Cariño linking for portfolio analysis

This short guide explains why and how to use Cariño linking in portfolio attribution analysis.

Sometimes, we need to perform a portfolio analysis and wish to use a simple sum to aggregate different periods. However, this method is not applicable. The solution is to link returns using the Cariño linking algorithm.

Here is an example:

This is our theoretical portfolio. As you can see, the simple return does not equal the compound return.

However, we can apply linking to adjust the numbers for a simple sum.

Here is an algorithm:

1. Calculate compound return:
   ((0.6 × 0.1 + 0.4 × 0.05) + 1) × ((0.6 × -0.02 + 0.4 × 0.04) + 1) — 1 = 0.08432
2. Calculate total returns coefficient:
   ln(1 + 0.08432) / 0.08432 = 0.9600695257
3. Apply this coefficient to calculate the adjustment coefficient per period ( Q1, Q2)
   Q1c = ln(1 + 0.08) / (0.08 × 0.9600695257) = 1.002024321
   Q2c = ln(1 + 0.004) / (0.004 × 0.9600695257) = 1.039513588
4. Now we need to apply Q1c and Q2c to our period respectively

Now we can use simple SUM to do our analysis: