Weight Effect

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:

    • A stock is a component of the S&P 500 with a weight of 1.5%.
    • 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

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

Hi Jeffrey,

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

Thanks,
Thomas