Passive equity portfolio management attempts to design a portfolio to replicate the performance of a specific index. The key word here is replicate. As discussed in Chapter 2, the portfolio man- ager who earns higher returns by violating the client’s policy statement should be fired; a pas- sive manager who isn’t really passive should likewise be dismissed. A passive manager earns his or her fee by constructing a portfolio that closely tracks the performance of a specified equity index (referred to as the benchmark index) that meets the client’s needs and objectives. If the manager attempts to outperform the index selected, he or she violates the passive premise of the portfolio.
In Chapter 6, we presented several reasons for investing in a passive equity portfolio. Strong evidence indicates that the stock market is fairly efficient. For most active managers, the costs of actively managing a portfolio (1 to 2 percent of the portfolio’s assets) are difficult to overcome.
As we saw earlier, the S&P 500 index typically outperforms most equity mutual funds on an annual basis. Note that, although the S&P 500 is the most popular index to track, a client can choose from among about 30 different indexes.2
Chapter 5 contained a summary description of many different market indexes. Domestic U.S.
equity indexes include the S&P 500, Industrials, and 100; the Major Market index; the Nasdaq composite index; and the Wilshire 5000. The Wall Street Journal publishes the daily values of indexes for the organized exchanges, the OTC market, and various industry groups. Indexes exist for small capitalization stocks (Russell 2000); for value- or growth-oriented stocks (Russell Growth index and the Russell Value index); and for numerous world regions (such as the EAFE index); as well as for smaller regions, individual countries, and types of countries (emerging markets). As passive investing has grown in popularity, money managers have created an index fund for virtually every broad market category.3
The goal of a passive portfolio is to match the returns to the index as closely as possible; but, because of cash inflows and outflows and company mergers and bankruptcies, securities must be bought and sold, which means that there inevitably will be differences between portfolio and benchmark returns over time. In addition, even though index funds generally attempt to mini- mize turnover and the resultant transactions fees, they necessarily have to do some rebalancing, which means that the long-run return performance of index funds will lag the benchmark index.
Certainly, substantial or prolonged deviations of the portfolio’s returns from the index’s returns would be a cause for concern.
There are three basic techniques for constructing a passive index portfolio: full replication, sam- pling, and quadratic optimization or programming. The most obvious technique is full replica- tion, wherein all the securities in the index are purchased in proportion to their weights in the index. This technique helps ensure close tracking, but it may be suboptimal for two reasons.
First, the need to buy many securities will increase transaction costs that will detract from per- formance. Second, the reinvestment of dividends will also result in high commissions when many firms pay small dividends at different times in the year.
The second technique,sampling, addresses the problem of numerous stock issues. Statistical theory teaches us that we don’t need to ask everyone in the United States for his or her opinion to determine who may win an election. Thus, opinion pollsters query only a small sample of the population to gauge public sentiment. Sampling techniques also can be applied to passive port- folio management. With sampling, a portfolio manager would only need to buy a representative sample of stocks that comprise the benchmark index. Stocks with larger index weights are pur- chased according to their weight in the index; smaller issues are purchased so their aggregate characteristics (e.g., beta, industry distribution, and dividend yield) approximate the underlying benchmark. With fewer stocks to purchase, larger positions can be taken in the issues acquired, which should lead to proportionately lower commissions. Further, the reinvestment of dividend cash flows will be less problematic because fewer securities need to be purchased to rebalance the portfolio. The disadvantage of sampling is that portfolio returns will almost certainly not track the returns for the benchmark index as closely as with full replication.
Rather than obtaining a sample based on industry or security characteristics,quadratic opti- mizationor programming techniques can be used to construct a passive portfolio. With quadratic programming, historical information on price changes and correlations between securities are input to a computer program that determines the composition of a portfolio that will minimize tracking error with the benchmark. A problem with this technique is that it relies on historical price changes and correlations, and, if these factors change over time, the portfolio may experi- ence very large tracking errors.
