衍生工具-第3章-宋凌峰

1、2021/8/21Chapter 3Hedging Strategies Using Futures2021/8/22Long & Short HedgesA long futures hedge is appropriate when you know you will purchase an asset in the future and want to lock in the priceA short futures hedge is appropriate when you know you will sell an asset in the future and want t

2、o lock in the price2021/8/23支持套期保值的观点支持套期保值的观点Companies should focus on the main business they are in and take steps to minimize risks arising from interest rates, exchange rates, and other market variables2021/8/24反对套期保值的观点反对套期保值的观点Shareholders are usually well diversified and can make their own he

3、dging decisionsIt may increase risk to hedge when competitors do notExplaining a situation where there is a loss on the hedge and a gain on the underlying can be difficult2021/8/25基差风险基差风险Basis is usually defined as the spot price minus the futures priceBasis risk arises because of the uncertainty a

4、bout the basis when the hedge is closed out2021/8/26Long Hedge for Purchase of an Asset DefineF1 : Futures price at time hedge is set upF2 : Futures price at time asset is purchasedS2 : Asset price at time of purchaseb2 : Basis at time of purchaseCost of assetS2Gain on FuturesF2 F1 Net amount paidS2

5、 (F2 F1) =F1 + b2交叉套期保值的情形F1 + (S2*-F2)+(S2-S2*)2021/8/27Short Hedge for Sale of an Asset DefineF1 : Futures price at time hedge is set upF2 : Futures price at time asset is soldS2 : Asset price at time of saleb2 : Basis at time of salePrice of assetS2Gain on FuturesF1 F2 Net amount receivedS2 + (F1

6、 F2) =F1 + b22021/8/28期货合约的选择期货合约的选择Choose a delivery month that is as close as possible to, but later than, the end of the life of the hedgeWhen there is no futures contract on the asset being hedged, choose the contract whose futures price is most highly correlated with the asset price. This is kn

7、own as cross hedging.2021/8/29Optimal Hedge Ratio (page 57)Proportion of the exposure that should optimally be hedged iswhere sS is the standard deviation of DS, the change in the spot price during the hedging period, sF is the standard deviation of DF, the change in the futures price during the hed

8、ging periodr is the coefficient of correlation between DS and DF.FShssr*2021/8/210Optimal Number of ContractsQA Size of position being hedged (units)QFSize of one futures contract (units)VAValue of position being hedged (=spot price time QA)VFValue of one futures contract (=futures price times QF)Op

9、timal number of contracts if no tailing adjustmentFAQQh*Optimal number of contracts after tailing adjustment to allow or daily settlement of futuresFAVVh*2021/8/211q MVHR假设决策者要通过调整期初持有的期货头寸来最小化期末的期现组合的价值的方差。假设现货价格变化期初为S0，期末为S1，期货价格期初为F0，期末位F1。那么最小化1单位的现货和h单位的期货构成的资产组合价值的方差的话，即 由于方差总存在最小值，仅考虑一阶条件，令 可

10、得 也可写成11最小方差套保比2021/8/212Example (Pages 59-60)Airline will purchase 2 million gallons of jet fuel in one month and hedges using heating oil futuresFrom historical data sF =0.0313, sS =0.0263, and r= 0.9287777003130026309280.*h2021/8/213Example continued The size of one heating oil contract is 42,000

11、 gallonsThe spot price is 1.94 and the futures price is 1.99 (both dollars per gallon) so that Optimal number of contracts assuming no daily settlement Optimal number of contracts after tailing 033700042000000277770.,.103658083000880377770.,.580830004299100088030000002941,.,.FAVV2021/8/214OLSOLS简单线性

12、回归方程要求模型的残差项是独立同分布的，简单线性回归方程要求模型的残差项是独立同分布的，若回归方程的残差项存在条件异方差，则估计出的若回归方程的残差项存在条件异方差，则估计出的 值不在值不在具有有效性和无偏性，针对这个问题，具有有效性和无偏性，针对这个问题，Engle(1982)Engle(1982)首先提首先提出了出了ARCHARCH模型对方差进行建模，模型对方差进行建模，Bollerslev(1986)Bollerslev(1986)将将ARCHARCH模型发展为广义模型发展为广义ARCHARCH模型（模型（GARCHGARCH）。）。大量实证研究表明大量实证研究表明GARCHGARCH模

13、型能够很好地描述金融变量的波模型能够很好地描述金融变量的波动特征。因此可以采用单变量动特征。因此可以采用单变量GARCHGARCH模型，通过最大似然估模型，通过最大似然估计（计（MLEMLE）求算最优套期保值比率）求算最优套期保值比率。GARCH(p,q)GARCH(p,q)模型的一般形式如下：模型的一般形式如下：残差项：残差项： 条件方差方程：条件方差方程： 基于基于GARCHGARCH模型求套保比模型求套保比2021/8/215股指期货合约股指期货合约2021/8/216美国期货合约美国期货合约S&P 500 股指期货股指期货合约标的合约标的S&P 500合约乘数合约乘数$

14、250报价单位报价单位指数点最小变动最小变动0.1点合约月份合约月份3月，6月，9月，12月每日价格变化限制每日价格变化限制最新2010年一季度的熔断变化点数为：110，220，330。当下降这些点数是熔断，上升不熔断。每季度重新计算一次。最后交易日最后交易日合约到期月份的第三个星期五前的星期四交割方式交割方式现金交割交割日期交割日期最后交易日下一日交易时间交易时间周一到周五: 8:30 a.m.-3:15 p.m保证金保证金Span系统计算最终结算价最终结算价Special Opening Quotation （通过最后交易日下一交易日的股票开盘价计算）头寸限制头寸限制20,000手净多头或

