Chapter 15: Indices Flashcards
m. Construction of indices
Explain what is meant by:
- chain-linking
- free float.
Weighted arithmetic indices
Chain-linking
- Process used to maintain continuity in index value when number of shares issued by constiuent company changes
- used to ensure that changes in the index value are due to changes in the underlying companies’ performance, rather than changes in the number of shares issued.
- changes in number of shares might be due to rights issue/share buybacks, New issue of shares, merger/takeover/breakup or changes in consituent companies.
Free float
- Percentage of shares freely available for purchase on open market.
- Adjust market cap for each share to excludes strategic holdings(SH)
- SH are held by LT investors for strategic purposes such as
holding companies or pension funds hedging their long-term liabilities.
m. Construction of indices
List four circumstances in which chain-linking would be required.
Weighted arithmetic indice
- rights issue/share buybacks by a constituent company
- New issue of shares in the sector covered by the index, e.g.,
- newly-formed company
- Privatisation
- demutualisation
- Merger/takeover or breakup involving the a constituent company or companies
- a change in the constituent companies in the index, resulting in a change in market cap due to share price movements. e.g., Q 100th largest company, share price of P changes so that theits market cap exceeds Qs.
m. Construction of indices
State the formula for a weighted arithmetic average capital value index.
Weighted arithmetic indices
i(t) = K (sum(w_i(P_i(t)/P_i(0)))/sum(w_i)
i(t) - capital index at t
K - constant related to the starting value of the index at 0 –> fixed so that index starts at 100 or 1000
w_i - weight applied to the ith constituent (market cap at 0)
P_i(t) - price at t
P_i(0) - price at 0 –> the last time at which there was a capital change
Weights are updated each time the number of shares issued change.
m. Construction of indices
State the formula for a weighted arithmetic average capital value index obtained by chain-linking and free-float.
Weighted arithmetic indices
I(t) = (sum(N_i(t) x P_i(t))/B(t)
Where:
- N_i(t) is the number of shares issued for i-th constituent at time t
- P_i(t) is price of i-th constituent at time t
- B(t) is the basee value, or divisor, at time t
- B(t) is obtained from B(t-1) through chain-linking process.
The numerator represents the total market cap of the index consituents
The formula only take into account changes in capital values
m. Construction of indices
Explain with aid of a formula what the ex-dividend adjustment represents.
Outline the assumptions that need to be made to allow for the effect of investment income.
Total return indices
xd_i(t) = N_i (t) x D_i(t)/B(t - 1) –> XD at the current time t (not an accumulation)
XD_i(t) = Sum_t (N_i (t) x D_i(t)/B(t - 1)) –> XD adjustment of ith share representing total dividends declared to date
XD(t) = Sum_i(XD_i(t)) –> XD adjustment accumulated to date for all constituent companies
Where:
- D_i(t) is the dividend per share declared by the ith constituent company at time t (net or gross, as required)
- B(t -1) is the divisor at the close of business on the previous day after allowing for any capital changes.
XD is reacts to the ex-dividend date rather than the date of receipt of dividends.
It is normally reset to zero at the start of each year.
An assumption needs to be made about:
- time of reinivestment of income
- whether it is reinvested net or gross of tax
- expenses of reinvestment
to allow for the effect of investment income
m. Construction of indices
State the formula of a holding period return.
Total return indices
TR(t) = (I(t) + XD(t) - I(t-1) - XD(t-1))/I(t-1) *100 –> holding period return
Generally:
HPR = (P(1) + d)/P(0)
Where:
- P(1) and P(0) are the vaues of the investment at the beginning and end of the period
- d is the income gennerated by the investment over the period.
- HPR is sometimes used as an approximation to IRR
- However, it is inaccurate, it fails to allow for the fact that part of the TR comes from reinvestment of d
This assumes implicitly 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.
m. Construction of indices
State the formula of the total return index obtained by linking successive HPRs.
