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

Assumption and Notation

  1. Same tax rate
  1. Borrow and lend money at the same risk- free rate
  1. Take advantages of arbitrage opportunity
  1. No transaction costs

Arbitrage opportunity

Should long or short?

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

Example (p.5 lecture slide)

Short: when future price > total loan repayment

Long: when future price < total loan repayment

No arbitrage when future price = total loan repayment

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

  1. Dividend paying stock: c = r -q
  1. Currency: c = r - rf
  1. Non- dividend- paying stock: c = r
  1. Commodity: c = r - q + u