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# Chapter 5 fx forwards

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### Chapter 5 fx forwards

1. 1. Managing Market Risk Under The Basel III Framework Copyright © 2016 CapitaLogic Limited Chapter 5 Foreign Exchange Forwards Managing Market Risk Under The Basel III Framework The Presentation Slides Website : https://sites.google.com/site/quanrisk E-mail : quanrisk@gmail.com
2. 2. Copyright © 2016 CapitaLogic Limited 2 Declaration Copyright © 2016 CapitaLogic Limited. All rights reserved. No part of this presentation file may be reproduced, in any form or by any means, without written permission from CapitaLogic Limited. Authored by Dr. LAM Yat-fai (林日林日林日林日辉辉辉辉), Principal, Structured Products Analytics, CapitaLogic Limited, Adjunct Professor of Finance, City University of Hong Kong, Doctor of Business Administration (Finance), CFA, CAIA, FRM, PRM.
3. 3. Copyright © 2016 CapitaLogic Limited 3 BIS statistics on FX derivatives Notional amount (USD bn) 75,87974,519Total 14,60013,558Options 24,20424.724Swaps http://stats.bis.org/statx/srs/table/d6?p=20151&c= 37,07637,238Forwards 20142015FX derivatives
4. 4. Copyright © 2016 CapitaLogic Limited 4 Time value of money Currency mis-match problem FX forwards analysis FX forwards market CNY non-deliverable forwards Outline
5. 5. Copyright © 2016 CapitaLogic Limited 5 Natural exponent and natural logarithm What is e? Natural exponent Natural logarithm ( ) ( ) N r r N N N a r lim 1+ = 2.718281828 = e N 1 lim 1 + = 2.718281828e = N b = e = exp a a = ln b →∞ →∞            
6. 6. Copyright © 2016 CapitaLogic Limited 6 Future value and present value Future value Value of an asset grows to after one or more compounding periods Present value Future value of an asset discounted by a periodic interest rate ( ) ( ) T T Future value = Present value 1 + Periodic interest rate Future value Present value = 1 + Periodic discount rate
7. 7. Copyright © 2016 CapitaLogic Limited 7 Risk-free security Functional purpose Created by financial economists For theory development Never exists in the world Proxy by top quality assets, e.g. domestic currency in a bank account Cash flows Out Principal at origination In Principal at maturity Scheduled interest
8. 8. Copyright © 2016 CapitaLogic Limited 8 Risk-free rate Annualized return of a risk-free security Discrete compounding Continuous compounding Conversion ( ) ( ) ( ) ( ) T T 0 T T T TT 0 T 0 0 T 0 0 S1 S = S exp rT S = S S S S = S 1 exp -rT r + r S = r = - 1 S1 + r = ln T S       ( )Continuous compounding = ln 1 + Discrete compounding
9. 9. Copyright © 2016 CapitaLogic Limited 9 Time value of currency STexp(rfT)S0 Foreign currency exp(rdT)1 Domestic currency T years laterTodayTime
10. 10. Copyright © 2016 CapitaLogic Limited 10 Time value of currency STS0exp(-rfT) Foreign currency 1exp(-rdT) Domestic currency T years laterTodayTime
11. 11. Copyright © 2016 CapitaLogic Limited 11 Long position and short position Long position You own a foreign currency Quantity is a positive number When the FX rate increases, you sell the foreign currency and make a profit Short position You borrow and sell a foreign currency Quantity is a negative number When the FX rate decreases, you buy and return the foreign currency and make a profit
12. 12. Copyright © 2016 CapitaLogic Limited 12 Time value of money Currency mis-match problem FX forwards analysis FX forwards market CNY non-deliverable forwards Outline
13. 13. Copyright © 2016 CapitaLogic Limited 13 A currency mis-match problem A trading firm Buys goods from United Kingdom Pays cost in GBP Sells goods to United States Receives revenue in USD Both cost in GBP and revenue in USD in three months are well estimated How to ensure that the revenue in USD which will be used to buy GBP, is sufficient to pay the cost in GBP, subject to the situation that the FX rate in three months is unknown?