Some passive portfolios are not based on a published index. Sometimes customized passive portfolios, called completeness funds, are constructed to complement active portfolios that do not cover the entire market. For example, a large pension fund may allocate some of its holdings to active managers expected to outperform the market. Many times, these active portfolios are overweighted in certain market sectors or stock types. In this case, the pension fund sponsor may want the remaining funds to be invested passively to “fill the holes” left vacant by the active managers. The performance of the completeness fund will be compared to a customized bench- mark that incorporates the characteristics of the stocks not covered by the active managers.
For example, suppose a pension fund hires three active managers to invest part of the fund’s money. One manager emphasizes small-capitalization U.S. stocks, the second invests only in Pacific Rim countries, and the third invests in U.S. stocks with low P/E ratios. To ensure adequate diversification, the pension fund may want to passively invest the remaining assets in a complete- ness fund that will have a customized benchmark that includes large- and mid-capitalization U.S.
stocks, U.S. stocks with normal to high P/E ratios, and international stocks outside the Pacific Rim.
Index Portfolio Construction Techniques
Still other passive portfolios and benchmarks exist for investors with certain unique needs and preferences.4Some investors may want their funds to be invested only in stocks that pay divi- dends or in a company that produces a product or service that the investor deems socially respon- sible. Benchmarks can be produced that reflect these desired attributes, and passive portfolios can be constructed to track the performance of the customized benchmark over time so investors’
special needs can be satisfied.5
If the goal of forming a passive portfolio is to replicate the essence of a particular equity index, the success of constructing such an investment fund lies not in the absolute returns it produces but, rather, in how closely its returns match those of the benchmark (e.g., the Standard & Poor’s 500 index). That is, the goal of the passive manager should be to minimize the portfolio’s return volatility relative to the benchmark. Said differently, the manager should try to minimize track- ing error.
Tracking error can be defined as the extent to which return fluctuations in the managed port- folio are not correlated with return fluctuations in the benchmark. A flexible and straightforward way of measuring tracking error can be developed as follows. Recalling the notation from Chap- ter 7, let
Wi=investment weight of asset i in the managed portfolio Rit=return to asset i in period t
Rbt=return to the benchmark portfolio in period t
With these definitions, we can define the Period t return to managed portfolio as
where:
N=number of assets in the managed portfolio
With these definitions, we can then specify the Period t return differential between the man- aged portfolio and the benchmark as
➤17.1
Notice that, given the returns to the N assets in the managed portfolio and the benchmark,∆is a function of the investment weights that the manager selects and that not all of the assets in the benchmark need be included in the managed portfolio (i.e., w=0 for some assets).
∆t i it bt pt bt i
N
w R R R R
= − = −
∑= 1
Rpt w Ri it
i
= N
∑= 1
Tracking Error and Index Portfolio Construction
656 CHAPTER 17 EQUITYPORTFOLIOMANAGEMENTSTRATEGIES
4Recall our discussion in Chapter 2 on investors’ objectives and constraints; two of the constraints were legal and regu- latory requirements and unique needs and preferences.
5See Sharmin Mossavar-Rahmani, “Customized Benchmarks in Structured Management,” Journal of Portfolio Manage- ment 13, no. 4 (summer 1988): 65–68; and Chris P. Dialynas, “The Active Decisions in the Selection of Passive Man- agement and Performance Bogeys,” in The Handbook of Fixed Income Securities, 5th ed., ed. Frank Fabozzi (Chicago, Ill.:
Irwin Professional Publishing, 1997).
For a sample of T return observations, the variance of ∆can be calculated as follows:
➤17.2
Finally, the standard deviation of the return differential is
so that annualized tracking error (TE) can be calculated as
➤17.3
where P is the number of return periods in a year (e.g., P=12 for monthly returns, P=252 for daily returns).
Suppose an investor has formed a portfolio designed to track a particular benchmark. Over the last eight quarters, the returns to this portfolio, as well as the index returns and the return dif- ference between the two, were:
The periodic average and standard deviation of the manager’s return differential (i.e., “delta”) relative to the benchmark are
Thus, the manager’s annualized tracking error for this two-year period is 2.0 percent (=1.0 per- cent × ).
