利率期货第六章讲

Basic principles

what's perfect hedging: completely
short hedge: be afraid of price decrease
long hedge: be afraid of price increase
cross hedge: asset to be hedged is different from the futures underlying assets. Use asset with related or opposite tendency
[rolling hedge](#Rolling the hedge forward)

Arguments for and against hedging

Favor

companies should focus on producing
should manage risk

Against

shareholders have done such things
may increase risk to hedge when competitors do not
loss on hedge and gain on the underlying asset

Basis risk

Basis is the difference between spot & futures:
$$ B = S - F$$
where B: Basis, S: Spot price, F: Future price
At expiration, basis equals 0, Before expiration, basis can be positive or negative
Support:

$S_x$ means spot price at $t_x$
$F_x$ means future price at $t_x$
$b_x$ means basis at $t_x$ and equals $S_x - F_x$

when $h=1$, we can get:

For short hedge

Effective price: $S_2 + (F_1 - F_2) = F_1 + b_2$

For long hedge

Effective price: $S_2 - (F_2 - F_1) = F_1 + b_2$

套保是用相对价格风险代替绝对价格变动风险

Strengthening of basis

basis increases
short hedger''s position improves
long hedger's position worsens

Weakening of the basis

basis decreases
short hedger''s position worsens
long hedger's position improves

从effective price方面考虑，基差扩大or缩小意味着$F_1 + b_2$的扩大和缩小
基差扩大，卖方赚的多了，买方付出多了
基差缩小，卖方赚的少了，买方付出少了

Choice of the contract

choosing underlying asset. Exact match is prefer but not always.
choosing the delivery month. As close as possible, but later than.

Optimal hedge ratio

the size of the position in futures contracts to the size of the exposure
If hedge ratio equals h: $Effective \ price = S_2 - h*(F_2-F_1)$
The minimum variance hedge ratio is:
$$h = \rho \frac{\sigma_S}{\sigma_F}$$
The optimal number of contracts:

$$N = \frac{h*Q_A}{Q_F}$$

or:

$$N = \frac{h*V_A}{V_F}$$

where Q means quantity and V means dollar value

Index futures

报价合约规模 = 指数*乘数(如：300元)
计算规模可以用$\beta$系数代替$h$，不完全替代

Example

套保效果：不论指数如何涨跌，都能获取无风险收益率
套保的好处：相比购买T-Bill或存银行，套保的流动性、避税效果更好

Changing $\beta$

short position to change $\beta$ from $\beta$ to $\beta^$:
$$N = (\beta - \beta^)\frac{V_A}{V_F}$$

Equity and Cash

Currency futures

货币期货用美元报价结算，分析时立于美国立场

出口商收到外币货款，担心外币贬值，需要做空外币
进口商付出外币货款，担心外币升值，需要做多外币

Rolling the hedge forward

the shorter the maturity is, the more liquid the contract is.
use a series of futures contracts to increase the life of a hedge. eg. four contracts with half year to hedge for two years.

Hedging strategy

Long hedge
short hedge
cross hedge
strip hedge
stack hedge
rolling hedge

1&2重点要求，4、5、6非重点

衍生工具 Chap 3