In the context of multiple assets, how is the number of correlations calculated?

The calculation of the number of correlations among multiple assets is determined by understanding how pairs are formed from a set of n assets. When considering correlations, you are looking at relationships between pairs of assets, meaning each correlation measures the relationship between two distinct assets.

To find out how many unique pairs can be formed from n assets, we can use the formula for combinations. The specific formula n(n - 1) / 2 takes into account that for each asset, you can create a pair with every other asset but only once (since correlation between asset A and asset B is the same as between asset B and asset A). This accounts for the need to avoid double counting when forming pairs.

The formula (n^2 - n) / 2 also conveys the same concept. Here, n^2 is the total number of ways to pair the n assets (including the duplicates, as you can pair an asset with itself as well), and subtracting n accounts for these duplicates. Essentially, you are left with the number of unique asset pairs, which is why both this formula and the formula for combinations result in valid results for determining the number of correlations.

As a result, understanding that the focus is on unique pairs leads to correctly identifying how many correlations