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Chapter 11 - International arbitrage. In this chapter, the learning objectives are: To define arbitrage and the no-arbitrage condition; to describe two-point, three-point and multi-point arbitrage in the foreign exchange market; to describe commodity arbitrage;…
Chapter 11 International Arbitrage Objectives • To define arbitrage and the no-arbitrage condition • To describe two-point, three-point and multi-point arbitrage in the foreign exchange market • To describe commodity arbitrage (cont.) Copyright 2010 McGraw-Hill Australia Pty Ltd PPTs t/a International Finance: An Analytical Approach 3e by Imad A Moosa Slides prepared by Afaf Moosa 11-2 Objectives (cont.) • To describe covered interest arbitrage and show how the no-arbitrage condition can be used to determine the forward exchange rate • To describe uncovered arbitrage and introduce the concept of carry trade Copyright 2010 McGraw-Hill Australia Pty Ltd PPTs t/a International Finance: An Analytical Approach 3e by Imad A Moosa Slides prepared by Afaf Moosa 11-3 Definition of arbitrage • Arbitrage is generally defined as capitalising on a discrepancy in quoted prices as a result of the violation of an equilibrium (no-arbitrage) condition • The arbitrage process restores equilibrium via changes in the supply of and demand for the underlying commodity, asset or currency (cont.) Copyright 2010 McGraw-Hill Australia Pty Ltd PPTs t/a International Finance: An Analytical Approach 3e by Imad A Moosa Slides prepared by Afaf Moosa 11-4 Definition of arbitrage (cont.) • The importance of arbitrage is that no-arbitrage conditions are used for asset pricing, such that the equilibrium price of a financial asset is the price that is consistent with the underlying no-arbitrage condition Copyright 2010 McGraw-Hill Australia Pty Ltd PPTs t/a International Finance: An Analytical Approach 3e by Imad A Moosa Slides prepared by Afaf Moosa 11-5 Two-point arbitrage • Also known as spatial or locational arbitrage, it arises when the following condition is violated: S A ( x / y) SB ( x / y) Copyright 2010 McGraw-Hill Australia Pty Ltd PPTs t/a International Finance: An Analytical Approach 3e by Imad A Moosa Slides prepared by Afaf Moosa 11-6 Two-point arbitrage with bid-offer spreads • With bid-offer spreads the no-arbitrage condition becomes: Sb , A x / y Sa, B x / y Sa, A x / y Sb , B x / y Copyright 2010 McGraw-Hill Australia Pty Ltd PPTs t/a International Finance: An Analytical Approach 3e by Imad A Moosa Slides prepared by Afaf Moosa 11-7 Three-point (triangular) arbitrage • It is triggered when cross exchange rates are inconsistent, that is, when the following condition is violated: S ( x / z) S ( x / y) S ( y / z) Copyright 2010 McGraw-Hill Australia Pty Ltd PPTs t/a International Finance: An Analytical Approach 3e by Imad A Moosa Slides prepared by Afaf Moosa 11-8 Profitable/unprofitable sequences (b) Profitable sequence (a) Unprofitable sequence x x S ( x / y) z S ( x / z) S ( y / z) y z Copyright 2010 McGraw-Hill Australia Pty Ltd PPTs t/a International Finance: An Analytical Approach 3e by Imad A Moosa Slides prepared by Afaf Moosa y 11-9 Multipoint arbitrage • The condition precluding multipoint arbitrage is: S ( x1 / x2 ) S ( x2 / x3 ) S ( xn / x1 ) Copyright 2010 McGraw-Hill Australia Pty Ltd PPTs t/a International Finance: An Analytical Approach 3e by Imad A Moosa Slides prepared by Afaf Moosa 11-10 Covered interest arbitrage • Covered interest arbitrage is triggered by the violation of the covered interest parity (CIP) condition, which describes the equilibrium relation between the spot exchange rate, the forward exchange rate, domestic interest rates and foreign interest rates Copyright 2010 McGraw-Hill Australia Pty Ltd PPTs t/a International Finance: An Analytical Approach 3e by Imad A Moosa Slides prepared by Afaf Moosa 11-14 Return on Investments Investor (K) Foreign investment Converting at spot rate Domestic investment K S Investing in foreign assets K (1 i ) S Reconverting at forward rate KF (1 i ) S K (1 i ) Copyright 2010 McGraw-Hill Australia Pty Ltd PPTs t/a International Finance: An Analytical Approach 3e by Imad A Moosa Slides prepared by Afaf Moosa 11-15 The CIP equilibrium condition F (1 i ) (1 i ) S i i f Copyright 2010 McGraw-Hill Australia Pty Ltd PPTs t/a International Finance: An Analytical Approach 3e by Imad A Moosa Slides prepared by Afaf Moosa 11-16 Covered interest arbitrage Foreign domestic Domestic foreign Borrowing domestic currency Converting at spot rate Investing at foreign rate 1 unit 1 unit 1 unit Converting at spot rate S S S Loan repayment Loan repayment (1 i ) S Reconverting at forward rate Borrowing foreign currency F (1 i ) S Investing at domestic rate S (1 i ) i i S ( 1 i ) F Covered margin Covered margin F (1 i ) S S (1 i ) F (1 i ) Reconverting at forward rate (1 i ) Copyright 2010 McGraw-Hill Australia Pty Ltd PPTs t/a