4w FinEcon 2024fall v2

Summary

The video script discusses the concept of basis risk in the context of futures and spot prices. It explains how basis risk arises due to uncertainty between the spot and future prices when closing out a hedge. The script uses examples to illustrate how gains or losses occur when taking long or short positions in futures contracts, such as with Samsung stock. It further explores cross hedging, where the underlying asset of the future contract differs from the asset being hedged, and introduces the concept of beta to explain the relationship and optimal hedge ratio between different assets.

Takeaways

• 📈 Basis risk arises from the uncertainty about the difference between the spot and future prices, known as the basis.
• 🔄 The basis is the difference between the spot price and the future price of an asset.
• 💼 To lock in a future price, one might take a short position in a forward contract, which can result in gain or loss depending on the final spot price.
• 💹 The gain or loss from a forward contract is calculated as the difference between the future price (strike price) and the spot price at maturity.
• 📉 If the spot price at maturity is higher than the forward price, a short position results in a loss, and vice versa for a long position.
• 💼 The net amount received from selling an asset and settling a forward contract depends on the initial and final spot prices and the forward price.
• 🌐 Basis risk can be mitigated by understanding the relationship between the asset and the future contract used for hedging, often represented by the beta coefficient.
• 📊 The beta coefficient indicates the sensitivity of the asset's price movement to the movement of another asset or index used as a hedge.
• 🔢 Cross hedging involves using a different but related asset or index future to hedge the price risk of the asset of interest.
• 🌐 In cross hedging, the optimal hedge ratio is crucial to minimize basis risk and is often determined by the beta coefficient.
• 📉 An increase in the basis, or the difference between the spot and future prices, can lead to unexpected losses even when the hedge is theoretically sound.

Q & A

What is basis risk?

Basis risk refers to the risk that arises from the uncertainty about the difference, or 'basis', between the spot price and the future price of an asset when a hedge is closed out.

Why does basis risk rise?

Basis risk rises due to the uncertainty about the basis when the hedge is closed out, which can lead to unexpected gains or losses.

Can you provide an example of how basis risk works with a stock like Samsung?

Yes, if you take a short position in a forward contract on Samsung with a strike price of 60,000 and the spot price at maturity is 70,000, you would have a gain of 10,000 if you had taken a long position. However, since you took a short position, you would incur a loss of 10,000.

What is the difference between a long and short position in a forward contract?

A long position means you expect the price to rise and you benefit from the increase. A short position means you expect the price to fall and you benefit from the decrease.

How does the spot price at maturity affect the outcome of a short position in a forward contract?

If the spot price at maturity is higher than the strike price of the forward contract, the holder of a short position will incur a loss equal to the difference between the spot price and the strike price.

What is meant by 'basis' in the context of futures and spot prices?

In the context of futures and spot prices, 'basis' refers to the difference between the spot price of an asset and its future price at a specific point in time.

Why might the basis change between the spot and future prices?

The basis can change due to various factors such as changes in supply and demand, storage costs, interest rates, and other market conditions that affect the spot and future prices differently.

What is the significance of the basis at maturity in a futures contract?

At maturity, the basis should theoretically be zero because the future price converges with the spot price. Any difference at this point represents basis risk.

What is a cross-hedge and why is it used?

A cross-hedge is a hedging strategy where a futures contract on one asset is used to hedge the price risk of another, related asset. It is used when there is no futures contract available for the exact asset you want to hedge.

How does beta relate to cross-hedge?

Beta is a measure of how much the price of one asset, like a stock, is expected to move in relation to another asset, like an index. In cross-hedge, beta is used to determine the optimal hedge ratio to minimize basis risk.

What is the optimal hedge ratio and how is it found?

The optimal hedge ratio is the ratio of the size of the hedging position (like the number of futures contracts) to the size of the exposure being hedged. It is found by analyzing the relationship between the asset being hedged and the hedging instrument, often using statistical methods like regression analysis.

Outlines

00:00

🔍 Understanding Basis Risk and Stock Forward Transactions

This paragraph introduces the concept of basis risk, which arises from uncertainty in the difference between spot and future prices at the time of closing a hedge. The example of selling a Samsung share with a short stock forward position is used to explain how basis risk occurs. It walks through the process of cash settlement at maturity, comparing the spot price (70,000 KW) and the strike price (60,000 KW). The scenario results in a gain of 10,000 KW from a long position, while a short position results in a loss of the same amount.

