Understanding Indices: Definition and Types

• An index measures change in a group of data points from company performance, prices, productivity, and employment
• These data points may come from various sources
• Indices track changes in economics or financial markets
• Index numbers show magnitude change in related variables
• Indices compare values between time periods, locations, or categories
• The Consumer Price Index (CPI) measures average price changes paid by urban consumers for goods and services

Types of Indices

Stock Market Indices

• Track the performance of a basket of stocks
• S&P 500, DJIA, and NASDAQ Composite are examples
• Provides an overview of market performance using methods like market capitalization, price, or equal weighting

Bond Indices

• Measures the performance of a group of bonds
• Factors tracked include total return, yield, and credit quality
• The Bloomberg Barclays U.S. Aggregate Bond Index is an example

Economic Indices

• Gives insights into economic health and performance
• Examples include CPI, PPI, and PMI
• CPI measures consumer goods and services price level changes
• PPI measures prices received by domestic producers
• PMI indicates manufacturing and service sectors' economic health

Commodity Indices

• Tracks the performance of commodities like precious metals, energy, and agricultural products
• The Bloomberg Commodity Index is an example

Real Estate Indices

• Tracks real estate market performance
• The S&P CoreLogic Case-Shiller Home Price Index is an example

Construction of Indices

Base Period

• A reference point is selected
• The index value is set to 100
• Subsequent values are relative to this base
• Base period choice affects interpretation

Weighting

• Determines each component's importance
• Common weighting methods include price, market capitalization and equal weighting
• Market capitalization weighting shows company significance

Calculation

• Depends on index type and weighting method
• The formula sums weighted component values, divides by a base value, and multiplies by 100

Rebalancing

• Indices are rebalanced for accuracy and relevance
• Adjusts component weights to reflect market value changes or new components
• Rebalancing frequency varies

Uses of Indices

Benchmarking

• They serve as benchmarks for evaluating investment portfolio performance
• Investors compare portfolio returns to an index to assess their performance
• Comparing a stock portfolio’s performance against the S&P 500 index is an example

Investment Vehicles

• Indices create investment vehicles like index funds and ETFs
• These funds replicate the performance of the chosen index
• Index funds and ETFs offer both diversification and low costs

Economic Analysis

• They are used by economists and policymakers to analyze economic trends, inflation, economic growth, and market sentiment
• Monitoring CPI to assess inflation is an example

Derivatives

• Indices are the underlying assets for derivatives like futures and options
• Derivatives allow speculating or hedging against index value changes
• Trading S&P 500 futures contracts is an example

Types of Index Formulas

Laspeyres Index

• Uses base period quantities as weights
• Measures the cost change of a fixed basket of goods and services
• Formula: ( I_t = \frac{\sum (P_{it} \times Q_{i0})}{\sum (P_{i0} \times Q_{i0})} \times 100 )
  • ( I_t ) = Index value at time t
  • ( P_{it} ) = Price of item i at time t
  • ( Q_{i0} ) = Quantity of item i in the base period
  • ( P_{i0} ) = Price of item i in the base period
• It tends to overestimate inflation when prices rise

Paasche Index

• Uses current period quantities as weights
• Measures the cost change of a current basket of goods and services compared to the base period
• Formula: ( I_t = \frac{\sum (P_{it} \times Q_{it})}{\sum (P_{i0} \times Q_{it})} \times 100 )
  • ( I_t ) = Index value at time t
  • ( P_{it} ) = Price of item i at time t
  • ( Q_{it} ) = Quantity of item i at time t
  • ( P_{i0} ) = Price of item i in the base period
• It tends to underestimate inflation when prices rise

Fisher Index

• The geometric mean of the Laspeyres and Paasche indices
• Corrects biases of the Laspeyres and Paasche indices
• Formula: ( I_t = \sqrt{Laspeyres \times Paasche} )
• It is considered a superior index number formula

Simple Aggregate Index

• Sum of current year prices divided by the sum of base year prices, multiplied by 100
• Does not account for the relative importance of the items
• Formula: ( I_t = \frac{\sum P_{it}}{\sum P_{i0}} \times 100 )

Weighted Aggregate Index

• Is similar to a simple aggregate index but incorporates weights to reflect the relative importance of the items
• Formula: ( I_t = \frac{\sum (P_{it} \times W_i)}{\sum (P_{i0} \times W_i)} \times 100 )
  • ( W_i ) = Weight of item i

Limitations of Indices

• Are subject to biases due to base period choice, weighting method, and components included
• May not accurately reflect all experiences
• Revisions and changes affect value comparability
• May be manipulated or misinterpreted