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Construction of indices: An investment index represents the

relative changes in the share/stock prices of the constituent companies or stocks which make up the index. The various methods of averaging those relative price changes are dealt with below.


here are many investment indices in use throughout the world,

T with each index having its own particular purpose and use. Each index will be constructed using certain eligibility criteria to determine the constituent companies from time to time.


Weighted arithmetic indices

Most investment indices are calculated on a weighted arithmetic average basis,


For investment indices, the weights used are

the market capitalisations of the constituents, usually the market capitalisations of the constituents at time 0. In the same way that a typical portfolio will be weighted towards the bigger companies, the index will be weighted towards the bigger companies.
The constant K is fixed when the index is first set up. Often it is fixed so that the index starts at a round number such as 100 or 1,000. For example, the FTSE 100 had a base value of 1,000 when it was started on 31 December 1983.


A new index is to be constructed in a share market that contains just two shares, in Companies A and B. At the starting date of the index, time 0, there are 100 shares in each company. Company A shares are priced at 3, whilst Company B shares are priced at 1.
. (i)  What is the market capitalisation at time 0? 

. (ii)  What are the weights to be used in the above formula? 

. (iii)  What value of the constant K is required if the index is to have a starting value of I (0) = 100 ? 

. (iv)  What is the value of the index at time 1 if the share prices have by then increased to 3.2 and 1.1 respectively?



The weights are updated

each time the number of shares issued by a constituent company changes and continuity is maintained by “chain-linking” the index on the new capital to that of the previous index.
It is now becoming common practice to restrict the weights to reflect the level of “free float” of shares available for purchase, thereby eliminating strategic holdings.
The free float of a share is the proportion of the shares that are freely available for purchase on the open market. It therefore excludes shares that are held for strategic purposes – eg by holding companies in subsidiaries – and are thus highly unlikely to be sold.


Chain-linking :The chain-linking process is set up so that:

  the index reflects the new market capitalisation of the constituents 

  the index value is not disturbed by the change in capital structure of its constituents. 
This is appropriate because if the aim of the index is to reflect the investment performance of its constituents, then the index value should change only in response to that investment performance and not in response to injections or withdrawals of funds into or out of the market itself.


Rights issues, for example, will

increase both the number of shares and the total market capitalisation. However, this does not mean that the index should be increased. After all, the value of a portfolio of shares would not jump upwards. For a portfolio to remain fully representative of the whole market, some of the holdings would have to be sold in order to take up an appropriate proportion of the rights issues.


List three circumstances in which chain-linking would be required.



Total return indices

In many cases, a measure of the total return, including income received, is required on an investment class. To provide this measure, a total return index is calculated from the capital index described above. Total returns can be calculated using ex-dividend adjustments or yield figures.


XD adjustment

The ex-dividend or XD adjustment represents the amount of income that has been received since the start of the year by the capital value index. It is assessed in the same terms as the main index. For example, on 12 December 2001, the index value for the FTSE 100 Index was 5,160.8. On the same day, the XD adjustment was 134.24 (ie 2.6% of the index value). In other words, by mid-December the dividend payments that had been paid by the FTSE 100 companies since 1 January 2001 were equal to 2.6% of their total market capitalisation.
To allow for the effect of investment income it is necessary to make assumptions about the time that the income is reinvested and whether it is reinvested net or gross of tax.
An allowance may also be required for the expenses of reinvestment.
Assuming that the dividend or interest payment is reinvested back in the index on the ex-dividend date, and that is it is added to the current market capitalisation, the corresponding increase in the index value would be the investment income divided by the base value,


The XD adjustment is t

he accumulated total of each constituent over the calendar year as each constituent company declares a dividend. It is returned to the value zero at the beginning of the year and a new accumulation is started.
This implicitly assumes that:
  dividends are subject to the rate of tax (if any) assumed in the calculation of the index 

  there are no expenses or losses incurred in reinvesting the dividends.
The figure calculated using the above expression is sometimes referred to as the holding 
period return, which is more generally defined as:


Explain how we can use the capital value index and the XD adjustment to estimate the total return yielded by an investment market over the period from time t to time t+1.



The holding period return is sometimes used

an approximation to the internal rate of return, but is inaccurate because it fails to allow for the fact that in practice part of the total return comes from the reinvestment of the income (d). However, by linking successive holding period returns together we can generate a total return index series. Thus, the total return index value at time t is related to the total return index value at time t–1 as follows:


Yield adjustment

For many published equity indices ex-dividend adjustments are not available but figures for the net dividend yield on the index are. The yield figures can then be used to estimate the dividend income over the period in order to calculate total return.