Total return indices
TRI(t) = TRI(t-1)[I(t)/(I(t) - income(t, t-1)]
where:
- TRI(t) is the total return index;
- income(t, t-1) is the income received from t - 1 to t (net or gross as required)
Alternatively, following formula can be used:
TRI(t) = TRI(t-1)[(I(t+1) + income(t, t-1))/I(t-1)]
The above is used more often
Total return between time a and b (b>a) is then given as:
TRI (b)/TRI(a) -1
m. Construction of indices
When do you assume the dividends are reinvested?
1.2 Total return indices
Usual assumption is to use the ex-dividend date. However, this may lead to problems if the index is used by index tracking funds, since they will not be able to reinvest the dividends until they actually receive it. The index fund might underperform the TRI due to the missed opportunity to earn returns on the immediate reinvestment assumed by the formula.
m. Construction of indices
Give two different ways of estimaiting the income received over the time period from t -1 to t from the index constituents.
1.2 Total return indices
- income(t-1, t) = XD(t) - XD(t-1)
where XD(t) is the ex-dividend adjustment at time t
- income(t-1,t) = I(t)*y(t)/n
where I(t) is the capital value index and y(t) dividend yield, both at time t and n is the number of time periods per annum.
m. Construction of indices
State the formula for an unweighted arithmetic index of capital values.
Unweighted (price) arithmetic indices
I(t) = Ksum_i(P_i(t)/P_i(0)
where:
- P_i(t) is price of the ith consituent at time t
- K is a constant
m. Construction of indices
Explain the main problems with such an index.
Unweighted (price) arithmetic indices
- Unsuitable for performance measurement:
This is unsuitable for performance measurement since actual performance reflects weights held, whereas this give equal weight to each share.
- Sensitivity to Stock Selection:
The index value is heavily influenced by the choice of stocks included. A single high-priced stock can significantly impact the index value compared to a low-priced stock, even if the high-priced stock’s performance isn’t representative of the broader market.
- Ignores Company Size:
The index doesn’t consider the market capitalization of companies. A small company with a high stock price can have the same weight as a large, established company with a lower stock price. This can misrepresent the overall market performance.
- Limited Diversification:
An unweighted index may not be well-diversified across sectors or industries. This can expose investors to higher risk if a particular sector or industry underperforms
- Potential for Manipulation:
Since the index is heavily influenced by the selection of stocks, there’s a potential for manipulation if the index composition isn’t carefully chosen and monitored.
6.* Difficulty with Reinvestment:*
The formula doesn’t explicitly account for dividend reinvestment. If dividends are not considered, the index might not accurately reflect the total return an investor would experience.
m. Construction of indices
State the formula for an unweighted geometric index of capital values.
Explain the main problem with this.
Geometric indice
I(t) = K[(multiplication function_i P_i(t)/P_i((0)]^(1/n)
m. Construction of indices
Describe three advantages and disadvantages of an unweighted geometric index relative to a weighted arithmetic index as a measure of price changes.
Geometric indice
Three advantages:
- It does not require weights – which might not be available in some circumstances;
- It is simpler to calculate and understand/explain (especially if it ignores corporate changes);
- It can be used to give an indication of short-term price movements;
- It gives a better representation of the broader market trend than an arithmetic index (due to the geometric index change being closer to the median of price changes).
Three disadvantages:
- The index goes to zero if one of the components goes to zero;
- Being unweighted makes it less relevant for performance measurement;
- The geometric index undershoots the arithmetic index in a rising market, and overshoots in a falling market
m. Construction of indices
List factors to consider when constructing an index.
- Purpose of index
- Consituents and basis for inclusion/exlcusion
- Type of index (weighted, freefloats)
- frequency of calculation of index values (& updating index constituents and weights)
- base date and value
- how to deal with income (XD adjustment, total return index)
- price data used (mid-market prices?)
- how to deal with capital gains changes.
