The Conditional Performance of Insider Trades

内幕交易

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B. ESPEN ECKBO and DAVID C. SMITH*

ABSTRACT

  This paper estimates the performance of insider trades on the closely held Oslo Stock Exchange (OSE) during a period of lax enforcement of insider trading regulations.

  Our data permit construction of a portfolio that tracks all movements of insiders in and out of the OSE firms.

  Using three alternative performance estimators in a time-varying expected return setting, we document zero or negative abnormal performance by insiders.

  The results are robust to a variety of trade characteristics. Applying the performance measures to mutual funds on the OSE, we also document some evidence that the average mutual fund outperforms the insider portfolio.

I. INTRODUCTION

  through direct employment or through participation on supervisory committees and boards, will from time to time possess information about the firm's future cash flow which is not yet reflected in the firm's stock price. Insiders who trade on the basis of such information tend to purchase stocks just prior to abnormal price increases and to sell just prior to abnormal price declines. Employing traditional event-study techniques, in which equal-weighted average abnormal stock returns are estimated over a fixed time period following insider trades, the extant empirical literature tends to support this "buy low and sell high" hypothesis. For example, Jaffe （$1974$） and Seyhun （$1986$） present evidence of significant abnormal stock returns following reported insider trades on the New York and the American Stock Exchanges. Similarly, Baesel and Stein （$1979$） and Fowler and Rorke （$1984$） conclude that insiders on the Toronto Stock Exchange earn abnormal profits, and Pope, Morris, and Peel （$1990$） reach a similar conclusion for firms in the United Kingdom.

  This paper develops a new empirical methodology that mimics the true performance of insider trades more accurately than the traditional event-study approach. This methodology, when applied to a stock market with a reputation for being an "insider's market," produces evidence of zero or negative abnormal insider returns. Moreover, it appears that portfolios formed from all insider holdings are outperformed by portfolios of managed mutual funds on the same stock exchange. We reach these conclusions using the population of more than $18,000$ reported insider trades on the Oslo Stock Exchange （OSE） from January 1985 through December 1992. Over this period, the OSE experienced a significant surge in investments by the general public as well as by foreign investors. Nevertheless, the ownership structure of OSE stocks continues to be concentrated, with insiders accounting for more than $14$ percent of the market. This ownership structure, combined with a relatively volatile stock market and lax enforcement of insider trading laws during our sample period, makes the OSE a particularly interesting laboratory for studying the potential profits from insider trades.

Our performance analysis is novel in that

• it tracks all changes in the level of insiders' individual stock holdings and
• it incorporates and extends performance measures recently developed in the literature on mutual funds.

  We draw inferences using various portfolios of insider holdings, as well as three different conditional performance measures, each allowing expected stock returns to be time-varying. Allowing for time-variation in expected stock returns is important in light of the growing evidence that publicly available information such as bond yields and past stock price movements to some extent predict future returns. For example, if current yield spreads indicate that a certain stock will have a relatively high expected return over the next period, an insider who conditions on this information when trading will exhibit superior performance relative to a benchmark portfolio that assumes （unconditional） constant expected returns. Because this insider has not exploited any private information, such "performance" is not considered superior in our context and therefore is eliminated.

  In our performance analysis,

• we first develop and estimate a conditional event-study measure that extends the traditional event-study technique to a conditional, multifactor setting.
• Second, we apply a conditional version of the so-called “Jensen's alpha,” also examined by Ferson and Schadt ($1996$) in the context of mutual funds.
• Third, we develop a conditional version of the portfolioweight performance measure first suggested by Cornell ($1979$) and applied in particular by Grinblatt and Titman ($1993$) to measure mutual fund performance.

  We find that a standard event-study analysis produces evidence of positive abnormal performance following insider sale transactions, not unlike the findings reported by Seyhun ($1986$). However, this abnormal performance disappears when insiders' actual value-weighted portfolio returns are used or when a multifactor market model allowing for time-varying expected returns is applied. Moreover, neither the conditional Jensen's alpha nor the conditional portfolio-weight performance measures indicate positive abnormal performance by insiders. In fact, there is some evidence of negative insider performance. These conclusions are robust with respect to trade size, size of holdings in the firm, whether the net trade in the firm is a purchase or a sale, or whether we weigh the trades by insiders' percentage holdings or total equity in the firm.

