Will the S&P 500 increase more or decrease less than the Nasdaq Composite from open on 1 February 2023 to close on 28 February 2023?
Increase is calculated per cent as 2 (p1 - p0) / (p1 + p0).
S&P 500
2023-02-01 open: 4070.07
2023-02-28 close: 3970.15
Per cent change:
2 (3970.15 - 4070.07) / (3970.15 + 4070.07) = −0.024855041
Nasdaq Composite
2023-02-01 open: 11573.14
2023-02-28 close: 11455.54
Per cent change:
2 (11455.54 - 11573.14) / (11455.54 + 11573.14) = −0.010213351
Sources:
https://www.wsj.com/market-data/quotes/index/SPX/historical-prices
https://www.wsj.com/market-data/quotes/index/COMP/historical-prices
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Math says this quirky resolution criteria is equivalent to SPX/4070.07 > IXIC/11573.14, so same as comparing performance as usual, the percent change for the month. Also equivalent to checking whether the SPX/IXIC ratio ends up above/below the initial 4070.07/11573.14 = ~0.3517.
In January, S&P 500 change was
2 (4076.60 - 3853.29) / (4076.60 + 3853.29) = 5.6321084%
lower than Nasdaq Composite's
2 (11584.55 - 10562.06) / (11584.55 + 10562.06) = 9.2338286%
Using the traditional method of calculation, the per cent changes were
(4076.60 - 3853.29) / 3853.29 = 5.7953074%
(11584.55 - 10562.06) / 10562.06 = 9.680782%
leading to a greater difference than using my formulas