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Week 3 (chapter 5): Determination of Forward and Future Prices (The cost…
Week 3 (chapter 5): Determination of Forward and Future Prices
Assets
Investment assets (i.e: stock, bonds, gold, silver)
Consumption assets (i.e: copper, oil, pork bellies)
Use
arbitrage
arguments to determine the forward and future prices of an
investment assets
but not consumption assets
Short selling
selling assets you do not own
your broker
borrows
the securities from another client and sells them in the market in the usual way => later, buy the securities back => profit if the stock price has declined
you must pay dividends and other benefits
the owner of the securities should receive on the shares
margin account: is
kept with the broker
to guarantee that you do not walk away from your obligations
Example (p.5 lecture slide)
Assumption and Notation
Same tax rate
Borrow and lend money at the same risk- free rate
Take advantages of arbitrage opportunity
No transaction costs
Arbitrage opportunity
Should long or short?
Short: when future price > total loan repayment
Long: when future price < total loan repayment
No arbitrage when future price = total loan repayment
Forward Pricing
Forward Pricing: Known income
(
separate into two components when using arbitrage
- read the lecture slide for detail example)
Forward Price: Known Yield
Valuing Forward Contracts
Forward vs Futures Pricing
If a strong positive correlation between IR and asset price => Futures price is slightly higher than forward price
Forward: profit realize on the end of settlement
Futures: profit realize daily
Forward and Futures on Currencies
Foreign currency: a security providing a dividend yield
Futures on Investment Commodities
Convenience yield (?)
benefits derived from holding physical assets
if inventories are low =>
shortages
=> convenience yield is usually higher
The cost of carry
cost of carry: relationship between futures prices and spot prices
cost of carry (c) = storage cost + interest cost - income earned
Dividend paying stock: c = r -q
Currency: c = r - rf
Non- dividend- paying stock: c = r
Commodity: c = r - q + u