In this brief note we argue that for investors that are serious about matching (the risks of) assets and liabilities, indexation is a doubtful proposition as significant autonomous changes may occur in the industry allocation and accompanying risk-return profile of the portfolio underlying the index. The name of the index may not change, but the underlying portfolio does!

Harry. M Kat

English

Research Papers in Economics

 
 
 
 
       
 
 
 
THE BUSINESS SCHOOL 
FOR FINANCIAL MARKETS 
The University of Reading 
 
 
 
 
 
Indexation Doesn't Make Sense 
 
 
ISMA Centre Discussion Papers in Finance 2002-26 
This version: 8 November 2002 
 
 
 
 
 
Harry M. Kat 
Associate Professor in Finance, 
ISMA Centre, University of Reading, UK 
 
 
 
Copyright © 2002 Harry M. Kat. All rights reserved. 
 
The University of Reading • ISMA Centre • Whiteknights • PO Box 242 • Reading RG6 6BA  • UK 
Tel: +44 (0)118 931 8239  • Fax: +44 (0)118 931 4741 
Email: research@ismacentre.rdg.ac.uk  • Web: www.ismacentre.rdg.ac.uk 
 
Director: Professor Brian Scott-Quinn, ISMA Chair in Investment Banking 
The ISMA Centre is supported by the International Securities Market Association   
   
    
This discussion paper is a preliminary version designed to generate ideas and constructive comment. The 
contents of the paper are presented to the reader in good faith, and neither the author, the ISMA Centre, nor 
the University, will be held responsible for any losses, financial or otherwise, resulting from actions taken 
on the basis of its content. Any persons reading the paper are deemed to have accepted this. 
 
 
 
 
 
Abstract 
 
In this brief note we argue that for investors that are serious about matching (the risks of) 
assets and liabilities, indexation is a doubtful proposition as significant autonomous 
changes may occur in the industry allocation and accompanying risk-return profile of the 
portfolio underlying the index. The name of the index may not change, but the underlying 
portfolio does! 
 
 
Contacting Author: 
Harry M. Kat 
ISMA Centre 
The University of Reading 
Whiteknights Park 
Reading RG6 6BA 
United Kingdom 
Tel. +44-118-9316428 
E-mail: h.kat@ismacentre.rdg.ac.uk 
From 2003: harry@airc.info or harry@harrykat.com  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
The author would like to thank BARRA for generously providing the data used in this 
paper. 
 ISMA Centre Discussion Papers in Finance 2002-26 
Copyright© 2002 Harry M. Kat 
1. INTRODUCTION 
Over the past 20 years, indexation has become very popular with institutional as well 
as private investors. Strongly advocated by big names from academia as well as the 
industry, assets under management by index funds have grown from almost negligible 
in 1976, when the first index fund was introduced, to far over $1 trillion now. It is 
estimated that (excluding so-called closet-indexing) currently 20-40% of 
institutionally managed assets are indexed, with US institutions quite far ahead of the 
rest of the world.   
 
The idea behind indexation is very straightforward: since modern capital markets are 
informationally highly efficient, the added value of chasing alpha can only be 
negative. There is plenty of evidence to support this hypothesis. No active investment 
manager seems to be consistently able to beat the index, while the average active 
manager underperforms the index by about 2% per year. This means that the only way 
to improve performance is to diversify and cut the costs of security analysis and 
trading to a minimum. This has lead many investors to abandon every form of security 
analysis and active trading and to just buy and hold the market as a whole in the form 
of the index.    
 
Although it sounds very plausible, the advice that investors should simply buy and 
hold the index does not follow logically from the idea that markets are informationally 
efficient. In an efficient market, collecting and analysing information cannot be 
expected to pay off in terms of a higher expected return. However, without collecting 
and analysing data investors would not know anything about the risk-return properties 
of the different assets available.  Every stock would look the same. The proper advice 
should therefore not be to throw in the towel and just buy and hold the largest stocks 
in the market, but simply to be very careful how one spends one’s money. There is 
little doubt that money spend on chasing alpha is money wasted. Money spend on 
gaining an understanding of the risk-return trade-offs available in the market, 
however, is not. It may not directly contribute to a higher return, but it does provide 
valuable and necessary insights and thereby contributes to better decision-making and 
risk management. Also, risk management procedures aimed at generating non-linear ISMA Centre Discussion Papers in Finance 2002-26 
Copyright© 2002 Harry M. Kat  2
payoff profiles, such as the convex payoff of portfolio insurance for example, will 
require active trading (or the purchase of options, in which case someone else does the 
trading). Again, the transaction costs involved in this are not money wasted. They are 
simply part of the price of generating the desired payoff profile.     
 