15、净空头2021/8/217使用股指期货保值使用股指期货保值(Page 61)To hedge the risk in a portfolio the number of contracts that should be shorted iswhere VA is the value of the portfolio, b is its beta, and VF is the value of one futures contractFAVVb2021/8/218ExampleS&P 500 futures price is 1,000Value of Portfolio is $5 m

16、illionBeta of portfolio is 1.5What position in futures contracts on the S&P 500 is necessary to hedge the portfolio?2021/8/219改变改变 BetaWhat position is necessary to reduce the beta of the portfolio to 0.75?What position is necessary to increase the beta of the portfolio to 2.0?2021/8/220Why Hedg

17、e Equity ReturnsMay want to be out of the market for a while. Hedging avoids the costs of selling and repurchasing the portfolioSuppose stocks in your portfolio have an average beta of 1.0, but you feel they have been chosen well and will outperform the market in both good and bad times. Hedging ens

18、ures that the return you earn is the risk-free return plus the excess return of your portfolio over the market.(获取收益）2021/8/221滚动对冲策略滚动对冲策略We can roll futures contracts forward to hedge future exposuresInitially we enter into futures contracts to hedge exposures up to a time horizonJust before matur

19、ity we close them out an replace them with new contract reflect the new exposureetc2021/8/222Liquidity Issues (See Business Snapshot 3.2)In any hedging situation there is a danger that losses will be realized on the hedge while the gains on the underlying exposure are unrealizedThis can create liqui

20、dity problemsOne example is Metallgesellschaft which sold long term fixed-price contracts on heating oil and gasoline and hedged using stack and rollThe price of oil fell.2021/8/223购销关系购销关系Castle公司公司 (客户)包销公司所有石油提炼产品，以最近月份的原油价格加成若干美元作为购买价格。 MGRM公司公司用户用户 以稍高于当时市价的固定价格定期提供给用户总量约1.6亿桶石油商品 十年长期合约十年长期合约

21、十年远期合同十年远期合同产生风险产生风险管理需要管理需要2021/8/224 “德国金属”必须为这个合约制定一套套期保值的策略，以把油品价格变动的风险转移到市场上去。它采用了在在NYME买入石油标准买入石油标准期货合约、在店头市场做互换合同期货合约、在店头市场做互换合同的方式来将它与用户的契约中引起的价格风险转移。这也符合其稳健的风格。2021/8/225交易结构交易结构2021/8/226油品价格涨跌的影响油品价格涨跌的影响价格上涨：期货盈利，互换盈利，现货亏损。价格下跌：期货亏损，互换亏损，现货盈利。价格上涨会使衍生物头寸有盈利。价格上涨会使衍生物头寸有盈利。2021/8/227市场反向变

22、化市场反向变化1993年6月:19美元/桶 1993年12月:15美元/桶2021/8/228市场反向变化市场反向变化OPEC油价下滑油价下滑反向变反向变正向正向保证金保证金追缴追缴 出现庞大 资金缺口 2021/8/229结局结局1在现货上积在现货上积累的大量潜累的大量潜在利润无法在利润无法变现变现 3花花1010亿美元亿美元解除与解除与CastleCastle能源能源公司的合约公司的合约 2在能源期货在能源期货和互换交易和互换交易上损失上损失1313亿亿美元美元 150150家德国和其它国际银行家德国和其它国际银行对MG公司采取了一个数额高达19亿美元的拯救行动，才使得MG公司避免了破产。

23、2021/8/230德国金属套保案例德国金属套保案例2021/8/231 为了说明MGRM的对冲方案所面临的基差风险，我们先将其简化。假定现在是1993年1月份，MGRM与顾客签订的远期合约是在1993年5月份交割。采取stack-and-roll策略对这一远期合约的空头进行套期保值：在1月，建立1993年2月到期的期货合约多头。到2月时，平掉2月期货的多头，同时建立3月到期的期货合约多头，以此类推到1993年5月时，平掉在4月份建立的5月期货的多头，同时在现货市场购进现货，兑现远期合约。 德国金属套保案例德国金属套保案例2021/8/232 假定远期合约中商定的交割价为S1(5)，在5月份，

24、现货价格为S5(5)；Fi(j)表示在第i个月里交割月为j的期货合约的价格。 现货市场盈利=S1(5) S5(5)期货市场盈利=F2(2) F1(2)+ F3(3) F2(3)+ F4(4) F3(4)+ F5(5) F4(5)德国金属套保案例德国金属套保案例2021/8/233现货与期货的总盈利= S1(5) S5(5)+ F2(2) F1(2)+ F3(3) F2(3)+ F4(4) F3(4)+ F5(5) F4(5) 由于临近交割时，期货价格趋近现货价格，所以我们大致可以认为S5(5) =F5(5),利用这一假定，重新排列总盈利公式，可得：总盈利=S1(5) F1(2)+ F2(2) F2(3)+ F3(3) F3(4)+ F4(4) F4(5)=S1(5) F1(2)+2月基差+3月基差+4月基差德国金属套保案例德国金属套保案例2021/8/234在远期升水的市场上,基差为负，这意味着每向前滚动一次，总盈利就要减少。 在远期贴水的市场上，基差为正，这意味着每向