Page 23 - FINAL CFA II SLIDES JUNE 2019 DAY 8

LOS 31.q: Explain the use of the arithmetic mean, READING 31: MARKET-BASED VALUATION: PRICE AND
the harmonic mean, the weighted harmonic mean, ENTERPRISE VALUE MULTIPLES
and the median to describe the central tendency of
a group of multiples. MODULE 31.4: EV AND OTHER ASPECTS

Consider two stocks: If in a portfolio,
• one priced at $10 with EPS of $1 (P/E = 10) and EPS = 1 + 2 = 3 and the “Price” of a portfolio share is 10 + 16 = 26.
• one priced at $16 with EPS of $2 (P/E = 8). The portfolio P/E = 26 / 3 = 8.67.

Any alternative measures of the mean P/E for the portfolio?
• arithmetic mean = (8 + 10) / 2 = 9
• weighted mean = (10 / 26) × 10 + (16 / 26) × 8 = 8.76 The P/E multiple for a stock index ≠ mean or weighted mean of
the P/Es of the portfolio stocks. Lets try other types of means!

Lets try other types of means!

The portfolio or index P/E (as well as other relative value ratios based on price) is not calculated a the arithmetic mean but
best as weighted mean or weighted harmonic mean P/E.

WHM (8.67) <HM (8.88) < AM (9); For an equal weighted portfolio, WHM = HM = AM

When there are extreme (high or low) outliers, the arithmetic mean will be the most affected.