SURVEY - MASTERING INVESTMENT: Mastering Investment
Financial Times; May 21, 2001

Part Two

This is the second issue of Mastering Investment, the FT's essential guide to the principles and practice of investment. Published in 10 weekly parts, the series covers all aspects of portfolio investment, from financial markets, bonds, equities and valuation to portfolio management and global investing. For a list of forthcoming topics, please turn to page 15.

Page 2

How to build a share index

The movements of financial indices such as the FTSE 100 or the Dow Jones Industrial Average are followed daily by bankers, economists, governments and investors. What can they tell us about financial conditions? On these pages Paul Marsh explains why indices are important and how they are constructed. He describes the way they are used to monitor the performance of investment professionals and to create index funds.

Page 6

A model weighting game in estimating expected returns

The estimation of expected returns is vitally important for money managers and corporate finance professionals, since it affects their decisions on what to invest in and which projects to carry out. However, this is no easy task. Here L'ubosù P!stor sets out some common approaches from asset pricing theory and assesses their effectiveness.

Page 8

Markets and the business cycle

The stock market and the wider economy are not always aligned, says Jeremy Siegel, yet over the past two centuries movements in the stock market have often presaged recession or recovery. For investors who think they can predict the state of the economy, the potential rewards are enormous. In fact, Siegel shows, our historical record for economic forecasting is decidedly poor.

Page 12

Consolidated limit order book: future perfect or future shock?

All stock markets have something in common: they bring together buyers and sellers. However, the ways in which they do so may differ greatly in practice, and such differences often benefit one group of at the expense of another. In this article Ken Kavajecz describes the current debate surrounding CLOB, a mechanism that enables greater transparency between investors.

Page 15

Corporate bonds and other debt instruments

In last week's issue Stephen Schaefer introduced the topic of bonds and showed how bond portfolios are managed. This week, he explains the special characteristics of corporate bonds and the strategic choices available to bond managers. Using derivatives alongside bonds, managers can now use their expertise in bonds to create portfolios that behave like equity portfolios.

We hope you will enjoy Mastering Investment and find the latest ideas in investment useful and interesting. If you have any comments about the series, please email mastering@ft.com.

Mastering Investment @ FT.com

Article summaries, background reading and further information are available at www.ft.com/investment.

How to build a share index

Stock market indices may not be a matter of life and death, but they are vital as investment benchmarks.

Paul Marsh explains how they are constructed

"Everything is looking decidedly wobbly ... Dow 9,500 is probably the most important number on the planet at the moment." The Blind Squirrel on the Motley Fool website.

an a stock market index number really matter so much? Clearly not, but to investors, it can seem so. Market indices are the benchmarks we use to monitor markets and judge performance. We love them, we hate them, but we cannot live without them. This article reviews the role of indices and gives guidelines for index construction. It describes how indices are used in performance measurement, index funds and measuring long-run returns.

We need indices

It would be hard to discuss investments without indices. We could not answer even such basic questions as "How's the market doing today?", "How did technology stocks perform last year?" or "Have shares beaten bonds over the long run?"

Indices have many purposes. First, they are used to monitor and measure market movements, whether in real time, daily, or over decades. A good index will tell us how much richer or poorer investors have become. Second, equity and bond indices are economic barometers, while equity indices are leading indicators. Monitoring markets and comparing movements with data such as wages, profits and inflation helps us to understand economic conditions and prospects.

Third, indices provide essential benchmarks in fund management. A managed fund can communicate its objectives and target universe by stating which index or indices serve as the standard against which its performance should be judged.

Fourth, indices underpin products such as index funds, exchange-traded funds, and options and futures on indices. These index-related products form a several trillion-pound business and are used widely in investment, hedging and risk management.

Finally, indices support research (for example, as benchmarks for evaluating trading rules, technical analysis systems and analysts' forecasts); risk measurement and management; and asset allocation and international diversification decisions.

Coverage

Indices are all-pervasive, with more than 4,000 in operation. Equity market indices, such as the Dow, Nikkei, Dax and FTSE 100 tend to be the best known. But indices are also important for other assets such as government and corporate bonds, commodities, currency baskets and retail prices.

As well as market indices, there are numerous sub-indices. For equities, these cover sectors, size bands, investment styles, and even ethical and religious dimensions; for bond indices they span maturities and credit risk categories. There are international indices that aggregate country indices into regions (such as Asia), currency zones (such as the euro), market types (such as emerging markets) and worldwide indices. While this article focuses on equity indices, the principles apply to all types of index.

