Actuarial Investments

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Actuarial Investments

• Shane Whelan
• L527

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Investment Indices
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Investment Indices

• Investment index one number to summarise how
  the market is performing. So it is some average
  of relative price changes.
• Like any single number to capture something
  complex, it has its limitations.
• Three distinct methods of calculation behind
  indices
• Weighted arithmetic indices
• Unweighted arithmetic indices
• Geometric indices

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Uses of Indices

• A measure of short-term market movements.
• A measure of long-term market movements history
  of movements/levels.
• Analysing sub-sectors of market.
• To help estimate/forecast/model future movements
  and the likelihood of future movements.
• Enables the scientific study of the markets.
• To use them as a benchmark to assess investment
  performance of portfolios.
• Valuing a notional portfolio.
• As a basis of index funds.
• As a basis to create derivative securities.

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Indices a history lesson

• First appearance of the first known stock index
  was 3rd July 1884 in the Afternoon News Letter
  (in 1885, Dow Jones renamed their newsletter
  The Wall Street Journal) it consisted of 11
  companies, 9 of which were railways (so called
  the Dow Jones Railway Average).
• First industrial only index, DJIA, on 26th May
  1896 comprising 12 companies and only GE
  remains to this day. Officially still known as
  the Dow Jones Industrial Average but generally
  referred to simply as the Dow.
• Method of construction was and is the arithmetic
  price-weighted return. Changed to adjusted
  divisor from 1928.
• Charles Dow opined in his editorials on the
  direction of the market. He died 1902 and next
  editor of the WSJ was William Peter Hamilton, who
  developed the Dow theory of stock price
  behaviour. This has evolved into an approach for
  selection of shares or timing trades known as
  technical analysis.

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Indices A History Lesson

• Cowles Commission in US set up capitalisation
  weighted price indices in 1933 and back-dated
  them to 1871. These latter became the SP
  indices.

• This improved method of construction was due to
  Irving Fisher (shown).

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Weighted Arithmetic Indices

• Indices, as weighted relative price changes of
  all constituent stocks
• Common weights adopted are total market
  capitalisation or free float
• What happens when weights change?
• Chain-linking change weights to reflect new
  relative weights without a discontinuity in the
  value of the index at the time of the change.
• e.g., after rights issue.

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Weighted Arithmetic Indices

• Weighted arithmetic indices are best, with
  suitable weights, because they accurately record
  the capital return to an investor holding those
  stocks in the given weights.
• Suitable weights are now considered to be the
  free float (that is, strategically held shares
  are excluded in the count) and, since June 2001,
  this is the weighting structure of the FTSE suite
  of indices.
• Must also measure income return on index to get a
  total return index, i.e., income plus capital
  return.
• But gross or net?
• When re-invested?
• Often the xd adjustment in calendar ytd is quoted
  beside capital index so total return, net of any
  income tax and assumed time of reinvestment, can
  easily be calculated.

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Unweighted or Price Weighted Arithmetic Indices

• Dow Jones Industrial Average (DJIA) price
  weighted!!
• Just 30 shares.
• Nikkei 225 an unweighted arithmetic index with
  its 225 components little changed since
  inception
• we prefer Nikkei 300, a cap. weighted arithmetic
  index of top 300 stock or Topix (c. 1,100 shares)
  
• DO NOT USE UNWEIGHTED INDICES TO MONITOR
  PORTFOLIOS/HISTORICAL RESEARCH.

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Geometric Indices

• Here the index is the geometric mean of the
  relative price changes.
• With n constituents, we have
• Geometic index lags an arithmetic index.
• Unsuitable to monitor portfolios -, e.g. Rolls
  Royce.
• Examples include the old FT30 Index and the old
  Actuaries Indices (dating from c.1930)

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UK Equity Market - the FTSE (Actuaries) Share
Indices

• Covering UK market, with good information
  average net dividend covergross and net yields,
  P/E ratio.
• FTSE 100 top 100 companies (by market
  capitalisation), giving 70 coverage of total
  market. Quoted continuously.
• FTSE 250. Quoted continuously.
• FTSE 350 the combination of FTSE 100 FTSE 250
  (about 90 of market captured), published daily.
  Has sub-indices, an ex-div adjustment and total
  return index.
• FTSE SmallCap Index below the top 350 but with
  market capitaliation above a certain limit. More
  than 500 companies in this index.

