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Yaq7 · 2021年10月28日

老师，这是答案是负数，即sell -84份contracts，是不是意思是要买？

  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, 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=(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)

因此，需要卖出84份股票期货合约。

做出来答案没问题，想确认一下解释

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1 个答案

Hertz_品职助教 · 2021年10月29日

嗨，从没放弃的小努力你好：


同学你好~

不是的哈

1.     原则是这样：根据下面这个公式计算出结果，当结果为正，则买；当结果为负，则卖。

2.     这也可以从公式中检验一下，当βT>βS的时候，这个结果是正数，即我们应该买入。这也是符合逻辑的，因为我们要调增β，买入期货合约才能达到这个目的嘛，反之亦然。


----------------------------------------------
虽然现在很辛苦，但努力过的感觉真的很好，加油！

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2024-10-05 12:29 1 · 回答

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