Averaging

Index construction is straightforward in principle, involving a process of averaging and weighting. Indices start at a base date when they are assigned an initial value, such as 100 or 1000. Later values depend on the weighted average return on the constituents.

Consider an index with base value 1000 and three constituents, shares A, B and C, which at the base date all had market values of Pounds 1bn. By the next day, assume the share prices had changed by +20%, +8% and -10%. The average return was (20 + 8 - 10)/3 = 6%, and hence the index value will be 1000 x 1.06 = 1060. The guiding principle is that the percentage change in the index (6%) should represent the change in value of the market. The market in our example contains three stocks, worth Pounds 3bn initially, and Pounds 1.2 + Pounds 1.08 + Pounds 0.9bn = Pounds 3.18bn on the next day. The percentage change in value is (Pounds 3.18bn/Pounds 3.00bn) - 1 = 6%, so our index value of 1060 is verified.

This example uses arithmetic averaging, that is, we totalled the three returns and divided by three. This is the correct method used by most indices. Some early indices used geometric averaging and this survives in indices such as the US Value Line Geometric Index and the FT Thirty Share Index. The geometric average of n returns is the nth root of the product of (one plus) the percentage returns, minus one. In our example, the geometric average return is:

(3Ã (1.2 x 1.08 x 0.9)) - 1 = 5.26%

This gives an index value of 1052.6, rather than the correct figure of 1060. The geometric average is always less than the arithmetic average, so investors can always beat a geometric index by buying and holding its constituents. One needs to be aware of this when looking at longer-term returns based on geometric indices.

Weighting

For indices to reflect changes in market value, they must be based on weighted-average returns, where the weights reflect each stock's value. Assume that companies A, B and C are no longer equal in size, but start with market capitalisations of Pounds 1bn, Pounds 2bn and Pounds 3bn. The value of our three-share market is Pounds 6bn. The weighted average return over the next day is:

(1 x 20% + 2 x 8% + 3 x -10%)/6 = 1%

Hence the index value is 1010. Again, we can check this corresponds to the change in market value. Initially, the market was worth Pounds 6bn. The next day, it was worth Pounds 1.2bn + Pounds 2.16bn + Pounds 2.7bn = Pounds 6.06bn. The percentage change was (Pounds 6.06bn/Pounds 6.00bn) -1 = 1%, so 1010 is correct.

Some early indices used equal, rather than market capitalisation, weighting. Such indices will give an unbiased estimate of the true market return only if large and small stocks perform in line, which is seldom the case. Other indices, including the Dow Jones Industrial Average (DJIA) and Nikkei 225, use share price weighting, so that higher price (rather than capitalisation) stocks receive greater weight. Although such indices are adjusted for stock splits, splits still lead to lower index weightings, and vice versa for consolidations. Price weighting has no economic rationale and is hard to justify or interpret.

Some complications

While index construction is simple in principle, there are many complications in practice. Share returns can be hard to compute for companies undergoing complex events and restructuring. International indices need to adjust for currency movements and exclude stocks that are unavailable to, or too illiquid for, foreign investors. Even capitalisation weighting has become controversial and many now argue for free-float weighting.

Many European stocks have large government or family holdings and many Japanese stocks have sizeable cross-holdings. Advocates of free float argue that if, say, 75 per cent of a stock is government-held, its index weighting should be 25 per cent. This reflects the "investable" weight or "free-floating" shares that public investors could hold. The concern is that if such stocks had 100 per cent weightings, this might stimulate demand, especially from index trackers, which could distort the market.

There is a distinction between cross-holdings and non-public holdings. Cross-holdings should be excluded to avoid double counting. The extreme case is closed-end investment companies, which consist solely of cross-holdings. Index providers recognise this by publishing variants of their indices without investment companies. But cross-holdings can also be prevalent for companies other than investment trusts, especially in Japan. Morgan Stanley Capital International (MSCI) estimates the average free float is just 65 per cent in Japan, versus 94 per cent in the US and 92 per cent in the UK, with much of this difference arising from cross-holdings.

Arguments are less clear-cut for non-publicly held shares. If an index is to approximate closely the "market portfolio" of financial theory, it should include, not exclude, the non-traded portion of a company's equity. There are also debates about how free float is defined. For example, why exclude family-held shares, which could be traded, but include shares held by index funds? Despite these caveats, major index providers, such as FTSE International, MSCI and Dow Jones Stoxx are all switching to free float.

