FORWARD CONTRACTS (REGULATION) ACT, 1952 - Kotak Anchored Ace
Forward Contracts - IES
Transcript of Forward Contracts - IES
Forward Contracts
International Finance ‐ 03
Outline
1. Valuing Forward Contract2. Using Forwards in Management
Outline
1. Valuing Forward Contract• Value of forward contract = price at which it can be traded on functioning market
• Contract A written at t‐5 vs contract B at t‐4• Their prices differ, but what is the value of outstanding contract?
• Why valuation? Useful for options or practical reasons:– Early settlement– Claim in case of default– Financial reporting by firms
Market Value of an Outstanding Forward" A contract" ‐ a forward purchase of 1 unit of FC
Outstanding contract is portfolio consisting of:
FC – denominated PN HC – denominated PNwith FV 1 as an asset with FV , as a liability
Get value in HC at t by discounting at risk‐free rate
⟹PVinFC ⟹PVinHC
transalte into HC via
where FV ‐ face value, PV ‐ present value, ‐ issue date, t ‐ today, T ‐maturity date, PN ‐ promissory note: financial instrument that contains a written promise by one party to pay another party a definite sum of money either on demand or at a specified future date (negotiable instrument if unconditional and salable).
Market Value of an Outstanding Forward
Market value of forward at t = ,
,
,
Market value of forward at t = ,
,
,
,
,
1
1 ,
1 ,
1 ,
,
1 ,
, ,
1 ,
where equality (*) comes from covered interest parity
PV of 1 FC
PV of 1FC PV ofAsset in HC HC liability
(*)
, by CIP
Market Value of an Outstanding Forward
So we know that
Market value of forward at t =,
,
,= , ,
,
If we consider a special case t = t (inception of contract), then
Initial value of a forward = , ,
,= 0
When signing forward contract we pay nothingThe value of forward contract is zero at the moment it is signedbecause the contract can be replicated at zero cost ‐• this inference comes from covered interest parity since you
can replicate the original forward contract with a synthetic one through spot and money markets
Market Value of an Outstanding ForwardSo we know that
Initial value of a forward = ,
,
,= , ,
,= 0
⟹presentvaluesofHCandFCdiscountedfromthefuturemustbeequal:
,
InotherwordsPVofuncertainfuturecashinflowgeneratedbythecontractcancelsoutagainstthePVoftheknownfutureoutflow ,
. isthepresentvalueoperator
Market Value of an Outstanding Forwardsince
,
⟹In a HC, the forward rate is the time‐t certainty equivalent offuture spot rate• while the future value of future sport rate at t is uncertain,
the forward rate , is certain at time t⟹
,
where (●) is certainty‐equivalent operator, like expected value operatorunlike expected value, CEQ(●) is risk‐adjusted expectationWhy? Forward rate , corrected for risk represents the market’s time t expectations of time T spot rate
Market Value of an Outstanding ForwardWhy CEQ(●) is risk‐adjusted expectation?• PV of risky cash flow equals its expectations discounted at
risk‐adjusted rate• Risk‐adjusted discount rate = risk‐free rate +risk premium• PV of risk‐free flow F is discounted at risk‐free rateFormally:
, ⟹
, ,
,
,
where , is the risk premium, which depends on the marketcircumstances at t and the asset to be bought at T
Market Value of an Outstanding ForwardWeusetheCEQnotationtoshowtherisk‐adjustedexpectedvalue
,1 ,
1 , ,⟹
1 ,1 , ,
11 ,
The fraction is called risk adjustmentwhere , is the risk premium, which depends on the marketcircumstances at t and the asset to be bought at T
Why Knowing the Value of Forward is Useful?
For valuation and hedging
VALUATION:• We can value FC assets and liabilities.
• We know that ,
• To value asset/liability we need to know forward rate, ‐ they are published
• we do not need to know expectation about future sport rates.
Why Knowing the Value of Forward is of Any Use for Us?
