Choosing a Value-at-Risk Model for Fund Portfolios
Summary
The document compares two ways to estimate one-day value at risk for a portfolio of funds: reconstruct and model the underlying assets, or treat each fund as a tradable asset. Modeling holdings directly can provide more information about constituent risk and underlying exposures, including derivatives when their underlyings are tracked. However, it may omit fund-level effects such as trading costs, rebalancing, fees, or management decisions. Using fund return histories captures those effects, but may lose statistical detail and can misrepresent current risk when fund holdings have changed over time.
The responses suggest weighing these limitations according to whether funds are active or benchmark-oriented, and propose a hybrid that models underlying market behavior while analyzing fund-specific residuals. Such a hybrid depends on the quality and history of holdings data; a synthetic history built from current holdings may diverge from the fund’s actual past portfolio. The document offers modeling considerations rather than a definitive method or comparative performance evidence.
Key ideas
- Modeling underlying holdings can provide detailed exposure data and represent derivatives through their underlying assets.
- Fund-level histories retain costs and management effects but may reflect past holdings that differ from current positions.
- The relative merits of the approaches depend partly on whether the funds are active or benchmark-oriented.
- A hybrid can model market behavior from holdings and analyze the remaining fund-specific effects.
- Synthetic histories based on current holdings may not represent the fund’s historical portfolio accurately.
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# VaR for portfolio of funds # 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? - flatten the portfolio and calculate VaR on a portfolio of assets - treat each fund as a tradeable asset and calculate VaR based on that? ## Answer by Quartz (score 4, accepted) https://quant.stackexchange.com/a/8113 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... ## Answer by Richi Wa (score 3) https://quant.stackexchange.com/a/8097 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).
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