The income received over shorter periods can be estimated by taking the relevant proportion of the annual amount but this will only give an approximation to the true value as income is not generally received uniformly over the year.
Having estimated the income in this way, a total return index series can then be calculated as described above.


Unweighted arithmetic indices

An unweighted, or price-weighted, arithmetic index is the arithmetic average of the relative price changes of the constituents. It is unsuitable as a benchmark for dynamic institutional portfolios. 
Although such indices are rather crude and generally inappropriate for performance measurement work, several of the world’s most famous indices are constructed using this method, eg the Dow Jones Industrial Average, the Nikkei 225.


Geometric indices

A geometric index is based on the geometric mean of the relative price changes of the constituents


An unweighted geometric index is

easy to calculate as only price data is required. It gives an indication of short-term price movements, but is totally unsuitable as a benchmark for investment strategy or portfolio investment measurement.
For example, if the price of one constituent falls to zero, then so does the index. Hence, constituents need to be changed, when necessary, to avoid this happening.


Would an (unweighted) arithmetic index rise faster or slower than a geometric index in a rising market?



uses to which indices can be put include:

  a measure of short-term market movements 

  providing a history of market movements and levels. 
All of the types of index described above can be used to give at least a broad indication of both whether the level of a particular investment market has increased or decreased, and the extent to which it has done so. 

  as a tool for estimating future movements in the market, based on past trends. 
Analysing how the investment market, as represented by the index, has moved in the past is likely to help us to predict how it may move in the future. Such technical analysis is discussed in detail in Chapter 21. 

  as a benchmark against which to assess the investment performance of portfolios. 
We discuss how this may be done in Chapter 15 of this course. 

  valuing a notional portfolio. 
This was discussed in detail in Subject A301. Recall that the fund split used could reflect either the actual split between equities and bonds (broad discounted cashflow approach) or an entirely notional split (notional portfolio approach). 

  analysing sub-sectors of the market. 
Many market-wide indices are built up from sub-indices, each of which represents a particular sub-sector of the total market. As an example, recall that in Chapter 13 we described how the FTSE industry classification system breaks down the UK equity market into ten industry groups that are further divided into sectors.

  as a basis for index funds that track the particular market. 
As the name suggests, index tracker funds aim to track or replicate the performance of an investment index. Thus, in order to construct an index tracker fund, we need an appropriate index to track. We discuss index tracking and index tracker funds in Chapter 20 of this course. 

  to provide the basis for the creation of derivative instruments relating to the market or a sub-section of the market. 
Many standardised derivative contracts are based on widely used indices, as opposed to individual securities. Such contracts are particularly useful if we wish to use derivatives to manage the risks arising from movements in an entire investment market. 
In particular for government bond indices:
  a standard against which yields on other fixed interest investments can be assessed 

  approximate valuation of a fixed interest portfolio.
The price indices can be used to obtain a quick, albeit approximate, valuation of 
a fixed interest portfolio without reference to all of the individual bond prices. 

  providing a picture of general yield structures of fixed interest investments. 
Yield indices provide a quick summary of the yield curve. 

  Yield indices allow comparison to be made with yields on ordinary shares as a measure of the yield gap between bonds and equities. 
Again, this is because yield indices summarise the yield curve.


Relevance of indices

  The investor’s investment objectives may be specified with reference to one or 
more indices – eg track or outperform a particular index. 

  Indices can be used in the development of the appropriate portfolio to best achieve those investment objectives – by helping us to predict the future possible returns on a particular investment market or sector. 

  Indices can be used to value the portfolio and can provide a benchmark against which to monitor its performance – as part of monitoring the investment experience. 
Fit for purpose 
When using any index it is vital to ensure that the index chosen is fit for purpose. In particular where an index is used to model a real world situation, it is important to ensure that the constituents of the index are a good match for the real world situation being modelled. 
This is particularly true when using indices compiled by commercial institutions. Such indices may have been established primarily for the sponsoring institution’s internal purposes, and later put into the public domain as a marketing tool. 
One example is that corporate bond indices produced by UK merchant banks often have a greater exposure to debt from financial institutions than does the bond market as a whole. Using such an index without care during the bond market turmoil in 2008-2009 could have generated significant model risk.