  For comparison, we also provide evidence on the conditional performance of seven major mutual funds on the OSE. In contrast to the decentralized (and partly independent) portfolio decisions by individual insiders, the managed fund portfolios have an administrative advantage in that asset allocation decisions can be optimized across the entire fund portfolio. Interestingly, we find little systematic evidence that the mutual funds outperform the OSE market but there is some evidence that the conditional performance of the average mutual fund exceeds that of the aggregate insider portfolio. Although this result is not pursued further in this paper, one possible explanation is that insiders enjoying corporate control benefits from their ownership positions decide against selling shares even when publicly available (conditioning) information suggests that such sales may increase average returns.

The rest of the paper is organized as follows.

• Section I characterizes our main empirical approaches to performance measurement.
• Section II describes our data on insider trades and mutual funds.
• Section III presents our estimates of insider performance,
• and the performance of mutual funds is discussed in Section IV.
• Section V concludes the paper.

II. Conditional Performance Evaluation: Methodology

  Let

• $r^{i}_{t+1}$ denote the excess return on asset $i$ in period $t+1$ (in excess of the risk-free rate $r^{f}_{t+1}$ and
• $E\left( r^{i}_{t+1}|Z^{*}_{t} \right)$ be the expected return conditional on a set of public information available at time $t$, $Z^{*}_{t}$.
• Suppose uninformed investors trade based on $Z^{*}_{t}$, generating time-varying expected returns of $E\left( r^{i}_{t+1}|Z^{*}_{t} \right)$, and
• that these investors' trades are otherwise independent of the assets' subsequent price changes. Informed investors use additional, private information $I_t$ to correlate trades with subsequent abnormal returns,

we have

$$\epsilon_{t+1}^{i} = r^{i}_{t+1} - E\left( r^{i}_{t+1}|Z^{*}_{t} \right)$$

  As a result of their ability to “buy low and sell high,” the conditional expected return to informed investors exceeds the expected return to uninformed investors; that is,

$$E\left( r^{i}_{t+1}|Z^{*}_{t}, I_{t} \right) - E\left( r^{i}_{t+1}|Z^{*}_{t} \right) > 0$$

  The purpose of our empirical analysis is to estimate this difference in conditional expected returns for portfolios of insider holdings as well as for managed mutual funds. In the following, we first discuss our choice of portfolio representations of insider holdings and trades. We next introduce the conditional event-study framework as well as the conditional Jensen's alpha approach. These methods require specification of a model relating the risk and return on a benchmark portfolio, which serves as a proxy for $E\left( r^{i}_{t+1}|Z^{*}_{t} \right)$. We then develop our third performance measure, which is the conditional covariance between individual portfolio weights at time $t$, $\omega_{t}^{i}$, and subsequent abnormal return realizations; that is,

$$Cov\left(\omega_{t}^{i}, \epsilon^{i}_{t+1}|Z^{*}_{t} \right).$$

  An advantage of the third measure, given data on portfolio weights, is that it does not require explicit specification of an expected return model.

A. Portfolio Aggregation

  It is common in the event-study literature on insider trading to estimate the equal-weighted average abnormal return over a fixed time period following insider trades. This approach, which is included as a special case here as well, is useful in terms of testing the hypothesis that insiders tend to trade prior to subsequent abnormal movements in stock prices. However, because a cross-sectionally fixed event window does not accurately represent insiders' actual holding periods, the event-study performance analysis does not produce estimates of the expected gains from insider trading.

  In this paper, we instead aggregate insider stock holdings each month, akin to an insider fund, and track the performance of this fund through time. Of course, individual insiders do not constrain their personal portfolio choices to the set of firms where they are insiders, so this aggregate insider portfolio is not optimal from the perspective of any individual insider. An analogous argument holds for mutual fund portfolios, unless the funds are viewed by all investors as belonging to the set of efficient portfolios. Regardless, the abnormal performance of this portfolio is of particular concern to uninformed investors or mutual fund managers actively trading in broadbased stock portfolios, and whose investment decisions depend on the expected loss from trading against (informed) insiders in the market. Moreover, the abnormal performance of the insider fund is directly comparable to the abnormal performance of managed mutual funds.