05:01

🤔 Losses from Short Positions in Stock Forward Contracts

This paragraph delves into the implications of taking a short position in a forward contract for Samsung shares. It explores how a short position leads to losses when the spot price at maturity exceeds the strike price. The example illustrates a loss of 10,000 KW due to the short position and explains how different sale prices of the share (e.g., 70,000 or 69,000 KW) affect the final amount received. The concept of basis risk is introduced again as the difference between spot and future prices, further emphasizing the risk of unexpected losses.

10:06

📈 Long Hedge Example: Asset Purchase with Future Price

This paragraph describes a long hedge example for purchasing an asset. It defines the future price at the time the hedge is set up (F1) and at the time of purchase (F2), with S2 representing the asset price at purchase. The future and spot prices are expected to converge at maturity. The paragraph details how gains are calculated by subtracting the initial future price from the final future price and subtracting net payment amounts. It explains how the basis, defined as the difference between the asset and future prices, can change and affect hedging outcomes.

15:09

🛡️ Short Position in Futures and Basis Risk Simplified

This section explores the mechanics of short positions in futures. It explains how selling shares at a future date after entering into a short futures position affects the final settlement. If there is no basis (i.e., no difference between spot and future prices), the amount received at maturity equals the forward price (F1). The paragraph simplifies the concept, stressing that noise from basis differences can occur but should not be a significant concern for understanding how a short position works.

20:10

📊 Cross Hedging and Optimal Hedge Ratio

This paragraph discusses cross hedging, where the underlying asset of a futures contract differs from the asset whose price is being hedged. The example of using a KOSPI 200 futures contract to hedge Samsung stock is provided, explaining that while Samsung is a component of the KOSPI 200 index, they are not identical. The paragraph introduces the concept of optimal hedge ratio, which helps balance the size of the futures position relative to the exposure. A regression model is mentioned to explain the relationship between the index and stock price changes.

25:14

📐 Sensitivity (Beta) in Cross Hedging

This paragraph expands on the idea of cross hedging by introducing the concept of beta, which measures the sensitivity of an asset's price to changes in an index. It explains how beta is used in regression models to estimate how Samsung's stock price responds to changes in the KOSPI 200 index. Various beta values (e.g., 1, 0.5, 2) are explained with corresponding examples of how a 10% change in the index would affect Samsung's stock price. This helps illustrate the importance of understanding sensitivity when cross hedging.

Keywords

💡Basis Risk

Basis Risk refers to the risk that the difference between the spot price and the futures price (the 'basis') will not be as expected. In the script, it is discussed in the context of uncertainty that arises when closing out a hedge. For instance, if one takes a short position in a stock forward to lock in a price, the basis risk comes into play because the actual spot price at the time of settlement could be different from the forward price, leading to potential gains or losses.

💡Spot Price

The spot price is the current market price of an asset. In the video, the spot price is used to illustrate the difference between the expected future price and the actual price at the time of settlement. For example, if the spot price of Samsung stock is 70,000 at the time of selling, it is compared to the forward price to determine the gain or loss from a short position.

💡Futures Price

The futures price is the price at which a contract to buy or sell an asset at a future date is agreed upon today. In the script, the futures price is compared to the spot price to understand the basis. It is used to explain how taking a short or long position in a futures contract can result in gains or losses depending on the movement of the spot price relative to the futures price.

💡Hedging

Hedging is a strategy used to reduce risk by taking an opposite position in a related security. The script discusses hedging in the context of locking in a future price for an asset, like Samsung stock, by taking a short position in a stock forward. The goal is to mitigate the risk of price fluctuations, but basis risk can still lead to unexpected outcomes.

💡Cash Settlement

Cash settlement refers to the process of settling a financial contract by paying or receiving cash based on the difference between the agreed-upon price and the actual price at maturity. In the script, it is mentioned that there is no physical delivery of the asset; instead, the difference between the forward price and the spot price at maturity is settled in cash.