FTSE UK Index Series

This is a series of indices covering the whole quoted UK equity market. All the indices used to be calculated on a weighted arithmetic average basis with the market capitalisations as the weights. As such they may be suitable for performance measurement purposes.
From June 2001 the weightings of all FTSE constituents were altered to reflect the availability of stock in the market. Where the actual “free float” is 5% to 15%, this percentage (rounded up to the next whole number) is used. Otherwise weightings are in bands according to the next higher of 20%, 30%, 40%, 50%, 75% and 100%.
The free float weighting of a share is the proportion of the company’s equity that is available for trading by the public. It therefore excludes any strategic holdings by holding companies in subsidiary companies.
In addition to the capital and total return index numbers:
  average net dividend cover 

  actual dividend yield 

  price earnings ratio 

  ex-dividend adjustment 
are given for each of the indices in the series. 
The dividend cover and dividend yield are based on the most recent year’s profits and declared dividend figures respectively, updated for interim changes and for any statements by companies forecasting future earnings and dividends. A euro index value is also computed. 
Data for the FTSE UK Index Series is published each day in the Financial Times. The indices are calculated by FTSE International Limited. Note that since July 1997, the total return index has been calculated on a net basis – ie assuming reinvestment of net dividends. 


FTSE 100 Index

This consists of the 100 largest quoted companies by market capitalisation, accounting for about 80 per cent of the total UK equity market capitalisation. It is the main indicator of short-term movements in the UK equity market and is used extensively as a basis for investment products, such as derivatives and exchange- traded funds. 
The capital value is the one that is widely quoted. It was started on 31 December 1983, with a base value of 1,000. At the close of play on 31 December 2014, the value was 6,566.10. 
The index is calculated on a real-time basis, ie continuously during the day, effectively every minute, and is based on the last trade prices. For continuity and administrative reasons, the constituents are changed once a quarter in accordance with predetermined rules. The index is also used as a basis for stock index derivatives, namely the FTSE 100 Index Futures and the FTSE 100 Index Options. 


 FTSE 250 Index

This index covers the 250 companies ranking below the top 100 companies by market capitalisation. 
Its constituents are also changed every quarter. It is calculated on a real-time basis and is another base for stock index derivatives.


 FTSE 350 Supersectors Index

This index combines the 100 and 250 indices. 
The 350 Index constituents account for over 90 per cent of the total UK equity market. Sub-indices are also calculated for high yielding and low yielding stocks.


FTSE SmallCap Index

This index covers all companies below the top 350 companies with a market capitalisation greater than a certain limit and whose shares are actively traded. It currently represents around 2% of the UK market capitalisation. 
The number of constituents is not fixed as with the previous indices – the chain-linking process enables the number of constituent companies to be varied. The index is calculated at the close of each day. 


 FTSE All-Share Index

This comprises the 350 and the SmallCap indices. It accounts for around 98 – 99 per cent of the total overall market capitalisation, and is calculated and updated every minute. 
Sub-Indices are calculated for industrial sub-sectors in accordance with the FTSE industry classification system described in the previous chapter.


FTSE Fledgling Index

This index consists of the remaining, sufficiently marketable, quoted companies which are too small to be included in the SmallCap index. 
As with the SmallCap index, each of the constituent companies must fulfil eligibility requirements concerning the level of active trading in their shares.


 FTSE Aim Index Series

This series of indices covers companies traded in the UK Alternative Investment Market. These are companies which are too small or too new to apply for a listing. The indices are calculated on a free-float basis.


Dow Jones

It is a very crude index because:
  it is based on only 30 shares 

  there is no weighting by market value. 
The basic principle of calculation is that you add up the share prices of all the constituents and divide by 30. Therefore, if the price per share of the company with the most costly share rises by 10%, it will have a disproportionate impact on the index – even if the company happens to be the smallest of the thirty companies. 
The divisor does get adjusted to reflect capital changes such as scrip issues. Consequently, the divisor now bears no resemblance to 30. However, the basic principle of summing the prices of the thirty shares and dividing by a constant remains. This is the best known and most widely quoted of the New York indices.
The Dow Jones Industrial Average, commonly known as the Dow Jones index, is made up of 30 shares. It is an unweighted arithmetic index. It is therefore unsuitable for performance measurement calculations.
It provides a quick guide to shares in the industrial sector, but it is not representative of the American equity market as a whole. It is, however, very widely reported.