14. 14. Copyright © 2016 CapitaLogic Limited 14 FX forward An agreement between an investor and a bank on a foreign currency such that The investor must buy from the bank the foreign currency at an agreed strike rate K at maturity T The bank must sell to the investor the foreign currency at an agreed strike rate K at maturity T
15. 15. Copyright © 2016 CapitaLogic Limited 15 At maturity ST above K The investor pays to the bank K units of domestic currencies The bank supplements ST - K buys one foreign currency at ST delivers to the investor one unit of foreign currency ST below K The investor pays to the bank K units of domestic currencies The bank pockets K - ST buys one foreign currency at ST delivers to the investor one unit of foreign currency
16. 16. Copyright © 2016 CapitaLogic Limited 16 Payoff The benefit to the investor resulting from a FX forward at maturity Single FX forward Payoff = ST - K FX forwards contract An agreement to enter many identical FX forwards in one transaction Contract payoff = Quantity × (ST - K)
17. 17. Copyright © 2016 CapitaLogic Limited 17 Payoff diagram -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 1.52 1.54 1.56 1.58 1.6 FX rate at maturity (USD per GBP) Payoff(USD) Payoff
18. 18. Copyright © 2016 CapitaLogic Limited 18 Moneyness < KOut-of-the-money KAt-the-money > KIn-the-money FX rate (S0)Moneyness
19. 19. Copyright © 2016 CapitaLogic Limited 19 Long position and short position Long position An investor has the right and obligation to buy from the bank the foreign currency at strike rate K at maturity T Short position The bank has the right and obligation to sell to the investor a foreign currency at strike rate K at maturity T An investor can choose to enter a short position The bank then enters the long position
20. 20. Copyright © 2016 CapitaLogic Limited 20 Time value of money Currency mis-match problem FX forwards analysis FX forwards market CNY non-deliverable forwards Outline
21. 21. Copyright © 2016 CapitaLogic Limited 21 Analysis of derivatives Functional purposes Hedging Investment Cash flows Outflows Inflows Valuation When there is market price Value = Quantity × Market price When there is no market price, how much does it worth? Market risk VaR Worst case loss
22. 22. Copyright © 2016 CapitaLogic Limited 22 Hedging Hedge To reduce the uncertainty in the value of a foreign currency To reduce the FX rate risk Complete hedge To eliminate completely the uncertainty in the value of a foreign currency To reduce the FX rate risk completely Partial hedge To eliminate the uncertainty in the value of part of a foreign currency To reduce the FX rate risk below a tolerance level
23. 23. Copyright © 2016 CapitaLogic Limited 23 Functional purposes Long position To hedge the value of a future outflow in a foreign currency To speculate on the up trend of a FX rate without upfront cash outflow To hedge a short position in a foreign currency Short position To hedge the value of a future inflow in a foreign currency To speculate on the down trend of a FX rate without borrowing and selling To hedge a long position in a foreign currency
24. 24. Copyright © 2016 CapitaLogic Limited 24 A reverse currency mis-match problem A trading firm Buys goods from United states Pays cost in USD Sells goods to United Kingdom Receives revenue in GBP Both cost in USD and revenue in GBP in three months are well estimated How to ensure that the revenue in GBP which will be sold and become USD, is sufficient to pay the cost in USD, subject to the condition that the FX rate in three months is unknown?
