@Quant Trader, the operative words in your notebook are: “...spxl is designed to get 3x the daily returns of SPY”. And as such will suffer slow return degradation. The reason is simple: (1 + 0.10)∙(1 - 0.10) = 0.99. And if you do this ten times, you get: (1 + 0.10)^10∙(1 - 0.10)^10 = 0.904. Which is what your chart show, as it should.

When it is done using small percentage change, it just takes longer to see the impact of the degradation.

3x Leveraged index ETFs like SPXL “seek daily investment results, before fees and expenses, which correspond to 3x the daily performance of the Standard & Poor’s 500 Index.”

There are two important points in that statement. Let's look at each one separately.

1."correspond to 3x the daily performance" Note that this doesn't say that it corresponds to the daily "value". Rather it's the daily 'performance' (ie the gain or loss). If SPY goes up 1% then SPXL will go up 3%. If SPY goes down 1% then SPXL will go down 3%. So far so good. Let's see how that plays out over time with some fictitious values.

Day 1 SPY 100  
Day 2 SPY 99 down 1.00%  
Day 3 SPY 98 down 1.010%  
Day 3 SPY 100 up  2.041%

Day 1 SPXL 100  
Day 2 SPXL 100 * (1 - 3 x .01000) = 97.00  
Day 3 SPXL 97.00 * (1 - 3 x .01010) = 94.06  
Day 4 SPXL 94.06 * (1 + 3 x .02041) = 99.82

Notice that while SPY is back at 100, SPXL is only at 99.82. This is because returns are not additive. A 10% loss followed by a 10% gain doesn't get you back to zero (unlike log returns which are additive). Anyway, that's the first point. Leveraged ETFs track gains and NOT the underlying value.

2."before fees and expenses" The second point. Note that the fund first tries to match the returns but then subtracts a bit for "fees and expenses". The fees for SPXL are about 1.1% (according to their web page). This is the amount deducted over the course of a year. So, expect to make about 1.1% less annually after the above discrepancy is factored in.

The bottom line is that long term a leveraged index ETF will always be lower than simply the compounded underlying index. Maybe take a look at this article in Kiplingers https://www.kiplinger.com/article/investing/T022-C009-S001-run-don-t-walk-from-leveraged-etfs.html .

Hope that helps.

Sorry, didn't really answer the original question. Basically, your premise of using the cumulative (sum) product is wrong.

 "As far as I'm aware, spxl is designed to get 3x the daily returns of SPY (positive or negative), so surely:  
np.cumprod(1+(3∗rx))−1=np.cumprod(1+ry)−1"  

That is incorrect. Algorithmic percentages are not additive like that. This WILL work with log returns but not simple returns. This is demonstrated in the above post.