Standard & Poor’s

The Standard & Poor’s Composite Index, sometimes known as the S&P 500, is a weighted arithmetic index. Its constituents are 500 leading companies in the USA representing a broad cross-section of all sectors of the market. 
It is often suitable to use for performance measurement of a fund’s portfolio of USA equities. 
Both the S&P 500 and the Dow Jones Industrial Average are used as the basis for stock index futures.



There are a number of other relatively comprehensive US equity indices such as the NASDAQ (National Association of Stock Dealers Automated Quotations). 
The NASDAQ composite index includes all common stocks (ie ordinary shares) traded on the NASDAQ market and currently includes about 5,000 different stocks. There are various sub indices for different industrial sectors, which reflect the large number of technologically based companies that are quoted on NASDAQ. In addition there are indices for the NASDAQ 100 (largest non-financial companies) and the NASDAQ Financial 100 (largest financial companies). 
The NASDAQ 100 is also used as the basis for stock index futures.



The Nikkei Stock Average 225 is an arithmetic index. The constituents are reviewed annually and the index is designed to reflect the overall market. It is the most widely used indicator of short-term movements in the Japanese market.
The Nikkei is an unweighted index with 225 constituents, which are not the largest 225 companies and so only represent about 50% of the market value of the Tokyo stock exchange.
The constituents are reviewed annually. The principle is that any illiquid stocks or unrepresentative stocks are replaced by more liquid stocks. In practice, the index still contains some small, illiquid and volatile stocks. Nevertheless, it is used as the basis for a stock index future.



The Tokyo Stock Exchange First Section Index, commonly known as Topix, comprises approximately 1,700 shares. It is a market capitalisation weighted arithmetic index reflecting “free float” from June 2006.
The constituents represent the leading companies in the market, so the index is much more comprehensive than the Nikkei index, and is more suitable for use in performance measurement.



The Deutsche Aktienindex (DAX) is a real-time index of thirty leading shares. It is a total return index.
There are other, older German indices which you may hear about from time to time (eg FAZ Aktien, Commerzbank), but the DAX is the most widely quoted and is used as the basis for a stock index future.



The main market index is the CAC General Index, comprising 250 shares. The CAC-40 consists of 40 of the largest stocks and was introduced as the vehicle for an index futures contract.


Which index would you use to assess the performance of the German equity component of a UK investment fund?



Why might you expect the DAX to increase more rapidly than the FTSE All-Share Index?




A number of indices have been created to measure the performance of the major European companies. These include the FTSE Eurotop 100 and FTSEurofirst 300 (formerly Eurotop 300), their Eurobloc equivalents and the Dow Jones Eurostoxx 50.
These indices provide a set of general European equity indices that can be used to assess European equity funds.


Volatility indices

The above indices all measure the performance of equities in price or total return terms. Another form of equity indices measures the volatility of equities, and such indices are typically used as an indication of the market perception of risk.


Suggest two ways in which the volatility of an equity share may be measured.

.1. Use an option pricing formula, typically Black-Scholes, and the actual market option price to estimate the unknown volatility parameter according to the formula. In reality, different estimates may be achieved depending on the strike price of the option. This would need to be taken into consideration along with any criticisms of the assumptions underlying the option pricing formula being used. 

2. Volatility is the same as annualised standard deviation. You could observe the sample standard deviation from historical values of the equity share and perhaps adjust it for any expected changes in the future. 


volatility indices 2

The most well known volatility index is the Chicago Board Options Exchange Volatility Index, commonly known as the VIX. This is essentially a weighted average of prices for a range of 30 day expiry put and call options on the S&P 500 index (see Section 3.9 above).
Intuitively, the level of the index, which is quoted in annualised percentage terms, is the risk neutral expectation of the volatility on the S&P index over a 30 day period.
The composition of VIX is quite sophisticated and uses the prices of options to calculate the implied volatility. Specifically, a higher option price implies greater volatility, other things being equal. Despite the sophistication, its predictive power is similar to that of simpler measures, such as observations of past volatility.


South Africa

The FTSE/JSE Africa Index Series was the result of a joint venture between the JSE Limited (JSE) and the FTSE Group (FTSE). The FTSE/JSE Africa Index Series replaced the JSE Actuaries indices on the 24th of June 2002. Until June 2002, the index weights were based on market capitalisation only. From June 2002, the indices were free float adjusted.
The most important equity indices in South Africa are the FTSE/JSE Africa Headline Indices comprising:
●  FTSE/JSE ALSI (All Share Index) consisting of 99% of all listed companies; 

●  TOP40: consists of the 40 largest stocks, constituting around 84% of the ALSI; 

●  Mid-cap index, made up of stocks from position 41 to 100, and around 14% of the ALSI; 

●  Small cap index, made up of stocks from position 101, and about 2% of the ALSI; 

●  Fledgling Index consisting of the 1% of listed companies not included in the ALSI.