HEDGING• You have to pay 1 unit of FC at T• FC debt is risky: we do not know what the future spot rate will be
• Cash (out)flow of 1 unit of debt will be worth • Solution is to buy forward ,
• To achieve risk‐free combined cash‐flow• We know thatexpiration value of forward = ,
Why Knowing the Value of Forward is of Any Use for Us?
HEDGING• Cash flows under hedging:
Cash (out)flow from debt repayment Value of forward purchase at expiration ,
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐Combined net cash flow ,
• Hedging the FC debt with forward purchase transforms the risky debt into risk‐free debt
• BUT….
Why Knowing the Value of Forward is of Any Use for Us?
HEDGING• Hedged debt in FC can result in worse‐off
situation ex post• If > , the situation is good, we pay less amount of the HC to repay the FC debt because of hedging
• BUT…• If < , we could pay less amount of the HC to repay the FC debt WHEN NOT HEDGING
Forwards
• We know forward currency contracts by now• There also exist forward contracts on interest rates
• These are not strictly international• …but, they may become so• Average of banks’ quotes (quotes for short maturities up to ten years)
• Purpose: hedging in budgeting, reduce financial distress
Forward Forward and Forward Rate Agreement
Two forward contracts on interest rates :• forward forward ‐ forward deposit on a loan: it fixesan interest rate today (time t) for a deposit or loan starting in a future at and expiring at
• forward rate agreement ‐ like forward forward, but the deposit is notional ‐ the contract is about a hypothetical deposit rather than an actual deposit• the holder will settle the gain or loss in cash and pay or receive the present value of (contracted forward rate ‐market rate at )
Basics – definition etc.Forward rate ,
It is the rate used for the contracts initiated at time t andmaturing at time T
, is also called the time‐t forward rate for delivery rate T
• not strictly organized market• Banks are market makers• Plus they search for counterparts via auction system and
brokers• Most active forward rates are for 30 and 90 days,
and up to 1 year
Remember: Forward rate , is the rate used for the contracts initiated at time t and maturing at time T
Quoting forward rates
Swap rate = Outright , ‐ Spot StOutright Premium or discounts, in cents
CAD per USD USD per CAD CAD per USD USD per CAD
U.S. Canada spot 1.3211 0.7569 1 month forward 1.3218 0.7565 +0.07 ‐0.043 months forward 1.3224 0.7562 +0.13 ‐0.076 months forward 1.3229 0.7559 +0.18 ‐0.10
If the CAD/USD forward rates > spot rate for all maturities ⟹ USD trades at a premiumIf USD/CAD forward rates < spot rate for all maturities ⟹ CAD trades at a discount
Important: (i) forward spread is always larger than spot spread, (ii) forward spread increases with time to maturity
Arbitrage In the Presence of SpreadsIn our diagram depicting money, spot and forward markets we ignored the existence of the spreads.How will the existence of spreads affect our diagram?Ex. A treasurer decides on the following questions1. A foreign customer has promised a large amount of FC, but today the company need HC to pay suppliers and does not like the exchange risk either. Should the company borrow FC or HC?2. The next day the excess liquidities of HC should be parked in. Should the company go for HC or FC deposit?
Arbitrage In the Presence of Spreads3. In six month the company will have to pay it FC liability. Should the company keep HC and buy forward or move into FC right away?4. The company received FC from a customer, but in 6 months it will have to pay foreign supplier in FC. Should the company keep FC?The market data are the following
Spot HC/FC Forward, 180d HC/FC
99.9‐100.01 109.98‐110.02
Interest rate on HC, 180 d Interest rate on FC, 180 d
20.9‐21.1% 9.9‐10.1%
Arbitrage In the Presence of SpreadsAns. 1. A foreign customer has promised a large amount of FC, but today the company need HC to pay suppliers and does not like the exchange risk either. Should the company borrow FC or HC?For simplicity, assume that the your customer will pay you 1 unit of FC.
