# Analysis

## Daily Price Difference

As we saw in the first figure, there seemed to be a share price offset between the funds. When I took the difference between both share prices for each day, we see that there is an increase in the difference over time. Nine years ago, SPY was only $10 more than VOO. Today, the difference is 250% greater at $25. On the other hand, in that same time, we can see the valuation of both stocks have tripled.

This is a good start but it only shows us raw price changes. It may be more useful to look at percent changes.

## Day-to-Day Percent Change

We can look at the day-to-day changes in percentages to analyze how the daily stock price fluctuations behaved. Using a simple percent change calculation, we can get a distribution of change between the two funds relative to SPY.

Based on this, it is clear that there is essentially no difference in how these stocks change on the daily. Looks like there is a 50–50 chance of seeing either fund increase more than the other on any given day. However, even if one increased more than the other, with the relative percent change, we see that there is very little difference between the two funds on daily fluctuations (within +/- 0.25%).

## Year-to-Year Percent Change

But how about the long-term, since most of us would be buying these funds expecting them to appreciate over time and not day-trading them. I redid the calculations and looked at the year-to-year percent change for shares prices on dates one year apart.

For the 1-year time span, the central tendency for SPY relative percent change shifted a little towards the negative side around -0.1%. This leads to VOO seeing a greater percent increase year over year for an overwhelming majority of the time. This is vastly different than the day-to-day percent changes we saw before where both funds had an equal number of increasing periods.

## 5-Year Percent Change

As we increase the investing duration to a 5-year period, we can see that VOO beats SPY in almost every 5-year period. There are only a few 5-year periods in the historical data where SPY beats VOO, and even those were barely greater than 0% difference. The average relative percent change continues to shift more negative, meaning SPY is consistently “underperforming” (increasing less) when compared to VOO. Seems like VOO gets slightly better over time.

When we compare the statistics between 1-day, 1-year, and 5-year periods, the average percent change between SPY and VOO increases in order of magnitude as investment duration increases. The median 1-day percent change differences manifest as 0.0003%, while the 1-year and 5-year periods increase to 0.0871% and 0.7158%, respectively. Range and standard deviation also increase as duration increases.

Lastly, I extended the duration to the maximum given by the dataset from 9/9/2010 to the current date and found that SPY increased 234.1% while VOO increased 236.5%, resulting in a 2.4% difference over 10 years.

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