# CFA Level 3 MPS

## CFA Level 3 MPS by Linear Discriminant Analysis

This posting is for CFA (Chartered Financial Analyst)  level 3 exam candidates and those with results who want to estimate their relative standing among candidates . I am a  bio-statistician with a strong interest in finance. In August 2014 I cleared all three levels. Like most level 3 candidates I was concerned about passing the highly competitive third and final level. I did a calculator to assess my chances of passing based on available 2013 scores. That is available at this page. Details on the updated calculator and scatter plot of passing and failing scores on the pooled 2013 and 2014 level 3 scores are provided below.

There have been many threads posted in the Analyst Forum on the MPS (Minimum Passing Score),  a statistic which is not released to the public by the CFA administrators. I thought I would try a more rigorous statistical methodology to assess the MPS than those at the  Analyst Forum threads. One of the analysts had kindly compiled a list of scores in the morning essay exam and afternoon exam for 91 2013 candidates who had posted their scores at the forum. The 91 scores were those of 80 passing candidates and 11 failing candidates. I also obtained the 74 scores from the results thread for 2014 which had 67 passing scores and 7 failing scores. So the sample was quite limited, especially for the failing candidates and is also subject to possible differences in a cohort that chooses to report their scores. However this is an improvement on the previous calculator — together we have 18 failing scores and 154 passing scores.

Further the linear discriminant analysis technique used here assumes equal covariance matrices in the pass and fail groups, an assumption which is not testable for small cohorts. The linear method, as opposed to the quadratic method, is easier to implement and display graphically.

The graphic below the calculator provides a scatter plot of the pass and fail scores in the CFA level 3 exam as well as a yellow line which attempts to separate the passing and failing groups. The green dots in the scatter plot are the 80 2013 passing scores, the green crosses are the 67 2014 passing scores, the 11 red dots in the graphic are the 2013 failing scores and the 7 red crosses are 2014 failing scores. The green triangle is the mean passing score and red triangle is the mean failing score. I apologize for the red, yellow and green traffic light coding – just using it to make it easier to read. I am sure there are a number of people who have passed (green – go) who are not really going anywhere and people who have failed (red-stop) who are unstoppable in many ways. The blue triangle is the author’s mean score in seven level 3 practice tests. The yellow line is obtained by the linear discriminant analysis. The precise formula for it is

You have a greater probability of passing than failing if

=0.563(AM Score) +0.827*(PM Score) – 86.84 >=  0