Lecture 3: Futures & Forward Pricing/Valuation

Question 1

What is the differences between Investment and Consumption assets?

Answer 1

1. IA held for investment purposes
2. IA can price forwards & futures off spot via arbitrage
3. CA held primarily for consumption/production
4. CA not able to price forwards & futures off spot via arb

Question 2

Describe short-selling

Answer 2

Borrowing an asset, selling at it and agreeing to purchase it back for an agreed price in the future

Question 3

Simple IA pricing

Answer 3

F0 = S0(exp)^rT

Question 4

IA: Known income pricing

Answer 4

F0 = (S0-I)(exp)^rT, where I is PV of income

Question 5

When pricing IA (known income), how do we treat different time horizons and rf’s between I and forward?

Answer 5

PV of I calc’d using the relevant rf and time horizon, then treat entire contract as per relevant rf and time horizon

Question 6

IA: Known yield pricing

Answer 6

F0 = S0(exp)^(r-q)T where q = average yield over the life of contract

Question 7

What are the two main known yield futures?

Answer 7

Currency futures & index futures

Question 8

IA: Currency pricing

Answer 8

F0 = S0(exp)^(r-rf)T where rf = foreign risk free rate

Question 9

Long spot short future currency arb process (US inv buying AUD)

Answer 9

1. Lock in price to sell AUD for at T
2. Borrow 1000 USD, buy AUD
3. Invest AUD
4. At T, sell AUD, receive USD
5. Repay USD debt, profit

Question 10

Short spot long future currency arb (US inv, buying AUD)

Answer 10

1. Lock in price to pay for AUD at T
2. Short sell AUD (borrow it at Aus rf and sell for USD)
3. Invest USD at US rf
4. At maturity/expiry, receive US investment return
5. Return AUD and maintain USD profit

Question 11

CA pricing

Answer 11

1. F0 = S0(exp)^(r+u)T where u is the storage cost per unit as a percent of asset value
2. F0 = (So+U) (exp)^rT where U = PV of storage costs

Question 12

Describe the convenience yield and its relationship with market expectations of future availability

Answer 12

Convenience yield is the benefit from holding the asset.
If the market expects future availability to be high, CY is low. If the market expects availability to be low, CY will be high

Question 13

How to price convenience yield?

Answer 13

F0 = S0(exp)^(r+u-y)*T

Solve for Y, take ln of each side, and simple algebra after

Question 14

Forward contract value at t=0?

Answer 14

0

Question 15

What is K and how do we calculate it?

Answer 15

K is the delivery of a price forward entered into previously

It remains constant

K = S0(exp)^rT

Question 16

How do we value a forward?

Answer 16

1. Calc K = S0(exp)^rT
2. Calc F1 = S1(exp)^rT
3. Calculate present value of forward: (F1 - K) (exp)^-rT

Logic is: calculate delivery price, then calculate F1, then take PV of F1 - K to get PV forward val

Question 17

Why is the futures price of a stock index always less than the expected future value of the index?

Answer 17

E(sT) = S0(exp)^(u-q)T whereas F0 = S0(exp)^(r-q)T, where u is always > r

u = investor expected return, r = rf

Question 18

1. Describe F0 as an unbiased estimator of E(sT)
2. Describe normal backwardation
3. Describe contango

Answer 18

1. F0 = E(sT)
2. F0 < E(sT)
3. F0 > E(sT)