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

[Gabor Grothendieck]

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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