Index Price Dynamics 2
Volkswagen and Siemens are both part of the DAX index. Volkswagen has an 8% share in the index, and Siemens has a 5% share. At a specific moment, the DAX index is valued at 13 000. If Volkswagen’s value increases by 4% due to strong car sales and Siemens’s value decreases by 2% after a quarterly report, by what percentage should the combined value of the remaining stocks change to keep the DAX index at the same value?
Answer
We have the following
\[
0.08\times13000 = 1040,\quad
0.05\times13000 = 650.
\]
\[
0.04\times1040 = 41.6,\quad
(-0.02)\times650 = -13.
\]
Net impact from VW and Siemens: \(41.6 - 13 = 28.6\), i.e. the index price rose by \(28.6\). On the other hamd, the remaining 87% of the index is:
\[
13000 - (1040 + 650) = 11310.
\]
To offset a +28.6 move, we need the remaining stocks to decrease by \(x\) where \(x\) is:
\[
11310 \times (x) = 28.6
\quad\Longrightarrow\quad
x = \frac{28.6}{11310} \approx 0.25\%.
\]
Thus, the remaining stocks must fall by about 0.25%.