- Sources and availability of data
- (costs of constructing the index)
m.i) the uses of investment indices
List the main uses of indices
Use of indices
- Portfolios
- as benchmark of Investment performance of pfs
- valuing a Notional pf
- to provide basis for the creation of Derivative instruments relating the market or sub-section of the market
- basis for Index tracker funds
- market movements
- Charting long-term history of market movements and levels
- Estimating future market movements based on past trends, ie for technical analysis
- Measure Short-term market movements
5. analysing Sub-sectors of the market
INDICES’S
m.i) the uses of investment indices
List (four) further uses of government bond indices.
Use of indices
- Benchmarking: A standard againt which yields on other fixed interest investments can be assessed.
- Yield curve Analysis: provide the general yield structures of fixed interest investments (summarise the yield curve). Provides information about market expectations for interest movements and economic conditions.
- approximate valuation of fixed interest pfs (without reference to all the individual bond prices)
- allow for comparison with yields on ordinary shares as a meausure of the yield gap between bonds and equities (as they summarise the yield curve).
- Portfolio construction: Helps with diversification by allocating investments across different segments of bond market
- Risk assessment: used to measure risk. High yields –> high credit risk and volatility vice versa. Also used to assess risk vs reward.
- Income planning: Investors seeking income-focused strategies use yield indices to identify segments of the bond market that offer attractive yield levels.
m.ii) principal indices in the SA and int stock and bond markets
Describe how the FTSE equity indices are calculated and list six figures, in addition to the capital value index, which are provided in respect of each FTSE index.
FTSE UK index series
- They are calculated on a weighted arithmetic average basis with market capilitisation as weights.
- weights based on free floats (which are rounded to a whole # according to the next higher band of 20%, 30%, 40%, 50% and 75% and 100%)
Other six figures:
1. actual dividend yield
2. price earnings ratio
3. total return index
4. ex-dividend adjustment
5. average dividend cover
6. Euro value index
m.ii) principal indices in the SA and int stock and bond markets
FTSE UK index series
m.ii) principal indices in the SA and int stock and bond markets
Outline the coverage of the following indices:
- FTSE 100
- FTSE 250
- FTSE 350 Supersectors
FTSE UK index series
FTSE 100:
- Consists the 100 largest quoted companies in the UK by market cap
- accounts for about 80% of the total equity market cap
- Main indicator ST market movements in the UK
- used as a basis for investment products (derivatives and EFT)
- for continuity and admnistrative reasons constituents changed once a quarter
FTSE 250:
- Consits of the 250 largest quoted companies ranking below the 100 companies by market cap
- Accounts for about 17% of total equity market cap
- Also a basis for stock derivatives
FTSE 350:
- Industry sector indexes derived from companies in the 100 and 250 indices.
- accounts for about 95% of total UK equity market
- sub-indices also calculated for high-yielding and low-yielding stocks
m.ii) principal indices in the SA and int stock and bond markets
Outline the coverage of the following indices:
- FTSE SmallCap
- FTSE All-Share
- FTSE Fledging
- FTSE AIM
FTSE UK index series
FTSE SmallCap:
- Covers all companies below the 350 with market cap above a certain limit and are actively traded
- about 350 constituents
- represents about 2% of the UK equity market cap
- index calculated at close of each day
FTSE All-Share
- Comprises of 100, 250 and SmallCap indices
- accounts for about 98% - 999% of the over total market cap
FTSE Fledging
- Consists of the remaining, sufficiently marketable, quoted copmanies that are too small to be included in the SmallCap index
FTSE AIM
- Covers some 1000 companies traded in Alternative investment Market.
- These companies are too small or too new to apply for full listing.
m.ii) principal indices in the SA and int stock and bond markets
List the main South African equity indices that comprise the FTSE/JSE Africa Headline Indices.
And list other indices published by the JSE.
FTSE UK index series
The most important equity indices in SA consist of:
- 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
- Fledging index consisting of the 1% of listed companies not included in the ALSI
In addition of the headlines indices, other indices published by the JSE Classification system:
- Sector and subsector indices that are consistent FTSE Global Classification System.
