward contracts, futures contracts and swaps
- Forward contacts can be written on equities, indexes, bonds, foreign currencies, physical assets or interest rates
Contingent Claim
Claim (to a payoff) that depends on a particular event
Options
Contingent claims that depend on a stock price at some future date
- Credit derivatives are contingent claims that depend on a credit event such as a default or ratings downgrade
Forward Contract
One party agrees to buy and the counter party to sell a physical or financial asset at a specific price on a specific date in the future
Uses of Forward Contracts
- To speculate on the future price of an asset
- Hedge an existing exposure to the risk of asset price or
interest rate changes - Reduce or eliminate uncertainty about future price of an asset which is planed to buy or sell at a later date
Forward Price
Price specified in the forward contract
- If the expected future price of the asset increases over the life of the contract, there is a right to buy at the forward price (Will have a positive value and the obligation to sell will have an equal negative value)
- If the expected future price of the asset decreases over the life of the contract, then the results is a right to sell
Long Forward Position
The party who agrees to buy the financial or physical asset (long)
Short Forward Position
The party who agrees to sell or deliver the asset (short)
Deliverable Forward Contract
Settled by the short delivering the underlying asset to the long
Cash-Settled Forward Contract
One party pays cash to the other when the contract expires based on the the difference between the forward price and the market price of the underlying asset (spot price) at the settlement date
- Also known as contracts for differences or non-deliverable forwards (NDFs)
Is a deliverable contract or a cash settled contract more economically favorable?
Apart from transaction costs, deliverable and cash-settled forward contracts are economically equivalent.
Futures Contract
Forward contract that is standardized and exchange-traded.
- Primarily traded in an active secondary market, subject to greater regulation, backed by a clearinghouse and require a daily cash settlement of gains and losses
Similarities between forwards and futures
- Can either be deliverable or cash-settled contracts
- Have contract prices set so each side of the contract has a value of zero at the initiation
Differences between forwards and futures
Futures
- Exchange traded
- Standardized
- Clearinghouse is the counterparty for futures
- Regulated by the government
Forwards
- Private contracts that don’t trade
- Custom contracts satisfying the specific needs of the parties involved
- Contracts with originating counterparty and therefore have counterparty (credit) risk
- Unregulated and don’t trade in organized markets
Tick Size
Minimum price fluctuation
Exchange-Traded Derivatives
- Organized
- Regulated
- The exchange sets the following for each contract:
- The minimum price fluctuation
- Daily price movement
- Settlement date
- Trading times
Settlement Price
The average of the prices of the trades during the last period of trading, called the closing period, which is set by the exchange (this reduces the opportunity of traders to manipulate the settlement price).
- Used to calculate daily gains and losses at the end of each trading day
- On the final day of trading, the settlement price equals the spot price of the underlying asset
Open Interest
The number of future contracts of a specific kind that are outstanding at any given time is known as the open interest
- Increases when traders enter new long and short positions
- Decreases when traders exit positions
Clearinghouse
Guarantees traders in the futures market will honor their obligations
- Splits each trade once it is made and acts as the opposite side of each (acts as buyer to sellers and vice versa)
- Traders can reverse or reduce their trades, which reduces risk
- The US Clearinghouse has never defaulted on a contract
Margin
Money that must be deposited by both the long and the short as a performance guarantee prior to entering into a futures contract
- No loan or interest charges
- Provides protection for the clearinghouse
- Each day the balance is adjusted for gains and losses based on the new settlement price (mark to market)
- Margin requirements are set by the clearinghouse
Mark-to-market
Adjusting the settlement price for gains and losses
Initial Margin
The amount that must be deposited in a futures account before a trade may be made
- Low per contract and equals about one day’s max price fluctuations on the total value of the asset
Maintenance Margin
Minimum amount of margin that must be maintained in a futures account. If the balance falls below the maintenance margin due to daily settlement of gains and losses, additional funds must be deposited to bring the margin balance back up to the initial margin amount
Price Limits
Exchange-imposed limits on how each day’s settlement price can change from the previous day’s settlement price. Exchange members are prohibited from executing trades at prices outside these limits.
- Common for futures
Swaps
Agreements to exchange a series of payments on periodic settlement dates over a certain time period. At each settlement date, two payments are netted so that only one net payment is made.