In addition to the above Headline Indices, other indices published by the JSE include:

●  Sector and Sub-Sector Indices consistent with the FTSE Global Classification System. 

●  Secondary Market Indices: The South African Market has three separate secondary markets – Development Capital (small to medium sized companies with limited profit history requiring start-up investment capital), Venture Capital (companies specialising in the holding of portfolio investments in venture capital projects and/or single venture companies) and Alternative Index (smaller companies not yet able to list on the main board). 

●  Specialist Indices: A number of specialist indices are published. Their constituents are not limited to the All Share or any specific industry sector, and include:
–  SWIX (Shareholder Weighted Index): For this index, the constituent weights have been adjusted for foreign shareholding. In other words, these counters’ free float shares have been reduced to reflect only the locally held shares. 

–  Style Indices: A style is defined as “an investment strategy that groups companies by apparent different rates of return” and published indices include Value and Growth. 

–  RAFI All-Share Index: This is an index where constituents are weighted by fundamental factors (sales, cashflow, book value and dividends) instead of market capitalisation. 
Total Return Indices are published at the end of each working day. The Total Return Indices are based on ex dividend adjustments.


International equity indices 4.1 FTSE Global Equity Index Series

Although equity market indices exist in each of the major world stock markets, in some markets they may not be:
  sufficiently comprehensive 

  calculated consistently 

  calculated accurately. 
The FTSE Global Equity Indices are an attempt to overcome some of these difficulties. 
The FTSE Global Equity Index Series covers over 8,000 securities in 48 countries and captures around 98% of the world’s equity markets in terms of investible market capitalisation. 
The index is divided into Developed, Advanced Emerging and Secondary Emerging segments. 
The indices are weighted arithmetic indices. From June 2001 the weightings of constituents reflect “free float”, as above. This applied to all new constituents from the beginning of 2000. 
Index numbers are shown for each country in US dollar and local currency terms. The local currency index gives a measure of the underlying performance of the particular market, and the dollar currency index shows performance adjusted for movements in the currency concerned. 
In addition to the indices in respect of each country, there are indices in respect of market type and region, for example, the FTSE Developed All Cap Index. Finally, there is a FTSE All-World Index comprising the Large/Mid-Cap aggregate of around 2,700 stocks from the Global Equity Series. 
The indices also include the gross dividend yield and a total returns index for each country.


Uses of interntional equity indices

Stocks not available to foreign investors are not included in the indices. This is not the case for most local indices, so the Global Index Series are often more suitable for performance measurement purposes than local indices. They also have the advantages of consistency between countries and are easier to obtain than some local indices.


Morgan Stanley Capital International Indices

These are a widely used series of international equity indices covering both developed and emerging markets. They are calculated on a market capitalisation weighted arithmetic basis and total returns are published both gross and net of withholding tax.
The MSCI ACWI (All Country World Index) Index is a free float-adjusted market capitalization weighted index that is designed to measure the equity market performance of developed and emerging markets. As of May 2015, the MSCI ACWI consisted of 46 country indices, comprising 23 developed and 23 emerging market country indices.


FTSE Gilts Index Series Bond indices

The indices cover conventional and index-linked gilts. Both price and yield indices are published, with the price indices being subdivided according to term and the yield indices subdivided according to term and coupon.
Both price indices and yield statistics are published each day in the Financial Times. They include indices for conventional and index-linked gilts across a range of durations.
For each category of the price indices, the information given includes the:
  index number 

  accrued interest 

  XD adjustment for the calendar year to date. 
The latter is the amount of gross income which has arisen on the index for the calendar year to date. 
Details of construction 
The principle of construction is to replicate the market value of a market portfolio of gilts. This assumes that the portfolio is rebalanced whenever there are changes to the market constituents. 
Price indices are constructed as weighted arithmetic indices, the weights being the market capitalisations of the stocks, dirty prices being used. The indices are chain-linked to allow for new issues, redemptions and movements of stocks between categories. 

