derivatives test one (ch 3 and 5)

Convenience Yield

-A non-monetary advantage of holding an asset. -consumption assets provide benefits of ownership not obtained by holding a futures contract -futures price can't be greater but it can be less than the futures price of an identical investment asset

Interest Rate Parity

-a situation in which the rates of return on assets in different currencies are equal -is an arbitrage condition

rules of thumb of assets and delivery month

-choose contracts that most closely matches your asset (in terms of price movements) -basis risk increases as the time difference between the hedge expiration and the delivery month increases. -choose a delivery month that is as close as possible to, but no earlier than, the expiration of the hedge

arguments in favor of hedging

-companies should focus on the main business they are in and take steps to minimize risks arising from interest rates, exchange rates, and other market variables

reasons for hedging an equity portfolio

-desire to be out of the market for a short period of time -desire to hedge systematic risk (appropriate when you feel that you have picked stocks that will outperform the market)

you must pay ____ and ________ the owner of the securities receives

-dividends and other benefits

if you believe that a stock is going to go down in price...

-go short -sell high buy low -means to simply take a negative position in the instrument -there are hefty margin requirements on shorts

Asset Mismatch

-if the asset to be hedged is NOT the one in which the futures contract is based, there is additional basis risk

Basis Risk

-in theory without market friction, the basis at time T is zero -this is not always possible in practice -basis risk arises because of the uncertainty about the basis when the hedge is closed out -for financial futures, basis risk tends to be small. this has to do with arbitrage being relatively easy to implement, and so prices are kept "in check"

is the futures price the same as the expected future spot price?

-none of our pricing equations utilize the expected spot price -do not expect any such relationship to hold

arguments against hedging (more subtle)

-shareholders are usually well diversified and can make their own hedging decisions -it may increase risk to hedge when competitors do not -explaining a situation where there is a loss on the hedge and a gain on the underlying can be difficult

long hedge

-take a long position in the futures market -appropriate for someone who expects to buy an asset and wants to lock in the price

short hedge

-take a short hedge in the futures market -appropriate when someone expects to sell an asset he already owns and wants to lock in the price

Hedge Ratio

-the ratio of the size of the position taken in futures contracts divided by the size of the exposure -HR= (size of futures position)/(size of exposure)

The purpose of hedging

-to remove uncertainty, not to improve the average wealth of the hedger -on average it doesn't make you wealthier, it just ensures that you won't have massive losses -think insurance -roughly 50% of the time you make more money by not hedging

desirable hedging using futures

-two counterparties with offsetting risks can eliminate risk -hedgers can also transfer price risk to speculators and speculators absorb price risk from hedgers -ex: a wheat farmer and a flour mill enter into a forward contract, they can eliminate the risk each other faces regarding the future price of wheat

3 major reasons why hedging does not always work perfectly

1. The hedger may be uncertain as to the exact date when the asset will be bought or sold. 2. The hedge may require the futures contract to be closed out before the expiration date. 3. The asset whose price is to be hedged may not be exactly the same as the asset underlying the futures contract.

Choice of contract (frequently a potential hedger will have to consider 3 things)

1. choice of asset underlying the futures contract 2. choice of the delivery month 3.choice of the contract size

Summary of gains or loss from basis risk: long hedge

Cost of short spot: -St Gain on long futures: Ft-F0 Net amount paid: -St+ (Ft-F0)= -F0- (st-Ft)= -F0-bt hedgers position improves: when bt decreases, weakening basis hedgers position worsens: when bt increases, strengthening basis

Investment assets vs consumption assets

Investment: primarily held for investment purposes (gold or silver) Consumption: primarily held for consumption or production purposes (copper or oil) -difference is that the typical investor is indifferent between holding an investment asset and holding a claim on that asset -consumption assets have a benefit of ownership that investment assets do no have (think oil shortage) -consumption assets usually provide no dividend income but can be subject to significant storage costs

when F0<S0^(r-q)T

an arbitrager buys futures and shorts the stocks underlying the index

when F0>S0^(r-q)T

an arbitrager buys the stocks underlying the index and sells futures

difference between backwardation and contango

backwardation: when the futures price is below the expected future spot price contango: when the futures price is greater than the expected future spot price

for non-financial futures, the basis is defined as:

basis= spot price of asset to be hedged - futures price of contract used -when b increases, we call it strengthening of basis (benefits of short hedger become more) -when b decreases, we call weakening of basis (benefits of short hedger become less

a forward contract is really just a form of

borrowing or lending money at the risk-free rate

a foreign currency is

comparable to a security providing a yield, which is the foreign risk-free interest rate

delivery of a forward vs futures contract

forward: take place on a particular day futures: party with short position chooses to deliver at any time during a certain period

Optimal Hedge ratio

h=p(sd of s/ sd of f) where S is the standard deviation of delta S (not S!), the change in the spot price during the hedging period, sF is the standard deviation of Delta F(not F!), the change in the futures price during the hedging period r is the coefficient of correlation between DS and DF.

Law of One Price

if two portfolios offer the same cash flows in all potential states of the world, then the two portfolios must sell for the same price in the market - regardless of the instruments contained in the portfolios -if law does not hold then an arbitrage opportunity exists

the difficulty with the hedge ratio

it tells us how many units of the hedge instrument to use for each unit of the primary instrument but does not take into account that with a futures contract you have to buy in integral units of the contract, so you cannot buy the exact number of hedge instruments that you might want to use

change in value of portfolio equation for long and short hedge

long (short asset + long futures): ΔS-h*ΔF short hedge (long asset + short futures): ΔF-h*ΔS

in any hedging situation there is a danger that

losses will be realized on the hedge while the gains on the underlying exposure are unrealized -we can use a series of futures contracts to increase the life of a hedge

expected futures spot price

market's average opinion about what the spot price of an asset will be at a certain future time

Summary of gains or loss from basis risk: short hedge

proceeds of long spot: St Gain on short futures: F0-Ft Net amount received: St+ (F0-Ft)= F0 + (St-Ft) = F0 + bt hedgers position improves: when bt increases, strengthening basis hedgers position worsens: when bt decreases, weakening basis

perfect hedging

short hedging: long position on the spot market + short position on the futures market

HR ratio symbol definitions

ΔS - change in spot price during hedge ΔF - change in futures price during hedge σs - standard deviation of ΔS σF - standard deviation of ΔF ρ - correlation coefficient between ΔF and ΔS h - hedge ratio (the ratio of the size of the position taken in futures contracts to the size of the exposure).

At the variance minimizing level...

δV/δh will be equal to zero -thus h=(p*σs)/σF -note it shows that the optimal ratio is not already equal to 1. only if the two assets are perfectly correlated, namely σs=σF, then h=1