  We examine two alternative definitions of the insider portfolio weight of security $i$ at time $t$, value weights, $\left[ \omega_{t}^{i} \right] ^{h}$ , and ownership weights, $\left[ \omega_{t}^{i} \right] ^{s}$ , where

$$\left[ \omega_{t}^{i} \right] ^{h} = \frac{h_{t}^{i}}{\sum_{i=1}^{N_{p}}h_{t}^{i}}\left( 1 \right)$$

$$\left[ \omega_{t}^{i} \right] ^{s} = \frac{\left( \frac{s_{t}^{i}}{S_{t}^{i}} \right)}{\sum_{i=1}^{N_{p}}\left( \frac{s_{t}^{i}}{S_{t}^{i}} \right)}\left( 2 \right)$$

and where

• $N_{p}$ is the total number of securities in the portfolio,
• $h_{t}^{i}$ is the total market value of all insiders' holdings in firm $i$ at the end of month $t$ , and
• $S_{t}^{i}$ denote the total number of shares outstanding held by insiders in firm $i$ at the end of month $t$, and
• $s_{t}^{i}$ denote total the number of shares held by insiders in firm $i$ at the end of month $t$.

  By construction, these weights sum to one.

  Both the value and ownership weights reflect the level of insider investment in firm $i$.

• The former $\left[ \omega_{t}^{i} \right] ^{h}$ assigns greater weight to firms with relatively large dollar values of insider investment, and
• the latter $\left[ \omega_{t}^{i} \right] ^{s}$ gives greater weight to relatively large proportional insider ownership in the firm.

Using these weights, we examine the performance of the total insider portfolio as well as subportfolios based on various trade characteristics such as the size and direction of the trade. Because trade-based portfolios zero out periods of nontrading from the return series, one can think of these as producing a marginal performance estimate. This contrasts with the average monthly performance estimate resulting from using both trading and nontrading periods in the estimation.

  The difference between the average and marginal performance estimates lies in the impact on portfolio returns of months with zero change in insider holdings. If a decision not to trade also reflects inside information, then the average performance estimate has greater power to detect superior performance. This is also the relevant portfolio concept for an analysis of the expected loss to outsiders from trading against insiders, and for comparing the performance of insiders to the performance of managed portfolios such as mutual funds. On the other hand, the possibility of loss of significant corporate control benefits may cause the typical insider not to trade except when inside information is particularly valuable. In this case, the marginal or trade-based performance concept has greater power to register abnormal performance.

  The standard event-study performance measure is similar to the marginal performance concepts in that it also conditions on an insider trade. However,the event study technique does not track insider trades during the fixed event window following the insider trade date. The typical event study also equally weighs abnormal returns across the securities with insider trades.Relative to our weights, such equal weights give greater weight to firms with smaller insider holdings.

B. Conditional Portfolio Benchmark Return Approach

  Assume that expected excess returns follow a $K$-factor equilibrium model （see, e.g., Connor and Korajczyk (1995)）,

$$E\left(r_{t+1}^{i} | Z_{t}^{*} \right) = \sum_{j=1}^{K} \left[ \beta^{ij} \left( Z_{t}^{*} \right) \lambda^{j} \left( Z_{t}^{*} \right) \right], \tag{3}$$

where

• $\beta^{ij} \left( Z_{t}^{*} \right)$ is the systematic risk of the $j^{th}$ factor, and
• $\lambda^{j} \left( Z_{t}^{*} \right)$ is the $j^{th}$ expected factor risk premium, $E\left(F_{t+1}^{j} | Z_{t}^{*} \right) - r_{t+1}^{f}.$

  In $E\left(F_{t+1}^{j} | Z_{t}^{*} \right) - r_{t+1}^{f}$, the factors $F^{j}$ are represented by traded securities, and both the systematic risks and expected risk premia are allowed to vary through time as a function of the publicly available information $Z_{t}^{*}$.

