15.401
15.401 Finance Theory
MIT Sloan MBA Program
Andrew W. Lo
Harris & Harris Group Professor, MIT Sloan School
Lectures 8–9: Forward and Futures Contracts
© 2007–2008 by Andrew W. Lo
,Critical Concepts 15.401
Motivation
Forward Contracts
Futures Contract
Valuation of Forwards and Futures
Applications
Extensions and Qualifications
Readings:
Brealey, Myers, and Allen Chapters 27
© 2007–2008 by Andrew W. Lo Slide 2
Lecture 8–9: Forwards and Futures
,Motivation 15.401
Your company, based in the U.S., supplies machine tools to
customers in Germany and Brazil. Prices are quoted in each country’s
currency, so fluctuations in the € / $ and R / $ exchange rates have a
big impact on the firm’s revenues. How can the firm reduce (or
‘hedge’) these risks?
Your firm is thinking about issuing 10-year convertible bonds. In the
past, the firm has issued straight debt with a yield-to-maturity of 8.2%.
If the new bonds are convertible into 20 shares of stocks, per $1,000
face value, what interest rate will the firm have to pay on the bonds?
You have the opportunity to buy a mine with 1 million kgs of copper for
$400,000. Copper has a price of $2.2 / kg, mining costs are $2 / kg,
and you can delay extraction one year. How valuable is the option to
delay? Is the mine a good deal?
© 2007–2008 by Andrew W. Lo Slide 3
Lecture 8–9: Forwards and Futures
, Motivation 15.401
Exchange Rates, 1995 – 2003
1.6 4.0
1.4 3.5
1.2 3.0
1.0 2.5
0.8 2.0
0.6 1.5
0.4 1.0
Euro / $ (left scale)
0.2 Real / $ (right scale) 0.5
0.0 0.0
Jan-95 Jan-96 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02 Jan-03
© 2007–2008 by Andrew W. Lo Slide 4
Lecture 8–9: Forwards and Futures
15.401 Finance Theory
MIT Sloan MBA Program
Andrew W. Lo
Harris & Harris Group Professor, MIT Sloan School
Lectures 8–9: Forward and Futures Contracts
© 2007–2008 by Andrew W. Lo
,Critical Concepts 15.401
Motivation
Forward Contracts
Futures Contract
Valuation of Forwards and Futures
Applications
Extensions and Qualifications
Readings:
Brealey, Myers, and Allen Chapters 27
© 2007–2008 by Andrew W. Lo Slide 2
Lecture 8–9: Forwards and Futures
,Motivation 15.401
Your company, based in the U.S., supplies machine tools to
customers in Germany and Brazil. Prices are quoted in each country’s
currency, so fluctuations in the € / $ and R / $ exchange rates have a
big impact on the firm’s revenues. How can the firm reduce (or
‘hedge’) these risks?
Your firm is thinking about issuing 10-year convertible bonds. In the
past, the firm has issued straight debt with a yield-to-maturity of 8.2%.
If the new bonds are convertible into 20 shares of stocks, per $1,000
face value, what interest rate will the firm have to pay on the bonds?
You have the opportunity to buy a mine with 1 million kgs of copper for
$400,000. Copper has a price of $2.2 / kg, mining costs are $2 / kg,
and you can delay extraction one year. How valuable is the option to
delay? Is the mine a good deal?
© 2007–2008 by Andrew W. Lo Slide 3
Lecture 8–9: Forwards and Futures
, Motivation 15.401
Exchange Rates, 1995 – 2003
1.6 4.0
1.4 3.5
1.2 3.0
1.0 2.5
0.8 2.0
0.6 1.5
0.4 1.0
Euro / $ (left scale)
0.2 Real / $ (right scale) 0.5
0.0 0.0
Jan-95 Jan-96 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02 Jan-03
© 2007–2008 by Andrew W. Lo Slide 4
Lecture 8–9: Forwards and Futures