Other principles

There are three other principles of index design. First, an index should provide the widest, most representative coverage of its target segment. Interestingly, the best-known indices fail this test. The Dow Jones, for example, covers just 30 US blue-chips. It survives through history and affection. It began in 1884 and was the first published index, then with 11 constituents. Charles Dow had neither computer nor calculator, hence his limited coverage. Today, 30 stocks are far too few.

Figure 1 shows the performance of four US indices over the year to the end of March 2001. All fell, but by different amounts. The DJIA, with its limited coverage and blue chip focus, fell 10 per cent. The more broadly based, but still large-cap oriented Standard & Poors 500 fell 23 per cent. In contrast, the Nasdaq, with its technology focus, fell a massive 60 per cent. The best measure of the US market is provided by the comprehensive Wilshire 5000, which, despite its name, covers more than 7,000 stocks. This fell by 26 per cent. The choice of index matters and it is ironic that the broadest and best index is the least known.

Total returns and dividends

Second, indices should measure total return. Investment returns comprise income plus capital gains or losses. Ignoring either leads to serious bias when measuring long-term returns. Yet many early equity indices measured just capital gains, ignoring dividends. Conversely, but equally seriously, early bond indices often recorded just yields, ignoring price movements. While short-run equity performance is driven by capital appreciation, long-term returns are driven by reinvested income.

Figure 2 shows this. It gives the cumulative capital gain and total return over the past 101 years on the ABN Amro/LBS UK Equity Index.

The sum of Pounds 1 invested in 1899 would have grown to Pounds 149 by 2001 if dividends had been spent or squandered. In contrast, with dividends reinvested, Pounds 1 would have grown by 108 times as much to Pounds 16,112. Clearly, unless indices incorporate reinvested dividends and so measure total return, they will be of little value for measuring long-term performance.

Trackability

Third, good indices must correspond to an investment strategy that could be set up in advance and followed in real life. Apart from dealing costs and taxes, an index tracker fund should be able to replicate index performance. This rules out geometric indices or those using price averaging, since these are not replicable. But there can also be other problems, relating to over-frequent rebalancing, and bias in back histories.

If indices are rebalanced too often, this can lead to bias and excessive turnover. In 1984, the Vancouver Stock Exchange had to announce there was a cumulative error in its index of more than 100 per cent. This was caused by bid-offer bias, a technical problem arising from over-frequent rebalancing. More recently, a different rebalancing problem occurred with the FTSE SmallCap Index.

All small-cap indices need periodic rebalancing so they continue to track smaller companies. Over-frequent rebalancing, however, is costly for tracker funds, as small-caps have high dealing costs. Given this trade-off, most small-cap indices rebalance annually.

The FTSE SmallCap not only rebalances annually, but also experiences constituent changes whenever there is a promotion to, or demotion from, the FTSE 350 (the largest 350 stocks). During 2000, there were so many promotions and demotions that an index fund seeking to track these changes would have led to turnover of 128 per cent, even ignoring the annual rebalancing. This is very high even compared with actively managed funds.

High turnover plus the impact of numerous constituent changes made the SmallCap hard to beat and three out of four small-cap fund managers failed even to match it (see Dimson and Marsh, 2001). In contrast, about half of these funds beat the more broadly based Hoare Govett Small Company Index, which is rebalanced yearly. This is what one would expect with a well-designed benchmark.

Avoiding bias

When a new index goes live, it is common practice to provide investors with a back-history of performance. When indices are constructed retrospectively, it is crucial to ensure they do not use hindsight. Serious biases arise if constituents are tilted towards stocks that subsequently survived or grew large, or towards sectors that later became important.

When the UK's FTSE 100 Index was launched in 1984, a British newspaper published a six-year back-history. This was constructed from the 100 largest stocks at the launch date of the index, rather than starting with the 100 that had been largest six years before. Clearly, six years earlier, investors did not know which stocks would subsequently perform best and grow largest. This led to back-history returns being erroneously overstated by 5 per cent a year.

A similar problem arose with the pre-1955 back history for the Equity-Gilt studies which, for over 40 years (from De Zoete and Gorton, 1955, to Barclays Capital, 1999) were regarded as the authoritative source of long-run UK returns. Research by Dimson, Marsh and Staunton (2000) using the more broadly based ABN Amro/LBS UK Equity Index from 1900 to 2000 found that, because of survivorship and success bias, the returns before 1955 in the Equity-Gilt studies were considerably overstated. The study has been revised by Barclays Capital (2000), although its early coverage remains limited.