  Below,

• in the event-study approach, we estimate an empirical version of equation ($3$) that adds a firm-specific intercept term as well as event parameters capturing abnormal performance.
• Under the Jensen's alpha approach, we estimate equation ($3$) without event parameters and where the intercept term itself measures abnormal performance.

B.1. Conditional Event Study

  We estimate abnormal returns over an event window consisting of $W$ months including and following the month of an insider trade (event month $0$). Let $\mu_{e_{p}}$ denote the $\left( W \times 1 \right)$ vector of monthly abnormal returns over the event window for portfolio $p$. The abnormal return vector $\mu_{e_{p}}$ is estimated jointly with the parameters in the following multifactor regression model:

$$r^{p}_{t+1}= \alpha^{p} + \left( \textbf{b}_{p} \right)^{T} \left( \textbf{F}_{t+1} \otimes \textbf{Z}_{t} \right) + {\mu_{e_{p}}}^{T} \textbf{D}_{t+1}^{p} + \epsilon^{p}_{t+1} \tag{4}$$

where

• $\textbf F_{\textbf{t+1}}$ is vectors of observable (traded) risk factors, and
• $\textbf Z_{\textbf{t}}$ is vectors of information variables.
• $\textbf b_{\textbf{p}}$ is a $\left( KL \times 1 \right)$ vector of coefficients associated with time-varying risk parameters, and
• $\textbf{D}_{\textbf{t+1}}^{\textbf{p}}$ is a $\left( W \times 1 \right)$ vector of zeros and ones.

$$\textbf{D}_{-1+1}^{p} = \left[\begin{matrix} 1 \\ 0 \\ ... \\ 0 \end{matrix}\right]_{W \times 1} \textbf{D}_{0+1}^{p} = \left[\begin{matrix} 0 \\ 1 \\ ... \\ 0 \end{matrix}\right]_{W \times 1} ,..., \ \ \textbf{D}_{m+1}^{p} = \left[\begin{matrix} 0 \\ 0 \\ ... \\ 1 \end{matrix}\right]_{W \times 1} ,..., \ \ \textbf{D}_{\left( W - 1 \right) + 1}^{p} = \left[\begin{matrix} 0 \\ 0 \\ ... \\ 0 \end{matrix}\right]_{W \times 1}$$

  When $t+1$ is outside the event window, $\textbf{D}_{t+1}^{p}$ is a vector of zeros.
  When $t+1$ is inside the event window, $\textbf{D}_{t+1}^{p}$ contains zeros and the value one for the corresponding month in the event window.

To illustrate, in Section III we use a total event window extending from the month of the insider trade (month $0$) through six months after the trade $\left( W = 7 \right)$. In this case, the month $0$ abnormal return is estimated as the first element of $\mu_{e_{p}}$ by setting $\textbf{D}_{t+1}^{p}$ equal to $\textbf{D}_{-1+1}^{p} = \textbf{D}_{0}^{p} = \left[\begin{matrix} 1 \\ 0 \\ ... \\ 0 \end{matrix}\right]_{7 \times 1}$.4

  The estimation proceeds in a standard event-study fashion:

  Let month $e_{1}$ be the first calendar month for which we have data on insider trades, and form a fixed-weight portfolio of all firms with nonzero net insider trades in this month. Assuming this portfolio is not empty, let $e_{1}$ denote “event month $0$ for portfolio $1$.” The excess return of portfolio $e_{1}$ is regressed using equation (4) over a total of $T$ months starting in event month $e_{1} - \left( T - W \right)$. The regression yields a vector of estimates of the event parameters for months $e_{1}$ through $e_{1} - \left( T - 1 \right)$, denoted $\mu_{e_{1}}$. Moving forward to the next month with nonzero net insider trades, denoted $e_{2}$ (“event month $0$ for portfolio $2$”), the regression is repeated, yielding a second vector of estimates $\mu_{e_{1}}$ . Moving forward in this manner through the entire sample period yields a total of $E$ vectors of event parameter estimates $\mu_{e_{1}}$, $p = 1, 2, ..., E$ ; that is, one vector for each of the $E$ portfolios. In Section III, we report the average value of mep across the $E$ portfolios.

