Fund of funds fees, survivorship bias and backfill bias

What does a fund of funds cost you?

A fund of funds invests in other funds, so it has its own management and incentive fees on top of the fees the underlying hedge funds charge. This is a double layer of fees . The fund of funds sees only what is left after the first layer, so the second layer is charged on that net return.

$$r_1 = r - m_1 - p_1\,r$$

$$r_i = r_1 - m_2 - p_2\,r_1$$

These forms assume fees calculated independently, management fees on beginning assets and a positive return. With a loss there is no incentive fee in that layer.

Fund of funds versus a single hedge fundthe investor pays two sets of fees

• Manager selection and monitoring Memorize due diligence done for you
• Diversification across funds Memorize one fund's loss offsets another's gain
• Access to closed funds Memorize the only way in to some managers
• Easier redemption Memorize cash buffers and special terms, sometimes

Why accept the extra cost? The extra layer buys manager selection and monitoring, diversification across funds, access to funds closed to new investors and, sometimes, easier redemption than a direct hedge fund investment. The example above assumes all the underlying funds earn the same return, which will not be true in practice. A good fund of funds may add value by selecting managers, and a poor one adds only cost.

When a fund of funds holds several hedge funds, it charges its fees on the combined portfolio, not fund by fund. Gains in one fund offset losses in another before the incentive fee is set.

$$R_{FoF} = V_1\,m_2 + \max\left[0,\; (V_1 - V_0)\,p_2\right]$$

Why do hedge fund indexes look better than reality?

Investors who care about risk-adjusted returns with low correlation to common asset classes track alternatives through relative returns , a fund’s performance compared with that of similar investments. They compare a fund with a benchmark : an index or peer group with similar features. For alternatives, the benchmark needs care, because both the peer group and the way it is built can mislead.

Hedge fund indexes suffer from selection bias : the funds in the database are not a fair draw of all funds. Two forms matter.

Selection bias in hedge fund databasesboth biases push reported returns up

• Survivorship bias Memorize funds that fail are dropped; only survivors remain
  • Cause poor performance, investor defections, closure
  • Effect average return overstated
• Backfill bias Memorize a fund joins the index and its earlier returns are added
  • Cause managers launch several funds and report only the best ones
  • Effect average return overstated

With survivorship bias , the problem is that funds that do badly attract withdrawals and close, and then drop out of the database. Studies suggest a large share of hedge funds fail within the first few years. An index that holds only funds that still exist leaves out the failures, so investors form overly optimistic expectations of return.

With backfill bias , the problem is when and how a fund enters the index. A manager may launch several funds at once and put only the most successful ones into an index a couple of years after launch. Adding their earlier returns afterward, selectively, raises the average reported return.

Bias	What happens	Effect on index returns
Survivorship	funds that close disappear from the database	overstated
Backfill	a fund joins after a good start and its earlier returns are added	overstated

Because of both biases, a hedge fund index may reflect only the funds that performed best early or that have not failed, rather than the average hedge fund.

Exam tip Failures vanish = survivorship. History arrives late = backfill. Either way, the index return is too high.

Fairer comparisons use like with like. For private equity and real estate, compare funds of the same vintage year, on an annual basis or since inception, because a composite benchmark can mislead when a fund is at a different life cycle phase from most of its peers. Compare hedge funds only with peers that follow the same strategy. And remember that lockups and illiquidity may stop an investor from acting on poor results, even when the comparison shows them.

Go deeper Survivorship bias outside hedge funds

The same bias affects any dataset built from today’s survivors: mutual fund databases that omit closed funds, and stock indexes tested only on companies that still exist. It comes back in the Quantitative Methods module on sampling and estimation.

Go deeper How much of the gross return do the two layers take?

In the 15% example the investor ends with 8.0%, so fees took 7.0 of the 15.0 points: about 47% of the gross return. A direct investor in the same hedge funds would keep 10.0%, and fees would take 5.0 points, one third. The comparison that matters is the extra 2.0 points against the value of the selection, diversification and access that the second layer provides.