The authors thank an anonymous referee whose comments have led to improvements in the paper.

# Agency and Institutional Investment

Article first published online: 17 MAR 2011

DOI: 10.1111/j.1468-036X.2011.00596.x

© 2011 Blackwell Publishing Ltd

Additional Information

#### How to Cite

Brennan, M. J., Cheng, X. and Li, F. (2012), Agency and Institutional Investment. European Financial Management, 18: 1–27. doi: 10.1111/j.1468-036X.2011.00596.x

#### Publication History

- Issue published online: 27 DEC 2011
- Article first published online: 17 MAR 2011

- Abstract
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### Keywords:

*portfolio choice*;*asset pricing*;*CAPM*;*institutional investors*

*G*110;*G*120;*G*230

### Abstract

- Top of page
- Abstract
- 1. Introduction
- 2. A Model of Institutional Investing
- 3. Data
- 4. Expected returns and the agency model
- 5. Institutional portfolio weights and the agency model
- 6. Conclusion
- Appendix
- References

*In this paper we summarise and extend the agency-based model of asset pricing of **Brennan (1993)** to show that the implied agency effects on asset pricing are too small to be empirically detectable: empirical tests confirm this and we show that the positive findings of **Gomez and Zapatero (2003)** are due to their choice of sample. We also derive new empirical implications for the composition of institutional investment portfolios and empirically confirm the major result, that institutional portfolios will be short the minimum variance portfolio.*

### 1. Introduction

- Top of page
- Abstract
- 1. Introduction
- 2. A Model of Institutional Investing
- 3. Data
- 4. Expected returns and the agency model
- 5. Institutional portfolio weights and the agency model
- 6. Conclusion
- Appendix
- References

In 1952 around 90% of US equities was held by domestic households according to US Federal Funds data. By 2007 that share had dropped to only 35%. Currently, domestic financial institutions own about 48% of the value of US stocks. Another 16% is held by foreigners and a large proportion of this is represented by foreign financial institutions. If we combine the foreign holdings with the holdings of domestic institutions, then the share of US equities held by institutions is of the order of 65%.

This growth in institutional investment makes traditional asset pricing models such as the CAPM problematic since they do not distinguish between individual and institutional investors, and there is reason to believe that the objectives, and therefore the portfolio holdings, of these two types of investor will differ because of the agency problem that arises from delegated portfolio management: while direct investors are typically concerned only with the return characteristics of their portfolios, investment managers, like corporate managers, have other concerns.^{1}

In this paper we examine the empirical predictions for asset pricing and for institutional portfolio allocations of a simple agency model of institutional investment managers whose performance is evaluated relative to a stock market index or benchmark. For such managers, the benchmark plays the role of the riskless asset in conventional portfolio theory and, as a result, in equilibrium the expected returns on securities which covary with the benchmark returns are depressed relative to the predictions of a classical asset pricing model, while institutional investment managers tilt their portfolios towards such securities.

The assumption that investment managers are concerned about their performance relative to a benchmark is consistent with Lakonishok *et al.* (1992) who report that most equity managers promise to beat the S&P 500 index by 200 to 400 basis points, and that pension fund sponsors allocate money among managers on the basis of their evaluations of the money managers’ ability to beat the index. Similarly, Stutzer (2003) cites the TIAA-CREF Trust company: ‘Accounts for clients who have growth objectives with an emphasis on equities will be benchmarked heavily toward the appropriate equity index – typically the S&P 500 index’. Different investment managers may be measured against different benchmarks, and since 1999 the SEC has required mutual funds to compare their historical returns with those of a passive benchmark.^{2}Chan *et al.* (2002) emphasise the differences in investment *styles* of different managers and claim that they can be analysed along size and value-growth dimensions.^{3}

There is also evidence that the decisions of institutional investment managers are affected by agency considerations. Thus Brown *et al.* (1996) argue that the mutual fund market has the characteristics of a tournament which creates incentives for mutual fund managers to change the risk characteristics of their portfolios during the year in response to their relative return ranking, and they find evidence of such behaviour. Chevalier and Ellison (1997) provide more detailed evidence on risk taking and the incentives created for mutual fund managers by the funds flow-performance relationship, and Chevalier and Ellison (1999) find evidence of career concerns in the behaviour of mutual fund managers.

Our model relies on the basic theoretical framework of the unpublished paper of Brennan (1993) which we extend to provide an *a priori* estimate of the magnitude of the effect of agency considerations on equilibrium rates of return, and to incorporate an analysis of the equilibrium portfolios of institutional investors. To operationalise the predictions of the model we assume that the aggregate benchmark portfolio for institutional investors can be represented by the S&P 500. The theory implies that if the benchmark is highly correlated with the market portfolio then the benchmark effect on expected returns should be small, and that is what we find. This is in contrast to Gomez and Zapatero (2003) who report a significant benchmark effect on expected returns during the period 1980–1996. This appears to be because Gomez and Zapatero restrict their sample to the ‘220 US securities that have been in the S&P 500 without interruption’ during the sample period. We show that the restriction to large firms significantly affects their empirical findings and that a more complete empirical analysis finds agency effects on asset pricing to be too small to detect.

The theory also implies that the portfolios of institutions consist of a long position in the market portfolio, a long position in the S&P 500 portfolio and a short position in the minimum variance portfolio. We find strong evidence that proxies for these three portfolios play an important role in institutional asset allocation and with the signs predicted by the theory. Moreover, this characterisation of institutional portfolios holds true, not only at the aggregate level, but also at the level of institutional type – bank, investment advisor etc. We also find that institutional portfolio allocations relative to aggregate market values are tilted towards stocks with high betas with respect to the component of the S&P 500 return that is orthogonal to the overall market return, which we refer to as the ‘S&P 500 residual’ beta. This association between asset allocations and the S&P 500 residual beta is robust across institutional groups and to the inclusion in the regression of the market beta of the security, firm size, and a dummy variable for membership in the S&P 500 portfolio.

### 2. A Model of Institutional Investing

- Top of page
- Abstract
- 1. Introduction
- 2. A Model of Institutional Investing
- 3. Data
- 4. Expected returns and the agency model
- 5. Institutional portfolio weights and the agency model
- 6. Conclusion
- Appendix
- References

We consider the simplest single period mean-variance setting with two classes of investor: *individuals* who invest directly on their own account and are mean-variance optimizers, and *agents* who manage equity portfolios on behalf of other investors.^{4} The supply of capital from these other investors is not modelled. However the reward to the agents is assumed to be proportional to the difference between the return on the managed portfolio and the return on a benchmark portfolio which is chosen exogenously by the suppliers of capital, and the agents are assumed to possess mean-variance preferences over this reward.

Without loss of generality, we assume that there is a single risk averse *agent* for each benchmark portfolio *i* (*i* = 1, … , *I*) which we denote by the vector of portfolio proportions **x**_{0i}, where **j**′ x _{0i}= 1 and **j** is a vector of units. The agent is assumed to have exponential utility defined over the excess return on the managed portfolio relative to the benchmark, and asset returns are assumed to be multivariate normal with parameters , where μ is an (*n* × 1) vector and is an (*n* × *n*) matrix . Then agent *i*, who is assumed to be constrained to hold all of the managed portfolio in equities,^{5}and to behave competitively, faces a mean-variance problem of the form:

- (1)

where *a _{i}* is the coefficient of absolute risk aversion and λ

_{i}is a Lagrange multiplier. The vector of optimal portfolio proportions is then:

- (2)

Imposing the constraint , it is seen that , the return on the global minimum variance portfolio. Thus, agents' holdings consist of a long position in their benchmark portfolio and an arbitrage portfolio which is at the point of tangency from the minimum variance portfolio expected return to the efficient set.

*Individual investors* are also assumed to have exponential utility functions, with coefficient of risk aversion *b _{j}*, and the portfolio problem faced by individual investor

*j*(

*j*= 1, … ,

*J*) is:

- (3)

where *R _{F}* is the risk free interest rate, and the optimal portfolio of risky assets is given by the familiar expression:

- (4)

As one would expect, the risky asset portfolio of individuals is the standard tangency portfolio.

