Review Session

Functions of Money Medium of Exchange Store of Value Unit of Accounting

Examples of Exchange Rates (1/29/13) Direct Quotes (U.S. Perspective) Swiss Franc 1.0852 CHF 1 = $ 1.0852 Euro 1.3491 € 1 = $ 1.3491 British Pound 1.5759 £ 1 = $ 1.5759 Japanese Yen 0.01103 ¥ 1 = $ 0.01103 http://finance.yahoo.com/currency?u Indirect Quotes Swiss Franc 0.9215 $1 = CHF 0.9215 Euro 0.7412 $1 = € 0.7412 British Pound 0.6346 $1 = £ 0.6346 Japanese Yen 90.6545 $1 = ¥ 90.6545

Examples of Exchange Rates (4/30/13) Direct Quotes (U.S. Perspective) Swiss Franc 1.0754 CHF 1 = $ 1.0754 Euro 1.3168 € 1 = $ 1.3168 British Pound 1.5534 £ 1 = $ 1.5534 Japanese Yen 0.010256 ¥ 1 = $ 0.010256 http://finance.yahoo.com/currency?u Indirect Quotes Swiss Franc 0.9299 $1 = CHF 0.9299 Euro 0.7594 $1 = € 0.7594 British Pound 0.6437 $1 = £ 0.6437 Japanese Yen 97.505 $1 = ¥ 97.505

The Basic Relationship (FA is a financial asset; RA is a real asset) MU money P  FA 1 2 L n RA

Suppose a Danish Krona buys 1 bag of good stuff 1 DKK

And $1 buys 5 bags of good stuff Then $1 = DKK 5 And DKK 1 = $ 0.20

Now, suppose $1 buys 2 bags of better stuff

And €1 buys 3 bags of the better stuff Then €1 = $1.50 And $1 = € 0.67

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

Generic Currency Arbitrage: Same Time New York Exchange rate Exchange rate Brussels London Exchange rate Requires three locations and means of exchange

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

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)

Yield Curve Upward sloping yield curve Flat yield curve Downward sloping yield curve R Convexity R Convexity R Convexity

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

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

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

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

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

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

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 http://www.smartmoney.com/investing/bonds/the-living-yield-curve-7923

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?

Examples of Exchange Rates (9/3/09) Direct Quotes (U.S. Perspective) Swiss Franc 0.9416 CHF 1 = $ 0.9416 Euro 1.4257 € 1 = $ 1.4257 British Pound 1.6321 £ 1 = $ 1.6321 Japanese Yen 0.0108 ¥ 1 = $ 0.0108 http://finance.yahoo.com/currency?u Indirect Quotes Swiss Franc 1.062 $1 = CHF 1.062 Euro 0.7014 $1 = € 0.7014 British Pound 0.6127 $1 = £ 0.6127 Japanese Yen 92.6950 $1 = ¥ 92.695

Examples of Exchange Rates (11/20/09) Direct Quotes (U.S. Perspective) Swiss Franc 0.9824 CHF 1 = $ 0.9824 Euro 1.4865 € 1 = $ 1.4865 British Pound 1.6508 £ 1 = $ 1.6508 Japanese Yen 0.0112 ¥ 1 = $ 0.0112 http://finance.yahoo.com/currency?u Indirect Quotes Swiss Franc 1.0179 $1 = CHF 1.062 Euro 0.6727 $1 = € 0.6727 British Pound 0.6059 $1 = £ 0.6059 Japanese Yen 88.905 $1 = ¥ 88.905

Examples of Exchange Rates (9/2/11) Direct Quotes (U.S. Perspective) Swiss Franc 1.2692 CHF 1 = $ 1.2692 Euro 1.4209 € 1 = $ 1.4209 British Pound 1.622 £ 1 = $ 1.622 Japanese Yen 0.01297 ¥ 1 = $ 0.01297 http://finance.yahoo.com/currency?u Indirect Quotes Swiss Franc 0.7879 $1 = CHF 0.7879 Euro 0.7038 $1 = € 0.7038 British Pound 0.6165 $1 = £ 0.6165 Japanese Yen 77.085 $1 = ¥ 77.085

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)

Examples of Exchange Rates (11/28/11) Direct Quotes (U.S. Perspective) Swiss Franc 1.0837 CHF 1 = $ 1.0837 Euro 1.3313 € 1 = $ 1.3313 British Pound 1.5502 £ 1 = $ 1.5502 Japanese Yen 0.01281 ¥ 1 = $ 0.01281 http://finance.yahoo.com/currency?u Indirect Quotes Swiss Franc 0.9228 $1 = CHF 0.9228 Euro 0.7511 $1 = € 0.7511 British Pound 0.6451 $1 = £ 0.6451 Japanese Yen 78.075 $1 = ¥ 78.075