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 is some average of
  relative price changes.
• Method of calculation
• 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.
• To help estimate/forecast future movements.
• To use them as a benchmark to assess investment
  performance of portfolios.
• Valuing a notional portfolio.
• Analysing sub-sectors of market.
• 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.
• First industrial only index, DJIA, on 26th May
  1896 comprising 12 companies and only GE
  remains to this day.
• 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.

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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 method of construction was due to Irving
  Fisher.

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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.
• 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?

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Weighted Arithmetic Indices

• Indices, as weighted relative price changes of
  all constituent stocks
• 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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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
  inceptionwe prefer Nikkei 300, a cap. Weighted
  arithmetic index of top 300 stock or Topix (1,100
  shares)
• DO NOT USE THESE 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.

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Complete Suites of Indices UK Market

• 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 amrket
  capitalisation), giving 70 coverage of total
  market. Quoted continuously.
• FTSE 250
• FTSE 350 the combination of FTSE 100 FTSE 250
  (about 90 of market captured)
• FTSE SmallCap Index below the top 350 but with
  market capitaliation above a cerain limit.

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Complete Suites of Indices UK Market

• FTSE (Actuaries) Share Indices (CONT)
• FTSE All-Share FTSE 350 plus FTSE SmallCap,
  giving about 98 of market.
• FTSE Fledgling Index the rest of market not in
  All-Share. All small companies.

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Complete Suites of Indices World Market

• Morgan Stanley Capital International Indices
  (MSCI) total return are publishes bnoth gross
  and net.
• FTSE Actuaries World Index.

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Other indices

• DAX total return index, cap. weighted
  arithmetic index of German market.
• CAC40 or (CAC General which has 250 shares)
  cap. weighted arithmetic index of French stock
  market.
• Etc.

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Example Operation of Equity Index

• Say, index at time 0 consists of three stocks,
  with price of each stock evolving as in the table
  below
• Time Stock 1 Stock 2 Stock 3
• 0 10 20 25
• 1 9 15 30
• 2- 12 14 32
• 2 11 14 32
• 3 10 15 35
• 4- 12 15 40
• 4 20 15 40
• 5 19 16 42
• Calculate a price unweighted arithmetic index at
  times 0,1,2,3,4,5 with radix at time 0 set at
  1,000.

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Example Operation of Equity Index

• Assuming there are 10,000 shares in issue in
  stock 1 25,000 in stock 2 and 50,000 in stock 3
  at time 0 and this does not alter up to time 4-,
  calculate a capitalisation weighted arithmetic
  index with radix at time 0 set at 1,000.
• Between time 4- and 4, stock 1 has a 1 for 2
  rights issue at 5. Calculate the theoretical
  ex-rights price and so show how the weights
  change in the index with this capitalisation
  change. Calculate the index value at time 5.
• Finally at time 2- stock 1 went ex-div, declaring
  a gross dividend of 2. Instantly the price fell
  by 1. How should we allow for this in our index
  construction?
• What is the capital return on an index in period
  1 to 5
• What is the total return to an investor who pays
  tax at the rate of 25 on income over the period
  1 to 5?
• What is the return on an (unweighted) geometric
  index between time 1 and 5?

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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 cerain limit. More
  than 500 companies in this index.

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UK Equity Market - the FTSE (Actuaries) Share
Indices

• 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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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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Complete Suites of Indices World Market

• We want consistent, comprehensive and accurate
  index for all markest in the world both equity
  and bond.
• Morgan Stanley Capital International Indices
  (MSCI) total return are publishes both gross
  and net.
• FTSE Actuaries World Index.
• FTSE Actuaries World Index
• give 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.

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Complete Suites of Indices World Market

• 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.
• But exclude 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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Other Equity Indices

• 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.
• DAX total return index, cap. weighted
  arithmetic index of German market.
• CAC40 or (CAC General which has 250 shares)
  cap. weighted arithmetic index of French stock
  market.
• Etc.

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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 on 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