# VaR for portfolio of funds

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?

1. flatten the portfolio and calculate VaR on a portfolio of assets
2. treat each fund as a tradeable asset and calculate VaR based on that?
• I would think #2 because #1 would contain correlations don't necessarily exist. May 21, 2013 at 14:54
• Why? Over the space of 1-10 days the funds NAV should track their assets' values rather closely. May 21, 2013 at 19:22
• Do you want to incorporate market inefficiencies such as the trading costs each fund makes? May 21, 2013 at 19:33
• @quant_dev best way without any more info as to whether the portfolios include short positions or not, whether there is overlap in the securities held among the funds, etc., is to run a backtest using each approach and pick the more conservative of the two, assuming either one is conservative enough at the threshold/time combination in question. May 21, 2013 at 21:18
• @quat_dev : Hi I would add the following remark to what has been said. Using only NAV for VaR then entails that you incorporate the history of reallocations of the funds, this is methodologically a poor proxy to the VaR you obtain using the "transparency" approach by true assets. Of course if those reallocations are limited the method works fine, and sometimes you simply don't have the choice... Best regards. May 22, 2013 at 6:29

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...

• "adding statistics of historical deviations of the fund portfolio from the (1) view" - do you mean tracking the difference between the fund valuation and the valuation of its assets using mid prices? May 30, 2013 at 12:29
• @quant_dev: For example, yes, that's the first & most basic step, but that will only capture some of the discrepancies since it's a static view. Then you can feed it back in your forecasts as an independent component. Improving on this one could first model dependencies with the other variates, and then sample joint forecasts. But to also capture temporal discrepancies, such as rebalancings, you should compare/model the running forecasts (returns conditional on the statistics on previous data) historically, in a kind of backtesting, not just the 2 valuations series. I'll expand if too cryptic. May 31, 2013 at 10:32
• Please do, this is interesting. Jun 3, 2013 at 8:49
• Is it clear/enough like this or shall it be edited further? I'm writing in a hurry from work so it might not be clear at a first read... I kept it more on the historical modeling there, other than referring to forecasts discrepancies which emerge as a consequence anyway. Jun 4, 2013 at 9:41

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).