Arbitrage In the Presence of Spreads(a) You can use the spot market and borrow in FC.• Since you will get 1 unit of FC at T, in term of today money you
can only borrow 1/ 1 0.101 of FC
• At the prevailing spot rates, in HC you will get.
99.9 90,74(b) Or you can borrow in HC and enter the forward contract.• At time T from the forward contract you will get 109.98 units
of HC
• At the current interest rate, you can borrow 109.98.
90.81⟹ option (b) is better
Arbitrage In the Presence of SpreadsAns. 2. The next day the excess liquidities of HC should be parkedin. Should the company go for HC or FC deposit?Let's assume that today you have 1 unit of HC(a) You invest into HC deposit• at time T you HC deposit will grow to 1.209.(b) If you invest into FC deposit• You have to convert 1 unit of HC into FC at the prevailing spot
rates ⟹ with 1HC you will buy 1/100.01 units of FC
• This investment will grow to .
1 0.099 FC
• At time T on the forward contract you will get.
1 0.099 109.98 1.21 HC⟹option (b) is better
Arbitrage In the Presence of Spreads
Ans. 3. In six month the company will have to pay it FC liability. Should the company keep HC and buy forward or move into FC right away?Let's assume that the company now has 1 unit of HC.
Arbitrage In the Presence of Spreads(a) The company can buy FC now and put into FC deposit• At the prevailing spot rates the company can buy 1 / 100.01 of
FC
• At time T the FC deposit will grow to.
1 0.0990.011 of FC
(b) The company can invest into HC and use the forward market• At time T HC deposit will grow to 1 + 0.209• At T you will also exercise the forward contract and get
(1 + 0.209) .
0.012of FC
⟹option (b) is better
Arbitrage In the Presence of Spreads
Ans. 4. The company received FC from a customer, but in 6 months it will have to pay foreign supplier in FC. Should the company keep FC?Let's assume that the company now has 1 unit of FC.
Arbitrage In the Presence of Spreads(a) The company makes FC deposit• At time T 1 unit of FC deposit will grow to (1 + 0.099) = 1.099
of FC(b) The company can invest into HC deposit and use the forwardmarket• At the prevailing spot rates 1 FC equals 99.9 units of HC• At T this HC deposit will grow to 99.9 (1 + 0.209) of HC• This HC you will exchange under the forward contract and get
99.9 (1 + 0.209).
= 1.098
⟹ option (a) is better
ArbitrageNote(!!!): in the presence of spreads, the synthetic forward rates are the worst possible combinations of the basic markets formula
ArbitrageDirect bid comes from ⟶ (you want to sell FC)Synthetic bid comes from synthetic sale trip
⟶ ⟶ ⟶
=.
99.99 1.209
⟹ synthetic , 109.798
Arbitrage
Direct ask comes from ⟶ (you want to buy FC)Synthetic ask comes from synthetic‐purchase trip
⟶ ⟶ ⟶
=. .
1.099
⟹ synthetic , 110.202
ArbitrageThe CIP basic principle:• the lowest possible combination for bid comes from
bid bid / ask• the highest possible combination for ask ‐ ask ask / bidCIP accounting for sperads⟹
, , ,1 ,
,
1 , ,1 ,
,
1 ,
Implication of Arbitrage and Shopping Around
What does the arbitrage ensure?• cases 1 and 2 will not exist – there would be no tradingWhat does the shopping around guarantee?• cases 3 and 4 do not persist for long time – arbitrage
opportunity evaporates fast
Hedging Contractual ExposureThere is contractual exposure when the firm has signed contracts that ensure a known inflow or outflow of FC on a well‐defined dateThe exposure ( , ): number telling by what multiple the HC value (asset, cash flow) changes when exchange rate changes
,
where ‐ is the change in the value in HC‐ change in the exchange rate
Hedging Contractual ExposureTo get the perfect hedge• match every contractual foreign currency inflow with a corresponding outflow• problem?
• denominate all contract in DC• problem?