- Secondary Market Indices: Development capital (small - medium sized with limited profit history); venture capital (CIS holding a pf of venture capital projects/single venture companies) and Alternative Index (smaller companies not yet listed on main board
Specialised Indices
- SWIX (shareholder weighted Index) - weights adjusted for foreign holding - freefloats reduced to reflect locally held shares
- ‘Style’ Indices - growth or value
- RAFI All-Share Index: Weights are by fundamental factors (sales, cashflow, bookvalue, dividends)
m.ii) principal indices in the SA and int stock and bond markets
Describe the FTSE Gilts Index series
Fixed Income indices
- Cover conventional and index-linked gilts
- Both price and yield indices are published…
- …with price indices subdivided according to term and yield indices subdivided according to term and coupon.
- Index numbers calculated using dirty prices, ie accrued interest included
- Accured interest and XD adjustment published for price index series
- price indices are constructed as weighted arithmetic indices, the weights being the market cap of the stocks
- indices are chain-linked to allow for new issues, redemptions and movements of stocks
m.ii) principal indices in the SA and int stock and bond markets
Describe the FTSE Gilts yield Index series (conventional gilts and index-linked gilts)
Conventional gilts:
- each yield index is constructed by fitting a curve to the gross redemption yields of the stocks in the particular category
- All irredeemable stocks are included in each coupon band to give stability to the long end of the curves.
- where stocks have optional redemption dates, whichever gives the lower redemption yield is used
Index-linkded gilts
- each yield index represents the average yields the stocks in that category
m.ii) principal indices in the SA and int stock and bond markets
List other figures published with the FTSE Gilt index
Fixed Income indices
Price indices:
- Index value
- accrued interest
- ex-dividend adjustment for the year to date
- day’s change
- total return index figure
- the weighting that each price index is given in the make-up of the all stocks index
- the gross redemption yield
- duration of the index
Yield indices:
- yesterday’s yield
- the yield the day before
- yield one year ago
m.ii) principal indices in the SA and int stock and bond markets
Describe the FTSE Global Bond Index series
Fixed Income indices
The series consits of four homogenously constucted bond families:
- FTSE Global Government bond indices comprising central government debt from 22 countries denomintated in the domestic currency (or Euros for Eurozone countries). Sub-indices ae segmented by maturity band.
- FTSE Covered Bond indices which consists of securitised issues.
- FTSE Corporate Bond Indices covering invesment grade bonds from corporate entities. Sub-inndices are available by maturity band, industry group and by credit rating
- FTSE Euro Emerging market Bond indices of Euro-denominited government bonds from emerging countries
m.ii) principal indices in the SA and int stock and bond markets
Describe the coverage and construction of the South African bond indices
Fixed Income indices
All Bond Index (ALBI)
- main fixed interest bond index
- Composite index containing top 20 fixed interest bonds ranked dually by liquidity and market cap.
- Split into two-sub-indices…
- …GOVI(Government bond Index) comprising top 10 government bonds issued by the Deparment of Finance
- …OTHI (other bond index)
Consituents and weightings changed in the following circumstances:
- Bond weightings change monthly based on issuance during period
- Constituent changes are effected quarterly.
CILI (Composite Inflation-Linked Index)
- main inflation linked bond index in SA
- split into three sub-indices…
- …IGOV
- …ISOE (state owned enterprises)
- …ICORP
- further split into four sub-indices by term (1 - 3 yr, 3-7, 7-12, 12+) similar to ALBI
ALBI and CILI include
- clean price index
- interest yield index
- total return index
m.ii) principal indices in the SA and int stock and bond markets
Describe the coverage and construction of the Global Equity indices.
International equity indices
- Cover over 8000 securities in 48 countries
- Captures around 98% of global equity markets by investible market cap
- indices divded into three segments: Developed, Advance emerging, Secondary emerging.
