Solutions Ch 4-6

# Solutions Ch 4-6 - Problem 4.2 Forward Premiums and...

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Problem 4.2 Forward Premiums and Discounts Calculate the percentage premium or discount. Quoted 180-day Percent premium Assumptions Spot rate Forward rate or discount Days forward 180 180 European euro (\$/euro) direct rate 0.8000 0.8160 4.0000% British pound (\$/pound) direct rate 1.5620 1.5300 -4.0973% Japanese yen (yen/\$) (Japanese Jen--> number would become too tiny --> indirect rate) 120.00 118.00 3.3898% Swiss franc (SF/\$) indirect rate 1.6000 1.6200 -2.4691% Hong Kong dollar (HK\$/\$) indirect rate 8.0000 7.8000 5.1282% Note that for the first two currency calculations (\$/euro and \$/pound), the calculation formula is: % premium = (F-S)/(S) x (360/180) While the calculation formula for the remaining currencies (all expressed as currency/\$) is: % premium = (S-F)/(F) x (360/180) Problem 4.4 Spot and forward quotes for the yen Calculate the forward premiums for the yen in Exhibit 4.5. a) Yen (yen/\$) Implied Calculated Assumptions Mid Rates Days Forward Forward Premium Spot 118.32 1 week 118.23 7 -5142.8571% 1 mo 117.82 30 -1200.0000% 2 mo 117.38 60 -600.0000% 3 mo 116.91 90 -400.0000% 4 mo 116.40 120 -300.0000% 5 mo 115.94 150 -240.0000% 6 mo 115.45 180 -200.0000% 9 mo 114.00 270 -133.3333% 1 yr 112.50 360 -100.0000% 2 yr 106.93 720 -50.0000% 3 yr 101.09 1,080 -33.3333% 4 yr 96.82 1,440 -25.0000% 5 yr 92.91 1,800 -20.0000% Forward premium = (S-F)/(F) x (360/days) b) The premium is gradually getting larger as the maturity lengthens to one year. After one year it seemingly stabilizes at about 5.5% to 5.6%. Problem 4.6 Traveling: Copenhagen to St. Petersburg What is the cross-rate? What is left? Assumptions Values Beginning your trip with Danish kroner 10,000.00 Spot rate (Dkr/\$) 8.5515 Spot rate (Roubles/\$) 30.962 a) Calculate the cross-rate Cross-rate (Dkr/rouble) 0.2762 cross-rate = (Dkr/\$) / (Rouble/\$) b) What would be the proceeds in Rubles? Converting your Danish kroner into Rubles 36,206.51 Proceeds = Danish kroner / (Dkr/rouble) Problem 4.7 Riskless profit on the franc Can you make a profit via triangular arbitrage? Assumptions Values Beginning funds in Swiss francs (SF) 10,000,000.00 Mt. Fuji Bank (yen/\$) 120.00 Mt. Rushmore Bank (SF/\$) 1.6000 JPY/USD = 80*1,6 = 128 --> better rate than going direct Matterhorn Bank (yen/SF) 80.00 Always convert back to the same currency we started with, otherwise we dont know if we made or lo Try Number 1: Start with SF to \$ Step 1: SF to \$ 6,250,000.00 Step 2: \$ to yen 750,000,000.00 Step 3: yen to SF 9,375,000.00 Profit? (625,000.00) A loss. Try Number 2: Start with SF to yen Step 1: SF to yen 800,000,000.00 Step 2: yen to \$ 6,666,666.67 Step 3: \$ to SF 10,666,666.67 Profit? 666,666.67 A profit. Forward rate > spot rate --> premium Forward rate < spot rate --> discount calculation flips A/B x B/C = A/C USD/CHF x CHF/EUR = USD/EUR If the USD/EUR is different possibility of arbitrage Not make Arbitrage to loose money

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Problem 4.8 Trans-Atlantic Arbitrage Can the arbitrager make a profit with these quotes? Assumptions Values Beginning funds \$1,000,000.00 Citibank NY quotes: Bid (\$/euro) we will sell at the bid rate 0.9650 Ask (\$/euro) we will buy at the ask rate 0.9670 Barclays London quotes: Bid (\$/euro) we will sell at the bid rate 0.9640 Ask (\$/euro) we will buy at the ask rate 0.9660 Arbitrage Strategy #1 Initial investment \$1,000,000.00 Buy euros from Barclays (at the ask rate) € 1,035,196.69 Sell euros to Citibank (at the bid rate) \$998,964.80 Arbitrage profit (loss) \$(1,035.20) Arbitrage Strategy #2 Initial investment \$1,000,000.00 Buy euros from Citibank (at the ask rate) € 1,035,196.69 Sell euros to Barclays (at the bid rate) \$997,929.61 Arbitrage profit (loss) \$(2,070.39) The arbitrager cannot make a profit using these quotes.
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