The danger of buying the index becomes more apparent if one realizes that stock 
market indices are created to reflect the overall movements of the stock market, not to 
be good investments. The stocks in most major indices are not selected based on their 
expected future performance or risk-return profile but simply on market capitalization. 
As a result, the composition of indices tends to be quite unstable. Based on their 
market capitalization, stocks come and go and their weight within the index changes 
continuously. The risk-return characteristics of the index can therefore change very 
substantially over a short period of time. This also has serious consequences for the 
returns that stock market indices generate. Although the name stays unchanged, the 
underlying portfolio doesn’t. In other words, what we record as ‘the return on the 
index’ is the return on a different portfolio every day. With the risk-return profile of 
indices changing over time, this means that historical index returns may not tell us too 
much about what to expect from an index replicating portfolio in the near future.  In 
this paper we investigate this matter in more detail. Throughout we concentrate on the 
S&P 500 index over the period January 1990 – July 2002.    
 
2. THE INDUSTRY WEIGHTING OF THE S&P 500 
One way to get an indication of how much the risk-return profile of a stock market 
index can change over time is to look at how the index is invested in the various 
industry sectors. Every industry has its own peculiar risk-return characteristics. A 
significant change in industry weightings can therefore be expected to change the 
risk-return profile of the index as well. Let’s look at how the industry weightings of 
the S&P 500 have changed over the last twelve and a half years. Doing so, we 
distinguish the following industry sectors: 
 
1. Basic materials – Mining and metals, forest products, paper, chemicals. 
2. Energy – Oil and gas exploration, production, refining, marketing.  ISMA Centre Discussion Papers in Finance 2002-26 
Copyright© 2002 Harry M. Kat  3
3. Consumer non-cyclical – Food, beverages, alcohol, tobacco, home products.  
4. Consumer cyclical – Durables, cars, clothing, construction, property. 
5. Consumer services – Publishing, media, hotels, restaurants, leisure. 
6. Industrials – Environmental services, heavy equipment, industrial parts. 
7. Utilities – Electricity and gas. 
8. Transportation – Railroads, airlines, trucking, shipping. 
9. Health care – Medical services and products, drugs. 
10. Technology – Electronics, computer chips and hardware, software, internet. 
11. Telecommunications – Telephone, cellular phones and pagers. 
12. Commercial services – Administration, advertising, consultancy, training. 
13. Financial services – Insurance, banks, thrifts, brokers, mutual funds. 
 
 
<< Insert Figure 1 >> 
 
Figure 1 shows how an S&P 500 index investor would have been invested in the 
above industry sectors by the end of January 1990, January 2000 and July 2002. From 
figure 1 we see that, with the exception of transportation and commercial services, in 
January 1990 an S&P 500 index investor would have between 5% and 10% percent 
invested in each of the above industry sectors. In January 2000, however, this would 
have changed completely. By then the same index investor would have 28% invested 
in technology stocks and 15% in financial services, which would have come at the 
cost of basic materials, energy, consumer non-cyclical, industrials and utilities.   
    
<< Insert Figure 2 >> 
 
Although the above change in industry allocation is extremely large, it took 10 years 
to materialize. This does not mean, however, that industry weightings always change 
slowly. Comparing the January 2000 and the July 2002 allocations shows that in only 
two and a half years time our index investor’s exposure to the technology sector 
would have come down from 28% to 15%. His exposure to the financial services 
industry on the other hand would have increased from 15% to 23%. Figure 2 shows 
the evolution of the weights of the sectors consumer non-cyclical, health care, 
technology and financial services over the period July 1997 – July 2002. From the ISMA Centre Discussion Papers in Finance 2002-26 
Copyright© 2002 Harry M. Kat  4
graph we clearly see how volatile the weights of these four sectors in the index have 
been over the past five years. During the first half of 2000, S&P 500 index fund 
investors were more than 30% invested in technology stocks; more than twice as 
much as in 1997-1998 and almost four times as much as in 1990-1993 (not shown). In 
2002, however, the weight was down to 15% again. 
 