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UK Equity Market - the FTSE Share Indices
Continued

• FTSE All-Share FTSE 350 plus FTSE SmallCap,
  giving about 98 of market. Published daily and
  has sub-sector indices.
• FTSE Fledgling Index the rest of market not in
  All-Share. All small companies.

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Other indices

• With global, regional, and national coverage
• e.g., Morgan Stanley Capital International
  Indices (MSCI) total return are published both
  gross and net.
• FTSE All-World Index FTSE Global Equity Index.
• Dow Jones series
• SP Global 1200a real time global index
  capturing 70 of market capitalisation.
• Local or national coverage but commonly used
• Standard Poors Composite (also known as SP
  500) remember this is a cap.-weighted price
  index with reasoable sub-sector indices and
  widely used to compare performance of US
  portfolios.
• Tokyo Stock Exchange First Section Index or Topix
  which, shortly will be available in free float as
  well as the existing cap. weighted version.
• DAX total return index, cap. weighted
  arithmetic index of German market available in
  real time.

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Other indices (continued)

• CAC40 or (CAC General which has 250 shares)
  cap. weighted arithmetic index of French stock
  market.
• Etc.
• Encourage you to look at Financial Times at
  least the Companies Markets section.

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Complete Suites of Indices World Market

• FTSE All-World Index
• Gives over 70 coverage of world equity markets
  and has a target of at least 70 within each
  national market. Same construction method as FTSE
  UK series of equity indices.
• FTSE Actuaries World Index Indices for each of 5
  currencies, gross div. yields given
• Country indices (about 30) build to regional
  indices which build to world index, always with
  relative weights given by relative market
  capitalisations.
• They exclude stocks that foreign investors (i.e.,
  non-nationals) are not allowed to hold.
• Until recently they excluded Taiwan, Korea,
• MSCI indices better in asia (and emerging markets
  generally). Also they have longer history. Give
  capital and total returns (the latter gross and
  net of withholding tax).

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Worked Example Operation of Equity Index
Question 7, Autumn 2002
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UK Gilt Market FTSE Actuaries Gov. Securities
UK Indices

• This index suite gives both price yield, and
  has ex-div. and acrued index sub-series. Indices
  are sub-divided by term and coupon. Prices used
  in index are dirty.
• Market-capitalisation weighted arithmetic indices
  with complete coverage of all fully paid
• chained-linked to allow for capitalisation
  changes/new issues/redemptions/shorteners/sliders.
  

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UK Gilt Market FTSE Actuaries Gov. Securities
UK Indices

• UK Gilts Indices have following sub-divisions
• Conventional
• All stocks
• Up to 5 years
• 5-15 years
• Irredeemables
• Index-linked
• All stock
• Up to 5 years
• Over 5 years
• Yields on conventionals for 5,15,and 2O year
  stock for each of high,medium, and low coupons,
  plus yields on irredeemables are published
  these yields are got by curve fitting.

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Example

• To calculate return on gilt index to investor
  subject to tax at 20 on income, between time 3
  and 5, given
• Time Gilt Index Ex-Div Adj. Accrued Int
• 3 158.23 5.17 2.85
• 5 217.09 6.87 1.20

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International Bond Indices

• Merrill Lynch, Salomon Brothers, and JP Morgan
  all have good bond indices, the first two with
  very wide geographical coverage.
• Care is needed to choose one which suits the
  investment brief by duration, by credit risk,
  by currency, by running yield.

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Usual Comparison Indices for Irish Pension Funds

• Irish Equity - ISEQ
• FTSE Eurobloc
• FTSE UK
• FTSE Europe ex UK
• FTSE North America
• FTSE Japan
• FTSE Pacific ex Japan
• FTSE World
• Merrill Lynch EMU G'ment gt 5 Year Bond
• 3 Month Interbank Deposit

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Property Indices

• Problems in getting reliable index
• Lack of reliable up-to-date market prices
• Uniqueness of each property
• Estimation of values is subjective and expensive
• Can be a long time ago since even similar
  property sold
• Sometimes prices are kept secret
• Two types of property indices
• Portfolio-based indices based on performance of
  actual portfolio of properties (as comprehensive
  as possible)
• Barometer type indices estimating full price on
  hypothetical rack-rented properties.More timely
  but more inaccurate than the former type.

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Completes Treatment of Market Indices