- Stocks not available to foreign investors excluded from indices, making them suitable for performance measurement
- Indices calculated in US dollar (performance adjusted for movements in currey concerned) and local currency (measure peformance of particular market)
- Weighted arithmetic capital indices, based on free floats
- Include dividend yield indices, total return index for each country.
m.ii) principal indices in the SA and int stock and bond markets
Describe briefly the FTSE Global Climate Index series.
International equity indices
Designed to reflect the performance of a global and diversifie basket of securities where their weights vary based on three types of climate related analysis (carbon emmissions, fossile fuel reserves, and green revenues data)
m.ii) principal indices in the SA and int stock and bond markets
Describe two main US equity indices
Equity indices
Dow Jones Industrial Average
- Unweighted arithmetic index based on only 30 industrial shares
- Just a very quick guide in the industrial sector
- very crude and unsuitable for performance
Standard & Poor’s Composite index ( S & P 500)
- Weighted arithmetic index.
- Constituents are leading 500 companies in the market representing a broad cross-section of all sectors of the market.
- Often suitable for performance measurement of portfolio of US equitie
Both are used as basis for stock index futures.
m.ii) principal indices in the SA and int stock and bond markets
State two key problems when constructing indices of unlisted or illiquid assets and list six problems in obtaining market prices of the constituents of such inidices.
Indices of unlisted or illiquid assets
Two key problems in constructing the property indices:
1. lack of reliable and up-to-date price data
2. heterogeneity of the assets included
Six problems in obtaining market values
1. Infrequent sales
2. price of deals/sales treated with degree of confidentiality
3. Valuations may be carried out at different points in time not necessarily when the index is calculated
4. Each asset may be unique and not representative of the sector or asset class overall.
5. Market values of asset may only be know when asset changes hands
6. Estimation of value is subjective and expensive process.
m.ii) principal indices in the SA and int stock and bond markets
Describe the two main Japanese equity indices
Equity indices
Nikkei Stock Average 225
- Unweighted arithmetic index with 225 (no largest stocks) representing about 50% of market value
- designed to reflect overall mark and an indicator of short term movements
- consituents are reviewed annually, but not representative of Japanese equity market
- not suitable for performance measurement
- used as basis for stock index futures
Tokyo Stock Exchange First Section Index
- Comprises of 1700 shares
- market cap weighted arithmetic index (reflecting free-float)
- constituents representing leading companies in the market
- more comprehensive than the Nekkei
- Suitable for performance measurment
m.ii) principal indices in the SA and int stock and bond markets
Explain what an equity volatility index is and list two main ways they may be calculated.
Equity indices
- Rather than recording market movements of equity price or total returns, these measure the volatility of equties.
- As such volatility indices are typically used as an indication of the market perception of risk.
They may be calculated in two ways:
- by using historical equity price movments
- by using the volatiility implied by option prices based on the equity being considered.
m.ii) principal indices in the SA and int stock and bond markets
Explain what is meant by a credit derivative index and give an example.
Equity indices
Whereas corporate bond indices blend interest andd credit risk, credit derivative indices are used to monitor prices of credit derivatives and hence more directly the price of credit risk.
Examples include the Markit iTraxx Europe index in Europe and in the CDX family in the US.
m.ii) principal indices in the SA and int stock and bond markets
Distinguish the two main types of property index.
Indices of unlisted or illiquid assets
Portfolio-based index
- measures the rental values, capital values and total returns of actual portfolio of rented properties
- responds slowly to changes in rental values
- behaves like actual property portfolio
- sometimes calculated on money-weighted basis
Barameter index
- based on estimates of hypothetical rack-rents
- response quickly to market conditions
- useful indicator of short-term movements in rents and yields
-unsuitable for performacne measurement
m.i) the uses of investment indices
outline the relevance of indices.
Use of indices
Indices are relevant to all stages of the asset management process.
- Objectives may be specified with reference to one or more indices - e.g. track or outperform
- 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
- Can be used to value the pf and can provide a benchmark against which to monitor it’s performance - as part of the monitoring the investment experience