💡Strike Price

The strike price is the price at which an option contract can be exercised or a futures contract is settled. In the video, the strike price is used to calculate the gain or loss from a futures contract. For example, if the strike price of a Samsung stock future is 60,000 and the spot price at maturity is 70,000, the gain would be the difference between these two prices.

💡Long Position

A long position is a stance in the market where an investor owns a particular asset or has bought futures contracts, expecting the price to rise. The script uses the term to contrast with a short position, explaining that a long position in a futures contract would result in a gain if the spot price at maturity is higher than the futures price.

💡Short Position

A short position is the opposite of a long position, where an investor sells an asset they do not own, or sells futures contracts, with the expectation that the price will fall. The script explains that taking a short position can result in a loss if the spot price at maturity is higher than the futures price.

💡Maturity

Maturity in the context of financial contracts refers to the date when the contract expires and the terms of the contract are fulfilled. The script discusses how the spot and futures prices at maturity can affect the outcome of a hedge, determining whether there is a gain or loss from a position taken in a futures contract.

💡Basis

The basis is the difference between the spot price and the futures price of an asset. The script explains how changes in the basis can lead to unexpected gains or losses when closing out a hedge. It is a critical factor in understanding basis risk and how it affects the effectiveness of a hedging strategy.

💡Cross Hedging

Cross hedging involves using a futures contract on one asset as a hedge for an exposure to another related asset. In the script, it is mentioned in the context of using the KOSPI 200 (CP 200) future to hedge the price risk of Samsung stock, acknowledging that the two are related but not identical, which introduces basis risk.

Highlights

Definition of basis risk as the difference between the spot and future prices.

Explanation of how basis risk arises due to uncertainty about the basis when the hedge is closed out.

Example given to illustrate the concept of locking in a price with a short forward position.

Description of cash settlement at maturity for a short forward position.

Explanation of the gain from a long forward position at maturity with a strike price of 60,000 and a spot price of 70,000.

Calculation of loss from a short position when the spot price is higher than the strike price at maturity.

Discussion on the impact of selling a share at a different price than expected on the net gain or loss.

Introduction to the concept of basis and its role in determining the net paid amount for a long position.

Explanation of how the basis changes when the spot price and future price diverge.

Example of a long hedge for the purchase of an asset and how it affects the net paid amount.

Definition of the basis as the difference between the future price and the spot price at maturity.

Discussion on the potential increase in basis risk when using a different asset for hedging, such as cross hedging.

Introduction to the concept of beta as a measure of sensitivity between the price changes of two assets.

Explanation of how beta can be used to determine the optimal hedge ratio in cross hedging scenarios.

Example of using the KOSPI 200 future as a proxy for hedging Samsung stock when Samsung futures are not available.

Discussion on the relationship between Samsung stock price changes and KOSPI 200 index changes using beta.

Explanation of how changes in the KOSPI 200 index can impact Samsung stock price based on beta sensitivity.

Illustration of the regression model showing the relationship between Samsung stock price and KOSPI 200 index.

Final conclusion on the importance of understanding the basis and beta sensitivity in hedging strategies.