#### 2.1. *Expected returns*

Let denote the wealth allocated to agent *i* for investment in equities, and let *W _{j}* denote the total wealth of individual

*j*. Then market clearing implies that where

*W*is the total value of the market portfolio and

_{m}**x**

_{m}is the vector of market value proportions. Substituting from (2) and (4) in the market clearing condition yields the following expression for the vector of equilibrium expected returns:

- (5)

where

**x**_{0} is the aggregate benchmark portfolio, which is a weighted average of the individual agent's benchmarks, where the weights are the amounts of wealth controlled by each agent.

Equation (5) expresses the expected return on a security as a linear function of the covariance of the security return with the return on the market portfolio, **x**_{m}, and with the return on the aggregate benchmark portfolio, **x**_{0}. θ_{1}, the price of market risk, is equal to the product of inverse of the wealth weighted average risk tolerance, *T*, and the fraction of total wealth that is invested in stocks, ρ. θ_{2} is equal to the product of the price of market risk, θ_{1}, and the fraction of the market that is held in agent controlled portfolios. Note that θ_{2} is positive so that the expected return is *decreasing* in the covariance with the benchmark portfolio. The equilibrium condition (5) can also be written in terms of the betas of the security with respect to the aggregate market and the aggregate benchmark portfolio so that the expected return on security *k*, μ_{k}, is given by :

- (6)

where β_{km} and β_{k0} are the usual coefficients from the (simple) regressions of the security return on the returns on the market and benchmark portfolio returns. θ*_{1}=θ_{1}*σ^{2}_{m} and θ*_{2}=θ_{2}*σ^{2}_{0} where σ_{m} and σ_{0} are the standard deviations of the returns on the market and the aggregate benchmark portfolios respectively. If we define the (aggregate) *benchmark residual* return *e* as the residual from the regression of the aggregate benchmark return, *R*_{0}, on the market portfolio return, *R _{m}*:

- (7)

then the equilibrium condition may be expressed also as:

- (8)

where , and β_{ke} is the coefficient of the aggregate benchmark residual return from either a simple regression of security returns on the residual return or, equivalently, from a multiple regression of security returns on market and aggregate benchmark residual returns. Since for the market portfolio β_{mm}= 1, β_{me}= 0, equation (8) implies that λ_{1}=μ_{m}− *R**_{F}, where μ_{m} is the expected return on the market portfolio. Then, subtracting the risk-free interest rate from both sides of (8), and using the fact that β_{0e}= 1, the expected return on the benchmark portfolio, μ_{0}, may be written as:

- (9)

Equation (9) shows that it is not possible to sign the CAPM ‘α’ of the benchmark portfolio in general because of the term (*R**_{F}− *R _{F}*). However, if β

_{0m}≈ 1 then the CAPM α of the benchmark portfolio will be approximately equal to −λ

_{2}.

Equation (8) also constrains the relative rewards to the market and residual betas^{6} since:

- (10)

where ψ≡σ^{2}_{e}/σ^{2}_{m}. When the benchmark has the same systematic risk as the market, β_{0m}≈ 1, the expression for the relative rewards reduces to:

- (11)

where χ≡θ*_{1}/θ*_{2}. If the total risk of the benchmark is close to that of the market then . Thus χ is approximately equal to the ratio of the total market value of all stocks divided by the total value of stocks managed by agents.

When the benchmark is ‘close to’ the market portfolio so that the σ^{2}_{e}≈ 0, the benchmark effect as measured by λ_{2}, the risk premium per unit of benchmark risk, will be small.

The equilibrium condition (5) may also be re-arranged to yield an expression for expected returns in terms of the market beta and the betas with respect to each of the individual benchmark residual returns:^{7}

- (12)

Chan and Lakonishok (2002, p. 1412) note that ‘in practice investment managers generally tend to break the domestic equity investment universe down into four classes: large-capitalisation or small-capitalisation growth stocks and large-capitalisation or small-capitalisation value stocks', and they present evidence that the Fama-French SMB and HML factors do a good job in summarising the investment styles of mutual fund managers.^{8}

If the benchmark portfolios of investment managers can be expressed as linear combinations of the S&P 500 and the Fama-French portfolios SMB and HML, the agency model may be written as:

- (13)

where β*_{kHML}, β*_{km} and β*_{kSMB} are the coefficients from the multiple regression of returns on three Fama-French factors and β_{ke} is the beta with respect to the S&P 500 residual. Under the agency model λ_{4} > 0 but λ_{2}, λ_{3} cannot be signed since they are associated with arbitrage portfolios that correspond to a long and a short position in two benchmark portfolios. Alternatively, a test of whether λ_{4} > 0 may be taken as a test of whether the agency model sign prediction is robust to the inclusion of the Fama-French factors.

It can also be shown that the expected return on the minimum variance portfolio, μ_{v}, is related to the shadow riskless interest rate by:

and that μ_{v} > *R**_{F} so long as the fraction of stock held by institutional investors is less than one.

#### 2.2. *Portfolio allocations*

The equilibrium portfolio of agent *i* can be expressed in terms of the exogenous parameters of the model by substituting for the vector of equilibrium expected returns, , from equation (5) in equation (2):

- (14)

Note that the vector is proportional to the vector of portfolio weights in the minimum variance portfolio. Then equation (14) expresses the agent's equilibrium portfolio as a linear combination of the personal benchmark portfolio, **x**_{0i}, the minimum variance portfolio, the market portfolio, **x**_{m}, and the aggregate benchmark portfolio, **x**_{0}.

When the agent-specific benchmark, **x**_{0i}, is identical to the aggregate benchmark portfolio, **x**_{0}, the expression for the agent's portfolio reduces to:

- (15)

where is the vector of portfolio proportions of the minimum variance portfolio. Equation (15) expresses agent *i*'s equilibrium portfolio as a linear function of the benchmark portfolio, **x**_{0}, the market portfolio, **x**_{m}, and the minimum variance portfolio, . While each agent holds a long position in the market portfolio and short position in the minimum variance portfolio, the position in the aggregate benchmark portfolio cannot be signed: on the one hand the portfolio is attractive because it is the zero risk portfolio for the agent; on the other hand, it is unattractive because its returns are depressed due to the demands of all agents which is reflected in the parameter θ_{2}. We summarise this result:

*Agent specific portfolios*

When the agent-specific benchmark portfolio is equal to the aggregate benchmark portfolio (**x**_{0i}=**x**_{0}), the portfolio of an individual agent is:

- • long the market portfolio
- • long or short the aggregate benchmark portfolio
- • short the minimum variance portfolio.

The aggregate portfolio held by agents, which we will refer to as the *institutional portfolio*, is obtained by multiplying equation (14) by , summing over *i* and dividing by to obtain:

- (16)

where . Since for , the institutional portfolio is short the minimum variance portfolio and is long the market portfolio. Finally, since *T ^{A}*θ

_{2}< 1, the institutional portfolio is long the aggregate benchmark portfolio. We summarise this result:

*Aggregate institutional portfolio*

The (aggregate) institutional portfolio is:

- • long the market portfolio
- • long the aggregate benchmark portfolio
- • short the minimum variance portfolio.

A natural measure of over-weighting of stock *k* by institution *i* is the ratio of the weight of the stock in the institutional portfolio *i* to its weight in the market portfolio which we denote by ρ^{i}_{k}≡ *x ^{i}_{k}*/

*x*. Under the CAPM the Tobin Separation Theorem implies that ρ

^{m}_{k}^{i}

_{k}= 1, ∀

*i*,

*k*.

The weight of security *k* in the benchmark portfolio, *x*^{0}_{k}, is related to its weight in the market portfolio, *x ^{m}_{k}* by:

where *I*_{0}= 0, 1 is an indicator variable for membership in the aggregate benchmark portfolio, and *W*^{0} is the total value of that portfolio.