- The party with the greater liability makes a payment to the other party
Tenor
The length of the swap contract, which ends on the termination date
Similarities between swaps and forwards
- Require no payment by either party at initiation
- Custom instruments
- Not traded in any organized secondary market
- Default risk is an important aspect of the contracts
- Most participants are large institutions and rarely individuals
Plain Vanilla Interest Rate Swap
One party makes a fixed-rate interest payment on the notional principal amount specified in the swap in return for floating-rate payments from the other party
Basis Swap
Involves trading one set of floating rate payments for another
Pay-Fixed Side of Swap
For plain vanilla interest rate swaps, the party that wants the floating-rate payments agrees to pay fixed rate interest, which is the pay-fixed side of the swap
Pay-Floating Side of Swap
The counterparty who receives the fixed payments and agrees to pay variable-rate interest
Option Contracts
Gives the owner the right, but not the obligation to either buy or sell an underlying asset at a given price (exercise or strike price).
- The buyer has the option, but the seller has the obligation
Call Option
The right to purchase the underlying asset at a specific price for a specified time period
Put Option
The right to sell the underlying asset at a specific price for a specified time period
Option Writer
Seller of an option
4 Possible Option Positions
- Long Call: Buyer of the call option has the right to buy the underlying option
- Short Call: Writer (seller) of a call option has the obligation to sell the underlying asset
- Long Put: Buyer of a put option has the right to sell the underlying asset
- Short Put: Writer (Seller) of a put option has the obligation to buy the underlying asset
Option Premium
The price of an option is often called option premium
American Options
May be exercised at anytime up to and including the contracts expiration date
European Options
Can be exercised only on the contracts expiration date
Credit Derivative
Contract that provides a bondholder (lender) with protection against a downgrade or a default by the borrower
Credit Default Swap (CDS)
Most common type of credit derivative. The bondholder pays a series of cash flows to a credit protection seller and receives a payment if the bond issuer defaults
Credit Spread Option
Call option that is based on a bond’s yield spread relative to a benchmark
- If the credit yield decreases, its yield spread will increase and the bondholder will collect a payoff on the option
Strike Price
The break-even point for the option buyer
Call Option Profits / Losses
- The maximum loss for the buyer is the premium paid on an option
- The potential profit to the buyer is unlimited and the potential loss to the writer (seller) is unlimited
- The call holder will exercise the option when the stock’s price exceeds the strike price at expiration date
- The sum of the profits between the buyer and seller of the call option is always zero, so option trading is a zero-sum game (The long profits = short losses)
- Seller of calls profit when the price of the underlying asset decreases
- Buyer of calls will profit when the price of the underlying asset increases
Put Option Profits / Losses
- The maximum loss for the buyer is the loss of the premium paid
- The maximum gain to the buyer is limited to the strike price less the premium
- The greatest profit the writer (seller) of a put can make i the premium
- The sum of the profits between the buyer and seller is always zero, so put option trading is a zero-sum game
- Buyer of puts profit when the price of the underlying asset decreases
- Seller of puts profit when the underlying asset price increases
Benefits to Derivatives Market
- Provide price information
- Allow risk to be managed and shifted among market participants
- Reduce transaction costs
Arbitrage
Arbitrage is riskless and is a concept used in valuing (pricing) derivative securities. If a return is greater than the risk-free rate can be earned by holding a portfolio of assets that produces a certain (riskless) return, then an arbitrage opportunity exists
- Opportunity arises when assets are mis-priced
- Trading by arbitrageurs will continue until they impact supply / demand and bring asset prices to efficient
(2 main arbitrages - 1. Law of one price 2. Investment arbitrage)
Law of One Price
Arbitrage Type
- Two securities or portfolios that have identical cash flows in the future regardless of future events, should have the same price
- If A & B have the identical future payoffs and A is priced lower, buy A and sell B. You have an immediate profit and the payoff of A will satisfy the (future) liability of being short on B.
