Table 3-1 reports exchange rates not only against the US dollar, but also against the euro and the pound sterling. (Each row gives the price of the dollar, euro, and pound, respectively, in terms of a different currency.) At the same time, the table gives the spot dollar prices of the euro 1$1.3221 per euro2 and the pound sterling 1$1.5539 per pound2. Pick any five currencies from the table and show that the three quoted spot exchange rates (in terms of dollars, euros, and pounds) approximately rule out triangular arbitrage. Why do we need to add the word "approximately"?

Exchange Rate Quotations TABLE 3-1 CURRENCIES FX EFFECTIVE INDICES Bank of England Indices 114 10T3 1003169 UK 1457 144.31434 USA 110.5 116 Switzerland 2434 M27 .7 811 Deer New Zealand 1146 Source: Bank of ErgandNew Sterling ERI boce Jan 2005 100ther indices base average 1990 90 1159 1218 Euro 603 950494.43 100, Indox rebased I/2/05, for furthor information about ER's se www.ban ofengland.co.uk 60 EURO DOLLAR POUND Clasing Day's Closing Day's Clsing Day's (Jey) 3 2025 0.0648 42338 0.71 49761 00959 ouble) 32 2100 0.0300 425833 0.0442 50.0495 00c01 Cosng Day's Cosing Day's Clasing Day's Md Cur (Peso) 5.3015 00077 70089 0 0240 82378 00198 Pland (AS 1.0545 0.0050 1.3941 185 00092 Roran. dlewLeu) 34133 .0.0294 45125-0.0300 5 3037-00408 Dina) 0.3770 Boliia (Bolan 69100 0.4985 00010 0.5858 0.0006 Russia 91354 00179 10.7371 00100 SArabia (R) 3.7503 0,0001 4981 0,0097 82T4 003 (S3) 12453 -0.0014 1.6464 0.0015 1.9350 00003 C$) 1.0208 ,01 10 1.3495-00119, 1.5861-00156 SuthAfrica (R) 99518-00399 131568-00268 154636-00436 Pesol 500.500.5.0500661 686-53619277 702-71138 suth Korea 1112ca 1.22501476 a3 4520tlasz as214 (SK) 65789 0.0018 5976 0.0195 102225 00123 S) 09351 0.0002 1 2362 .0027 14530 00017 (TS) 7180 0.0795 39 2887 0.0276 46.1773 0003 ( 306300 0.0300404944 0.1192 47.5944 00909 (Dinar) 16248 -0.0049 21481 0,0023 2.5247 00052 (Lira) 18774 -0.0188 24320 -0.0199 2.9171 00265 Drhamo36729 0.0000 48558 0.0095 5.7072 00052 (RS) 2.1309 0.0027 2.8172 00090 3.3111 00072 u 6.1335 00027 8.1088 00124 9.5305 00047eden Pso 1897.17 136300 2508.15 130615 29472 18 4083 tzerland Costa Rca (Colon 498.980 00300 659 677 12573 775341 06772 lawan Caech Rap (ocua) 19.3473 0.1597 255780 0105 30.0627 02200 Denntark 5.6394 00115 7,4555 0006 87627 00098u 92398 00182 10.8598 00102 10.2625 0002 120619 00113 Egyp 6.980 UK(06436)" ro onth 15539 0.0014 03509 0.0010 Font) 223.101 3.1794 2949503 6150 346 655 4.6122 R 57.0750 0.1850 75.4560 03925 88.6850 03699 ladres (Rapah 980500 12500129627 419965 152355 336230 178038 (Sh) 3.6120 0.0023 4.7753 0E4 5.6125 0.0017 15529 0.0000 03518 0,0000 5510 0.0003 08544 0.0000 6232 8 31 9241 19078.9 Uraine (rywna) 81376 0.0150 10.7532 0.0014 12.6445 00115 (Peso) 20 3250 0.4500 27:5317 0.649 323590 0.23 Y 97.3850 0.9900 128.748 0630 151322 1.3957 973715-00010 128750 - 151270 .0.0014 97.3382 00021 128.75100037 151 160 0.0013 1.3221 0.0026 15539 0.0014 97.0400 00110 128584 00522 150509 00441 e ear One ar enezuela Bdinat Fuerte) 62921 3251 0.0003 1.5510 00003 83135 0.0164 9.7770 00091 Dorg) 210180 .0000 277358 61.2433 32668.8 382180 112.242 02203 131922 01231 Diror)0.2847 00003 03764 00004 0.4424 (M5) 3.0935 00105 4.0888 00219 48058 00207 Mexioo(New Pesz) 12.7217 01774 168187 02009 19.167 02669 New Zeeland (NZS)1.2652 00106 16726 00173 1659 00183 Euro(0 554) (Euro) 13221 0.0020 Naira) 159.700 08000 211.131 14703 248150 1.4735 One Month 1.1749 00000 57702 00076 75285 00050 8650 0.0035 Three Month 98.4750 0100 130,189 02093 153.015 0.1583 One Yor Pakistanu (Nen Sel)2.7280 00060 36066 00003 4.2389 00054 Phippines 42.2400 1000 55.8434 02418 65.6347 02165 0.6597-0,0011 08721 0.0002 0250-00007. Rates are derived from WWResters at 4pm(Londen time The dlosing mid-pointrates for the Euro and Cagainst the S are shawn in brackets The other Figunesis the dolar columnof both the Euroand Serlig ro sa e ist e reciprocal kr in ire w market colier on erecy deno nate y 1 . Sone w uesa ronded by the FT. Thee chang, rates printed this table are a oa a ble ntereet at http:/rww.FT.cominarketsdata Euro Locking Rates Austrian Schling 13.7603 B pun/Lembourz 340.75 Irish Punt 0.787 564, Itallian Lira193627, Matn 0 4293 Netherlands Guilder 2.20371,Portuguese Esxcudb 200.482, Slovenia Tolar 239.64,Spanibh Peseto 166386 franc 40 3399. Cyprus 0.585274.Finnish Markka 5.94572, Franch Franc 6.55057,Gorman Mark 1.95583, Greek Drachma