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cenwandada · 2024年04月11日

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

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:

A.

long 200 contracts.

B.

long 220 contracts.

C.

long 280 contracts.

D.

long 240 contracts.

解释:

D is correct.

考点:Hedging With Stock Index Futures

解析:

(1.81.2)100,000,001,000×250=0.6×400=240(1.8-1.2)\frac{100,000,00}{1,000\times250}=0.6\times400=240

where 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。

1 个答案

李坏_品职助教 · 2024年04月11日

嗨,爱思考的PZer你好:


因变量变化了啊。一个投资组合对应一个β。


一开始是一个充分分散化的投资组合,价值100million,它的β是1.2.

现在由于我们加仓买入了240份SP500股指期货合约,所以新的投资组合变成了:原来的100million组合 + 240份股指期货,这个新的投资组合的β=1.8

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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

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