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# Weight Effect

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• #61323
Thomas
• Topics: 88
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Hi,

this time I have a really special question about the effect of a stock change it has on the stock index of which the stock is a component.

Here is an example:
1. – A stock is a component of the S&P 500 with a weight of 1.5%.
2. – This stock is expected to decline 30% in two months.

Question: “What is the effect for the S&P 500 when the stock declines 30% and this stock has a weight of 1.5% in the S&P 500?”

Calculation:
Is my calculation correct when I calculate 1.5% of 30% as the effect on the S&P 500? In this example the effect would be a decline of 4.5% (1.5 % of 30%) in the S&P 500 when this stock declines 30% and has a weight of 1.5% in the S&P 500.

In the calculation above I have assumed that the decline of 30% would happen on one day. This is of course not realistic. The decline of 30% is expected to happen in around two months.

Because the decline is expected to happen in around two months, the effect on the S&P 500 would be in “parts”, distributed over a period of two months but when the decline of 30% is over the total effect on the S&P 500 would be a decline of 4.5% if all other stocks in the S&P 500 would be unchanged.

As already mentioned a really special question. I appreciate any comment.

Thanks,
Thomas

• This topic was modified 1 month, 3 weeks ago by Thomas.
#61327
Jeffrey A.
• Topics: 26
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• Posts: 60

Hi Thomas,

I think you might be off by a decimal:
0.015×30 = 0.45% (less than a half of percent) the effect the S&P would incur with a 30% change in a component that has a 1.5% weighting. There may be better formula

Unless I’m wrong in my understanding, think about it as if that stock with the 1.5% weighting went to zero in one day, it would affect the S&P by  -1.5%.. therefore a 30% down move in the stock would result in S&P moving down about a third of that or 0.45% if all other components stayed still

If it happens slowly over time,  the quarterly rebalancing of market cap weighting structure of s&p 500 would affect the results too in this model

Jeff

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#61329
Thomas
• Topics: 88
• Replies: 118
• Posts: 206

Hi Jeffrey,

thank your very much for your fast response. You are surely right with your calculation and assumptions.

Thanks,
Thomas

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