Basis for construction
For conventional gilts, each yield index is constructed by fitting a curve to the gross redemption yields of the stocks in the particular category. All the irredeemable stocks are included in each coupon band to give stability to the long end of the curves. Where a stock has optional redemption dates the earliest or latest date is used, whichever gives the lower redemption yield.For index-linked gilts, each yield index represents the average yield of the stocks in that category.


International bond indices FTSE global bond index series

These are a series of fixed income indices covering the principal bond markets, including, France, Germany, the US and Japan and global emerging markets. The series comprises four homogenously constructed bond families:
  FTSE Global Government Bond indices comprising central government debt from 22 countries denominated in the domestic currency (or Euros for Eurozone countries). Sub-indices are segmented by maturity band. 

  FTSE Covered Bond indices which consist of securitised issues. These include Jumbo pfandbrief from Germany and Obligations Foncieres from France. 
The Jumbo Pfandbrief index was introduced in 1995 to attract international investors to the German bond market. 

  FTSE Corporate Bond indices covering investment grade bonds from corporate entities. Sub-indices are available by maturity band, by industry group and by credit rating. 

  FTSE Euro Emerging markets Bond indices of Euro-denominated government bonds from emerging countries. Indices are published in US dollars, Euro, sterling, yen and local currency versions.


Markit iBoxx fixed income indices

Markit iBoxx fixed income indices
These indices cover Euro, Sterling, Asian, US dollar and European High Yield bond markets. These indices comprise liquid investment grade bond issues in six categories:
1. sovereigns 

2. sub-sovereigns 

3. collateralised 

4. corporates 

5. financials 

6. non-financials. 

They are based on bid and ask bond prices supplied throughout the trading day by leading investment banks. From these, consolidated bid and ask prices are calculated and used for index calculation. Geographic, rating, sector and maturity sub-indices enable multi-dimensional analysis.


Other international bond indices

Other international bond indices
Investment banks such as Barclays Capital, Merrill Lynch, Saloman and J P Morgan also produce indices covering all aspect of the fixed income market including inflation-linked and swaps indices. These are published as:
  global / multicurrency and 

  regional / single currency benchmarks 
and a large number of standard sub-indices are available within each index family. 
(Prior to 2008, Lehman Brothers benchmark indices were also widely quoted. These have now been rebranded as Barclays Capital indices. ) 
These other indices include:
  Salomon Smith Barney World Government Bond Index, which covers government bonds in sixteen different countries, broken down by maturity. Indices are produced for different maturities in each country. 

  JPMorgan EMBI (Emerging Markets Bond Index), which tracks total returns on bonds in emerging markets 
The market for Japanese corporate bonds is covered by the Nikko Bond performance index.


Credit derivative indices

In addition to corporate bond indices, there are indices of credit default swaps (CDS). Whereas corporate bond indices blend interest and credit risk, CDS indices can be used by analysts and investors to monitor more directly the price of credit risk.
A CDS is an OTC credit derivative, whereas a CDS index is a completely standardised credit security and may therefore be more liquid and trade at a smaller bid-offer spread. This means that it can be cheaper to hedge a portfolio of credit default swaps or bonds with a CDS index than it would be to buy many single name CDS to achieve a similar effect.
There are currently two main families of CDS indices, the iTraxx and the CDX.



The most well known index in Europe is the Markit iTraxx Europe index (often referred to as iTraxx Europe Main). Different index series are established each six months, and the constituents of the index are the top 125 names in terms of CDS volume traded in the six months prior to this. The index is quoted for 3, 4, 5, 7 and 10-year maturity CDS and the index is the unweighted average of the CDS premium for the constituents.
The constituents of the indices are changed every six months, a process known as "rolling" the index.
There are also a number of sub-sector indices for different industries.
This means that it may be possible to invest in a CDS index for a basket of bonds issued by pharmaceutical companies, say.



The corresponding US indices are the CDX family. CDX indices contain North American and Emerging Market companies and are administered by CDS Index Company.


South African bond indice

The main fixed-interest bond index in South Africa is the ALBI (All Bond Index), a composite index containing the top 20 fixed interest bonds ranked dually by liquidity and market capitalisation. The ALBI is split into two sub-indices, the GOVI (Government Bond Index) comprising the top 10 government bonds issued by the Department of Finance, and the OTHI (Other Bond Index).
The constituents and weightings of the ALBI are changed in the following circumstances:
●  Bond weightings change monthly based on issuance during the period. 