Then equation (15) can be written as

Define the relative minimum variance portfolio weight of security , as the ratio of its weight in the minimum variance portfolio to its weight in the market portfolio: . Then equation (15) can be written as

- (17)

To obtain the relative portfolio weight in the aggregate institutional portfolio, ρ^{I}_{k}, multiply equation (17) by *W _{i}*, sum, and divide by Σ

_{i}

*W*, to obtain:

_{i}- (18)

The agency model then predicts that the institutional portfolio overweighting of stock *k*, ρ^{I}_{k}, is negatively related to its relative minimum variance portfolio weight, .

*Relative institutional portfolio weights*

The relative institutional portfolio weight of a security is:

- • higher for securities that are included in the aggregate benchmark portfolio;
- • decreasing in the relative minimum variance portfolio weight of the security.

The agency model also predicts that, under reasonable assumptions, the benchmark residual beta of the institutional portfolio will be positive, where the benchmark residual, *e*, is defined as the residual from equation (7), the regression of the aggregate benchmark return, *R*_{0}, on the market portfolio return, *R _{m}*.

It is shown in Appendix A that the benchmark residual beta of agent *i*'s portfolio, β^{i}_{e}, can be written as:

- (19)

where we have used the fact that the residual beta of the benchmark portfolio (*x*′_{0}β_{e}) is equal to unity and that of the market portfolio (*x′ _{m}*β

_{e}) is equal to zero. Equation (19) implies that the residual beta of the institutional portfolio (β

^{I}

_{e}) is:

- (20)

The first term in (20) is positive and the second term will close to zero if the benchmark beta is close to unity. Since we expect the aggregate benchmark portfolio market beta to be close to unity there is a presumption that the benchmark residual beta is positive.

In the following we shall present empirical evidence bearing on the composition of institutional investment portfolios.

### 3. Data

- Top of page
- Abstract
- 1. Introduction
- 2. A Model of Institutional Investing
- 3. Data
- 4. Expected returns and the agency model
- 5. Institutional portfolio weights and the agency model
- 6. Conclusion
- Appendix
- References

The basic data that are used in our empirical analysis are the returns and market values of all stocks listed on the CRSP tape during the period December 1925 to December 2009. We take as our proxy for the aggregate market index the returns on the CRSP value weighted index. Anecdotal evidence suggests that the S&P 500 is the most commonly used benchmark for US equities,^{9} and therefore we proxy the aggregate benchmark returns by the returns on the S&P 500 index which are taken from Global Financial Database.^{10} The Fama French factors and the 1-month Treasury Bill rate are taken from the website of Ken French.

In our analysis of institutional portfolio holdings quarterly data on institutional holdings of equity securities were obtained from the CDA Spectrum database for the period from March 1980 to September 2008. Institutions with more than $100 million of assets under discretionary management are required by the SEC to report their holdings on the 13F form within 45 days of the end of each quarter. Holdings are reported only for the assets for which the institutions have investment discretion. For example, an investment advisor will report holdings for the assets under his management while the beneficial owner of the assets could be a mutual fund or a corporate pension plan. In the case of shared-defined investment decisions, care has been taken to prevent double counting.^{11}

Institutional investors are classified into five categories: (1) bank, (2) insurance company, (3) investment company, (4) independent investment advisor, and (5) other. The first category includes banks and bank trust departments that manage personal trust funds and certain contracted pension assets. Insurance companies invest their own property-casualty and life insurance funds, and also invest on behalf of their clients. Investment companies are mutual fund families including closed-end funds and open-end funds. Investment advisors are money management firms that exercise investment discretion on behalf of clients. They include most of the large brokerage firms as well as independent advisory firms. The other ‘category’ mainly consists of private and public pension funds, and also includes university and private endowments, philanthropic foundations, and law firms acting as trustees.^{12}

For each stock in the CDA Spectrum database, the institutional ownership was aggregated by manager type. Observations for which the stock's permanent identification number (PERMNO) could not be identified, and the observations with reported total institutional ownership greater than 100% were dropped to eliminate obvious errors. The historical S&P 500 stock list was obtained from CRSP.^{13} and financial information on individual firms was taken from the Compustat industry annual files from 1978 to 2008.

### 4. Expected returns and the agency model

- Top of page
- Abstract
- 1. Introduction
- 2. A Model of Institutional Investing
- 3. Data
- 4. Expected returns and the agency model
- 5. Institutional portfolio weights and the agency model
- 6. Conclusion
- Appendix
- References

Panel A of Table 1 reports summary statistics for returns on the CRSP Value Weighted market index, the proxy for the market portfolio; the S&P 500 index, the proxy for the aggregate benchmark portfolio; and the S&P 500 residual return, *e*, which is is obtained by regressing the index return on the CRSP value weighted index return for the whole sample period. As one might expect, the S&P 500 is a fairly good proxy for the wider market index: its beta is between 0.95 and 1.05, the volatilities of the two portfolio are very close, and the correlation between the two portfolio returns is close to 0.99. The mean returns on the two portfolios differ by only 1 *basis point* per month during the second half of the sample period, and by 4 *basis points* per month during the first half. However, the volatility of the S&P residual is around 80 basis points per month, and the maximum tracking error is of the order of 4-5% per month. Clearly, our proxy for the market portfolio is not a perfect substitute for the S&P 500 for an agent whose benchmark is the S&P 500.

January 1931–December 2009 | |||
---|---|---|---|

CRSP _{VW} | S&P 500 | S&P residual | |

Maximum | 38.37% | 42.87% | 4.40% |

Minimum | −29.01% | −29.63% | −5.09% |

Mean | 0.93% | 0.89% | 0.00% |

Median | 1.29% | 1.16% | −0.02% |

Standard Deviation | 5.55% | 5.51% | 0.82% |

ρ(CRSP, _{VW}S&P 500) = 0.99, β_{0m}= 1.01 | |||
---|---|---|---|

January 1931–June 1970 | |||

CRSP _{VW} | S&P 500 | S&P residual | |

Maximum | 38.37% | 42.87% | 4.33% |

Minimum | −29.01% | −29.63% | −5.53% |

Mean | 0.91% | 0.84% | 0.00% |

Median | 1.22% | 1.14% | 0.00% |

Standard Deviation | 6.43% | 6.44% | 0.82% |

ρ(CRSP, _{VW}S&P 500) = 0.99, β_{0m}= 1.05 | |||
---|---|---|---|

July 1970–December 2009 | |||

CRSP _{VW} | S&P | S&P residual | |

Maximum | 16.56% | 16.81% | 4.64% |

Minimum | −22.53% | −21.54% | −4.96% |

Mean | 0.95% | 0.94% | 0.00% |

Median | 1.30% | 1.17% | −0.01% |

Standard Deviation | 4.63% | 4.48% | 0.76% |

ρ(CRSP, _{VW}S&P 500) = 0.98, β_{0m}= 0.95 |

Panel B: CAPM regressions for the S&P 500 portfolio This table reports the coefficients from the regression of the excess returns on the S&P 500 portfolio, R_{0t}− R, on the excess returns on the CRSP value weighted market index, _{Ft}R − _{mt}R: _{Ft}R is proxied by the Fama one month risk free rate from WRDS. α is reported in _{Ft}per cent per month. t-ratios are in parentheses. | |||||||

Jan 1931 | Jan 1931 | Jul 1970 | Jan 1931 | Oct 1950 | Jul 1970 | Apr 1990 | |

Dec 2009 | Jun 1970 | Dec 2009 | Sep 1950 | Jun 1970 | Mar 1990 | Dec 2009 | |

α_{0} | −0.00 | −0.02 | 0.01 | −0.06 | 0.04 | 0.03 | 0.00 |

(0.82) | (0.54) | (0.68) | (0.97) | (0.78) | (0.66) | (0.02) | |

β_{0m} | 1.01 | 1.04 | 0.95 | 1.05 | 0.98 | 0.96 | 0.95 |

(203.74) | (167.48) | (125.74) | (143.57) | (76.27) | 106.37) | (76.21) |

#### 4.1. *Asset shares and relative risk prices*

As shown in expression (10), the agency model places restrictions on the relative values of the risk prices, λ_{1} and λ_{2}, in terms of the wealth share managed by agents, (1/χ), the ratio of the variance of the benchmark residual return to that of the market return (ψ), and the benchmark beta (β_{0m}). The estimates from the second half of the sample period in Table 1 imply ψ= 0.027 and β_{0m}= 0.95. If we use the institutional wealth share of 65% which is the value for 2007, this implies a value of λ_{2}/λ_{1} of 0.046. Earlier values of the institutional wealth share imply correspondingly lower values of the λ_{2}/λ_{1}. For example, a 40% institutional wealth share, which is approximately the value for 1983, implies a value for the ratio of only 0.02. Using the average excess return on the CRSP value weighted index for the period 1931–2010 yields a simple estimate of λ_{1}= 0.5% per month which, for λ_{2}/λ_{1}≈ 0.05, implies a value of λ_{2} of about 35 *basis points* per year or 3*bp* per month. Thus, the implied agency effect on expected returns is small, and is unlikely to be detectable using standard methods. This is what we find.

