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NO.PZ2019052801000026

问题如下：

Suppose we have a well-diversified $100 million equity portfolio. The portfolio beta relative to the S&P 500 is 1.2. The current value of the 3-month S&P 500 Index is 1,000. The multiplier is 250. If we want to adjust the portfolio beta to 1.8, how many S&P 500 contracts we need?

选项：

long 200 contracts.

long 220 contracts.

long 280 contracts.

long 240 contracts.

解释：

D is correct.

考点：Hedging With Stock Index Futures

解析：

$(1.8-1.2)\frac{100,000,00}{1,000\times250}=0.6\times400=240$

where beta = 1.2, target beta = 1.8, A = 250 x 1,000, P = $100 million

还是long或者short这个方向搞不懂。 如果我先计算beta1.2的时候，需要short480份，再计算beta01.2，需要short720份，从-480到-720，不是应该short160吗？ 老师我这个算法和思路是错误的吗？

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1 个答案

pzqa39 · 2024年02月19日

嗨，从没放弃的小努力你好：

Number of contracts = (β target - β) * current value of the portfolio/current value of the futures contract.

如果得出的值大于0，就是long；小于0，就是short。

本题 β target=1.8 β=1.2 ，代入公式后结果值为240，大于0，所以是long 240。

假如题目β target是0.6，那么代入公式后结果值为-240，小于0，那么就是short 240。

同学不需要想的太复杂，根据结果值正负判断long short即可。

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NO.PZ2019052801000026问题如下Suppose we have a well-versifie$100 million equity portfolio. The portfolio beta relative to the S P 500 is 1.2. The current value of the 3-month S P 500 Inx is 1,000. The multiplier is 250. If we want to aust the portfolio beta to 1.8, how many S P 500 contracts we neeA.long 200 contracts.B.long 220 contracts.C.long 280 contracts.long 240 contracts.is correct.考点Heing With StoInx Futures解析(1.8−1.2)100,000,001,000×250=0.6×400=240(1.8-1.2)\frac{100,000,00}{1,000\times250}=0.6\times400=240(1.8−1.2)1,000×250100,000,00=0.6×400=240where beta = 1.2, target beta = 1.8, A = 250 x 1,000, P = $100 million稍微较个真，贝塔数学角度理解就是因变量相对于某个自变量单位变化的变动，按道理不管咋弄因变量还是那个熟悉，贝塔不会变呀。

2024-04-11 00:37 1 · 回答

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NO.PZ2019052801000026 long 220 contracts. long 280 contracts. long 240 contracts. is correct. 考点Heing With StoInx Futures 解析 (1.8−1.2)100,000,001,000×250=0.6×400=240(1.8-1.2)\frac{100,000,00}{1,000\times250}=0.6\times400=240(1.8−1.2)1,000×250100,000,00=0.6×400=240 where beta = 1.2, target beta = 1.8, A = 250 x 1,000, P = $100 million 这个就是1.8—1.2。全面一道题是1.1—0.75 什么情况下beta在前面。什么情况下要在计算时就把负号加进去

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2019-11-03 07:39 1 · 回答

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1 个答案

Number of contracts = (β target - β) * current value of the portfolio/current value of the futures contract.

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