Finance Problems
and Solutions Collection
Finance Theory I
Part 2
Fall 2025
1
,CONTENTS CONTENTS
Contents
1 Questions 4
1.4 Forward and Futures ............................................................................. 4
1.5 Options ................................................................................................... 9
1.6 Risk & Portfolio Choice ...................................................................... 19
1.7 CAPM ................................................................................................... 31
1.8 Capital Budgeting ................................................................................ 42
2 Solutions 45
2.4 Forward and Futures ........................................................................... 45
2.5 Options ................................................................................................. 55
2.6 Risk & Portfolio Choice ...................................................................... 79
2.7 CAPM ................................................................................................... 90
2.8 Capital Budgeting .............................................................................. 104
3
, 1 QUESTIONS
1 Questions
1.4 Forward and Futures
1. During the summer you had to spend some time with your uncle, who
is a wheat farmer. Your uncle, knowing you are studying for an MBA
at Sloan, asked your help. He is afraid that the price of wheat will fall,
which will have a severe impact on his profits. Thus he asks you to
compute the 1yr forward price of wheat. He tells you that its current
price is $3.4 per bushel and interest rates are at 4%. However, he also
says that it is relatively expensive to store wheat for one year. Assume
that this cost, which must be paid upfront, runs at about $0.1 per
bushel. What is the 1yr forward price of wheat?
2. The Wall Street Journal gives the following futures prices for gold on
September 6, 2006:
Futures price ($/oz) 635.60 641.80 660.60 678.70
and the spot price of gold is $633.50/oz. Compute the (effective annu-
alize) interest rate implied by the futures prices for the corresponding
maturities.
3. Suppose that in 3 months the cost of a pound of Colombian coffee will
be either $1.25 or $2.25. The current price is $1.75 per pound.
(a) What are the risks faced by a hotel chain who is a large purchaser
of coffee?
(b) What are the risks faced by a Colombian coffee farmer?
(c) If the delivery price of coffee turns out to be $2.25, should the
farmer have forgone entering into a futures contract? Why or
why not?
4. Consider a 6-month forward contract (delivers one unit of the security)
on a security that is expected to pay a $1 dividend in three months.
The annual risk-free rate of interest is 5%. The security price is $20.
What forward price should the contract stipulate, so that the current
value of entering into the contract is zero?
5. Spot and futures prices for Gold and the S&P in September 2007 are
given below.
4
, 1.4 Forward and Futures 1 QUESTIONS
07-September 07-December 08-June
COMEX Gold ($/oz) $693 $706.42 $726.7
CME S&P 500 $1453.55 $1472.4 $1493.7
Table 1: Gold and S&P 500 Prices on September 7, 2007
(a) Use prices for Gold to calculate the effective annualized interest
rate for Dec 2007 and June 2008. Assume that the convenience
yield for Gold is zero.
(b) Suppose you are the owner of a small gold mine and would like
to fix the revenue generated by your future production. Explain
how the futures market enables such hedges.
6. Use the same set of information given in the problem above.
(a) Use S&P 500 future prices to calculate the implied dividend yield
on S&P 500. For simplicity, assume you can borrow or deposit
money at the rates implied by Gold’s futures prices.
(b) Now suppose you believe that we are headed for a slow-down in
economic activity and that the dividend yield will be lower than
the value implied in part (a). What June-2008 contracts you would
buy or sell to make money, assuming your view is correct? Again,
assume you can borrow or deposit money at the rates implied by
Gold’s futures prices.
7. The Wall Street Journal gives the following futures prices for crude oil
on September 6, 2006:
Futures price ($/barrel) 67.50 69.60 72.66 73.49
and the spot price of oil is $67.50/barrel. Use the interest rates you
found in the previous problem.
(a) Compute the net convenience yield (in effective annual rate) for
these maturities. (You can use the market information provided
in the above problem.)
(b) Briefly discuss the convenience yield you obtained.
8. The data is the same as in the two problems above. You are running a
refinery and need 10 million barrels of oil in three months.
(a) How do you use oil futures to hedge the oil price risk? The contract
size is 1,000 barrels for futures.