B.2. Conditional Jensen's alpha

  Following Ferson and Harvey (1993) and Ferson and Korajczyk (1995), model ($3$) can be estimated for a portfolio $p$ with an intercept term $\alpha^{p}$. A portfolio strategy that depends only on information $\textbf{Z}_{\textbf{t}}$ will generate abnormal returns that have mean zero and are uncorrelated with $\textbf{Z}_{\textbf{t}}$. Consequently, such a portfolio strategy will yield an estimate of $\alpha^{p}$ that is equal to zero. The constant term $\alpha^{p}$ is a conditional version of the classical “Jensen's alpha” developed and applied by Jensen (1968) in the context of the unconditional single-factor capital asset pricing model (CAPM). Active fund management causes the fund's systematic risk to vary through time; estimation of Jensen's alpha assuming constant systematic risk produces a bias in the estimate of Jensen's alpha (see Grinblatt and Titman (1989) for details). But because equation ($3$) allows systematic risks to vary with the public information $Z_{t}^{*}$, our conditional model framework mitigates this bias.

  The performance measure $\alpha^{p}$ is estimated using the following system of moment conditions:

$$\textbf{u1}_{t+1}^{p} = \textbf{F}_{t+1} - \left( \gamma^{p}\right)^{T} \textbf{Z}_{t} \tag{5}$$

$$\textbf{u2}_{t+1}^{p} = \left[ \textbf{u1}_{t+1}^{p} \left( \textbf u1_{t+1}^{p} \right)^{T} \right] \left( \gamma^{p} \textbf{Z}_{t}\right) - \textbf{u1}_{t+1}^{p}r_{t+1}^{p} \tag{6}$$

$$u3_{t+1}^{p} = r_{t+1}^{p} - \alpha^{p} - \left[ \left( \gamma^{p} \right)^{T} \textbf{Z}_{t} \right]^{T} \left( \gamma^{p} \textbf{Z}_{t}\right) \tag{7}$$

$\left(\right)$
  If the model is well specified, the following orthogonality conditions must hold:

$$E\left( \textbf{u1}_{\textbf{t+1}}^{\textbf{p}}\textbf{Z}_{\textbf{t}}^{T}, \textbf{u2}_{\textbf{t+1}}^{\textbf{p}}\textbf{Z}_{\textbf{t}}^{T}, u3_{t+1}^{p}\right) = 0, \tag{8}$$

which we estimate using Hansen's ($1982$) generalized method of moments （GMM） estimator.

  The system (5) through (7) has an intuitive interpretation:

  First, equation (5), when multiplied by $\textbf{Z}_{\textbf{t}}$, forms L OLS normal equations for each regression of the factors in $\textbf{F}_{\textbf {t+1}}$ on the information variables $\textbf{Z}_{\textbf{t}}$. That is, we assume that the “unrestricted” conditional expected factor returns are linear in

$$\textbf{Z}_{t} : E \left( \textbf{F}_{\textbf{t+1}} | \textbf{Z}_{\textbf{t}} \right) = \left( \gamma^{\textbf{p}} \right)^{T} \textbf{Z}_{\textbf{t}}$$

  The fitted values, $\left( \hat{\gamma}^{\textbf{p}} \right)^{T} \textbf{Z}_{\textbf{t}}$ , are used to model the conditional expected risk premia, and the residuals $\left( \hat{u}1^{\textbf{p}}_{\textbf{t+1}} \right)^{T}$ are used to estimate conditional variances and covariances.

  Second, defining the conditional factor betas as

then equation (6) is the pseudoregression of the estimates bpt on the instruments Zt, yielding the L 3 K matrix of regression coefficient estimates kp.

  The fitted values kp' Zt then represent our estimates of the time-varying betas. Third, equation (7) defines the average abnormal performance parameter ap to be the difference in the realized unconditional excess return on portfolio p and the unconditional mean of the product of the conditional beta estimates and estimates of the conditional risk premia. In sum, ap measures the average return on portfolio p relative to the return on a time-varying benchmark portfolio.

  Ferson and Harvey （$1991$） and Evans （$1994$） argue that time-variation in conditional betas for passive portfolios is economically and statistically small in the United States. On the other hand, Ferson and Schadt （$1996$） find that time-varying betas are important in their measurement of the performance of managed U.S. mutual funds. Because no comparable study exists for the Oslo Stock Exchange, the subsequent empirical analysis reports estimates of ap assuming both time-varying and constant conditional betas.