25. 25. Copyright © 2016 CapitaLogic Limited 25 At maturity ST below K The investor pays to the bank one foreign currency The bank sells the foreign currency at ST supplements K - ST delivers to investor K units of domestic currencies ST above K The investor pays to the bank one foreign currency The bank sells the foreign currency at ST pockets ST - K delivers to investor K units of domestic currencies
26. 26. Copyright © 2016 CapitaLogic Limited 26 Payoff of a short position in FX forward -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 1.52 1.54 1.56 1.58 1.6 FX rate at maturity (USD per GBP) Payoff(USD)
27. 27. Copyright © 2016 CapitaLogic Limited 27 Investment in FX rate with FX forward Long position Short position ( ) T T T T Payoff = S - K > 0 if S > K Payoff = - S - K > 0 if S < K
28. 28. Copyright © 2016 CapitaLogic Limited 28 Investment in FX rate with FX forward When an investor expects that the FX rate will go up Long a FX forward When an investor expects that the FX rate will go down Short a FX forward In either case, no upfront cash is required Chance to create profit without principal The most important characteristic of FX forwards
29. 29. Copyright © 2016 CapitaLogic Limited 29 Modelling a FX forward S0: Current FX rate rd: Annualized risk-free rate of domestic currency rf: Annualized risk-free rate of foreign currency K: Strike rate T: Maturity in years ST: FX rate in T years f: Value a FX forward
30. 30. Copyright © 2016 CapitaLogic Limited 30 Cash flows – physical settlement Foreign currencyK Out flow at maturity K = S0exp[(rd - rf)T] Foreign currency None Long Strike rate K In flow at maturity Cash flow at origination ShortPosition
31. 31. Copyright © 2016 CapitaLogic Limited 31 Cash flows – cash settlement K = S0exp[(rd - rf)T] ST - K None Long Strike rate K - ST Cash inflow at maturity Cash flow at origination ShortPosition
32. 32. Copyright © 2016 CapitaLogic Limited 32 Principles of derivatives valuation Mark-to-market Value = Quantity × Relevant and recent transaction price But, FX forwards have no available transaction prices Mark-to-model Value calculated by valuation models and available market data FX rate, interest rate Transaction price ≠ Model value Transaction price = Model value + Administrative cost + Profit Subject to supply and demand in the financial market Model value is a proxy of transaction price for risk management and financial reporting purposes
33. 33. Copyright © 2016 CapitaLogic Limited 33 Valuation – long position f Payoff Strike rate S0exp(-rfT) - Kexp(-rdT) Value of a FX forward today ST - K Benefit to long position K Long position pays at maturity ST FX rate at maturity
34. 34. Copyright © 2016 CapitaLogic Limited 34 Value of a FX forward Forward value Intrinsic value Caused by payoff Time value Caused by time to maturity ( ) [ ] [ ]{ } 0 f d 0 0 f d f = S exp(-r T) - Kexp(-r T) = S - K + S exp(-r T) - 1 - K exp(-r T) - 1 [ ] [ ] 0 T 0 f d Intrinsic value = S - K = S - K at maturity Time value = S exp(-r T) - 1 - K exp(-r T) - 1 = 0 at maturity
35. 35. Copyright © 2016 CapitaLogic Limited 35 Value of a FX forward -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 1.52 1.54 1.56 1.58 1.6 Current FX rate (USD per GBP) Value(USD) Intrinsic value Time value
36. 36. Copyright © 2016 CapitaLogic Limited 36 Forward rate The strike rate at which the value of a FX forward is zero Interest rate parity In general, forward rate moves in the same direction as current FX rate Standard FX forwards are originated at forward rate to avoid cash outflow from either party The most important characteristic of FX forwards ( ) 0 f d 0 d f f = S exp(-r T) - Kexp(-r T) = 0 K = S exp r - r T Forward FX rate = Current FX rate × Interest rate differential effect    Example 5.3
37. 37. Copyright © 2016 CapitaLogic Limited 37 Delta The sensitivity of a FX forward to its underlying foreign currency Change in FX forward value if the FX rate increases by 1 [ ] [ ] ( ) [ ] [ ] 0 0 f d 0 0 f d 0 0 f f S = S exp(-r T) - Kexp(-r T) f S +1 = S +1 exp(-r T) - Kexp(-r T) Delta = f S +1 - f S = exp(-r T) 1≈
