Week 8 - Forwards & futures

Question 1

Forward contract

Answer 1

An OBLIGATION to buy/sell a certain quantity of an asset for a pre-specified, FORWARD PRICE at a particular future, MATURITY/EXPIRATION DATE

• Over the counter, not exchange traded
• No money changes hands on inception date

Question 2

Futures contract

Answer 2

Similar to forward contract except that gains & losses (cash flows) are settled DAILY
^MARKED TO MARKET

• You have to post the initial margin, unlike in forwards contract
• standardised {ie. non-negotiable contract}
• traded on an exchange

Question 3

3 possible scenarios for no arbitrage pricing of a forward contract on an investment ASSET that… + their formulae

Answer 3

1. An investment asset that pays no income
   F0,T = S0(1+rrf)^T
2. pays fixed known income
   F0,T = (S0-I)(1+rrf)^T
3. pays fixed known yield
   F0,T = S0(1+rrf-y)^T

Question 4

2 possible scenarios for no arbitrage pricing of a forward contract on investment COMMODITIES with… + their formulae

Answer 4

1. Investment commodities with fixed known storage costs
   F0,T = (S0+U)(1+rrf)^T
2. with net convenience yield
   F0,T = S0(1+rrf-NCY)^T

Question 5

Pricing forwards on foreign currency formula

Currency spot exchange rate formula

Answer 5

F0,T(HC/FC) = S0(HC/FC) [(1+rHome)/(1+rForeign)]^T

Spot exchange rate = HC/FC

Question 6

Arbitrage strategy involving foreign currency

eg. sell forward at t=0, arbitrage profit at t=1

Answer 6

• sell more expensive currency, buy cheaper currency

Portfolio 1 (forward)
t=0, sell forward (no cash flow at time 0)
t=1, collect __

Portfolio 2
t=0,
1. Borrow __
2. Buy __ at spot rate
3. Invest __ at risk-free rate
t=1,
1. Repay __ with interest
2. Collect __ with interest

Question 7

Arbitrage strategy involving commodities

eg. sell forward at t=0, arbitrage profit at t=1.
Commodity is gold.

Answer 7

eg. short sell forward contract (b/c more expensive), long replicating portfolio

Portfolio 1 (forward)
t=0, sell forward
t=1, collect PAYOFF = K - ST

Portfolio 2
t=0,
1. Borrow
2. Buy gold
3. Pay storage
t=1,
1. Repay at EAR
2. Gold position, +ST

Question 8

3 main uses for derivatives

Answer 8

1. Hedge risk
   - derivatives used to remove/reduce the risks associated w/ their economic activities or investment portfolios
2. Speculation (making bets)
   - if you don’t actually own the underlying asset. Risky strategy, can either win or lose a lot.
3. Create arbitrage portfolios
   - replicate payoffs of derivative portfolio

Question 9

Net convenience yield, NCY, for Commodities (instead of investment assets)

{also taken from 2016 paper}

Answer 9

NCY = y - s
= convenience yield - storage cost
= the value of having an inventory - storage cost

Convenience yields can differ seasonally, eg. harvest times, heating season

• Storage costs: physical commodities cost money to keep hold of
• Convenience yields: there might be a utility benefit to having a physical store of a commodity rather than a derivative claim to that commodity.

Question 10

2 pros of Futures

Answer 10

1. NO DEFAULT RISK
   - The contract says once goes below 1000, you need to top up (prevention of default mechanism)
2. Can get off the contract BEFORE maturity date by using the EXCHANGE