Generally speaking, there is an inverse relationship between a passive portfolio’s tracking error relative to its index and the time and expense necessary to create and maintain the portfo- lio. For example, full replication of the S&P 500 would have virtually no tracking error but would necessitate positions in 500 different stocks and require frequent rebalancing. As smaller samples are used to replicate the S&P index’s return performance, the expense of forming the managed portfolio would decline but the potential tracking error is likely to increase. Thus, the art of being a manager of a passive equity portfolio lies in balancing the costs (larger tracking error) and the benefits (easier management, lower trading commissions) of using smaller sam- ples. Exhibit 17.2 estimates the tracking error that occurs from such sampling.
4
Average ∆
∆
= − + + + − ÷ =
= − − + − + + − − ÷ − =
[ . . . . ] . %
( . . ) ( . . ) ( . . ) ( ) . %
0 4 1 0 0 8 1 6 10 0 2
0 4 0 2 2 1 0 0 2 2 1 6 0 2 2 10 1 1 0
K σ K
PERIOD MANAGER INDEX DIFFERENCE(∆)
1 2.3% 2.7% –0.4%
2 –3.6 –4.6 1.0
3 11.2 10.1 1.1
4 1.2 2.2 –1.0
5 1.5 0.4 1.1
6 3.2 2.8 0.5
7 8.9 8.1 0.8
8 –0.8 0.6 –1.6
TE= σ∆ P
σ∆ = σ∆2 =periodic tracking error σ∆
∆ ∆
2
2 1
= 1
−
−
∑= ( )
( )
t t
T
T
Although investors can construct their own passive investment portfolios that mimic a particular equity index, there are at least two “pre-packaged” ways of accomplishing this goal that are typ- ically more convenient and less expensive for the small investor. These are (1) buying shares in an index mutual fund or (2) buying shares in an exchange-traded fund (ETF).
Index Funds As we discuss in Chapter 25, mutual funds represent established security port- folios managed by professional investment companies (e.g., Fidelity, Vanguard, Putnam, AIM) in which investors can participate. The investment company is responsible for deciding how the fund is managed. For an indexed portfolio, the fund manager will typically attempt to replicate the composition of the particular index exactly, meaning that he or she will buy the exact secu- rities comprising the index in their exact weights and then alter those positions anytime the com- position of the index itself is changed. Since changes to most equity indexes occur infrequently, index funds tend to generate low trading and management expense ratios. A prominent example of an index fund is Vanguard’s 500 Index Fund (VFINX), which is designed to mimic the S&P 500 index. Exhibit 17.3 provides a descriptive overview of this fund and indicates that its historical return performance is virtually indistinguishable from that of the benchmark.
The advantage of index mutual funds is that they provide an inexpensive way for investors to acquire a diversified portfolio that emphasizes the desired market or industry within the context of a traditional money management product. As with any mutual fund, the disadvantages are that investors can only liquidate their positions at the end of the trading day (i.e., no intraday trad- ing), usually cannot short sell, and may have unwanted tax repercussions if the fund has an unforeseen need to sell a portion of its holdings, thereby realizing capital gains.
Exchange-Traded Funds ETFs are a more recent development in the world of indexed investment products than index mutual funds. Essentially, ETFs are depository receipts that give investors a pro rata claim on the capital gains and cash flows of the securities that are held in deposit by the financial institution that issued the certificates. That is, a portfolio of securities is placed on deposit at a financial institution or into a unit trust, which then issues a single type of certificate representing ownership of the underlying portfolio. In that way, ETFs are similar to the American depository receipts (ADRs) described in Chapter 3.
Methods of Index Portfolio Investing
658 CHAPTER 17 EQUITYPORTFOLIOMANAGEMENTSTRATEGIES
Expected Tracking Error
(Percent) 4.0 3.0 2.0 1.0
500 400 300 200 100 0
Number of Stocks
EXHIBIT 17.2 EXPECTED TRACKING ERROR BETWEEN THE S&P 500 INDEX AND PORTFOLIOS COMPRISED OF SAMPLES OF FEWER THAN 500 STOCKS
EXHIBIT 17.3 DETAILS OF THE VANGUARD 500 INDEX TRUST MUTUAL FUND
© 2002 Bloomberg L.P. All rights reserved. Reprinted with permission.