One takes on a position that exactly offsets the existing exposure ‐ one can reach that w/ forward contract
Issues Related to Hedging1. Imperfect hedging:• futures may be cheaper, but hard to tailor the required size
and expiration date• options do not entirely eliminate uncertainty, but remove the
downside risk; on the other hand, there is a price to be paid2. Credit riskIn the case of debtor's default you have to add the reverse forward.⟹ There is 50% probab. that the reverse hedge may bring loss• the risk, arising when a hedged exposure disappears, is called
reverse risk
Issues Related to Hedging3. Hedging of pooled cash flows• the treasurer may prefer to group into time buckets
• allows for netting over time ‐ the differencebetween inflows and outflows will be hedged
• scale economies in transaction costs ‐ it is cheaper to enter 1 big contract then a couple of smaller
SpeculationSpeculation ‐ intentional underdiversification with the aim of getting extra returnsThe speculators bet on market mispricing• he/she spots mispricing which the market has not yet noticed
• the market will soon see the error and come around to the speculator's view
• the gain from that hoped‐for price adjustment justifyunderdiversification
Speculation1. Speculating on the future spot rate
Buy forward: betting on appreciation – will pay more units of HC for 1 FC in future at spot => 1 FC from forward will yield more units of HC when sold at spot => difference is profitSell forward: betting on depreciation – opposite situation: sell forward, after depreciation buy at spot and honor the forward delivery
Speculation2. Speculating on the forward rateOne speculates on the future forward rate ,
• at t (today) you buy forward for delivery at • at close out ‐ sell forward for delivery at
• at you will lock in the cash , ,
• what is your bet about , , ? what does it imply?
, , > 0 ⟹ speculating on the rise in the forward rate
Speculation
The reverse position is• at t (today) you sell forward for delivery at • at close out ‐ buy forward for delivery at what are you betting on now?
, , ‐ you are speculating on the drop of in the forward rate
Speculation3. Speculating on swap rate (w)
Position Action at t Action at Payoff at
Bet on ↑ Buy forward Sell forward , 100.7
Hedge Sell forward Buy spot 100.3
Combined Forward‐forwardswap "out"‐ thetransaction for thenearest date takesout of FC
Sport‐forwardswap „in" ‐ thetransaction for thenearest date takesus into FC
,100.7 100.3
, 0.7 03.
Forward contracts can be used to minimize the Impact of Market Imperfections
• In perfect market shopping around is pointless – the same output for a given trip from both directions
• But… markets are not prefect• Imprefections:
– Bid‐ask spreads– Asymmetric taxes– Information asymmetries (leading to inconsistent aid‐ask spreads)
– Legal restrictions
Minimizing the Impact of Market Imperfections
1. Shopping aroundto minimize costsUse our diagram
Identify START position indentify the END position calculates the outputs for each routes from START to
END ‐ choose the best one
Minimizing the Impact of Market Imperfections
2. Swapping for tax reasons• advantages due to the difference in the taxation ofdeposits/loans
• tax asymmetries ‐ capital losses and gains are treateddifferently (examples: capital gain tax exempt, capital loss not tax deductible, income tax brackets etc.)
3. Swapping for information‐cost reasons• due to credit risk loans in FC can have higher spreads
Minimizing the Impact of Market Imperfections
4. Replicating bank‐to‐back loans• To support GBP during Bretton Woods
– Bank of England occasionally borrowed USD fromBundesbank
– to guarantee the loan Bank of England deposited equal value of GBP with Bundesbank
– eventually the loan and deposit is returned and the interests on both are paid
• companies post government securities as guarantee to a loan
• there are three firms: X, Y, Z (Z is a subsidiary of Y): Y lends X in FC, but X lends Z in HC
Key Ideas for Arbitrageurs, Hedgers, and Speculator
In the imperfect markets it is a near certainty that one route will be cheaper because:• Differences in taxation of capital gains/losses and interest income/cost ‐ routes produce differentoutcomes
• Information asymmetries can induce different risk spreads by different banks and if the loans differ in currency ‐ go for the best spread
• With pooled hedging, there is still interest rate risk• etc.