Tricky!Whereas means are additive so that mean(year1+year2) = mean(year1) + mean(year2), medians are not. The medians of the individual years can be arbitrarily different from the median of the multi-year aggregate.Consider this example of three instruments measured annually for two years (Year1,Year2), biannually (BothY), and then annualized (AnnY):Year1: 2%, 4%, 18%; Mean = 8%; Median = 4%Year2: 36%, 8%, 2%; Mean = 16%; Median = 8%BothY: 38%, 12%, 20%; Mean = 24%; Median = 20%AnnY: 19%, 6%, 10%; Mean = 12%, Median = ??? The annualized median is not 10% although Alan's suggestion does work in this case. Whether Alan's suggestion works with higher numbers of instruments and years is less clear, but it seems like a usable approximation.The deeper issue here is that medians, which are robust to extreme outliers within a time series, are NOT robust to anti-correlated patterns of outliers that aggregate over time in a more sparsely-sampled time series. You might want to think about why you are using the median function and how fat-tail outliers in individual years and individual instruments will affect the median. If returns are anti-correlated across the years, the median of infrequently sampled series will be markedly different from the medians of an annually-sampled series.
Last edited by Traden4Alpha
on March 29th, 2015, 10:00 pm, edited 1 time in total.