#### 4.2. *A direct estimate of* λ_{2}

Since the market beta of our proxy for the aggregate benchmark portfolio is close to unity, equation (9) predicts that the CAPM ‘α’ of the portfolio will be negative and approximately equal to *minus* λ_{2}. Panel B of Table 1 reports the intercept and slope coefficients from the regression of the return on the S&P 500 index in excess of the riskless interest rate on the excess return on the market portfolio for the period January 1931 to December 2009 and various subperiods. The point estimates of α are all close to zero and insignificant. However, the standard errors are of the order of 3 *basis points* which, we have argued, is the magnitude of the coefficient itself implied by the agency model. Thus this direct estimation procedure does not have enough power to reject the null hypothesis of no agency effects.

#### 4.3. *Cross-sectional estimates of* λ_{2}

We form 25 portfolios based on estimates of β_{km} and β_{ke}. Then, at the beginning of each year from 1931 to 2009, the monthly returns on each security *k* that has at least 24 observations over the previous 60 months are regressed on the return on the CRSP value weighted index, and on the S&P 500 residual returns to obtain estimates of the market beta, β_{km}, and the benchmark (residual) beta, β_{ke}. Then the securities are assigned, first to quintiles on the basis of the estimated market beta, and then within each market beta quintile to one of five portfolios on the basis of the estimated benchmark beta. This procedure yields 25 portfolios with a spread in both market and benchmark betas. The returns on the portfolios for the next 12 months are then calculated assuming first equal portfolio weights at the beginning of the year and no rebalancing within the year (EW) and, secondly, assuming a value weighted portfolio at the beginning of the year where the weights are based on market capitalisations at the end of the previous year, again without rebalancing within the year (VW). Finally the time series of EW and VW returns on each portfolio *p*, (*p* = 1, … , 25) are regressed on the aggregate market index and the S&P 500 residual returns to obtain final estimates of the betas, β_{pm}, and β_{pe}:

For each month the average size of the firms in a portfolio, *Size*, is defined as the equal or market value weighted average of the log of the market capitalisations.

The characteristics of the two sets of portfolios are not reported in order to save space. However, the *t*-*ratios* for the two betas are highly significant in most cases. The correlation between the two betas is 0.44 (−0.35) for the EW(VW) portfolios. However, the benchmark beta is highly correlated with the measure of average firm size of the portfolios: 0.83 (0.90) for the EW(VW) portfolios: the returns on large firms (many of which will be in the S&P 500) tend to be more sensitive to the idiosyncratic element of the S&P 500 return. The spreads of market betas of the portfolios are from 0.68 to 1.83 (EW) and from 0.67 to 1.81 (VW), and the spreads of the S&P 500 residual betas are from −3.61 to 0.01 (EW) and from −3.22 to 1.44 (VW). Both the market and S&P 500 residual betas are monotonic in the portfolio rankings in these variables, confirming that our sorting procedure is effective. The *Size* variable displays much less proportional variation across the portfolios: from 9.76 to 11.60 (EW) and from 11.71 to 14.73 (VW).

In Table 2 we report the results of GLS estimates of regressions of average returns on the estimated market beta, β_{pm}, and the estimated benchmark beta, β_{pe}, for both EW and VW portfolios. We also include the measure of firm size, *Size*, in the regression to ensure that any return effect associated with β_{pe} is not in fact a firm size effect. Thus the final regression is:

Equally weighted portfolios | Value weighted portfolios | |||||||
---|---|---|---|---|---|---|---|---|

λ_{0} | λ_{1} | λ_{2} | λ_{3} | λ_{0} | λ_{1} | λ_{2} | λ_{3} | |

1931–2009 | 0.75 | 0.43 | 0.03 | 0.68 | 0.33 | −0.01 | ||

(7.06) | (2.03) | (0.75) | (4.90) | (1.50) | (0.24) | |||

1.46 | 0.46 | 0.00 | −0.06 | 0.95 | 0.32 | −0.02 | −0.02 | |

(1.53) | (2.15) | (0.09) | (0.75) | (1.10) | (1.47) | (0.39) | (0.32) | |

1931–68 | 0.67 | 0.46 | 0.10 | 0.62 | 0.47 | 0.05 | ||

(4.29) | (1.41) | (1.45) | (3.60) | (1.41) | (0.77) | |||

3.41 | 0.35 | 0.02 | −0.24 | 0.22 | 0.50 | 0.06 | 0.03 | |

(2.23) | (1.07) | (0.24) | (1.80) | (0.22) | (1.46) | (0.84) | (0.39) | |

1969–2009 | 0.97 | 0.07 | 0.06 | 0.96 | −0.05 | 0.01 | ||

(7.59) | (0.25) | (1.08) | (4.93) | (0.19) | (0.14) | |||

0.85 | 0.04 | 0.06 | 0.01 | 1.87 | 0.02 | −0.05 | −0.06 | |

(1.09) | (0.11) | (0.92) | (0.16) | (1.95) | (0.06) | (0.67) | (0.96) | |

1931–49 | 0.14 | 0.80 | 0.11 | 0.25 | 0.66 | 0.03 | ||

(0.60) | (1.39) | (1.11) | (0.98) | (1.12) | (0.37) | |||

2.14 | 0.64 | 0.06 | −0.18 | 0.28 | 0.66 | 0.03 | −0.00 | |

(1.32) | (1.10) | (0.58) | (1.24) | (0.26) | (1.07) | (0.33) | (0.02) | |

1950–68 | 1.15 | 0.24 | 0.07 | 0.88 | 0.38 | −0.02 | ||

(7.22) | (0.84) | (0.77) | (4.35) | (1.28) | (0.32) | |||

1.76 | 0.27 | 0.05 | −0.05 | 0.79 | 0.38 | −0.02 | 0.01 | |

(1.31) | (0.91) | (0.46) | (0.46) | (0.87) | (1.27) | (0.19) | (0.10) | |

1969–87 | 1.46 | −0.46 | −0.02 | 1.21 | −0.32 | 0.02 | ||

(6.96) | (1.11) | (0.28) | (3.67) | (0.68) | (0.27) | |||

1.20 | −0.55 | −0.00 | 0.03 | 5.95 | −0.18 | −0.25 | −0.34 | |

(1.45) | (1.10) | (0.03) | (0.33) | (3.95) | (0.37) | (2.35) | (3.23) | |

1988–2009 | 0.74 | 0.34 | 0.08 | 0.75 | 0.22 | −0.04 | ||

(5.90) | (1.06) | (1.15) | (4.12) | (0.68) | (0.60) | |||

1.09 | 0.42 | 0.06 | −0.03 | 0.85 | 0.23 | −0.04 | −0.01 | |

(0.96) | (1.02) | (0.65) | (0.31) | (0.75) | (0.67) | (0.48) | (0.09) |

Considering first the EW portfolio results, the estimate of λ_{2}, while positive except in the period 1969–87, is negative in all the other regressions. The magnitude of the point estimate of this parameter is consistent with our ball-park calculation of 3 *basis points*, but in all cases the standard error is too large for us to reject the null hypothesis of no benchmark effect.

