If they say "It's up 20%," it's always 20% relative to whatever time they are comparing it to. If it was 21%, they'd say that.
It sounds like you're asking if, on Wednesday, they'd see it went up 10% Monday, 10% Tuesday, and then add those together. They wouldn't. They'd look at the current value, then look at some past value they want to compare to, and calculate.
If market closed Friday with the stock worth $100, and on Monday close it was worth $110, but then on Tuesday close it was worth $121, at market open on Wednesday, they would never say it's up 20% so far on the week even if it is 2 days of consecutive 10% increases. They'd say it's up 21%, because that's the comparison of $121 to $100. They wouldn't do $121 compared to $110 and $110 compared to $100 and add the results; they'd just go straight to comparing $121 to $100.
They will always report by calculating from the values they are comparing, not by adding percentages, because adding percentages is both inaccurate and of no value to anyone.
I agree with deltatango
Big Rig, you are overthinking this. It is simple.
The S&P500 for example, all indexes work the same,
has 500 stocks they follow that represents the market all as whole. When one stock no longer matches the criteria of the 500 they drop it and choose another. At any given time throughout the day
they average the gain or loss of those 500 stocks in terms of percentage that is was before the stock market opened.
Thr next day they do the exact same thing
You seem to be comparing the magic of compounding interest with the magic of stock prices rising.
They are not the same animal .
Over the long term the magic of the market will beat the magic of any interest rate you can get, it is not even close
The answer to your question is the stock prices do incorporate compounding
Stock broker salesmen have a very misleading poster that truefully graphs the rise of the market since 1930. $100 invested then would be worth over $1,300,000 today because the market averages 11.5% gain every year since 1930. This is true but very misleading because you bought the stock at its lowest point IE the great depression and when you bought it means everything. The rise of the market is irrelevant, the rise since you bought it is what counts.
Bad investors panic when the market falls and sell then buy when it rises. IE they sell low and buy high which is the opposite of what you should do.
As market timing is impossible you should just buy and hold.
Since 1960 the S&P has risen 6.5 % annually, on average, and that is what you should reasonably expect not the 11.5% rise since the great depression when the market was at a historic low
Because we realize the annual rate the market rose in retrospect, we have to compound that rate like a interest rate to see what the value would be if we had invested. We do not have to use the rise every single day just the annualized return, I think, but I not sure I am correct. The answer to the question I just asked seems to be what is confusing you and it is an interesting question
