# [R-sig-finance] Fund ratios with lagged correlations

Patrick Burns patrick at burns-stat.com
Fri Mar 10 15:25:11 CET 2006

```One solution to the problem is in Burns, Engle and Mezrich(1998)
"Correlations and Volatilities of Asynchronous Data".
The working paper version is available at ucsd.edu.

That solution is to fit a multivariate MA(1) and then
transform to get synchronized values.  The paper is
written in terms of multivariate GARCH estimation, but
my impression is that the MA estimation is quite robust
to GARCH effects even if you don't fit them.

The idea of using lower frequency returns has been
suggested.  In experiments that I've tried (on equity
indices), it looked like weekly returns was about right
to get rid of the asynchrony.  (Though if your series
are close in time, you might be able to get away with
less aggregation.)

Patrick Burns
patrick at burns-stat.com
+44 (0)20 8525 0696
http://www.burns-stat.com
(home of S Poetry and "A Guide for the Unwilling S User")

Enrique Bengoechea wrote:

>
>
>Hi, I'm having a problem computing funds ratios such as alpha, beta, tracking error, etc, and maybe the list wisdom can be of help  :-)
>
>I have daily NAVs and values of luxembourg funds and their benchmarks. Most funds investing in the US have a delay on its NAV of 1 day with respect to benchmarks such as S&P500. I find this easily using the ccf function, and then I just compute the ratios
>of the delayed (returns of the) NAVs with respect to (returns of) the benchmark.
>
>The problem is that with some markets (e.g. south american funds) the correlation between the fund and its benchmarks is splitted between the current day and the previous day. I find this by testing that none of the series exhibits significant serial
>autocorrelation, but the cross-correlations are high for both the 0 and 1 lag (say 0.5 and 0.5, or 0.7 and 0.4). With products that trade continuously I can solve this problem by taking into account timezones and using prices at specific times of the day,
>but with funds and many indexes only end-of-day values are available.
>
>Has someone faced this problem? How do you adapt the beta/correlation/etc computations to handle this issue and come up with sensible estimates? Any paper dealing with this topic?
>
>
>Enrique
>
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```