International Finance: An Analytical Approach 3e by Imad A Moosa Slides prepared by Afaf Moosa 11-17 Profit from covered arbitrage (domestic→foreign) π F (1 i ) (1 i ) S π i i f Copyright 2010 McGraw-Hill Australia Pty Ltd PPTs t/a International Finance: An Analytical Approach 3e by Imad A Moosa Slides prepared by Afaf Moosa 11-18 The interest parity forward rate F i S i Copyright 2010 McGraw-Hill Australia Pty Ltd PPTs t/a International Finance: An Analytical Approach 3e by Imad A Moosa Slides prepared by Afaf Moosa 11-19 Covered arbitrage with bid-offer spreads (domestic→foreign) π Fb (1 ib ) (1 ia ) Sa π ib ia f m Copyright 2010 McGraw-Hill Australia Pty Ltd PPTs t/a International Finance: An Analytical Approach 3e by Imad A Moosa Slides prepared by Afaf Moosa 11-20 Covered arbitrage with bid-offer spreads (foreign→domestic) π Sb (1 ib ) (1 ia ) Fa π ib ia f m Copyright 2010 McGraw-Hill Australia Pty Ltd PPTs t/a International Finance: An Analytical Approach 3e by Imad A Moosa Slides prepared by Afaf Moosa 11-21 Arbitrage with bid-offer spreads Foreign domestic Domestic foreign Borrowing domestic currency Converting at spot offer rate Investing at foreign bid rate Reconverting at forward bid rate 1 unit 1 unit 1 unit Borrowing foreign currency Converting at spot bid rate Sa Sb S Loan repayment Loan repayment (1 ib ) Sa Fb (1 ib ) Sa Sb (1 ib ) ia Covered margin Fb (1 ib ) Sa Investing at domestic bid rate (1 ia ) ia Sb (1 ib ) Fa Reconverting at forward offer rate Covered margin Sb (1 ib ) Fa (1 ia ) Copyright 2010 McGraw-Hill Australia Pty Ltd PPTs t/a International Finance: An Analytical Approach 3e by Imad A Moosa Slides prepared by Afaf Moosa 11-22 Uncovered interest arbitrage • Uncovered arbitrage is triggered by the violation of the uncovered interest parity (UIP) condition It is described as ‘uncovered’ because, unlike covered arbitrage, the long currency position is not covered in the forward market but rather left uncovered or open Copyright 2010 McGraw-Hill Australia Pty Ltd PPTs t/a International Finance: An Analytical Approach 3e by Imad A Moosa Slides prepared by Afaf Moosa 11-23 Carry trade • Carry trade is a kind of uncovered interest arbitrage in which a short position is taken on a low-interest currency and a long position is taken on a highinterest currency Copyright 2010 McGraw-Hill Australia Pty Ltd PPTs t/a International Finance: An Analytical Approach 3e by Imad A Moosa Slides prepared by Afaf Moosa 11-24 Return on domestic investment and foreign investment (with uncovered position) Investor (K) Foreign Investment Converting at spot rate Domestic Investment K S Investing in foreign assets K (1 i ) S Reconverting at expected spot rate KS e (1 i ) S K (1 i ) Copyright 2010 McGraw-Hill Australia Pty Ltd PPTs t/a International Finance: An Analytical Approach 3e by Imad A Moosa Slides prepared by Afaf Moosa 11-25 The UIP condition i i i Se (1 i ) S S e Copyright 2010 McGraw-Hill Australia Pty Ltd PPTs t/a International Finance: An Analytical Approach 3e by Imad A Moosa Slides prepared by Afaf Moosa 11-26 Uncovered interest arbitrage Foreign domestic Domestic foreign Borrowing domestic currency Converting at spot rate Investing at foreign rate 1 unit S0 1 unit 1 unit Converting at spot rate S0 S Loan repayment Loan repayment (1 i ) S0 Reconverting at spot rate Borrowing foreign currency S1 (1 i ) S0 Investing at domestic rate S0 (1 i ) i i S0 (1 i ) S1 Covered margin Covered margin S1 (1 i ) S0 S0 (1 i ) S1 (1 i ) Reconverting at spot rate (1 i ) Copyright 2010 McGraw-Hill Australia Pty Ltd PPTs t/a International Finance: An Analytical Approach 3e by Imad A Moosa Slides prepared by Afaf Moosa 11-27 Uncovered arbitrage with bid-offer spreads Foreign domestic Domestic foreign Borrowing domestic currency Converting at spot offer rate Investing at foreign bid rate Reconverting at spot bid rate 1 unit Borrowing foreign currency 1 unit 1 unit Converting at spot bid rate Sa Sb S Loan repayment Loan repayment (1 ib ) Sa Sb1 (1 ib ) Sa Sb 0 (1 ib ) ia Covered margin Sb1 (1 ib ) Sa Investing at domestic bid rate (1 ia ) ia Sb (1 ib ) S a1 Reconverting at spot offer rate Covered margin Sb (1 ib ) S a1 (1 ia ) Copyright 2010 McGraw-Hill Australia Pty Ltd PPTs t/a International Finance: An Analytical Approach 3e by Imad A Moosa Slides prepared by Afaf Moosa 11-28 ... McGraw-Hill Australia Pty Ltd PPTs t/a International Finance: An Analytical Approach 3e by Imad A Moosa Slides prepared by Afaf Moosa 1 1- 6 Two-point arbitrage with bid-offer spreads • With bid-offer... Copyright 2010 McGraw-Hill Australia Pty Ltd PPTs t/a International Finance: An Analytical Approach 3e by Imad A Moosa Slides prepared by Afaf Moosa 1 1- 11 Commodity arbitrage • The no-arbitrage condition... condition Copyright 2010 McGraw-Hill Australia Pty Ltd PPTs t/a International Finance: An Analytical Approach 3e by Imad A Moosa Slides prepared by Afaf Moosa 1 1- 5 Two-point arbitrage • Also known