3. BARRA RISK INDEX EXPOSURES OF THE S&P 500 
Another way to gain some insight into the changing risk-return profile of the S&P 500 
is to have a look at the evolution of the BARRA Risk Index Exposures. These are 
sensitivities to a number of risk indices, computed each month by combining 
fundamental and market data. Risk index exposures are expressed as standardized 
numbers. The average stock in the estimation universe (11,500+ US stocks) has an 
exposure of zero. BARRA distinguishes the following twelve risk indices: 
 
1. Volatility - Captures relative volatility using measures of both long-term 
historical volatility and near-term volatility (such as high-low price ratio, daily 
standard deviation, and cumulative range over the last 12 months).  
2. Momentum - Captures common variation in returns related to recent stock 
price behaviour. 
3. Size - Captures differences in stock returns due to differences in market 
capitalization of companies. 
4. Size non-linearity - Captures deviations from linearity in the relationship 
between returns and log of market capitalization. 
5. Trading activity - Measures the amount of relative trading in each stock. 
Stocks that are highly traded are likely to be those with greater institutional 
interest. Such stocks may display different returns. 
6. Growth - Uses historical growth and profitability measures to predict future 
earnings growth.  
7. Earnings yield - Combines current and historical earnings-to-price ratios with 
a measure of analyst-predicted earnings-to-price. 
8. Value - Distinguishes between value stocks and growth stocks using the ratio 
of book value of equity to market capitalization.  ISMA Centre Discussion Papers in Finance 2002-26 
Copyright© 2002 Harry M. Kat  5
9. Earnings variability - Measures the variability in earnings and cash flows 
using both historical measures and analyst predictions.  
10. Leverage - Measures financial leverage of a company. 
11. Currency - Measures the sensitivity of a company's stock return to the return 
on a basket of foreign currencies.  
12. Dividend yield - Computes a measure of predicted dividend yield using the 
past history of dividends and the market price behavior of the stock. 
 
 
<< Insert Figure 3 and 4 >> 
 
Similar to figure 1, figure 3 shows the risk index exposures of an S&P 500 index 
investor by the end of January 1990, January 2000 and July 2002. From the graph we 
see that the risk index exposures of the S&P 500 do not only deviate significantly 
from the average stock in BARRA’s estimation universe (which by construction has  
risk index exposures equal to zero), but also that they may vary considerably over 
time.  Figure 4 shows the evolution of the S&P 500’s exposures to volatility, 
momentum, trading activity, growth and earnings yield. Comparing this graph with 
figure 2 shows that the change in these risk index exposures closely follows the rise 
and fall of the relative importance of technology stocks in the S&P 500.  
 
In sum, whether one simply looks at the way the S&P 500 is spread over the various 
industry sectors or approaches risk in a more sophisticated way, it is clear that buying 
and holding the S&P 500 will leave an investor with a portfolio with risk-return 
characteristics that may show significant autonomous swings over time. For investors 
that are serious about matching (the risks of) assets and liabilities this makes 
straightforward passive indexation a doubtful proposition. 
 
 
 
 
 
 
 ISMA Centre Discussion Papers in Finance 2002-26 
Copyright© 2002 Harry M. Kat  6
4. CONCLUSION 
In this brief note we have argued that simply buying and holding the index in an 
attempt to minimize costs and thereby improve performance can be a dangerous 
strategy as significant autonomous changes may occur in the industry allocation and 
accompanying risk-return profile of the underlying portfolio. The name of the index 
may not change, but the underlying portfolio does! Leaving job protection aspects 
aside, indexation appears to be the result of taking the implications of market 
efficiency just a little to far. As long as it is not purely aimed at beating the market, 
there is nothing wrong with spending some money on data, analysis and trading. 
Investors need to collect and analyse data to find out what risk-return profiles are on 
offer in the marketplace. In addition, they may need to trade quite actively to ensure 
their portfolio stays in line with their risk-return requirements or desired payoff 
profile. It is a fact of life that responsible investment management requires one to 
incur costs. The trick is to avoid those costs that have little or no value added, but not 
to avoid making costs altogether.    
     
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ISMA Centre Discussion Papers in Finance 2002-26 
Copyright© 2002 Harry M. Kat  7
Figure 1: Sector weights S&P 500 index 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 2: Sector weights S&P 500 index over July 1997 – July 2002 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
0
5
10
15
20
25
30
1 2 3 4 5 6 7 8 9 10 11 12 13
Jan-90
Jan-00
Jul-02
5
10
15
20
25
30
35
7/31/2002 1/31/2000 7/31/1997
3
9
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13ISMA Centre Discussion Papers in Finance 2002-26 
Copyright© 2002 Harry M. Kat  8
Figure 3: BARRA risk index exposures S&P 500  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4: BARRA risk index exposures S&P 500 over July 1997 – July 2002 
 
 
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
1 2 3 4 5 6 7 8 9 10 11 12
Jan-90
Jan-00
Jul-02
-0.3
-0.25
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-0.15
-0.1
-0.05
0
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0.1
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7/31/2002 1/31/2000 7/31/1997
1
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7

Indexation doesn't make sense

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Indexation doesn't make sense

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