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hyi725 · 2023年08月27日

duration

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=(βTβSβf)(Sf)=(0.001.200.95)($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/?

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) 我总是搞不清f应该用哪个数,题目里的远期合约价格105300在什么时候会用到?

2024-10-05 12:29 1 · 回答

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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