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Outline the challenges of managing risk when money is invested in hedge funds.

FRM® Part II · Risk Management and Investment Management · VaR and Risk Budgeting in Investment Management · FRM2.IM.6.d

The idea

Investing in hedge funds makes risk management harder for several reasons. Transparency is limited, so the investor usually cannot see positions or leverage and cannot compute position-based VaR. It must work from reported returns. Return histories are short and non-normal, with option-like payoffs and fat tails, so a normal VaR from history is unreliable. Illiquid holdings priced infrequently produce smoothed returns with positive serial correlation, which understates volatility. For a first-order autoregressive pattern with coefficient ρ, long-horizon variance is the independent-return variance multiplied by this factor: Multiplier = (1 + ρ) ÷ (1 − ρ). Lockups and redemption notice periods mean exposure cannot be cut quickly, so the horizon should be longer. Correlations with other assets tend to rise in stress, and operational and style-drift risks need due diligence. Exam point: historical hedge fund VaR usually understates true risk.

Formulas

Annual volatility of smoothed hedge fund returns

σ annual = σ monthly × √12 × √[(1 + ρ) ÷ (1 − ρ)]

σ monthly
the reported monthly volatility
ρ
the first-order autocorrelation of reported returns

For a first-order autoregressive pattern with positive ρ, the factor raises volatility. Scaling by √12 alone assumes independent returns and understates risk.

A practice question

From the question bank, with the reason each wrong option is wrong.

What is the main obstacle to computing a position-based VaR for an investor's allocation to an external hedge fund?

  1. Hedge funds are not allowed to report returns.Why not: They do report returns, and returns are what investors use.
  2. VaR cannot be computed for a portfolio that has more than ten separate positions.Why not: No such limit exists; VaR is computed for portfolios of any size.
  3. Hedge fund returns are perfectly normal, so VaR is meaningless.Why not: The opposite: returns are typically non-normal, with fat tails and option-like payoffs.
  4. Limited transparency: positions and leverage are not fully disclosed, so the investor relies on returns. - correct

Investors usually cannot see positions, so VaR must come from returns and factor models. Limited transparency and non-normality make this approach less reliable.

A harder one

An investor's VaR for a hedge fund holding breaches its internal limit. The fund has a 12-month lockup and requires 90 days' notice for redemptions. What does this imply for risk management?

  1. The investor cannot cut exposure quickly, so the VaR horizon should be at least as long as the redemption delay. - correct
  2. Redeem at the next month-end, since a breach gives the right to exit.Why not: Ignores the lockup and the notice period; a breach does not override redemption terms.
  3. Ignore the breach, because a lockup stabilises the fund and so lowers the investor's market risk.Why not: Confuses stability of capital with market risk; the investor still bears losses it cannot exit.
  4. Use a one-day VaR, because hedge funds trade daily.Why not: The relevant horizon is the investor's time to exit, not the fund's trading frequency.

The risk horizon is set by how quickly the investor can reduce exposure. With a lockup plus notice period, losses can accumulate over a long window.

The hardest tier

A hedge fund reports monthly return volatility of 3.0 percent. The returns are smoothed and follow a first-order autoregressive pattern with coefficient 0.4, for which long-horizon variance is the independent-return variance multiplied by (1 + rho) / (1 - rho). The adjusted annual volatility is closest to:

  1. 10.4 percentWhy not: Scales by the square root of 12 only, which assumes independent returns.
  2. 15.9 percent - correct
  3. 6.8 percentWhy not: Applies the autocorrelation factor in the wrong direction, dividing instead of multiplying.
  4. 12.3 percentWhy not: Uses only the (1 + rho) part of the factor and omits the (1 - rho) denominator.

Naive annual vol = 3.0 x sqrt(12) = 10.39. Factor = sqrt(1.4/0.6) = 1.528, so adjusted vol = 15.9 percent. Smoothing hides risk at the monthly level.

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