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Marina_0122 · 2022年02月25日

可以详细解释一下吗?看了其他解释没看懂

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, the number of stock index futures needed to sell is? Based on the following information:

  • ŸThe stock index value is at 1,200, multiplier is $250, the beta is 0.95
  • ŸThe 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)

因此,需要卖出84份股票期货合约。

可以详细解释一下吗?看了其他解释没看懂

2 个答案
已采纳答案

Hertz_品职助教 · 2022年02月25日

嗨,从没放弃的小努力你好:


同学你好~

1.     题干说一个pension fund规模是100million,其中80million是股票,20million是债券。现在想要调整一下比例,改为60million的股票和40million的债券。

2.     然后看一下问题,问的是需要卖掉的股指期货合约的份数是多少。

根据问题可以知道,问的是股指期货合约,这个合约是用来调股票头寸的,因此就是问我们将80million的股票头寸调节至60million的股票头寸,需要卖掉的期货合约份数。

因此题干中所有关于债券的信息是不需要的。

3.     计算合约份数,直接按照公式计算即可:

4.     当然,如果真正实现将股票:债券的比例由8:2调整成6:4,还是需要买入bond futures的。但是本题没有问,所以就不用管这部分了。

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

Hertz_品职助教 · 2022年03月02日

嗨,爱思考的PZer你好:


同学你好

是的哈,因为这个数据是 bond futures contract 的价格,从上面的分析可知咱们需要使用的只是股指期货合约的条件喔

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努力的时光都是限量版,加油!

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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?

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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.-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) The priof bonfutures contrais $105,300 with impliemofieration of 6.5.这个条件用不上对吗?为什么这里用beta算不用ration算呢/?

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