Turning to the VW portfolio results, the point estimates of λ_{2} range from *minus* 4 to *plus* 6 and again, while the estimates are consistent with our ball-park calculation of 3 basis points, they are never significantly different from zero. In the subperiod 1969–87, the estimate of λ_{2} is not significant if the *Size* variable is not included, but in the presence of *Size* the estimate is *minus* 25 basis points per month, so that stocks with high benchmark residual betas are earning positive abnormal returns. This is consistent with the finding of Chan and Lakonishok (1993) that stocks in the S&P 500 had higher returns during the period 1977–91 after adjusting for size and beta as we do, as well as for other variables. They attribute this outperformance to the growth in the popularity of index investing during this period, and we note that while the agency model predicts a negative reward for the benchmark residual beta, it is a static model which takes no account of the effects of an increase in agency considerations: intuition suggests that a more complete, dynamic, model would predict positive returns associated with the benchmark residual beta for periods in which agency considerations become more important.

To explore the possibility that the difference between our results and those of Gomez and Zapatero (2003) are due to the restriction of their sample to large firms that are included in the S&P 500 we repeated our analysis using three different groups of firms classified according to firm size. At the beginning of each year, securities were classified into 3 size groups. If the market capitalisation of a security at the end of the previous year is smaller than the 30% break-point,^{14} the security is classified as ‘Small’; if its size is below or at the 70% break point and above or at the 30% break point, it is classified as ‘Medium’; if it is above the 70% break point, it is classified as ‘Large’.

Within each of the three size classifications, we assign each security to one of 25 portfolios according to its estimated values of β_{im} and β_{ie}. As before, we then compute the EW and VW returns over the next 12 months and, linking these returns across the whole sample period, use them to calculate β_{pm} and β_{pe}. We also calculate each portfolio's average *Size*, based on the log of market capitalisations.

The results of estimating the parameters of the model for the three size groups separately are summarised in Panel A of Table 3 which reports the estimates of λ_{2}, the coefficient of −β_{pe}. An interesting pattern emerges. There is no significant benchmark effect in the first half of the sample period, and none for the *Medium* size group of firms. On the other hand the *Large* firm size group yields a significant estimate for λ_{2} of 14 *basis points* per month for the period 1969–2009, while the *Small* firm size group yields a significant estimate of λ_{2} of *minus* 30 *basis points* for the same period. The significant positive estimate for the *Large* firm size group is due mainly to the period 1969–87, while the negative estimate for the *Small* firm size group is more evenly spread across the two final quarters of the sample period. The *Small* firm size group results in the second half of the sample period, 1969–2009, are clearly inconsistent with the predictions of the simple agency model, and *Large* firm size group point estimates are also too large to be consistent with our ballpark calculate for λ_{2}. The positive estimate of λ_{2} for large firms in the second half of the sample period is consistent with the finding of Gomez and Zapatero (2003) who restricted their sample to S&P 500 firms.

A. λ_{2} estimates for different firm size groups | |||
---|---|---|---|

Large | Medium | Small | |

1931–2009 | 0.03 | 0.02 | −0.25 |

(0.62) | (0.51) | (4.11) | |

1931–68 | −0.05 | 0.09 | −0.05 |

(0.80) | (1.18) | (0.43) | |

1969–2009 | 0.14 | −0.02 | −0.30 |

(2.44) | (0.27) | (4.20) | |

1931–49 | −0.06 | 0.11 | 0.03 |

(0.71) | (1.07) | (0.25) | |

1950–68 | −0.03 | −0.00 | −0.04 |

(0.40) | (0.01) | (0.28) | |

1969–87 | 0.15 | −0.11 | −0.21 |

(2.12) | (1.07) | (2.29) | |

1988–2009 | 0.05 | 0.06 | −0.24 |

(0.73) | (0.78) | (2.64) |

B. λ_{4} estimates from extended agency model | ||||
---|---|---|---|---|

All | Large | Medium | Small | |

1931–2009 | 0.05 | 0.08 | 0.13 | −0.01 |

(0.32) | (0.57) | (0.85) | (0.07) | |

1931–68 | 0.04 | 0.06 | −0.02 | −0.09 |

(0.26) | (0.44) | (0.12) | (0.42) | |

1969–2009 | 0.03 | 0.13 | −0.05 | −0.14 |

(0.24) | (0.81) | (0.29) | (0.72) | |

1931–49 | 0.41 | 0.17 | 0.17 | 0.10 |

(2.00) | (0.89) | (0.88) | (0.42) | |

1950–68 | 0.05 | 0.08 | −0.09 | −0.16 |

(0.32) | (0.56) | (0.60) | (0.94) | |

1969–87 | −0.09 | −0.17 | −0.01 | −0.12 |

(0.68) | (1.11) | (0.06) | (0.80) | |

1988–2009 | 0.01 | 0.17 | 0.02 | −0.14 |

(0.05) | (0.98) | (0.09) | (0.78) |

#### 4.4. *Multi-benchmark model*

It is possible that the large benchmark effect that we have found for *Large* firms and the negative estimate of λ_{2} for *Small* firms are due to the omission of important factors that affect expected returns. It is also possible that the omission of these factors increases the standard error of the λ_{2} estimate. Therefore, as a robustness check, we also estimate the extended agency model (13). First, the S&P 500 residual was estimated by regressing the S&P 500 portfolio returns on the returns on the market portfolio, proxied again by the CRSP Value Weighted portfolio. Then, at the beginning of each year from 1931 to 2009, the monthly excess returns on each security *k* with at least 24 observations over the previous 60 months were regressed on the excess return on the CRSP value weighted portfolio, the HML and SMB returns, and the S&P 500 residual returns to obtain estimates of the market beta, β*_{km}, and the benchmark (residual) beta, β_{ke}. Then, as before, the securities were assigned, first to quintiles on the basis of the estimated market beta, and then within each market beta quintile to one of five portfolios on the basis of the estimated benchmark beta. This procedure yielded 25 portfolios with a spread in both market and benchmark betas. Then equal weighted and value weighted portfolio returns were calculated as before.

The estimates of the FF factor loadings for the 25 portfolios, range from −0.13 to 0.72 for β*_{p,SMB}, and from −0.25 to 0.34 for β*_{p,HML}. There is some tendency for firms that have intermediate values of the S&P 500 residual beta, β_{pe}, to have higher values of β*_{p,HML}. Higher values of β*_{p,SMB} are associated with higher values of the S&P 500 residual beta and higher values of the market beta, β_{pm}.

The extended agency model (13) was estimated using both EW and VW portfolios. For the EW portfolios the estimated coefficients of neither β*_{pm} nor β_{pe} are significant for any sub-period, thus providing no support for the agency model. Of the coefficients of the three Fama-French betas, only the coefficient of β*_{p,SMB} is significant: it is strongly positive in the first half of the sample period.

The estimates of λ_{4} derived from the extended agency model using the VW portfolios are shown in the first column of Panel B of Table 3: the point estimates are of the same magnitude as those obtained from the simple agency model. The extended model was also estimated using three different samples of firms according to firm size and the resulting estimates of λ_{4} are also shown in Panel B. Comparing the estimates in Panels A and B, we see that the effect of introducing the three Fama-French betas is to eliminate the significance of the coefficient of the benchmark residual beta for both *Large* and *Small* firm size groups.

#### 4.5. *Summary*

We have shown that the magnitude of the benchmark effect predicted by the agency model is of the order of 3 basis points per month. The standard errors of the estimates of λ_{2} derived either from the ‘alpha’ of the benchmark portfolio itself or from cross sectional regressions of portfolio returns on the benchmark residual beta are all in excess of this, so that as expected our tests lack power to reject either the null hypothesis of no agency or benchmark effect, or the null hypothesis of the agency model itself. For the full sample of firms the point estimates of λ_{2} in the simple agency model are of the order of 1–8 basis points per month in absolute value except for the subperiod 1969–1987 when the *Size* variable is also included in the regression; in this case for the value weighted portfolios the estimate of λ_{2} is *minus* 25 basis points per month and is statistically significant. When the total sample is divided up by firm size the estimate of λ_{2} is around 14 basis points per month for the *Large* firm sample in the second half of the sample period and *minus* 20–39 basis points per month for the *Small* firm sample. However, when the simple agency model is extended to include the Fama-French HML and SMB factors, the estimates of the benchmark effect become insignificant for all three size groups.

