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Review Session
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Functions of Money Medium of Exchange Store of Value
Unit of Accounting
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Examples of Exchange Rates (1/29/13)
Direct Quotes (U.S. Perspective) Swiss Franc CHF 1 = $ Euro € 1 = $ British Pound £ 1 = $ Japanese Yen ¥ 1 = $ Indirect Quotes Swiss Franc $1 = CHF Euro $1 = € British Pound $1 = £ Japanese Yen $1 = ¥
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Examples of Exchange Rates (4/30/13)
Direct Quotes (U.S. Perspective) Swiss Franc CHF 1 = $ Euro € 1 = $ British Pound £ 1 = $ Japanese Yen ¥ 1 = $ Indirect Quotes Swiss Franc $1 = CHF Euro $1 = € British Pound $1 = £ Japanese Yen $1 = ¥
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The Basic Relationship (FA is a financial asset; RA is a real asset)
MU money P FA 1 2 L n RA
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Suppose a Danish Krona buys 1 bag of good stuff
1 DKK
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And $1 buys 5 bags of good stuff
Then $1 = DKK 5 And DKK 1 = $ 0.20
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Now, suppose $1 buys 2 bags of better stuff
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And €1 buys 3 bags of the better stuff
Then €1 = $1.50 And $1 = € 0.67
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Would be equilibrium if €1 = £0.90
Cross Rate Example: $1,035,000 - $1,000,000 = $35,000 $1,000,000 New York Dollar Weakens Dollar Strengthens €1 = $1.50 $1 = £ 0.60 Brussels London £ 1 = € 1.15 € 690,000 £ 600,000 Pound Weakens Would be equilibrium if €1 = £0.90
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Generic Currency Arbitrage: Same Time
New York Exchange rate Exchange rate Brussels London Exchange rate Requires three locations and means of exchange
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Generic Currency Arbitrage: Across Time
NY today FRA today Exchange rate %i or prices %i or prices NY later FRA later Exchange rate 2 locations, 2 dates Means for transition
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Lessons Learned from Currency Arbitrage:
Interest Rate Parity Real rate same for every currency Purchasing Power Parity A Dollar (or Euro, or Pound, or Franc, etc.) buys same stuff in every country (except for cost of transport)
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Yield Curve Upward sloping yield curve Flat yield curve
Downward sloping yield curve R Convexity R Convexity R Convexity
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Generic Rate Arbitrage: No Coupon
Day 90 Interest rate or derivative Interest rate Day 120 Initial Time Interest rate Requires three dates and means of transfer across time
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Generic Interest Rate Arbitrage: Different Coupons
(Example: 8%) Price too high Sell two bonds C+x (Example: 10%) C–x (Example: 6%) Buy one of each Requires three equally-spaced coupons, with prices out of balance
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Generic Interest Rate Arbitrage: Different Coupons
C+x (Example: 10%) C–x (Example: 6%) Sell one of each C (Example: 8%) Price too low Buy two bonds Requires three equally-spaced coupons, with prices out of balance
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Generic Interest Rate Arbitrage: Same Coupon, Different Maturities
(Example: 7 yrs) Price too high (YTM too low) Sell two bonds M–x (Example: 6 yrs) M+x (Example: 8 yrs) Buy one of each Requires three equally-spaced maturities, with prices out of balance
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Generic Interest Rate Arbitrage: Same Coupon, Different Maturities
M–x (Example: 6 yrs) Sell one of each M+x (Example: 8 yrs) M (Example: 7 yrs) Price too low (YTM too high) Buy two bonds Requires three equally-spaced maturities, with prices out of balance
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Lessons Learned from Bond Arbitrage:
Yield curve behavior must be monotonous in any currency If upward sloping anywhere, must be upward sloping overall If downward sloping anywhere, must be downward sloping overall Slope must gradually move toward zero at ever diminishing rate until curve becomes flat Once curve becomes flat, it must remain flat There can be no kinks in the curve Yield curves for different risk classes (say, AAA versus junk) may rest at different risk levels, but quality gap must be same overall
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Lessons Learned from Bond Arbitrage:
Yield curves may have different shapes for bonds in different currencies, but Once bond prices are adjusted for forward currency exchange rates, yield curves must have same shape Once bond prices are adjusted for forward currency exchange rates, quality gap must be same overall Derivatives can be very useful in managing interest rate risk Interest rate derivatives must conform to the shape of the yield curve
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Questions for discussion:
What is the marginal utility of money? What is the price of money? What is the marginal utility of a financial asset? What is the marginal utility of a real asset? Consider the ratio of marginal utility to price. What does it mean for this ratio to be the same for all financial assets and real assets in the world?
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Examples of Exchange Rates (9/3/09)
Direct Quotes (U.S. Perspective) Swiss Franc CHF 1 = $ Euro € 1 = $ British Pound £ 1 = $ Japanese Yen ¥ 1 = $ Indirect Quotes Swiss Franc $1 = CHF 1.062 Euro $1 = € British Pound $1 = £ Japanese Yen $1 = ¥
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Examples of Exchange Rates (11/20/09)
Direct Quotes (U.S. Perspective) Swiss Franc CHF 1 = $ Euro € 1 = $ British Pound £ 1 = $ Japanese Yen ¥ 1 = $ Indirect Quotes Swiss Franc $1 = CHF 1.062 Euro $1 = € British Pound $1 = £ Japanese Yen $1 = ¥
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Examples of Exchange Rates (9/2/11)
Direct Quotes (U.S. Perspective) Swiss Franc CHF 1 = $ Euro € 1 = $ British Pound £ 1 = $ 1.622 Japanese Yen ¥ 1 = $ Indirect Quotes Swiss Franc $1 = CHF Euro $1 = € British Pound $1 = £ Japanese Yen $1 = ¥
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A Helpful Concept: Arrow-Debreu Securities
MU money P FA 1 2 L n RA Arrow-Debreau securities: One of these pays a dollar if a specific state of the world occurs at a specific time, but pays nothing otherwise (a lottery ticket also works this way, but covers a very limited span of events)
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Examples of Exchange Rates (11/28/11)
Direct Quotes (U.S. Perspective) Swiss Franc CHF 1 = $ Euro € 1 = $ British Pound £ 1 = $ Japanese Yen ¥ 1 = $ Indirect Quotes Swiss Franc $1 = CHF Euro $1 = € British Pound $1 = £ Japanese Yen $1 = ¥
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