Passive management

Passive management is the strategy where a fund manager makes portfolio decisions so as to mimic the performance of a externally specified index. Funds which utilise passive management are called 'index funds'. The ethos of an index fund is aptly summed up in the injunction to an index fund manager: Don't just do something, sit there!

Passive management is most common on the equity market, where index funds track a stock market index. Today, there is a plethora of market indexes in the world, and thousands of different index funds tracking many of them.

Rationale

Questions -- Why are index funds interesting? Why would it make sense to sit there and do nothing? What is the empirical performance of index funds?

Implementation

At the simplest, an index fund is implemented by purchasing securities which make up the index. Most sensible indexes are market-capitalisation weighted, so the index fund also has to invest in the securities in the index in proportion to their market capitalisations. Such an index fund is said to utilise full replication.

There is a common misconception that index funds have to trade every time prices change. This is not required, because the index fund weights change in exact synchrony with changes in market prices.

Example: Suppose an index is made of two companies, which have prices $1 and $2, and are made up of 100 and 200 shares. Thus the market capitalisations are $100 and $400. Suppose an index invests in these to the extent of $1 and $4, i.e. buying 1 and 2 shares.

Now suppose the prices change to $2 and $3. This makes the new market capitalisations to $200 and $600. The index fund which had a portfolio (1,2) now has values of $2 and $6, which is correctly on market capitalisation weights.

This example illustrates that an index fund can simply sit tight when prices fluctuate. This portfolio will correctly track the changing weights of alternative stocks in the index.

The index fund needs to trade when corporate actions (such as an SEO) take place, or when funds flow in/out of the fund.

Metrics

At the simplest, an index fund is judged on it's "tracking error". This is defined as the annualised standard deviation of the [tracking error]? between the returns on the index fund and the returns on the index that it is supposed to replicate. Tracking error is computed using the following steps:

  
 Over a stated time-period, compute daily returns on the index fund and daily 
       returns on the index. The computation of returns on the index fund should
       fully account for the fees and expenses that the end-investor suffers.
       The computation of returns on the index should give full credit for dividends
       or interest payments that accrue to the index portfolio. The index variant
       which does this is called the "total return index" (see [index construction]?).
  
 Subtract the two, to obtain a daily time-series of the error between the
       index fund return and the total return index return.
  
 Compute the standard deviation of the error time-series.
  
 Annualise this by multiplying by the square-root of the number of trading
       days a year, which is roughly sqrt(250).

Tracking error is the standard deviation of the random variable, which is the error between index fund return and TR index return over one year. Assuming this error is normally distributed, we can then make inferences such as "The actual error is likely to be smaller than twice the tracking error with a 95% probability". For example, if an index fund exhibits a tracking error of 0.3%, then we can be 95% sure that over a one--year period, the error between the index fund returns and the TR index will be smaller than 0.6%.

Tracking error penalises discrepencies between the index fund and the index, but it does not directly concern itself with portfolio strategies which obtain systematically higher or lower returns. These include fees, riskless efforts to obtain superior returns such as stocklending, and index arbitrage, etc. Hence, an alternative measure that is often preferable in judging index funds is the "information ratio", which is defined as the [Sharpe's Ratio]? of the error time-series. It is the reward divided by risk, i.e. it is the average outperformance of the index fund divided by the tracking error.

Taxonomy

At the simplest, we have plain vanilla index funds, which only invest in securities using the weights specified in the index. These funds will, in general, underperform the index since the index fund suffers transactions costs and management fees. Alternatively, we can have index plus funds, which utilise stocklending and index arbitrage to add positive errors to the index fund performance. This may increase tracking error, but generally improves the information ratio. Finally, we can have synthetic index funds, which utilise index futures and index options in implementing the index fund - they don't actually own any shares.

These terms are not universally agreed upon. The above is an attempt at reflecting a broad consensus on terminology. However, there are shades of gray and certain difficulties with terminology.

Sometimes, a fund which is apparently under [active management]? may actually be substantially invested in an index. This is called closet indexation. Sometimes, the fund manager is under a contractual obligation that while he can do active management, his tracking error will not exceed a stated level. This fund manager seeks opportunities to outperform the index while basically staying close to index performance. Sometimes the term index plus fund is used to describe such a policy also.

Further reading

  
 AJAY SHAH and KSHAMA  FERNANDES.  "The relevance of index funds for
   pension  investment  in  equities."  In:  "New  Ideas  About  Old  Age
   Security:  Toward  Sustainable  Pension  Systems in the 21st Century,"
   (editors) ROBERT HOLZMANN and JOSEPH STIGLITZ. World Bank, 2001. This is
   a survey article on index funds. It can be accessed at 
   http://www.igidr.ac.in/~ajayshah/public_html/PDFDOCS/ShahFernandes2001_indexfunds.pdf

Related entries -- [index construction]?, [active management]?, [performance evaluation]?, [fees and expenses in fund management]?, Vanguard?, [State Street]?, [Barclays Global]?, [[Standard & Poors]], [[S&P 500]], [index futures]?, [Pension fund management]?.