Let's assume we need to calculate a 1-day VaR for a portfolio of funds. Funds are traded, they can be bought and sold every day. We know exactly what the assets in each fund are. What is the right way to calculate VaR?
Both approaches have drawbacks, so if one must choose among the two then one shall compare those drawbacks in the specific case. Or another way would be devising a hybrid of the two (e.g. adding statistics of historical deviations of the fund portfolio from the (1) view etc...).
Among the drawbacks of (1): trading costs, rebalancings, management fees etc are all lost/not accounted for. For (2): you might lose in information & statistical efficiency (especially if number of constituents > funds) compared e.g. to a factor model; one also loses the ability to deal properly with derivatives (available in (1) by also tracking underlyings).
Of course it's important what kind of funds you're dealing with, which will change the relative importance of the above mentioned drawbacks; e.g. are they active or passive/benchmarked? Obviously passive will mean (1) is less problematic than with active ones (but this doesnt eliminate the need for a comparison altogether)...
If you have time I would suggest going for a hybrid to get the best of both approaches. Some detail on this joint model:
(1) has the advantage of detailed statistics on the invested universe and its dynamics
(2) additionally to the underlying investment (2a) (which is not accessible directly, and might also have lower statistical power) also includes the above mentioned additional dynamics proper of the fund & management (2b).
The first goal of the hybrid model is of course to extract that second component (2b), by subtracting the market behaviour which we assume is known in more detail by (1).
As a second step of course one can then simulate forecasts of the combined model (1)&(2b) and calculate a VaR on them.
So the trickery is mostly in deriving (2b). If the history of fund holdings is also known besides obviously the history of the underlying prices too (let's call this ideal case 1A), then additional information e.g. on rebalancings can enter (2b) (to help identify residuals such as fees, if they´re not known explicitely) and the comparison between (1) and (2a) is proper in the first place. All the market dynamics in the funds is correctly modeled so that the residual fund behaviour can be analysed. Otherwise -keeping a fixed fund composition (1B)- you must take care that far away in the past this present view induces a static "synthetic" fund history which might be diverging from the correct dynamic syntetic fund history (1A), and thus the resulting discrepancies among the two views (2)-(1B) that you are analysing for (2b) might not be very realistic. So here one shall do atleast some additional exponential weighting or so...
No matter how you calculate the VaR (historical simulation, covariance approach, MC) I assume that you work on historical data or data derived from the history of assets, risk factors and theresuch.
If this assumption is correct then I would use approach (1). If you know the exact positions today of the (sub-)funds, then (except from some technicalities) you have all these assets in your fund-of-funds.
If you use approach (2) then the historical time series will be biased as the (sub-)fund might have traded a lot in the past (changed duration, equity long/short). Then the history of the (sub-)fund itself does not reflect the risk of the current positions today (!)
If you subfunds are rather benchmark based and stick close to it, then (1) and (2) will not differ that much. To be on the safe side I recommend (1).
