I got a question in one of the Schweser Mock exams that gave the following info : “Gupta noted that the largest 5 companies in the industry had market shares of 35%, 10%, 20%, 5%, and 30%. Gupta used the Hefindahl index for the industry in order to make inferences about the industry concentration in terms of its equivalence to that of an industry with a particular number of equal- size firms.” I am still unclear as to what the question is asking and the logic behind the answer. I always calculated the HHI as the sum of squared mkt shares of the firms in the industry with a max of 10,000 (100% squared for monopolies). However in this particular question they used the decimal form of squared deviations (ie. 0.35 squared + 0.10 squared + 0.20 squared + …) to yield 0.265 for the Herfindahl index. Then the reciprocal of this number was taken to yield the equivalent number of firms of 3.8. Anyone come across a similar question, or able to explain the logic behind the calculation and what is meant by the equivalent number of firms? (Could not find this in the CFA curriculum)
Have not seen this.
you gotta know this backward and forward.
Where is it in the CFAI texts?
How many ‘equal’ size firms does it takes to produce equivalent HHI = .1225+.01+.04+.0025+.09 = .265 1/x 3.77358 or 3.8 firms.
How does the inverse of .265 equal the amount of firms needed to produce that HHI number? I checked the number and 3.8 firms (100%/3.8)^2 then times 3.8 because each firm has this, to get the sum – this in fact matches up. But can anyone provide a brief explanation as to how this logic actually works, can’t seem to get it down and would like to understand.
HHI Index for the original firms =x equal size equivalent = n. We have 1/x= n --> each of the n has a market share 100% /n = x % market share. To calculate the HHI for the n equal size [x^2]*n = x*x/x =x i.e., same as old HHI. Try it yourself with the numbers in this case. x = .265 n = 3.77 --> each firm has share of 26,5%. New HHI for the .266^2*3.77 = .265