Transcripts

basis risk as coming from hatching what

is the

basis uh between uh the spot and future

basis is difference between spot and

future uh let me uh explain

further basis risk rise because of

uncertainty about the basis when the

hatch is closed out uh let's see this

example suppose you are going to sell

one share of

Samsung in one

year to lock in the price you have taken

a short position of stock forward on

Samsung

already where no physical delivery but

only cash settlement in one year yeah

this is a condition after one year here

when the satell price is determined at

around 7

70,000

KW which

means you are going

to um hold on a second hold a

second

okay

uh at maturity and

maturity and maturity you are going to

make a in know cash uh

settlement see uh this

way uh effect I mean uh Samsung

forward

price

exactly speaking like a strike

price strike

price let's say this uh you know

was

60,000 uh hold on a second hold on a

second uh

60 60,000

6,000 uh

the so take a short position short

position

6,000

okay yeah so uh you know this is Strike

price and uh at at one one year at one

year maturity the spot spot price

is

7,000

70,000 this is L

again forward forward

a

spot

minus strike price this is

gain

right this is

gain

so you have you know you take a long

portion of effect you take a long

portion of stock forward and this is

gain in one year and

maturity

now

70 yeah

7 uh s is 70,000 K is

60,000 how

much

gain

10,000 this 10,000 gain is from what if

you taken if you taken long

position if Tak long

position uh if if you take a long

position on uh samung forward where

strike price

is

60,000 at maturity spot is in one year

spot is

70,000 and from long position of FX long

position of equ forward long position of

Samsung

forward yeah you gain

10,000 however

here question

is you know you are going

to you're going to take on a short

position or long position short position

short position

means your pel is like

this minus because this is

long this is

short

so from short

position

panl can be like

this got

it which

means you make a loss around

10,000

now based on this information think

about think about

what uh I don't want to be uh too much

technical sorry about it uh uh see

from

from yeah from uh you know uh from the

scratch now

strike strike price

is

60,000 of one Samsung

Share to take a short

position

means the purpose is you know you like

to lck in one share Samsung

at

60,000 but you know once you have taken

a short position

on Samsung forward but it R here spot

is

70,000 so from your short position you

make a loss how much

yeah 10,000 yeah you make a Closs

now now you have in know one year share

already you like to sell it to the

market then how much you are going to

sell if you sold out you one of shares

exactly

at

70,000 then how much you have you are

receiving

70,000 and your loss is 10,000

already how much you have in your

pocket

60,000 what if you sold out one share of

Samsung

at

60

9,000 then how much you have

10,000 Lo 10,000 loss

from short forward and then you

receive

69,000 how much you

have

59,000 so what if uh you know you're

not uh

selling

selling your one of

shares

at 70,000

then you make a further

loss that loss it's not

expected that loss is coming from a

basis basis

what S and

K yeah this is the basis so forget about

you know uh you know this technical

things just uh simply you know spot and

for future but other than uh I mean

there could be some uh basis between uh

spot price and future uh price so

on uh let's see uh you know one more

example long hatch for purchase of an

asset now F1 is future

price at time

H is set up like a initial future price

F2 future

price at time asset is purchased like a

future price at maturity that is initial

future price and final future price ns2

is asset price at time of purchase in

one year so basis we Define like this

in

now

c

f future price in one

year there is S1 in one year that is

F2 and

also

S2 usually in one year

maturity

equal to S2 because this is future price

but uh you are arriving at

maturity uh where you know you have uh

also like a spot age traded so future

price and the spot price you know could

be converged such as I already uh you

know explained in the previous session

this is Future

and is spot it's a maturity

yeah based on this you know we can say

this now possible asset

means uh you are going to spend uh this

uh much amount money to buy underline

asset in one year that's why you spend

you need to pay S2 for buying your

underly asset and the gain on future is

this one this is

initial uh future price you know when uh

you entered into uh future transaction

and this is price at one year so gain

is FS2 minus FS1 this is

gain net paid amount

in one year and uh you're going to pay

uh this

much and

also this is gain this is pay out this

is gain so you know you need to make a

uh in a

minus then this is another

yeah

expression from this and

finally this what is

this E2 basis so a net paid amount in

one year is how much if you take a you

know H

position yeah short position

is sorry a long position then FY

plus

B2 this is your net paid

amount what if you know S2 went up and

S2 down and B2 is different because S2

minus F2 is BAS

B2 S2 is going down and base Bas is

different Bas is change it

I should hat for a sale of an asset now

asset online the future contract is the

same as asset whose price being hatch

now we are still talking about there is

no uh mismatch between underlying asset

and also the

asset uh whose price to be hatch to

Define mutual price

at time patch set up and the future

price at Time s is sold and S price time

of sale and basis at time of sale now

price of

ss and S2 now gain on future is like

this because this is short

position previous

one yeah this is gain from previous one

that is long position

long so F4 fub1 F2

so FS2 is uh uh more than uh F1 then you

know this is

gain

however we are talking about the you

know short positions so gain uh will be

a negative of this one so this

one yeah this is gain so n received

amount is

S2

because you're going to sell you're

going to sell and you receive

S2 and

gain

right this can be exess this

way yeah this

is

two and

um let's make a in a simple as

[Music]