5
and Solutions Collection
Finance Theory I
Part 2
Fall 2025
1
,CONTENTS CONTENTS
Contents
1 Questions 4
1.4 Forward and Futures ............................................................................. 4
1.5 Options ................................................................................................... 9
1.6 Risk & Portfolio Choice ...................................................................... 19
1.7 CAPM ................................................................................................... 31
1.8 Capital Budgeting ................................................................................ 42
2 Solutions 45
2.4 Forward and Futures ........................................................................... 45
2.5 Options ................................................................................................. 55
2.6 Risk & Portfolio Choice ...................................................................... 79
2.7 CAPM ................................................................................................... 90
2.8 Capital Budgeting .............................................................................. 104
3
, 1 QUESTIONS
1 Questions
1.4 Forward and Futures
1. During the summer you had to spend some time with your uncle, who
is a wheat farmer. Your uncle, knowing you are studying for an MBA
at Sloan, asked your help. He is afraid that the price of wheat will fall,
which will have a severe impact on his profits. Thus he asks you to
compute the 1yr forward price of wheat. He tells you that its current
price is $3.4 per bushel and interest rates are at 4%. However, he also
says that it is relatively expensive to store wheat for one year. Assume
that this cost, which must be paid upfront, runs at about $0.1 per
bushel. What is the 1yr forward price of wheat?
2. The Wall Street Journal gives the following futures prices for gold on
September 6, 2006:
Futures price ($/oz) 635.60 641.80 660.60 678.70
and the spot price of gold is $633.50/oz. Compute the (effective annu-
alize) interest rate implied by the futures prices for the corresponding
maturities.
3. Suppose that in 3 months the cost of a pound of Colombian coffee will
be either $1.25 or $2.25. The current price is $1.75 per pound.
(a) What are the risks faced by a hotel chain who is a large purchaser
of coffee?
(b) What are the risks faced by a Colombian coffee farmer?
(c) If the delivery price of coffee turns out to be $2.25, should the
farmer have forgone entering into a futures contract? Why or
why not?
4. Consider a 6-month forward contract (delivers one unit of the security)
on a security that is expected to pay a $1 dividend in three months.
The annual risk-free rate of interest is 5%. The security price is $20.
What forward price should the contract stipulate, so that the current
value of entering into the contract is zero?
5. Spot and futures prices for Gold and the S&P in September 2007 are
given below.
4
, 1.4 Forward and Futures 1 QUESTIONS
07-September 07-December 08-June
COMEX Gold ($/oz) $693 $706.42 $726.7
CME S&P 500 $1453.55 $1472.4 $1493.7
Table 1: Gold and S&P 500 Prices on September 7, 2007
(a) Use prices for Gold to calculate the effective annualized interest
rate for Dec 2007 and June 2008. Assume that the convenience
yield for Gold is zero.
(b) Suppose you are the owner of a small gold mine and would like
to fix the revenue generated by your future production. Explain
how the futures market enables such hedges.
6. Use the same set of information given in the problem above.
(a) Use S&P 500 future prices to calculate the implied dividend yield
on S&P 500. For simplicity, assume you can borrow or deposit
money at the rates implied by Gold’s futures prices.
(b) Now suppose you believe that we are headed for a slow-down in
economic activity and that the dividend yield will be lower than
the value implied in part (a). What June-2008 contracts you would
buy or sell to make money, assuming your view is correct? Again,
assume you can borrow or deposit money at the rates implied by
Gold’s futures prices.
7. The Wall Street Journal gives the following futures prices for crude oil
on September 6, 2006:
Futures price ($/barrel) 67.50 69.60 72.66 73.49
and the spot price of oil is $67.50/barrel. Use the interest rates you
found in the previous problem.
(a) Compute the net convenience yield (in effective annual rate) for
these maturities. (You can use the market information provided
in the above problem.)
(b) Briefly discuss the convenience yield you obtained.
8. The data is the same as in the two problems above. You are running a
refinery and need 10 million barrels of oil in three months.
(a) How do you use oil futures to hedge the oil price risk? The contract
size is 1,000 barrels for futures.
5
