F0 = S0 e(r–q )T
where q is the average dividend yield on the portfolio represented by the index during life of contract
5.20
Stock Index
(continued)

For the formula to be true it is important that the index represent an investment asset In other words, changes in the index must correspond to changes in the value of a tradable portfolio
5.19
Stock Index (Page 110-112)

Can be viewed as an investment asset paying a dividend yield The futures price and spot price relationship is therefore

The Nikkei index viewed as a dollar number does not represent an investment asset
(See Business Snapshot 5.3, page 111)
5.21
Index Arbitrage


When F0 > S0e(r-q)T an arbitrageur buys the stocks underlying the index and sells futures When F0 < S0e(r-q)T an arbitrageur buys futures and shorts or sells the stocks underlying the index
Consider a 6-month forward contract on an asset that is expected to provide income equal to 2% of the asset price once during a 6-month period. The risk free rate of interest is 10% per annum. The asset price is $25. The yield is 4% per annum, it follows that q=0.0396(=2ln(1+4%/2)).
5.6
Notation for Valuing Futures and Forward Contracts
S0: Spot price today F0: Futures or forward price today
T: Time until delivery date(in years) r: Risk-free interest rate for maturity T
F0 = (S0 – I )erT
where I is the present value of the income during life of forward contract. In our example, So that,
5.12
When an Investment Asset Provides a Known Yield
5.7
Forward price for an investment asset
5.8
When Interest Rates are Measured with Continuous Compounding
F0 = S0erT
if
远期价格大于即期价格
F0 > S0erT ,arbitrageurs can buy the asset and short forward contracts on the asset. if F0 < S0erT , they can short the asset and enter into long forward contracts on it. This equation relates the forward price and the spot price for any investment asset that provides no income and has no storage costs. 5.9
5.4
Example
The investor is required to maintain a margin account with the broker.
5.5
Assumptions
1.
2.
3.
4.
The market participants are subject to no transaction costs when they trade. The market participants are subjects to the same tax rate on all net trading profits. The market participants can borrow money at the same risk-free rate of interest as they can lend money. The market participants take advantage of arbitrage opportunities as they occur.
(Page 107, equation 5.3)
F0 = S0 e(r–q )T
where q is the average yield during the life of the contract (expressed with continuous compounding)
5.1 of Forward and Futures Prices
Chapter 5
5.1
Consumption vs Investment Assets


Investment assets are assets held by significant numbers of people purely for investment purposes (Examples: stock, bond, gold, silver) Consumption assets are assets held primarily for consumption (Examples: copper, oil)
5.3
Short Selling
(continued)


If at any time while the contract is open the broker is not able to borrow shares, the investor is forced to close out the position, even if not ready to do so, called shortsqueezed(挤空，挟仓). You must pay dividends and other benefits the owner of the securities receives
5.2
Short Selling (Page 99-101)



Short selling involves selling securities you do not own Your broker borrows the securities from another client and sells them in the market in the usual way At some stage you must buy the securities back so they can be replaced in the account of the client
5.23
Futures and Forwards on Currencies (Page 112-115)



A foreign currency is analogous to a security providing a dividend yield The continuous dividend yield is the foreign risk-free interest rate It follows that if rf is the foreign risk-free interest rate ( r r f )T 0 0
5.14
Valuing a Forward Contract
Page 108


Suppose that K is delivery price in a forward contract and F0 is forward price that would apply to the contract today The value of a long forward contract, ƒ, is ƒ = (F0 – K )e–rT Similarly, the value of a short forward contract is (K – F0 )e–rT
5.17
The value of a long forward contract
No income income
Known yield
5.18
Forward vs Futures Prices