Portfolio % Stock PE Stock AAA 60% 10 Stock BBB 40% 15 Which of the following is closest to the weighted harmonic mean of these two PE ratios? Is there an easy way to do this on the calc? hoping to avoid any formulas i can. 1/[(0.60 × 1/10) + (0.40 × 1/15)] = 11.54
my 2 cents: focus on the relations btw weighted harmonic, harmonic, arthimatic means, i could see them asking something like, when does the weighted harmonic = harmonic ? or evaluate the statement: the harmonic mean is greater than the arthimatic. YES! sry if this was a tangent
^^ Harmonic is always the lower. For all data sets containing at least one pair of nonequal values, the harmonic mean is always the least of the three means, while the arithmetic mean is always the greatest of the three and the geometric mean is always in between.
completely mis-stated that, thanks for the correction, Am > Gm > Hm!
Harmonic mean is based on the averaging down theory. The most common application is when buying stock at different prices. The idea is that the investor would invest the same amount of money at each price. For example, buying stock A at 10/share and 15/share. The easiest way to calculate the harmonic mean is as follows. Assume that the investor invests 1000 each time. Total number of shares bought = (1000/10) + (1000/15). HM = 2000/number of shares bought. In this case, however, there is different weight on each stock. But we can still apply the same concept. For this case, assume that we invest 1000. So 1st calculate the contributing factor of each stock to the portfolio PE. 600/10 and 400/15. Next, HM is simply 100/(the sum of the values calculated earlier).