May 09

Consumer Good Industry P/E Confidence Interval - Practice Question (Par 3+ difficulty)

by David Harper, CFA, FRM, CIPM

FRM | Quant |

I pulled the latest price-earnings ratios for 35 publicly traded companies in the industry Consumer Goods:Processed & Packaged Goods (the actual data on the second tab of EditGrid below). This group includes, for example, Campbell Soup and Kellogg. Here are the summary statistics.

  • Average P/E ratio: 22.5
  • Sample standard deviation of P/E ratios: 13.82
  • Sample: n = 35 companies

Question:

Construct a 90% confidence interval for the true P/E ratio (i.e., the random interval that has a 90% chance of containing the population P/E ratio).

(don't peek until you try)

 

 

 

 

 

Answer:

See the EditGrid below for calculations. I get 18.6 < X < 26.5.

Note that we use the student's t distribution because we don't know the population variance; however, our sample is above 30, so the this outcome will approximate the use of the normal anyhow.

EditGrid:

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