●  Constituent changes are effected quarterly. Changes are driven by changes in eligibility criteria ie outstanding market value, turnover and outstanding term to maturity. Bonds are also excluded if they fall below 1 year during the next period for which constituents apply. The Index Committee meets quarterly to discuss the constituents. 
The main inflation-linked bond index in South Africa is the CILI (Composite Inflation- Linked Index), which is split into three sub-indices to reflect bonds issued by Government (IGOV), State owned enterprises (ISOE) and corporates (ICORP). As for the ALBI, the CILI is further split into four sub-indices based on term to maturity (1- 3yr, 3-7yr, 7-12yr, 12+yr). 
Indices produced for both the ALBI and CILI include a clean price index, an interest yield index, and a total return index. The total return index assumes coupons are reinvested immediately after payment. 
Credit Indices are also produced by the JSE for listed corporate bonds. The three indices include Credit Fixed, Credit Floating and Credit Composite. The Credit Composite Index is a weighted average index of the Credit Fixed and Credit Floating Indices. The trio of indices enables investors to choose the benchmark most appropriate for their credit portfolios. In addition to the above indices, term split sub-indices are also produced based on term to maturity (1-3yr, 3-7yr, 7-12yr, 12+yr) for all of the Credit Indices. Index weights and constituents are reviewed quarterly, and index values are calculated and published daily following the close of the market. 


For money market instruments

the Short Term Fixed Interest (STeFI) Composite index is used in South Africa. It is a benchmark index originally constructed by Alexander Forbes, and is now calculated and published daily by the Johannesburg Stock Exchange (JSE). It has become the industry benchmark for cash equivalent investments (ie up to 12 months). It is comprised of:
1. 15% of the STeFI Call Deposit Index which is based on an Interbank Call rate; 

2. 30% of the STeFI 3 month NCD Index which is based on 3 month NCD instruments; 

3. 35% of the STeFI 6 month NCD Index which is based on 6 month NCD instruments; and 

4. 20% of the STeFI 12 month NCD Index which is based on 12 month NCD instruments.


Property indices
Problems in constructing property indices

There are two key problems encountered when constructing property indices:
1. the lack of reliable and up-to-date data on property prices 

2. the heterogeneity of properties. 

The root of the problem is therefore mainly a lack of reliable data on prices.


Lack of price data

The production of reliable indices requires knowledge of the market values of the constituents of the indices at frequent intervals. There are a number of problems in obtaining such information for property:
  Each property is unique. 

  The market value of a property is only known for certain when the 
property changes hands. 
Just because a property sells for X on a given day does not mean that an identical property next door will also achieve X on an immediate sale. 

  Estimation of value is a subjective and expensive process. 

  Valuations will be carried out at different points in time. 

  Sales of certain types of investment property are relatively infrequent. For example, very few large shopping malls are bought/sold in any one day! 

  The prices agreed between buyers and sellers of properties are normally treated with a degree of confidentiality. 
For this reason, some of the major firms of surveyors produce property price indices from their own client database. Similarly, different building societies develop their own indices for residential properties. 


Using surveyors’ valuations as an alternative to actual sale prices has problems too:

  subjectivity – different surveyors would give different values for the same property 

  cost – it can be time-consuming and expensive 

  circularity – the indices would be based too heavily on the surveyors’ views, but 
the surveyors would form their views on the trends of the indices! 
Clearly, surveyors’ valuations would not give the independent measure of the market’s behaviour that an index strives to provide. 
Hence there typically isn’t a universally accepted index for property prices. 
The heterogeneity of property magnifies the problems of obtaining price data. It is difficult to group properties into usefully homogeneous groups and still obtain sufficient price data for each group.


Types of property index

There are two main types of investment property index – portfolio-based indices, which are the most common, and barometer indices.
Their different characteristics mean that each is useful for different purposes.


Portfolio-based indices

Portfolio-based indices measure rental values, capital values or total returns of actual rented properties. Different indices of this type will give different results because the underlying portfolio of properties will vary in size, regional spread and sector weighting (office, retail etc).
As these actual properties may be sold very infrequently, the valuations upon which the index is based will largely reflect the prices at which comparable properties are sold. Even these valuations may be out-of-date if the comparables themselves do not come up for sale very often.
The rates of return will typically be money-weighted, meaning that the timing and magnitude of cashflows into the particular property fund will influence the results.
However, some property indices in the UK have now moved to a time-weighted calculation basis.

