Fall 2018 Question #16 - Investment Yield
For this question, I don't quite understand the investment yield part of the calculation for letter G.
The formula shown to determine investment yield is 2 x NII / [ (invested assets)_beg2017 + (invested assets)_end2017 - NII].
Can you provide more intuition behind the numerator and denominator of this formula? (I'm aware this formula is from the MSA.Ratios reading)
Comments
There's another long thread related to your question at the link below. You have to scroll up a little bit to see all the posts from September 1, 2021, but it is a very similar question to yours:
Anyway, let's step back and look at a simple example. Suppose you start the year with $100 of invested assets and by the end of the year, those assets have grown to $108. That means the investments earned $8 and then the investment yield is:
But this is too simple because a real life company would be receiving premiums throughout the whole year and they would presumably be investing a portion of these premiums. For example, at the beginning of February, they may have total invested assets of $120 and would start earning interest on the additional $20.
An accurate way to calculate investment yield is to look at the invested assets A at the beginning of every day. If those invested assets earn $x of interest then the investment yield for that day would be:
You could then take a weighted average of the investment yield for each day over the whole year to calculate the overall annual investment yield. Of course, this is too much work, so the formula for investment yield used in this problem is an approximation. This part of the formula:
can also be written as:
This denominator is the basis on which the investment yield is calculated. It's just the average of the beginning and ending invested assets. So the investment yield is almost:
There's just one catch. We don't want NII (investment income earned during the year) to be included in the basis because that would skew the results. That's why NII is subtracted from the denominator. If we didn't subtract NII from the denominator, the investment yield would come out lower than it really is.