38. 38. Copyright © 2016 CapitaLogic Limited 38 Replicating portfolio A portfolio comprising A long position in exp(-rfT) units of foreign currency A short position in exp(-rdT) units of domestic currency Replication Long a FX forward is equivalent to long Delta units of foreign currency and short a risk-free security Short a FX forward is equivalent to short Delta units of foreign currency and long a risk-free security 0 f df = S exp(-r T) - Kexp(-r T)
39. 39. Copyright © 2016 CapitaLogic Limited 39 Hedge the risk of a foreign currency Long position in ONE FX forward Short position in ONE FX forward Approximation Long position in exp(rfT) quantity of FX forward Short position in exp(rfT) quantity of FX forward Forward hedge ShortLongFX position
40. 40. Copyright © 2016 CapitaLogic Limited 40 Approximations to risk calculations Value and forward rate Direct impact to profit and loss Must look accurate Value-at-risk A projection of potential loss in the future Model error always exists Convenience is over accuracy Approximations For FX forwards where the maturity in general less then one year, under the current low interest environment, the quantities exp(rdT), exp(-rdT), exp(rfT), exp(-rfT), exp[(rd-rf)T)] and exp[(rf-rd)T)] are close to ONE
41. 41. Copyright © 2016 CapitaLogic Limited 41 Hedged worst case loss Value0 0 Worst case value Expected value Value-at-risk 1 - q% q% T days ValueT Unrealized loss Worst case loss Acquisition cost Hedging Hedged worst case loss Example 5.4 Example 5.5
42. 42. Copyright © 2016 CapitaLogic Limited 42 FX rate risk of a FX forward Foreign currency has FX rate risk Domestic currency has no risk FX rate risk Equivalent to Delta units of foreign currency Approximately equivalent to ONE unit of foreign currency Example 5.6 Example 5.7 0 f df = S exp(-r T) - Kexp(-r T)
43. 43. Copyright © 2016 CapitaLogic Limited 43 FX rate risk factors for FX forwards portfolio FX rate risk Value Quantity Holding period dispersion FX rate Standard deviation Holding period Diversification effect Concentration of foreign currencies % change dependency
44. 44. Copyright © 2016 CapitaLogic Limited 44 Hedge the risk of a FX forward Long position in another FX forward Short position in another FX forward Forward hedge Long position in a foreign currency Short position in a foreign currency Foreign currency hedge ShortLong Forward position
45. 45. Copyright © 2016 CapitaLogic Limited 45 Time value of money Currency mis-match problem FX forwards analysis FX forwards market CNY non-deliverable forwards Outline
46. 46. Copyright © 2016 CapitaLogic Limited 46 Hypothetical sale of a FX forward A long position at time 0 Forward rate at time τ Value of a long position at time τ Sell and deposit cash until maturity T [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] ( ) [ ] ( ) 1 0 0 f 1 d 1 0 d f 2 0 d f τ f 2 d 1 τ τ f 1 d 2 d 1 d 2 1 d 2 1 f = S exp(-r T) - K exp(-r T) = 0 K = S exp (r -r )T K = S exp (r -r )(T-τ) S exp -r (T-τ) = K exp -r (T-τ) f = S exp -r (T-τ) - K exp -r (T-τ) K exp -r (T-τ) - K exp -r (T-τ) = K - K exp -r (T-τ) K - K exp - = [ ] [ ]d d 2 1r (T-τ) exp r (T-τ) = K - K
47. 47. Copyright © 2016 CapitaLogic Limited 47 A long-short portfolio Enter a long position at time 0 Enter a short position at time τ At maturity Selling of a FX forward = Entering a reverse position [ ] [ ] [ ] [ ] ( ) ( ) 1 0 0 f 1 d 1 0 d f 2 τ τ f 2 d 2 0 d f 1 2 T T T 1 T 2 2 1 f = S exp(-r T) - K exp(-r T) = 0 K = S exp (r -r )T f = S exp -r (T-τ) - K exp -r (T-τ) = 0 K = S exp (r -r )(T-τ) f - f = S - K - S - K = K - K
48. 48. Copyright © 2016 CapitaLogic Limited 48 Reverse position Long position Entering a short position with the same maturity day At maturity Net payoff = (ST - K1) - (ST - K2) = K2 - K1 Equivalent to close a long position Short position Entering a long position with the same maturity day At maturity Net payoff = (ST - K2) - (ST - K1) = K1 - K2 Equivalent to close a short position
49. 49. Copyright © 2016 CapitaLogic Limited 49 Closing a position Standard FX forwards contract Customized for investor in terms of foreign currency, maturity and quantity A bilateral agreement between an investor and a bank Cannot be transferred No secondary market An investor can NOT sell his FX forwards contract Market maker A bank which is always ready to quote a forward rate to enter a FX forwards contract with an investor An investor can always enter a position or a reverse position with a market marker By entering a reverse position, an investor can always reverse and close his existing FX forwards position A liquid FX forwards market Selling a FX forwards contract in fact means closing a FX forward position by entering a reverse position Market markers create a liquid FX forwards market
50. 50. Copyright © 2016 CapitaLogic Limited 50 Close out netting agreement An agreement between an investor and a bank Covering all FX forwards entered between the two parties Allowing FX forward positions with same underlying currency and maturity to offset among one another for settlement at maturity
51. 51. Copyright © 2016 CapitaLogic Limited 51 Spot market vs forward market Spot market Domestic currency and foreign currency are exchanged on spot in accordance with the current FX rate Forward market A market in which FX forward transactions are entered by quoting the forward rates directly without any upfront cash flows Forward market is compatible in size with spot market As such, the forward FX rates take an active role to drive the current FX rates through the interest rate parity
52. 52. Copyright © 2016 CapitaLogic Limited 52 Over-the-counter An investor and a bank enter a FX forward through private negotiation High degree of customization High confidentiality Loosely regulated Subject to default risk Primarily protected by contract law through civil litigation Resulting unknown systemic risk to regulators Nowadays, banks in many developed countries must report their FX forwards positions to the Central Trade Repository
53. 53. Copyright © 2016 CapitaLogic Limited 53 Bank business model – service based Revenue A bank enters a FX forward with an investor Charges a service fee Due to the strong competition among banks, very slim profit is made for providing services on FX forwards
54. 54. Copyright © 2016 CapitaLogic Limited 54 Bank business model – position based If the bank’s position is consistent with its expectation on the trend of FX rate Keep the position If the bank’s position is consistent with its expectation on the trend of FX rate Enter a reverse position with foreign currency or another FX forward
55. 55. Copyright © 2016 CapitaLogic Limited 55 Default risk Default At maturity, an investor obligated to pay does not pay the bank Regular settlement Before maturity The long position deposits K - S0 to the short position when S0 < K The short position deposits S0 - K to the long position when S0 > K In almost all cases, for a period of less than one year | S0 - K | < 25% of K
56. 56. Copyright © 2016 CapitaLogic Limited 56 Time value of money Currency mis-match problem FX forwards analysis FX forwards market CNY non-deliverable forwards Outline
57. 57. Copyright © 2016 CapitaLogic Limited 57 CNY non-deliverable forwards Developed by the HKMA, TMA and major retail banks in Hong Kong Launched in late 2005 To facilitate the growing market of CNY due to the hedging and investment objectives of small and medium size investors in retail market Small transaction size USD 10,000 Short maturities 1, 2, 3, 6, 12 months Available from retail banking services Lower service fee due to strong competition
58. 58. Copyright © 2016 CapitaLogic Limited 58 Product description Indirect quote for FX ratesDirect quote for FX rates ShortBank payoffLongInvestor payoff Quantity × K Notional amount CNYQuantity 1 / KForward rateKStrike rate 1 / ST Settlement rate ST FX rate at maturity Product descriptionLecture convention
59. 59. Copyright © 2016 CapitaLogic Limited 59 Payoff ( ) T T Forward rate Payoff = Notional amount × 1 - Settlement rate 1 K= Quantity × K× 1 - 1 S = - Quantity × S - K                  
60. 60. Copyright © 2016 CapitaLogic Limited 60 Other features No explicit service charge Embedded in strike rate For a long position, strike rate higher than theoretical rate For a short position, strike rate lower than theoretical rate Market marker When there is an enquiry, the bank must propose a strike rate No secondary market Hold to maturity Collaterals Notional amount of liquid assets Example 5.8