In the following section we turn to explore the portfolio implications of the agency model.

### 5. Institutional portfolio weights and the agency model

- Top of page
- Abstract
- 1. Introduction
- 2. A Model of Institutional Investing
- 3. Data
- 4. Expected returns and the agency model
- 5. Institutional portfolio weights and the agency model
- 6. Conclusion
- Appendix
- References

Prior empirical evidence on institutional stock holding includes Gompers and Metrick (2001) who show that institutional investors invest in stocks that are larger and more liquid than the average stock; institutional ownership is also associated with share turnover, firm age, and S&P 500 membership; Falkenstein (1996) finds that mutual fund portfolios are tilted toward large liquid firms about which there is a lot of information. On the other hand Bennett *et al.* (2003) report that although institutional investors have a preference for large capitalisation stocks, over time they have shifted their preferences toward smaller, riskier securities. In our empirical tests we shall take into account S&P 500 membership and the possibly time-varying effect of firm size. In order to test the implications of the agency model for institutional portfolios it is necessary first to construct empirical proxies for the minimum variance portfolio, the market portfolio, the aggregate benchmark portfolio and the institutional portfolio.

#### 5.1. *Institutional, market, benchmark and minimum variance portfolio weights*

The *institutional portfolio* weights, *x ^{I}_{kt}*,

*k*= 1, …

*N*were calculated each quarter

_{t}*t*from March 1980 to September 2008 for every non-ADR stock

*k*by first multiplying the number of shares held by institutions at the end of the quarter as reported by CDA Spectrum by the stock price at the end of the quarter as reported by CRSP; this yields the dollars of institutional investment in stock

*k*. Dividing the dollar investment in stock

*k*by the summation of the institutional investments in all non-ADR stocks yields the institutional portfolio weight,

*x*.

^{I}_{kt}The *market portfolio* weights were calculated by multiplying the number of shares of each non-ADR stock listed on the CRSP file outstanding at the end of the quarter by the share price to obtain the market value of each firm and then dividing by the sum of the market values.

Construction of the *minimum variance portfolio* requires an assumption about the covariance structure of security returns. While many possibilities suggest themselves, we adopted the simple expedient of assuming that the residuals from the Fama-French (1993) three-factor model are independent. This has the advantage of parsimony and yields an easily invertible covariance matrix. To the extent that the minimum variance portfolio is mis-estimated we should find it harder to detect a relation between the institutional investment portfolio weights and those of the estimated minimum variance portfolio. The procedure for calculating the minimum variance portfolio was as follows. At the end of each quarter the FF model was estimated for each non-ADR security with returns on the CRSP file for at least 24 of the preceding 60 months. These returns were used to estimate the FF factor loadings and residual variances. The resulting estimates, as well as the covariances of Fama-French 3 factors estimated by using the Fama-French 3 factors in the preceding 60 months, were then used to solve the minimum variance portfolio choice problem, from which the weights of the minimum variance portfolio were calculated.

As in our study of asset pricing, the *aggregate benchmark portfolio* was taken as the S&P 500 portfolio.

#### Institutional portfolio weights

The agency model implies that individual agents will be long the market portfolio and short the minimum variance portfolio, and that the aggregate institutional portfolio will be long the market portfolio, long the aggregate benchmark portfolio and short the minimum variance portfolio. To test these predictions the following regression was estimated:

where are the portfolio weights for security *k* in the institutional portfolio, the S&P 500 portfolio, the estimated minimum variance portfolio and the CRSP value weighted portfolio. The theory predicts that for any institutional portfolio *a*_{3} > 0, *a*_{2} < 0 and that for the aggregate institutional portfolio *a*_{1}, *a*_{3} > 0, *a*_{2} < 0

In order to take account of correlation in the errors of the equation, the equation was estimated each quarter and the coefficients were averaged over time in the fashion of Fama and MacBeth (1973). Standard errors were calculated following Newey and West (1987) with 5 lags.

Panel A of Table 4 reports the results of Fama-MacBeth regressions of the institutional portfolio weights on the market, S&P 500 and minimum variance portfolio weights using the quarterly portfolio data; there are an average of 5150 securities in the cross-section regressions. In addition to reporting results for the aggregate institutional portfolio we also report results for the portfolios managed by groups of institutions: investment advisors, investment companies, banks, insurance companies and other institutions. Under portfolio separation with homogeneous beliefs as in the CAPM we should expect the coefficient of the market portfolio weights to be unity and all the other coefficients to be zero. The agency model predicts that the coefficient of the market weight will be positive while that of the minimum variance portfolio weight will be negative for all institutional portfolios. It predicts that the coefficient of the S&P 500 weight will be positive for the aggregate institutional portfolio, though not necessarily for individual institutional portfolios.

Panel A | Panel B | ||||||
---|---|---|---|---|---|---|---|

a _{0}× 10^{4} | a _{1} | a _{2} | a _{3} | a _{0} | a _{1} | a _{2}× 10^{3} | |

All institutions | 0.26 | 0.24 | −0.017 | 0.65 | 0.53 | 0.64 | −0.55 |

(18.38) | (17.58) | (-6.13) | (28.01) | (25.21) | (38.18) | (-7.16) | |

Investment advisors | 0.45 | 0.10 | −0.029 | 0.71 | 0.71 | 0.49 | −0.76 |

(19.65) | (5.12) | (-6.18) | (23.66) | (20.73) | (15.50) | (-7.54) | |

Investment companies | 0.52 | 0.10 | −0.025 | 0.67 | 0.49 | 0.76 | −0.61 |

(13.31) | (3.04) | (-5.08) | (20.42) | (55.86) | (67.59) | (-9.60) | |

Banks | −0.05 | 0.50 | −0.001 | 0.54 | 0.37 | 0.74 | −0.27 |

(-2.02) | (25.38) | (-0.29) | (18.89) | (36.96) | (56.02) | (-5.71) | |

Insurance companies | 0.27 | 0.25 | −0.015 | 0.63 | 0.43 | 0.74 | −0.47 |

(15.14) | (8.40) | (-4.43) | (21.14) | (57.09) | (60.85) | (-9.52) | |

Other institutions | 0.14 | 0.31 | −0.005 | 0.63 | 0.42 | 0.74 | −0.54 |

(6.41) | (7.80) | (-1.67) | (15.75) | (7.89) | (12.22) | (-5.69) |

For *all institutions* (i.e. the aggregate institutional portfolio) the estimated coefficient from the regression of the portfolio weight on the market portfolio weight is 0.65 (*t* = 278.01), on the S&P 500 weight 0.24 (*t* = 17.58), and on the minimum variance portfolio weight is −0.017 (*t* = 6.13). Our simple theory which is based on homogeneous beliefs predicts that the institutional portfolio vector will be an exact linear combination of the market, S&P 500 and minimum variance portfolio vectors. In reality, institutional portfolios will be affected by informational advantages, both real and imagined, as well as other considerations such as liquidity; moreover, our empirical proxy for the minimum variance portfolio is surely imperfect. Therefore we do not expect the exact linear relation to hold in practice: on average the quarterly cross-section regression explains 93% of the variance in the institutional portfolio weights. We can easily reject the null that the coefficient of the market portfolio weight is unity as predicted by the CAPM. Thus, each of the coefficients is highly significant and is of the sign predicted by the agency model. Particularly striking is the sign of the coefficient on the minimum variance portfolio weight since our procedure identifies this portfolio with error.

The signs and significance of the estimated coefficients on the market weight and the S&P 500 weight are maintained across the institutional groups. It is noteworthy however that the importance of the S&P 500 weight is less for Investment Advisors and Investment Companies than it is for Banks, Insurance Companies and Other Institutions. The sign and significance of the coefficient of the minimum variance portfolio weight is maintained for the institutional groups except for Banks and for Other Institutions where it is insignificant. The importance of the minimum variance portfolio weight is greater for both Investment Advisors and Investment Companies than it is for the other groups.