Investment Arbitrage
If a portfolio of securities or assets will have a certain payoff in the future, there is no risk in investing in that portfolio
- To prevent profitable arbitrage, the return on the portfolio must be at the risk free rate
- If the return on the portfolio is greater than the risk free rate, the arbitrage would be to borrow at Rf, invest in the portfolio, and keep the excess of the portfolio return above the risk free rate that must be paid on the loan
- If the portfolio return is less than the Rf, sell the portfolio, invest the proceeds at Rf, and earn more than it will cost to buy back the portfolio at a future date
Investor Risk Tolerance
- Risk-Averse: require positive premium (higher returns)
- Risk-Neutral: require no risk premium and would discount the expected future value on an asset or future cash flows at the risk-free rate
No-Arbitrage Condition
The valuation of derivates is based on a no-arbitrage condition with risk-neutral pricing. Since the risk of a derivative is based on the risk of the underlying asset, we can construct a fully hedged portfolio and discount its future cash flows at the risk-free rate
- No arbitrage condition is expected because if there was an arbitrage it would be exploited quickly
Forward Contract Price
Value of the asset combined with a short forward position (Fo(T)
- Asset is delivered at the settlement date for the forward contract price
- With time 0, the value of an asset of So, and a forward price of Fo(T), it must be that Fo(T) / So = (1+ Rf)^T
- Fo(T) = So x (1+Rf)^T
Riskless Transactions
Should return the riskless rate of interest. Since the payoff at time T (settlement date) is from a fully hedged position, its time T value is certain. The asset will be sold at time T at the price specified in the forward contract
When to take a short position
If Fo(T), the no-arbitrage price, is greater than: So x (1+Rf)^T - Could then buy the asset and take a short position in the forward contract to receive an arbitrage profit of Fo(T) - So x (1 + Rf)^T at time T (If it's less, then we sell the asset short, invest the proceeds in a pure discount bond at Rf and take a long position in the forward contract. At settlement, we could use the proceeds of the bond to buy the asset at Fo(T) to cover the short position and retain the bond proceeds in excess of the forward price (So x (1+Rf)^T - Fo(T) as an arbitrage profit
No-Arbitrage Price Derivative
When Fo(T) = So x (1 +Rf)^T
- We know the risk-free rate, the spot price of the asset and the certain payoff at time T, the no-arbitrage pice can be solved for (The investor’s risk aversion isn’t considered, so the no-arbitrage price is called the risk-neutral pricing)
- Assumes there is no benefit or cost to hold the asset other than the opportunity cost of the future asset. There may be additional costs of owning an asset such as storage and insurance costs. Financial asset costs are very low and insignificant. There may be monetary (dividend payment) and non-monetary benefits to holding an asset.
Replication
Replicating the payoffs on one asset or portfolio with those of a different asset or portfolio
Risk-Neutral Pricing
Risky bond + credit protection = bond valued at the risk-free rate
Forward price vs. value
The contract price at which the long forward will purchase the asset in the future does not change over the life of the contract, but the value of the forward contract almost surely will
Value of Forward at t
The value of the forward contract is the spot price of the asset minus the present value of the forward price
Vt(T) = St-Fo(T) / (1+Rf)^T-t
- note at settlement T=t, since there is no time left in the contract
Payoff of Long Foward
The difference between the spot price of the asset at expiration and the price of the forward contract
ST - Fo(T)
Monetary Benefits of Holding Asset
Dividend payment
Non-Monetary Benefits of Holding an Asset
Convenience yield (This is difficult to measure and only significant for some assets-mostly commodities)
Benefits of Selling an Asset
Shortage of the asset may drive prices up, making sale of the asset in the short term profitable
Assets with Costs and Benefits
Fo(T) = So + PV(cost) - PVo(benefit)^T
- Both the present value of the costs of holding an asset and the benefits decrease as time passes and as time to settlement (T- t) decreases
Value of forward contract at any point in time
Vt(T)= St + PVt(cost)- PVt(benefit) - Fo(T) / (1 + Rf)^T-t
- The benefits of holding the asset until settlement are zero, so that the payoff of the long forward at time T is St - Fo(T), the difference between the spot price of the asset at settlement and the forward price of the contract
Net Cost of Carry (Carry)
PV(Benefits of holding the asset) - PV(Cost of holding the asset)
- When benefits (CF yield and convenience yield) exceed the cost (storage and insurance) of holding the asset, the net cost of carry is positive
Forward Rate Agreement (FRA)
Derivative contract that has a future interest rate, rather than an asset. Locks in the interest rate for parties.
- One party pays the other party the difference between a fixed interest rate specified in the contract and the market interest rate at settlement
- Libor is usually the underlying rate
- Company that expects to borrow 90-day funds in 30 days will have higher interest costs if 90-day Libor 30 days from now increases, so a long position in the FRA (pay fixed and receive floating) will receive a payment that offsets the increase in borrowing costs from the increase in the 90 day Libor
Uses of Forward Rate Agreements (FRAs)
Hedge the risk of borrowing and lending in the future
- Perfect hedge means the firm’s borrowing costs will not be higher if the rates increase, but will also not be lower if rates decrease
- Firm that intends to have funds to lend (invest) in the future, a short position in an FRA can hedge its interest rate risk. If rates declined, there would be a decrease in return on the funds, but the FRA would have a positive payoff and augment the returns so that the return from both the short FRA and loaning funds is the no-arbitrage rate
No-Arbitrage Rate
Price of Forward Rate Agreement (FRA) at initiation
Synthetic Forward Rate Agreement (FRA)
Rather than enter into two FRAs, the same payment structure can be created with two LIBOR loans