Performance measurement

Indices are widely used as benchmarks in performance measurement. For a general UK equity fund, for example, the FTSE All-Share Index provides a suitable naive benchmark. We say "naive" because an investor with no stock selection skills could match the FTSE All-Share simply by holding its constituents and running a tracker fund.

When measuring performance, we are therefore seeking evidence of the fund beating its benchmark by at least the incremental management fees charged. If not, the fund manager has added no value.

Performance measurement is naturally more complex than this and three caveats are needed.

First, comparing fund performance with indices is slightly unfair, because indices incur no dealing or other costs. Some transaction and administrative costs are involved in running even an index tracker, although for large market tracker funds, such costs should be low.

Second, performance measurement should embrace risk as well as return and there are many ways of adjusting for risk (see a standard textbook, such as Alexander, Sharpe and Bailey, 2001). The important question that risk adjustment addresses is whether the fund manager took on a higher or lower level of risk than the benchmark index and whether this can explain any apparent out- or under-performance.

Third, performance should be judged only over long periods. This is because markets are volatile and luck plays a major role. Skilful managers can experience runs of poor performance, while a monkey picking stocks from a hat would have successful years, and even good multiyear runs. Research shows that few equity fund managers can expect to outperform by more than 1 per cent a year after fees and costs. With this level of skill, it takes at least 25 years to confidently tell luck from judgment.

Index funds

A second major use of indices is to underpin a wide-range of financial products, the most important of which are index funds. These portfolios track an index. They are passively managed, that is, no views are taken about which stocks are over- or under-valued and transactions are limited to those needed to keep the portfolio in line with index changes.

Index funds first appeared in the US in 1971 following academic studies that found active fund managers had mostly failed to beat market indices by enough to cover their expenses. Index funds also offered maximum diversification at a low cost. Dealing costs were low because there were few transactions, while management fees were minimised, since portfolios could be managed mostly by computers.

Over the past 30 years, index funds have become enormously successful, with trillions of pounds invested worldwide. Their subsequent growth has been fuelled by further research continuing to cast doubt on the value of active management.

Today, about 30 per cent of US funds and 10-20 per cent of UK funds are directly indexed. A far larger proportion of fund managers (perhaps a majority) surreptitiously track their benchmark index, or match closely index weightings. These are known as "closet indexers" or "index huggers". Whatever the merits of this, indices have clearly had a huge influence on investment management practices.

Measuring the risk premium

Indices also allow us to measure long-run rates of return and the reward investors have received from investing in equities rather than risk-free investments. This reward for risk is known as the equity risk premium and is measured as the difference between returns on equities and those on either government bills or bonds.

The equity risk premium is extremely important. It is central to projecting investment returns, calculating the cost of capital, valuing companies and shares, appraising projects within companies and determining fair rates of return for regulated utilities. All these applications require an estimate of the prospective risk premium, whereas, by definition, the only premium we can measure is the historical premium.

Figure 3 shows the historical risk premium for 15 countries relative to both bonds and bills. Relative to bills, the annualised premium is 4.7 per cent for the UK, 5.6 per cent for the US, and 5.1 per cent averaged across all 15 countries. Relative to bonds, the premia are slightly lower: 4.4 per cent for the UK, 5.0 per cent for the US and 4.7 per cent for the 15-country average.

Over the 20th century, equity investors enjoyed a substantial risk premium and over the past 50 years, it was higher still. What does the future hold? Are these figures a good guide to the future? No one knows, but the study from which these estimates were taken concluded that the premium will be lower over the next 100 years. We can be certain of only one thing. If in 100 years' time we wish to check this prediction, to do so, we will continue to be reliant on high quality, well-constructed indices.

Paul Marsh is Esm}e Fairbairn Professor of Finance at London Business School. He has designed several indices and worked with Elroy Dimson on the FTSE 100.

Further reading

* Alexander, G.J., Sharpe, W.F. and Bailey, J.V. (2001) Fundamentals of Investments, 3rd ed., New Jersey: Prentice-Hall.

* Barclays Capital (1999) and (2000) Equity-Gilt Study 1999 and Equity-Gilt Study 2000, London: Barclays

Capital.

* De Zoete and Gorton (1955) Equities and Fixed Interest Investment, London.

* Dimson, E. and Marsh, P. (2001) "Index rebalancing and the technology bubble", Journal of Asset Management, 3(1), 1-10.

* Dimson, E., Marsh, P. and Staunton, M. (2000) The Millennium Book: A Century of Investment Returns, and (2001) Millennium Book II: 101 Years of Investment Returns, London: ABN Amro/London Business School.

Signpost

See the article on mutual fund performance in part seven, June 25.l

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