A “fund of funds” (FOF) is an investment strategy of holding a portfolio of other investment funds rather than investing directly in stocks, bonds or other securities. This type of investing is often referred to as multi-manager investment. A fund of funds may be “fettered”, meaning that it invests only in funds managed by the same investment company, or “unfettered”, meaning that it can invest in external funds run by other managers.
There are different types of FOF, each investing in a different type of collective investment scheme (typically one type per FOF), for example a mutual fund FOF, a hedge fund FOF, a private equity FOF, or an investment trust FOF. The original Fund of Funds was created by Bernie Cornfeld in 1962. It went bankrupt after being looted by Robert Vesco.
Investing in a collective investment scheme may increase diversity compared with a small investor holding a smaller range of securities directly. Investing in a fund of funds may achieve greater diversification. According to modern portfolio theory, the benefit of diversification can be the reduction of volatility while maintaining average returns. However, this is countered by the increased fees paid both at FOF level and at the level of the underlying investment fund.
In its article on Funds of Funds, Investopedia notes that, “Historically, a fund of funds showed an expense figure that didn’t always include the fees of the underlying funds. As of January 2007, the SEC began requiring that these fees be disclosed in a line called ‘Acquired Fund Fees and Expenses’ (AFFE).”  
After allocation of the levels of fees payable and taxation, returns on FOF investments will generally be lower than what single-manager funds can yield. However, some FOFs waive the second level of fees (the FOF fee) so that investors only pay the expenses of the underlying mutual funds. 
Pension funds, endowments and other institutions often invest in funds of hedge funds for part or all of their “alternative asset” programs, i.e., investments other than traditional stock and bond holdings.
The due diligence and safety of investing in FOFs has come under question as a result of the Bernie Madoff scandal, where many FOFs put substantial investments into the scheme. It became clear that a motivation for this was the lack of fees by Madoff, which gave the illusion that the FOF was performing well. The due diligence of the FOFs apparently did not include asking why Madoff was not making this charge for his services. 2008 and 2009 saw FOFs take a battering from investors and the media on all fronts from the hollow promises made by over-eager marketers to the strength (or lack) of their due diligence processes to those carefully explained and eminently justifiable extra layers of fees, all reaching their zenith with the Bernie Madoff fiasco.
These strategic and structural issues have caused fund-of-funds to become less and less popular. Nonetheless, fund-for-funds remain important in particular asset classes, including venture capital and for particular investors in order for them to be able to diversify their too low or too high level of assets under management appropriately.
The FOF structure may be useful for asset-allocation funds, that is, an “exchange-traded fund (ETF) of ETFs” or “mutual fund of mutual funds”. For example, iShares has asset-allocation ETFs, which own other iShares ETFs. Similarly, Vanguard has asset-allocation mutual funds, which own other Vanguard mutual funds. The “parent” funds may own the same “child” funds, with different proportions to allow for “aggressive” to “conservative” allocation. This structure simplifies management by separating allocation from security selection.
A target-date fund is similar to an asset-allocation fund, except that the allocation is designed to change over time. The same structure is useful here. iShares has target-date ETFs that own other iShares ETFs; Vanguard has target-date mutual funds that own other Vanguard mutual funds. In both cases, the same funds are used as the asset-allocation funds. Since a provider may have many target dates, this can greatly reduce duplication of work.