Quantitative Methods - Index Numbers

Question 1

What is the idea of indices in relation to the stock market?

Answer 1

They are used to describe how prices of securities in general have moved. A base date will be established and ascribed an index value of say 100. Subsequent valuations of the items will be carried out and compared to the original base value to establish the revised index value. There are no rules in the selection of a base date, though it shouldn’t have an extreme value

Question 2

What are indexes used for in their simplest form?

Answer 2

Calculating % change and % points movement between any two years

Question 3

How can analysts use movements in a market index?

Answer 3

They give an indication of general trends and also indicate whether the market appears over or under priced relative to previous years. Indices may give some input into when we should buy and sell

Question 4

For an index to be useful what must it be?

Answer 4

It must be indicative of realistically achievable performance for the period being considered, and great efforts must be made to ensure the index is both relevant and comparable.

Question 5

What is particularly important to know about an index in terms of their pricing?

Answer 5

How the index deal with the payment of income by a security (dividends and interest). Normally quoted FTSE indices do not include dividend income in their valuation, however bond indices eg. Salmon Brothers World Government Bond Indices most frequently do and hence represent total return indices

Question 6

If I wanted to construct an index of price changes, what would th first step be?

Answer 6

Start with a price-relative index, this would take the price at the base date as the reference price and measure the current price against this.

Question 7

What is the issue with the price relative idea?

Answer 7

Whilst it works well when considering the change in the price of a particular standard item it can’t be as easily applied to share as it doesn’t take into account of things like a one for four bonus issue.

Question 8

What is the price relative index?

Answer 8

The current price divided by the base date price multiplied by 100

Question 9

What does a weighted index do?

Answer 9

It will weight the prices by multiplying them by the number of shares

Question 10

How do you calculated a weighted index?

Answer 10

Current share price multiplied by the current number of shares/base share price multiplied by base number of share

Multiplied by base index value

Question 11

What is a composite index?

Answer 11

An index which deals with several items

Question 12

What are the two approaches to composite indexes?

Answer 12

Arithmetically or Geometrically

Question 13

What is a re based index?

Answer 13

When the index is reset to a new base value

Question 14

When a index is debased what must be done for it to still be useful

Answer 14

It will need to be re-evaluated based on the new base year, or the new index values based on the old base year

Question 15

What is an index?

Answer 15

A number that gives the value of something relative to some base value

Question 16

Which will be higher the unweighted geometric or arithmetic index?

Answer 16

The geometric index will always be lower!

Question 17

What is the problem with unweighted geometric and arithmetic indexes?

Answer 17

They take no account of the number of shares and as such would only give an average portfolio price, not the value of the portfolio.

Question 18

Out of geometric and arithmetic unweighted index, which is more appropriate for portfolio performance measurement and why?

Answer 18

Arithmetic index, as returns on a portfolio will be the sum of the returns of the individual stocks within the portfolio, not the product.

Question 19

What are two important things to note about the geometric index?

Answer 19

It is unlikely to be representative of anything that can be achieved (the return on a portfolio is the sum of the constituents, not the product) hence the geometric index is unsuitable as a benchmark

A geometric mean tends to understate the performance relative to an equivalently arithmetic index, since it is less sensitive to large increase in prices and more sensitive to large price falls

Question 20

What weighting do we use for investment indices?

Answer 20

In relation to arithmetic means, Original quantity for original prices and current quality for current prices

Question 21

Historically what was the purpose of indices and what are they used for more commonly now?

Answer 21

The used to used to give an indication of the mood of the market however now they are more frequently used as a benchmark for performance assessment

Question 22

What characteristics are required to render an index suitable as a benchmark?

Answer 22

It must be

Specified and unambiguous
Appropriate to the preferences of the fund and the currency
Investable - composed of investments that could conceivably be held in the fund
Measurable - the return can be calculated on a frequent basis as required
Representative of achievable performance - it has an arithmetic weighted composition
Measures the relevant component of performance - total return indices for total return performance and capital value indices for capital growth

Question 23

How are share indices measured and what are they useful for?

Answer 23

Share indices measure appreciation of the capital value of the relevant shares, taking no account of the income generated. As such they they are a good benchmark for comparing capital gains but not dividend income.

To reflect different sizes of companies in the index the most common construction is arithmetic weighted.

Question 24

Are bond and share indices universally accepted?

Answer 24

Some share indices are however no bond indices are right now.

Question 25

How are bond indices calculated?

Answer 25

Bond indices are generally total returns indices that include both capital gain and income reinvested for bonds with particular characteristics. They are also generally unweighted or price relative as the level of investment in a bond issue is unlikely to be linked to the size of the issue but is more likely to depend on cash flows, yields and duration.

Question 26

For UK bond indices what determines which of the available indices is chosen as a benchmark?

Answer 26

The consideration of the duration

Question 27

What is the free-float indices?

Answer 27

Free-float indices ensure that the index satisfies the benchmark requirement of being investable. The weighting should only reflect the number of shares available to the public as otherwise there would be significant demand for the few available shares (even if only from trackers trying to replicate this weighting from the limited supply available) distorting the price upwards and distorting the index

Question 28

Indices for UK government bonds are available covering all fully paid up stocks in issue for which timeframes?

Answer 28

0-5 years
5-10 years 
5-15 years
10-15 years
>15 years
Irredeemables