possible you

have you know one share that is s and

forget about

basis

uh you like to you know

sell in one

year to do that you take a short

position on

future

fure the

price

F1 yeah this is

now in one year in one

year you still have

S and

then

this

future uh should be uh

settled how you how you're going to be

settled

you delivered

s and you

pay you paid back you you

return

F1 from new account party so

finally in know net received amount in

one year is how

much F1 against what

you delivered

shares so FS1 + B2 is the same meaning

where you know there is no basis so

there is no basis when you have uh you

know shares but you're going to sell in

one year and to do that you enter into

uh short position on a future and

finally in one year you're are going to

deliver s and you are going to get paid

F1 so net receive amount in one year is

how

much

F1 if there is Basis between uh spot and

a future and there there might be some

noise but forget about the you know

noise that could happen but uh from your

an you know you don't worry about noise

as simply as possible a net receiv

amount in one year and you are going to

receive

FY this

is uh you know we we can say you know

you are lacking the

price

right now you know based on this one uh

you know we are extending

to a cross setting cross setting is

underline

underly uh

asset of

future and uh your

asset this is a this is b a is not B

yeah this case you know we can say uh

cross

hatching

um in case of asset underlying future

contract is not the same as asset whose

price being hatched it's somewhat

expected for basis stre to increase

hence we should find Optimal hch

ratio where you know it's the ratio of

size of hatching position such as future

contact to the size of exposure being

hatching now suppose we try to lock in

the price of Samsung stock using

CP 200 fature because we assumed there

is no uh you know Samsung

Futures so you cannot lock in the price

instead instead of in a Samsung uh

future you're going to use po p 200

future for

hatching again pop 200 is not identical

with Samsung because Samsung is one of

you know one of uh you know component

one of

shares uh to comprise uh cost speed 200

but cost speed 200 has you know 200

different

Shares are you know included so anyway

there might be some relationship between

Samsung and cby 200 but cby 200 is not

equal to Samsung shares in terms of you

know exposure

okay to make a cross setting uh let's

think about a simple relationship such

as a beta beta means let's say know

probably you have

Samsung Samsung rate of return this is

going

to uh be explained by kind of uh

regession model such as

beta0 beta 1 here

here c p

200 rate return and know and atat time

this

is

regession model this regression

formula I like to uh you know borrow

idea here from this regression model is

beta one beta one is kind of a

sensitivity

how much uh you know change in cost P

200 and how much

Samsung price is changing so simply uh

you know we we can say this

one Samsung

price rable change you know Samsung

stock price

changes can

be explained

by

sensitivity beta

times po p

200 index change so simply uh let's see

uh this is um

[Music]

um

kpy API c p and this is L let's throw

uh

okay cost P2 cost P 200 uh changes

increased like a 10% in uh

price and and uh if uh in know in the

case

samung uh stock increase 10%

means what it's a in a

linear under you know

45 degree angle so which means

RS

one or

kpy so

whatever you know change

percentage it will be

directly impact to the same uh change

because

sensitivity AG one what about the you

know this you know beta sensitivity is

0.5 which means

what

if po p 200 shares

changeing in 10% and Samsung price

change how much

5% yeah then in this

case regression uh graph is like

this this is previous one it's a better

uh sorry

sorry

yeah yeah this one is beta is one yeah

here beta is one and this new one beta

is how much beta is

0.5 this is

sensitivity so rly you know Samsung

today price uh 70,000 and tomorrow 70 uh

77,000 uh means like 10% increase and

cost p uh 200 today 300 and tomorrow

let's say uh 3 15 then 5% increase then

in this case we can utilize this

information

to in know a drive this uh regulation

formula Lely let's

say this case Samsung

is

two

times

apy then based on this one uh let me uh

draw another line such as

here this this time you know uh the

sensitivity beta this is beta

sensitivity

is two beta is two slop is more steppen

right step is you know step more stepper

you you know the slope is more steeper

sens sensitivity wise increase and slope

is going

higher and this is regression model uh

you know Samsung is dependent variable

and cost P 200 independent variable how

uh they are related uh through beta so

finally

uh we can say this

is uh relationship between uh Samsung

and Cosby so and sensitivity wise this

is two this is a better

again KP uh CP

200 changes

10% then Samsung stock price changed how

much 20 % because sensitivity is two

yeah based on uh this

information