In addition, as the current rental income is fixed until the next rent review, any response to movements in rental values will be sluggish.
Portfolio-based indices are used mainly for performance measurement.


Barometer indices

As the name suggests, these are designed to act as a barometer of current market conditions.
The barometer type of index aims to track movements in the property market at large by estimating the maximum full rental values of a number of hypothetical rack-rented properties.
As with portfolio-based indices, different barometer indices are produced in practice for different property sectors and (hypothetical) regional spreads. The values underlying the index are based on valuers’ estimates of current rack rents, rather than actual rents, and should therefore give an earlier indicator of changes in market rent levels. In order to calculate meaningful index values, strict guidelines are required covering both the constituent hypothetical properties to be valued and the assumed lease terms of those properties – eg length of lease, who is responsible for repairs etc
The main use of this type of index is in highlighting short-term changes in the level of the market in terms of rents and yields. But an index of this type is unsuitable for portfolio performance measurement since an investor could not closely match its movement with an actual portfolio of property holdings.


Index providers

There are a number of index providers who produce property indices that are suitable as benchmarks for property investors. Indices are typically divided into residential and commercial indices, and where sufficient data exists the commercial indices are often further subdivided into industrial, office and retail categories.
Within the European market, IPD is a leading index provider for commercial property indices and several of these indices are sufficiently robust to have been used as a basis for pricing property derivative contracts. A property derivative is a financial derivative whose value is based on the value of an underlying property. Because properties can be hard to accurately price, property derivative contracts are typically written based on a real estate property index. Trading in property derivatives is also known as synthetic real estate.


What is the main weakness of a barometer index?

.The main weakness of a barometer index is that the rental values on which it is based are subjective estimates for hypothetical properties – as opposed to actual rents for actual properties.


Alternatives to property indices

Collective investment schemes investing in real property have the same issues surrounding producing regular valuation as those identified above. However a large scheme with a wide range of investments may be trading and valuing sufficiently frequently to smooth out the main difficulties. Thus using the published prices of a scheme as a proxy for an index may be a practical alternative to using an index, particularly in property markets where the indices that exist are unrepresentative of the property assets held by an investor.
It will be necessary to adjust prices for any regular management or other charges. As with all indices it is necessary to choose the collective investment scheme with care. Many schemes invest significantly in property company shares as well as in real property, which will distort the results.


The uses to which indices can be put include:

  a measure of short-term market movements 

  providing a history of market movements and levels 

  as a tool for estimating future movements in the market, based on past trends 

  as a benchmark against which to assess the investment performance of portfolios 

  valuing a notional portfolio 

  analysing sub-sectors of the market 

  as a basis for index funds which track the particular market 

  to provide the basis for the creation of derivative instruments relating to the market or a sub-section of the market. 
In particular for government bond indices: 

  a standard against which yields on other fixed interest investments can be assessed 

  approximate valuation of a fixed interest portfolio 

  providing a picture of general yield structures of fixed interest investments 

  a measure of the yield gap between bonds and equities.


The FTSE UK Index Series are market capitalisation weighted arithmetic indices. In addition to the capital and total return index numbers they give:

  average net dividend cover 

  actual dividend yield 

  price earnings ratio 

  ex-dividend adjustment.


The FTSE 100 index is

based on the 100 largest companies in the UK equity market and covers about 80% of the market by value. It is calculated every minute, is the most widely quoted of the FTSE UK Index Series and is used as the basis for derivatives contracts.


Circumstances in which chain-linking would be required include:

  a rights issue or a share buy-back by a constituent company 

  a new issue of a share in the sector covered by the index – eg newly-formed company, privatisation, demutualisation 

  a merger, takeover or break-up involving a constituent company or companies 

  a change in the constituent companies in an index, resulting from a change in relative market capitalisations due to share price movements. For example, the share price of Company P increases so that its overall market capitalisation now exceeds that of Company Q, which was formerly the 100th largest company. Thus, P replaces Q in the index of the largest 100 companies.


main uses of the FTSE Gilts Index Series are:

  a measure of short-term market movements 

  providing a history of market movements and levels 

  a tool for estimating future movements in the market, based on past trends 

  a benchmark against which to assess the investment performance of portfolios 

  analysing sub-sectors of the yield curve (eg shorts, mediums etc) 

  providing a standard against which yields on other fixed interest investments can be assessed 

  approximate valuation of a fixed interest portfolio 

  providing a picture of general yield structures of fixed interest investments.