Overall, these regressions provide strong support for the predictions of the agency model. However, given the extreme variation in firm sizes, the errors terms in the quarterly cross-sectional regressions underlying the Fama-MacBeth estimator are likely to be highly heteroscedastic. Therefore we turn to regressions in which the dependent variable is the relative portfolio weight–the weight of a security in a portfolio divided by its weight in the market portfolio–which should reduce the problem of heteroscedasticity and yield more efficient parameter estimates.

#### Relative institutional portfolio weights

The theory predicts that the relative institutional portfolio weight of a security is higher for stocks that are included in the aggregate benchmark portfolio and decreasing in the relative minimum variance portfolio weight of the security. Panel B of Table 4 reports Fama-MacBeth estimates of the parameters of a regression of the relative institutional portfolio weight on an S&P membership dummy, *SPdum*, and the relative weight of the security in the minimum variance portfolio:

Consistent with the theory, the estimate of *a*_{2} is negative and strongly significant, not only for the aggregate institutional portfolio, but also for each of the institutional groups. The *t*-statistic for the aggregate institutional portfolio is in excess of 7, and for the individual groups is in excess of 5. Similarly the estimate of *a*_{1} is positive and highly significant, for both the aggregate portfolio and for each of the institutional groups. While the finding that institutions overweight securities in the S&P 500 portfolio is not altogether surprising, the finding that they significantly underweight securities with high weightings in the minimum variance portfolio is a new prediction of the agency model.

#### Benchmark residual beta of institutional portfolios

We have seen that the agency model predicts that the beta of the aggregate institutional portfolios with respect to the benchmark residual is positive if the (market) beta of the aggregate institutional portfolio is close to unity. Panel A of Table 5 reports Fama-MacBeth estimates of the coefficients from a regression of institutional portfolio weights on the market and S&P 500 residual betas of the securities. We expect the coefficient of the S&P 500 residual beta to be positive, so that institutions overweight securities that have high covariance with the part of the S&P 500 return that is orthogonal to the market return. The betas were estimated from time series regressions over the 60 months prior to the quarter end for securities for which at least 24 months of return data were available. Securities for which betas could not be calculated in a given quarter were omitted from the regression. On average the quarterly cross-sectional regressions explain around 2–3% of the portfolio weights. It must be remembered that the individual security betas contain considerable measurement error. Consistent with our prediction, the coefficient of both the market beta and the benchmark residual beta is positive and significant in all cases. The *t*-statistic associated with *a*_{2} is of the order of 8.

Panel A | Panel B | |||||
---|---|---|---|---|---|---|

x = ^{I}_{kt}a_{0}+ a_{1}β^{m}_{kt}+ a_{2}β^{e}_{kt} | ρ^{I}_{kt}= a_{0}+ a_{1}β^{m}_{kt}+ a_{2}β^{e}_{kt} | |||||

a _{0}× 10^{4} | a _{1}× 10^{4} | a _{2}× 10^{4} | a _{0} | a _{1} | a _{2} | |

All institutions | 2.85 | 0.35 | 0.62 | 0.02 | ||

(14.26) | (7.73) | (53.35) | (5.35) | |||

2.67 | 0.26 | 0.37 | 0.51 | 0.11 | 0.02 | |

(8.52) | (1.93) | (8.73) | (23.75) | (6.71) | (7.27) | |

Investment advisors | 2.76 | 0.32 | 0.77 | 0.01 | ||

(14.34) | (7.59) | (36.91) | (3.31) | |||

2.41 | 0.42 | 0.34 | 0.60 | 0.18 | 0.02 | |

(9.16) | (3.85) | (8.46) | (16.99) | (9.23) | (5.14) | |

Investment companies | 2.76 | 0.32 | 0.60 | 0.02 | ||

(14.82) | (8.08) | (34.17) | (5.44) | |||

2.45 | 0.39 | 0.35 | 0.45 | 0.15 | 0.02 | |

(8.67) | (3.10) | (9.17) | (27.79) | (8.93) | (7.03) | |

Banks | 2.99 | 0.40 | 0.49 | 0.02 | ||

(15.00) | (8.57) | (37.75) | (9.14) | |||

2.98 | 0.08 | 0.41 | 0.48 | 0.02 | 0.02 | |

(8.94) | (0.55) | (9.59) | (18.53) | (1.23) | (10.75) | |

Insurance companies | 2.86 | 0.36 | 0.55 | 0.02 | ||

(14.80) | (8.20) | (45.05) | (10.14) | |||

2.67 | 0.28 | 0.38 | 0.45 | 0.10 | 0.03 | |

(8.59) | (2.03) | (9.33) | (25.44) | (5.94) | (11.44) | |

Other institutions | 2.91 | 0.37 | 0.51 | 0.01 | ||

(14.24) | (7.82) | (13.73) | (3.83) | |||

2.83 | 0.16 | 0.39 | 0.41 | 0.11 | 0.02 | |

(8.59) | (1.09) | (8.78) | (11.10) | (8.23) | (6.86) |

To the extent that institutional portfolio weights are greater for large firms which are more likely to be included in the S&P 500 benchmark, the regressions reported in Panel A do not necessarily confirm an institutional bias towards high S&P 500 residual beta stocks. Therefore the analysis was repeated using the relative institutional portfolio weight, ρ^{I}_{it}, as the dependent variable in place of the portfolio weight and the results are reported in Panel B of Table 5. The CAPM of course predicts that the relative institutional weight for all stocks will be unity, independent of their risk characteristics. Panel B shows however, that the relative institutional weight is increasing in both the market beta and the residual beta. Moreover, this relation holds for all institutional groups. A unit increase in the market beta is associated with an 11 percentage point increase in the relative institutional weight, while a unit increase in the benchmark residual beta is associated with a 2 percentage point increase in the relative institutional weight. Since the standard deviation of the S&P 500 residual beta is approximately 4.5, a one standard deviation change in the residual beta is associated with a 9 percentage point increase in the relative institutional weight.

It is possible of course that the role of the benchmark residual beta in determining institutional ownership is entirely due to the effect of indexing. To check this the regressions were re-run to include both a dummy variable for S&P 500 membership and the market portfolio weight which serves as a measure of (relative) size. The results are presented in Table 6. The coefficient of the S&P dummy is positive and highly significant. Inclusion of a stock in the S&P index is associated with a 60.5 percentage point increase in the relative institutional weight. However, the coefficients of both market beta and S&P 500 residual beta remain positive and strongly significant for both the aggregate institutional portfolio and for each of the institutional groups. Thus the role of the benchmark residual beta in determining the allocation of institutional portfolios cannot be attributed to simple indexing. After allowing for *Size* and S&P 500 membership a one standard deviation change in the residual beta is associated with a 4.5 percentage point increase in the relative institutional weight.

a _{0} | a _{1} | a _{2}× 10^{2} | a _{3} | a _{4} | |
---|---|---|---|---|---|

All institutions | 0.439 | 0.100 | 1.008 | 0.605 | 13.332 |

(21.62) | (7.65) | (4.90) | (57.67) | (4.56) | |

Investment advisors | 0.542 | 0.170 | 0.934 | 0.483 | −8.406 |

(13.43) | (10.18) | (3.46) | (21.40) | (-2.28) | |

Investment companies | 0.365 | 0.142 | 1.090 | 0.735 | −2.172 |

(35.79) | (9.27) | (4.65) | (47.02) | (-1.08) | |

Banks | 0.394 | 0.003 | 1.254 | 0.649 | 42.541 |

(19.93) | (0.30) | (7.86) | (40.21) | (16.80) | |

Insurance companies | 0.370 | 0.086 | 1.408 | 0.677 | 20.171 |

(31.26) | (6.60) | (8.99) | (55.99) | (7.71) | |

Other institutions | 0.321 | 0.098 | 0.549 | 0.695 | 27.629 |

(7.52) | (9.49) | (3.99) | (13.76) | (6.45) |

Interestingly enough, the role of the size variable varies across the institutional groups. While its coefficient is positive and significant for the aggregate institutional portfolio and for most of the institutional groups, it is negative and marginally (not) significant for Investment Advisors (Investment Companies).

