[R-sig-Finance] Confidence intervals for spread returns

[David Kane]

We are creating an R package for simple backtests. One part will
involve creating decile (or whatever) portfolios and then looking at
the spread return between the top and bottom decile. So, for example,
the top decile might return 10% and the bottom decile 2%, yielding an
8% spread return if one were to go long the top decile and short the
bottom.

Question: How might one calculate a reasonable confidence interval
around this 8% spread return?

The obvious intution is that more securities in each decile should
lead to more narrow confidence interval. For example, if there are 100
securities in each decile, then the 8% result is fairly accurate. If
there are only 2 securities per decile, then the 8% could easily be
very wrong.

One hack might be to argue the spread is sort of a weighted mean
calculation in which the weights are 1 for the long decile and -1 for
the short decile. If there are N securities total, there would be N/10
in each decile or 2*N/10 in the bottom/top together. If sd(r) is the
standard deviation of the returns of these securities (just those in
the extreme deciles), the standard error would be:

SE = sd(r) / sqrt(N/5)

This would suggest that a reasonable confidence interval around 8%
might be +/- 2 times SE. Does that make sense?

Thanks,

Dave Kane