[R-sig-Finance] Confidence intervals for spread returns
Krishna Kumar
kriskumar at earthlink.net
Sun Jun 25 20:26:27 CEST 2006
are the portfolio weights found using simulation. i.e. You simulate the
underlying asset returns and then optimize
on the simulated paths?. Bootstrapping seems like a natural way to get
the conf.intervals.
Krishna
David Kane 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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