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DaiDai · 2023年08月27日

duration

  1. CFA III
  2. Derivative

NO.PZ2018113001000003

问题如下：

A $100 million pension fund with 80% stock and 20% bond. The beta of equity portion is 1.2 and the duration of bond portion is 5.0. In order to adjust the allocation to 60% stock and 40% bond.

Calculate the number of stock index futures needed to buy.

Based on the following information:

  • The stock index value is at 1,200, multiplier is $250, the beta is 0.95
  • The price of bond futures contract is $105,300 with an implied modified duration of 6.5.

选项：

A.

-88

B.

-84

C.

-95

解释：

B is correct.

考点：用futures contract 调整组合的头寸

解析：

现需要将股票头寸从80%降至60%，即需要将20%*100,000,000=$20,000,000的股票的beta调整为0（转成cash）

需要的stock index futures contract数量为：

Nf=(βT−βSβf)(Sf)=(0.00−1.200.95)($20,000,0001,200×$250)=−84.21(−84rounded)N_f=(\frac{\beta_T-\beta_S}{\beta_f})(\frac Sf)=(\frac{0.00-1.20}{0.95})(\frac{\$20,000,000}{1,200\times\$250})=-84.21(-84rounded)

负号代表卖出，即需要卖出84份股票期货合约, 对应的也就是买入（-84）份合约，选B。

（注意，本题中问的是需要的股指期货合约的份数，因此关于债券的信息是用不到的）

  • The price of bond futures contract is $105,300 with an implied modified duration of 6.5.

这个条件用不上对吗？


为什么这里用beta算不用duration算呢/？

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1 个答案
已采纳答案

pzqa31 · 2023年08月28日

嗨，从没放弃的小努力你好：


因为题目问的是用多少股指期货来调整，没问怎么调整债券头寸。

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NO.PZ2018113001000003问题如下 A $100 million pension funwith 80% stoan20% bon The beta of equity portion is 1.2 anthe ration of bonportion is 5.0. In orr to aust the allocation to 60% stoan40% bon Calculate the number of stoinx futures neeto buy. Baseon the following information: The stoinx value is 1,200, multiplier is $250, the beta is 0.95 The priof bonfutures contrais $105,300 with impliemofieration of 6.5. A.-88B.-84C.-95 B is correct.考点用futures contra调整组合的头寸解析现需要将股票头寸从80%降至60%，即需要将20%*100,000,000=$20,000,000的股票的beta调整为0（转成cash）需要的stoinx futures contract数量为Nf=(βT−βSβf)(Sf)=(0.00−1.200.95)($20,000,0001,200×$250)=−84.21(−84rounN_f=(\frac{\beta_T-\beta_S}{\beta_f})(\frSf)=(\frac{0.00-1.20}{0.95})(\frac{\$20,000,000}{1,200\times\$250})=-84.21(-84rounNf​=(βf​βT​−βS​​)(fS​)=(0.950.00−1.20​)(1,200×$250$20,000,000​)=−84.21(−84roun负号代表卖出，即需要卖出84份股票期货合约, 对应的也就是买入（-84）份合约，选（注意，本题中问的是需要的股指期货合约的份数，因此关于债券的信息是用不到的） 在一些具体数据上不知道哪个ration用在谁的BPV上，可以展示一下具体的过程吗？谢谢

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NO.PZ2018113001000003 问题如下 A $100 million pension funwith 80% stoan20% bon The beta of equity portion is 1.2 anthe ration of bonportion is 5.0. In orr to aust the allocation to 60% stoan40% bon the number of stoinx futures neeto sell is? Baseon the following information: ŸThe stoinx value is 1,200, multiplier is $250, the beta is 0.95 ŸThe priof bonfutures contrais $105,300 with impliemofieration of 6.5. A.-88 B.-84 C.-95 B is correct.考点用futures contra调整组合的头寸解析现需要将股票头寸从80%降至60%，即需要将20%*100,000,000=$20,000,000的股票的beta调整为0（转成cash）需要的stoinx futures contract数量为Nf=(βT−βSβf)(Sf)=(0.00−1.200.95)($20,000,0001,200×$250)=−84.21(−84rounN_f=(\frac{\beta_T-\beta_S}{\beta_f})(\frSf)=(\frac{0.00-1.20}{0.95})(\frac{\$20,000,000}{1,200\times\$250})=-84.21(-84rounNf​=(βf​βT​−βS​​)(fS​)=(0.950.00−1.20​)(1,200×$250$20,000,000​)=−84.21(−84roun因此，需要卖出84份股票期货合约。 老师好 怎么问法是 用40MM （=20M +20M）来做？像课上例题 3.1（截图)中把 50M +50M = 100M 来转？

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