A. Description
VANGUARD 500 INDEX FUND—INV OBJECTIVE—INDEX FUND—LARGE CAP Vanguard 500 Index Fund is an open-end fund incorporated in the United States. The Fund’s objective is to match the
performance of the Standard & Poor’s 500 Index, which is dominated by the stocks of large U.S. companies. The Fund invests all or substantially all of its assets in the stocks that make up the Index.
BLOOMBERG CLASSIFICATION DATA CURRENT/OPERATIONAL DATA
Asset Class Equity
Style Index Fund
Market Cap Focus Large Cap
Geographic Focus U.S.
PERFORMANCE RANKING
AS OF3/28/02 RETURN %ALL %OBJ
3) TRA 1 Month 3.74 51 72
YTD .24 50 86
1 Year .69 39 86
5 Year 9.64 81 91
2001 –12.02 34 86
B. Historical Returns
CURRENT RETURN PERCENTILE
AS OF3/28/02 FUND SPX DIFFERENCE ALL OBJECTIVE
3) TRA 1 Week –.53 –.52 –.01 24 59
1 Month 3.74 3.76 –.02 51 72
3 Month –.88 –.84 –.04 31 84
4) COMP YTD .24 .27 –.03 50 86
1 Year .69 .87 –.18 39 86
3 Year –2.47 –2.43 –.04 19 84
9) HRH 5 Year 9.64 9.68 –.04 81 91
HISTORICAL FUND SPX DIFFERENCE ALL OBJECTIVE
2001 –12.02 –11.89 –.13 34 86
2000 –9.06 –9.10 .04 27 87
1999 21.07 21.04 .03 68 92
1998 28.61 28.58 .03 92 81
1997 33.21 33.38 –.17 95 88
1996 22.86 22.96 –.10 89 89
1995 37.45 37.62 –.17 94 89
1994 1.18 1.33 –.15 86 74
1993 9.89 10.06 –.17 33 82
1992 7.45 7.62 –.17 48 n.a.
20
10
0
–10
–20
20
10
0
–10
–20 29MAR 31JAN02
30NOV 28SEP
31JUL 31MAY 30MAR01
1 Yr Performance vs. Benchmark Indexes
VFINX SPX
1) GP NAV $ 105.85
Assets(mil) 12/31/01 $ 86,000.00
Inception Date 8/31/76
660 CHAPTER 17 EQUITYPORTFOLIOMANAGEMENTSTRATEGIES
There are several notable example of ETFs, including (1) Standard & Poor’s 500 Depository Receipts (SPDRs or “spider” as they are sometimes called), which are based on a basket of all the securities held in that index; (2) iShares, which recreate indexed positions in several global developed and emerging equity markets, including countries such as Australia, Mexico, Malaysia, the United Kingdom, France, Germany, Japan, and China; and (3) sector ETFs, which invest in baskets of stocks from specific industry sectors, including consumer services, indus- trial, technology, financial services, energy, utilities, and cyclicals/transportation. Exhibit 17.4 shows descriptive and return data for the SPDR Trust certificates. Notice once again how closely the returns to these shares track the overall index.
A significant advantage of ETFs over index mutual funds is that they can be bought and sold (and short sold) like common stock through an organized exchange or in an over-the-counter market. Further, they are backed by a sponsoring organization (e.g., for SPDRs, the sponsor is PDR Services LLC, a limited liability company whose sole member is the American Stock Exchange where SPDR shares trade) who can alter the composition of the underlying portfolio to reflect changes in the composition of the index. Other advantages relative to index funds include no payment of a management fee, the ability for continuous trading while markets are open, and the ability to time capital gain tax realizations. ETF disadvantages include the bro- kerage commission and the inability to reinvest dividends except on a quarterly basis.