As a final test of the model prediction, monthly returns on the aggregate institutional portfolio and the portfolios of the institutional subgroups were regressed on the market return and the S&P 500 residual return and the results are reported in Table 7. The market beta for all institutional subgroup portfolios is very close to unity. The benchmark residual beta is positive and significant for All Institutions and for all subgroups except Investment Advisors and Investment Companies for which the coefficient is very small and is insignificant.

α× 10^{3} | β_{m} | β_{e} | N | R ^{2} | |
---|---|---|---|---|---|

All institutions | 0.107 | 1.019 | 0.237 | 345 | 0.99 |

(0.48) | (208.55) | (8.56) | |||

Investment advisors | −0.124 | 1.052 | 0.006 | 345 | 0.99 |

(-0.42) | (164.76) | (0.15) | |||

Investment companies | −0.119 | 1.054 | 0.031 | 345 | 0.99 |

(-0.39) | (158.36) | (0.81) | |||

Banks | 0.789 | 0.953 | 0.724 | 345 | 0.99 |

(3.44) | (189.73) | (25.44) | |||

Insurance companies | −0.018 | 1.014 | 0.431 | 345 | 0.99 |

(-0.07) | (184.44) | (13.81) | |||

Other institutions | 0.211 | 0.989 | 0.399 | 345 | 0.99 |

(0.78) | (167.05) | (11.88) |

#### 5.2. *Summary*

In this section we have shown that the composition of institutional portfolios conforms well to the predictions of the agency model. We find that the *aggregate institutional* portfolio consists of a long position in the market portfolio, a long position in the aggregate benchmark portfolio as proxied by the S&P 500 portfolio, and a short position in our proxy for the minimum variance portfolio. On average, a linear combination of these three portfolios explains 93% of the variance in the institutional portfolio weights. Similar results obtain for each individual type of institution. When the institutional portfolio weight is replaced by the relative institutional portfolio weight (the weight in the institutional portfolio divided by the weight in the market portfolio), even stronger results are obtained. Finally, institutions were shown to overweight stocks with positive S&P 500 residual betas even after allowing for the effects of S&P 500 membership and firm size.

### 6. Conclusion

- Top of page
- Abstract
- 1. Introduction
- 2. A Model of Institutional Investing
- 3. Data
- 4. Expected returns and the agency model
- 5. Institutional portfolio weights and the agency model
- 6. Conclusion
- Appendix
- References

In this paper we have presented a simple model of asset pricing and allocation with agency which, we argue, is likely to be more descriptive of contemporary capital markets than the classical capital asset pricing model, because it takes account of the fact that a substantial proportion of equity portfolios are now managed by financial institutions on an agency basis. The model assumes that the capital market is populated by a mix of individual investors and institutions who manage money on an agency basis. The agents are assumed to be concerned, not with the raw return on their portfolios, but with the return relative to a benchmark portfolio. Assuming normal distributions of returns and exponential preferences for both individuals and agents, we demonstrate that the resulting equilibrium is a multi-beta asset pricing model. The first beta is the classical market beta and the second beta is with respect to the component of the return on the weighted average benchmark portfolio that is orthogonal to the market return. The market price of the market beta risk is positive as in the classical setting, but the market price of benchmark risk is negative. The intuition for the latter result is that agents bid up the price of assets which load strongly on the benchmark return since the benchmark plays the role of the riskless asset for them. However, we show that for realistic values of the residual risk of the benchmark portfolio the agency effect will be small – of the order of 3 basis points per month. Using returns on common stocks from CRSP for the period 1931–2009 we find benchmark effects of that order of magnitude but they are not statistically significant.

While the asset pricing implications of this model of agency are theoretically and empirically insignificant, the implications for portfolio allocations are more interesting. We have found that institutional asset allocations can be represented as consisting of long positions in the market portfolio and the benchmark portfolio as represented by the S&P 500 portfolio, and a short position in the minimum variance portfolio, plus security specific noise. We also find that institutional portfolios are tilted towards securities with high market betas and high benchmark residual betas, and this result is robust to allowing for S&P 500 membership and for firm size.

### Appendix

- Top of page
- Abstract
- 1. Introduction
- 2. A Model of Institutional Investing
- 3. Data
- 4. Expected returns and the agency model
- 5. Institutional portfolio weights and the agency model
- 6. Conclusion
- Appendix
- References

#### Appendix A: The Benchmark Residual Beta of the Institutional Portfolio

Using the equilibrium condition (5), the expected return of the minimum variance portfolio is

Substituting for μ_{v} in (15), agent *i*'s portfolio may be written as

The benchmark residual beta of stock *k* is

Define the vector of the benchmark residual betas of all stocks as

Then the benchmark residual beta of agent *i*'s portfolio is

The benchmark residual beta of the institutional portfolio is the weighted average of the benchmark residual betas of all the agents' portfolios, so that:

- 1
For a detailed discussion of the agency problems in the management of corporate defined benefit pension plans see Lakonishok

*et al.*(1992). - 2
- 3
Russell and BARRA both produce indices that capture size and value effects. Cornell and Roll (2005, p. 61) remark that ‘Many benchmarks are available, including diversified international indexes, technology indexes, bond indexes, and specialized indexes designed for industrial sectors or “sin-free” stocks … the most common benchmarks are S&P 500, Wilshire 5000, or the MSCI (Morgan Stanley Capital International) indexes’.

- 4
Cornell and Roll (2005) use a similar model framework to discuss the theoretical implications of ‘delegated-agent asset pricing’ but do not present any empirical evidence. In their model, unlike the one we develop, there are only active and passive portfolio managers or agents, but no individual investors.

- 5
Restrictions on the compositon of institutionally managed portfolios are almost universal: Almazan

*et al.*(2004) document the prevalence of portfolio constraints in investment management contracts in the mutual fund industry. - 6
We are grateful to a referee for pointing this out.

- 7
Stutzer (2003) derives a similar expression in a setting in which the agents who manage equity portfolios are also able to invest in the riskless asset.

- 8
Dimson and Nagel (2002) argue that value has been a salient investment strategy characteristic in the US since the 1930s, while firm size emerged only after the classic study of Banz (1981). Sensoy (2009) shows that in 2004 33.5% of mutual fund assets were benchmarked against size and value/growth benchmarks. Sharpe (1992) appears to have been the first to draw attention to the implications of investment style for performance measurement and therefore to have suggested the use of portfolios other than proxies for the market portfolio as appropriate benchmarks.

- 9
Sensoy (

*op.cit.*) reports that on average 61.3% of US mutual fund assets were benchmarked against the S&P 500 over the period 1994-2004. - 10
The origins of the Standard & Poor's 500 Index go back to 1923, when the Standard Statistics Company presented a series of indices that included 233 companies grouped into 26 industries. In 1957 S&P introduced the S&P 500 and has expanded its representation over the years to encompass approximately 90 specific industry groups. Prior to 1957 the ‘S&P 500’ series is actually the precursor series, the ‘all stock’ index. For a detailed discussion see Wilson and Jones (2002).

- 11
According to SEC's website, “If you control another entity (or are controlled by another entity), you should report shared-defined investment discretion. This category includes parent corporations and their subsidiaries (e.g., a bank holding company and its subsidiaries), investment advisers and mutual funds that they advise, and insurance companies and their separate accounts.”

- 12
Thompson Financial has reported that many institutions are incorrectly classified as type 5 (‘other’) from 1998 on. We correct this problem by investigating the institutions classified as type 5 from 1998: if the institution was also classified as type 5 before 1998, no change was made; if the institution had been classified as ‘other’ before 1998 and changed to type 5 in or after 1998, it was reclassified as the type assigned immediately before the change.

- 13
From the file msp500list.sas7bdat.

- 14
The breakpoints, which are described in Fama and French (1993), are based on the size distribution of NYSE firms. They were downloaded from Ken French's website.

### References

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- Abstract
- 1. Introduction
- 2. A Model of Institutional Investing
- 3. Data
- 4. Expected returns and the agency model
- 5. Institutional portfolio weights and the agency model
- 6. Conclusion
- Appendix
- References

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