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Going to the World Cup (and what it says about arbitrage )

Going to the World Cup (and what it says about arbitrage ). Roberto Chang January 2014 Econ 336. The “ problem ”. A number of people I know are thinking about going to Brazil for the World Cup It is very expensive , so we need to make efficient financing decisions.

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Going to the World Cup (and what it says about arbitrage )

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  1. Going to theWorld Cup(and whatitsaysaboutarbitrage) Roberto Chang January 2014 Econ 336

  2. The “problem” • A number of people I know are thinkingaboutgoing to BrazilfortheWorld Cup • Itisveryexpensive, so weneed to makeefficientfinancingdecisions

  3. Theexchangeratequestion • Theysaytheywillneed, say, about 24000 Brazilianreais (BRL) each, byJuly (sixmonthsfromnow). • Friday’sspot exchangerate: 2.40 BRL per US$ • So, at currentrates,theamountinvolvedisabout US $ 10,000 • Butthe BRL/US$ exchangerate can move a lot, we are wonderingwhatisthebestway to plan to havethatamountfortheJulytrip.

  4. http://www.xe.com/currencycharts/?from=USD&to=BRL&view=5Y

  5. Coveringwith a forward contract • A forward contractisanagreementtoexchangecurrencies at a given date in thefuture, at a givenprice (theforward rate) • So, oneway to have 24000 BRL in sixmonthsis to set asidetodaysomeamount of dollars (say, x) in aninterestbearingaccount and enter a forward contract to exchange x*(1 + i$) dollarsforreais in July

  6. LetFBRL/$ be the forward exchangerate. • Thenforthe plan tosucceed, x * (1 + i$) * FBRL/$ = BR 24000 thatis, x = BRL 24000 / [(1 + i$) * FBRL/$ ]

  7. Isthere a cheaperway? • Thereisanalternative: onecouldtakesomeamount of dollarstoday, say z dollars, exchangethemforreaistoday, and savethereais in aninterestbearing BRL account • Ifthe (spot) exchangeratetoday (reais per dollar) is EBRL/$ and theinterestrateon BRL depositsisiBRL, weneed z* EBRL/$ *(1+ iBRL) = BRL 24000

  8. z* EBRL/$ *(1+ iBRL) = BRL 24000 Or, equivalently, z = BRL 24000/[EBRL/$ *(1+ iBRL) ]

  9. Thereis no free lunch! • Summarizing, there are twoways to plan to have 24000 BRL byJuly: x = BRL 24000 / [(1 + i$) * FBRL/$ ] z = BRL 24000/[EBRL/$ *(1+ iBRL) ] • But x and z must be equal!! • Why? Suppose x < z. Thenbyborrowingthe BRL 24000, obtaining z dollarstoday, and investing x in dollars, onewouldmake z – x instantly, at no cost, and withoutrisk.

  10. Implications of No Arbitrage • Itfollowsthat no arbitragerequires: x = BRL 24000 / [(1 + i$) * FBRL/$ ] = z = BRL 24000/[EBRL/$ *(1+ iBRL) ] thatis (1 + i$) * FBRL/$ = EBRL/$ *(1+ iBRL) or FBRL/$ = EBRL/$ *(1+ iBRL)/ (1 + i$)

  11. CoveredInterestParity • Thecondition FBRL/$= EBRL/$ *(1+ iBRL)/ (1 + i$) isknown as coveredinterestparity. As seen, itisanimplication of no arbitrage. • This can be usedtoinferthe forward exchangerate. Today, EBRL/$ = 2.4, and (approximately) i$ = 0.001, iBRL = 0.05025, so the forward rateshould be: FBRL/$ = 2.4* (1.05025)/(1.001) = 2.52

  12. Concepts • Exchange Rates: Spot and Forward • No Arbitrage • InterestParity

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