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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 1.0852CHF 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 Franc0.9215$1 = CHF 0.9215
• Euro 0.7412
• $1 = € 0.7412
• British Pound 0.6346$1 = £ 0.6346
• Japanese Yen 90.6545$1 = ¥ 90.6545
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Examples of Exchange Rates (4/30/13)
Direct Quotes (U.S. Perspective)
• Swiss Franc 1.0754CHF 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 Franc0.9299$1 = CHF 0.9299
• Euro 0.7594$1 = € 0.7594
• British Pound 0.6437$1 = £ 0.6437
• Japanese Yen 97.505$1 = ¥ 97.505
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The Basic Relationship (FA is a financial asset; RA is a real asset)
MU money
P moneyMU FA1
P FA1
MU FA2
P FA2
L MU FAnP FAn
MU RA1
P RA1
MU RA2
P RA2
L MU RAnP RAn
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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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Cross Rate Example:
NewYork
London Brussels
$1 =
£ 0.6
0€1 = $1.50
£ 1 = € 1.15
$1,035,000 - $1,000,000 = $35,000
£ 600,000 € 690,000
DollarWeakens
Pound Weakens
DollarStrengthens
$1,000,000
Would be equilibrium if €1 = £0.90
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Generic Currency Arbitrage: Same Time
NewYork
London Brussels
Requires three locations and means of exchange
Excha
nge r
ateExchange rate
Exchange rate
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Generic Currency Arbitrage: Across Time
FRAtoday
2 locations, 2 dates
NYtoday
FRAlater
%i or prices
NYlater
%i or prices
Means for transition
Exchange rate
Exchange rate
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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
Initial Time Day 120
Requires three dates and means of transfer across time
Inter
est r
ateInterest rate
or derivative
Interest rate
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Generic Interest Rate Arbitrage: Different Coupons
C(Example: 8%)
C–x(Example: 6%)
C+x(Example: 10%)
Requires three equally-spaced coupons, with prices out of balance
Price too high Sell two bonds
Buy one of each
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Generic Interest Rate Arbitrage: Different Coupons
C(Example: 8%)
C–x(Example: 6%)
C+x(Example: 10%)
Requires three equally-spaced coupons, with prices out of balance
Price too low Buy two bonds
Sell one of each
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Generic Interest Rate Arbitrage: Same Coupon, Different Maturities
M(Example: 7 yrs)
M–x(Example: 6 yrs)
M+x(Example: 8 yrs)
Requires three equally-spaced maturities, with prices out of balance
Price too high (YTM too low)
Sell two bonds
Buy one of each
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Generic Interest Rate Arbitrage: Same Coupon, Different Maturities
M(Example: 7 yrs)
M–x(Example: 6 yrs)
M+x(Example: 8 yrs)
Requires three equally-spaced maturities, with prices out of balance
Price too low(YTM too high)
Buy two bonds
Sell one of each
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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
http://www.smartmoney.com/investing/bonds/the-living-yield-curve-7923
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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 0.9416CHF 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 Franc1.062$1 = CHF 1.062
• Euro 0.7014$1 = € 0.7014
• British Pound 0.6127$1 = £ 0.6127
• Japanese Yen 92.6950$1 = ¥ 92.695
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Examples of Exchange Rates (11/20/09)
Direct Quotes (U.S. Perspective)
• Swiss Franc 0.9824CHF 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 Franc1.0179$1 = CHF 1.062
• Euro 0.6727$1 = € 0.6727
• British Pound 0.6059$1 = £ 0.6059
• Japanese Yen 88.905$1 = ¥ 88.905
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Examples of Exchange Rates (9/2/11)
Direct Quotes (U.S. Perspective)
• Swiss Franc 1.2692CHF 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 Franc0.7879$1 = CHF 0.7879
• Euro 0.7038$1 = € 0.7038
• British Pound 0.6165$1 = £ 0.6165
• Japanese Yen 77.085$1 = ¥ 77.085
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Examples of Exchange Rates (11/28/11)
Direct Quotes (U.S. Perspective)
• Swiss Franc 1.0837CHF 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 Franc0.9228$1 = CHF 0.9228
• Euro 0.7511$1 = € 0.7511
• British Pound 0.6451$1 = £ 0.6451
• Japanese Yen 78.075$1 = ¥ 78.075