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Cheli · 2021年04月05日

期货部分一个月后价值

NO.PZ2018113001000005

问题如下:

The equity portfolio has a market value of $6,000,000, The pension fund plans to use a futures contract priced at $250,000 in order to increase the beta from 0.9 to 1.2 for the period of one month. The futures contract has a beta of 0.95. One months later, the return of equity market is 5%, the market value of equity portfolio is $6,250,000, the price of futures contract is $262,000.

The effective beta of the equity portion of the fund is closest to:

选项:

A.

1.15.

B.

1.20

C.

1.05

解释:

A is correct.

考点:计算effective beta

解析:

将beta从0.9调整为1.2需要的合约数量为:

Nf=(βTβSβS)(Sf)=(1.20.90.95)($6,000,000$250,000)=7.58N_f=(\frac{\beta_T-\beta_S}{\beta_S})(\frac Sf)=(\frac{1.2-0.9}{0.95})(\frac{\$6,000,000}{\$250,000})=7.58

因此,需要买入8份期货合约。

一个月之后:

期货合约所带来的利润=8×(262,000-250,000)=$96,000

股票组合的市场价值变为6,250,000,加上期货合约的收益可以得到整个头寸的价值=$6,250,000+$96,000=$6,346,000,

整个头寸的收益=$6,346,000/$6,000,000-1=0.0577

又因为市场的收益率为5%,而组合的收益率为5.77%,所以组合的有效贝塔为:

0.0577/0.05=1.154

期货部分一个月后价值计算为什么是收益部分而不是250k*8?
1 个答案

Hertz_品职助教 · 2021年04月06日

嗨,从没放弃的小努力你好:


同学你好~

期货合约一开始的价格是250,000,后来涨到了262,000,所以一份期货合约我们赚262,000-250,000. 我们买入了8份合约因此需要×8,就有了“期货合约所带来的利润=8×(262,000-250,000)=$96,000”。

注意:期货合约的价值就是期货合约可以给我们带来的好处(所以我们不能用25000×8,而应该是用收益部分×8),因此,96,000就是我们买入8分合约的价值,也就有了解析中的“股票组合的市场价值变为6,250,000,加上期货合约的收益可以得到整个头寸的价值=$6,250,000+$96,000=$6,346,000”。

(如有疑问,欢迎追问)

----------------------------------------------
就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

徐威廉 · 2021年10月21日

期末时刻期货价值等于(262000-250000)*Nf我可以理解,是不是只针对本题long futures增加贝塔的情况,如果换个short头寸这里期货的价值就是负的了,也就是说还是要考虑期货头寸问题的,对吧?

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