Confidence intervals for spread returns
You might want to provide for the user to choose normal theory or bootstrap confidence intervals in the design. The actual implementation could be left to a later release if you already have your hands full.
On 6/21/06, David Kane <dave at kanecap.com> wrote:
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
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