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简ying · 2023年07月02日

问题如下

  1. CFA III
  2. Derivative

NO.PZ2022123002000061

问题如下：

Jacob wants to eliminate systematic risk in the equity portion of the fund by using futures on the FTSE 100 Index, which is the benchmark for the fund’s equity portfolio. She collects the information shown in Exhibit 2.

Exhibit 2 Bold Beverages Pension Fund and Market Data

Three months after Jacob implements the hedge, the FTSE 100 Index is up 3.75%. The equity portion of the Bold Beverages Pension Fund is up 3.50% and the level of the expiring three month FTSE 100 futures contract that Jacob sold is 4,824. The trustees ask Jacob to assess the effectiveness of the hedge that has been in place.

D. Determine the effective beta of the Bold Beverages Pension Fund equity portfolio, including the futures, assuming that Jacob sold 5,200 futures contracts. Show your calculations.

选项：

解释：

Correct Answer:

The new value of the equity portfolio is GBP 235,400,000 × 1.035 = GBP 243,639,000 or a gain of GBP 8,239,000.

The profit on the futures is (4,824 – 4,667) x GBP 10 × (-5,200) = - GBP 8,164,000 or a profit of -3.468%.

So, the overall profit is GBP 8,239,000 – GBP 8,164,000 = GBP 75,000 and the ending value of the overall portfolio is GBP 235,475,000.

This is an overall return of GBP 75,000/GBP 235,400,000 = 0.0003 or 0.03%

Since the market was up 3.75%, the effective beta was 0.0003/0.0375 = 0.0085.

这个题，如果用X表示目标beta，那么根据公式（X-1.04）/0.98*235.4million/46670=-5200，倒推那个X，计算出的目标beta值就和答案里的计算结果不一致，这个计算公式为啥在这个时候不能用了？

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1 个答案

pzqa31 · 2023年07月03日

嗨，爱思考的PZer你好：


因为题目让求的是effective beta。


beta的意思是说当大盘变动1%，我们手里的头寸变化多少。当我们头寸就是stock portfolio时，我们一般就称他为beta了；但是当我们的头寸既包括了股票又包括了futures时，就像本题，我们就叫做effective beta了。同学做题的时候也应该发现了：让我们求effective beta的时候，我们的portfolio一般都是包括了futures的，但其实beta还是那个beta，就是换了个称呼，都是在说大盘变动1%，自己手里的组合变动多少，从其定义来看也是在说收益率变化的概念。


按照你的算法，只是计算了stock的部分，没有算futures的部分，因此和不一致。

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

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NO.PZ2022123002000061 问题如下 Jacob wants to eliminate systematic risk in the equity portion ofthe funusing futures on the FTSE 100 Inx, whiis the benchmark for thefuns equity portfolio. She collects the information shown in Exhibit 2. Exhibit 2 BolBeverages Pension FunanMarket taThree months afterJacob implements the hee, the FTSE 100 Inx is up 3.75%. The equity portionof the BolBeverages Pension Funis up 3.50% anthe level of the expiringthree month FTSE 100 futures contrathJacob solis 4,824. The trusteesask Jacob to assess the effectiveness of the hee thhbeen in place. terminethe effective beta of the BolBeverages Pension Funequity portfolio, inclungthe futures, assuming thJacob sol5,200 futures contracts. Show yourcalculations. CorreAnswer: The new value ofthe equity portfolio is G235,400,000 × 1.035 = G243,639,000 or a gain ofG8,239,000.The profit on thefutures is (4,824 – 4,667) x G10 × (-5,200) = - G8,164,000 or a profit of-3.468%.So, the overallprofit is G8,239,000 – G8,164,000 = G75,000 anthe enng value of theoverall portfolio is G235,475,000.This is overallreturn of G75,000/G235,400,000 = 0.0003 or 0.03%Sinthe marketwup 3.75%, the effective beta w0.0003/0.0375 = 0.0085. 老师，effective beta是什么考点，好像没见过

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