C. Conditional Portfolio Weight Measure

  As pointed out by Grinblatt and Titman (1989, 1993), absent superior information and assuming expected returns are constant, the average covariances of portfolio weights with future returns should be zero:

$$\sum_{i=1}^{N_{p}} cov \left( w_{t}^{i}, r_{t+1}^{i} \right) = \sum_{i=1}^{N_{p}} E \left\{ \left[ w_{t}^{i} - E \left( w^{i} \right)\right] \left[ r_{t+1}^{i} - E\left( r^{i} \right) \right] \right\}$$

$$\sum_{i=1}^{N_{p}} E\left\{w_{t}^{i} \left[ r_{t+1}^{i} - E\left( r^{i} \right) \right] \right\} = 0 \tag{9}$$

where $w_{t}^{i}$ is the portfolio weight of asset $i$ selected at time $t$ and held from time $t$ through $t + 1$. Insiders with superior information will generate a positive estimate of equation (9) because they are able to correlate this period's trade with next period's return. Grinblatt and Titman（$1989$）, in the context of managed portfolios, demonstrate that a risk-averse manager with superior information will generate a positive estimate of the covariance measure (9) if the manager's level of Rubinstein（$1973$） absolute risk aversion is nonincreasing.

In the presence of nonconstant expected returns, the covariance in equation (9) will exhibit a bias when investors have no superior information, but use publicly available information to forecast returns and trade on these forecasts. To avoid this potential bias, we extend equation (9) to a conditional setting:

$$\sum_{i=1}^{N_{p}} cov \left( w_{t}^{i}, r_{t+1}^{i} | Z^{*}_{t} \right) = \sum_{i=1}^{N_{p}} E\left\{w_{t}^{i} \left[ r_{t+1}^{i} - E\left( r^{i} \right) \right] | Z^{*}_{t} \right\} \tag{10}$$

  The conditional covariance in equation (10) measures whether a manager's portfolio weights are correlated with the unforecastable portion of portfolio returns, where the forecasts use only $Z^{*}_{t}$.6

We estimate equation (10) as follows:

Let $\textbf{r}_{\textbf{t+1}}^{\textbf p}$ denote the $\left( N_{p} \times 1 \right)$ vector of excess returns and $\textbf w_{\textbf{t+1}}^{\textbf p}$ the $\left( N_{p} \times 1 \right)$ vector of portfolio weights. Moreover, define

$$\textbf u1_{\textbf{t+1}}^{\textbf p} = \textbf{r}_{\textbf{t+1}}^{\textbf p} - \left( \gamma^{p}\right)^{T} \textbf{Z}_{\textbf{t}}$$

$$u2_{t+1}^{p} = \left( \textbf w_{\textbf{t+1}}^{\textbf p} \right)^{T} \textbf u1_{\textbf{t+1}}^{\textbf p} - \Phi^{p}$$

with the following orthogonality restrictions:

E~u1p,t+1Zt' ,u2p,t11Zt ! 5 0. (13)

The $N_{p} \times 1$ vector $\textbf u1_{\textbf{t+1}}^{\textbf p}$ when multiplied by $\textbf Z_{\textbf{t}}$ forms a set of seemingly unrelated regressions of the asset returns from the portfolio on the time t information set, producing estimates of the parameters summarized in the Np 3 L matrix Dp. The GMM estimate of the parameter Fp is an average of the conditional covariance of equation (10). The second term in equation (13) imposes the restriction that this covariance be orthogonal to the information set Zt.

  We now turn to the empirical analysis of the three performance measures mp, ap, and Fp, applied to portfolios of insider stock holdings as well as to managed mutual funds.

III. Data and Sample Characteristics

A. Insider Trades and Holdings

  Our empirical analysis focuses on all individuals defined as “insiders” according to the 1985 amendment to the Norwegian Securities Trading Act. The definition of an insider includes the CEO, the top managers of the firm, members of the board of directors and supervisory boards, the firm's auditor and investment advisor, and close family members of these individuals. Each quarter, all OSE-listed firms must report to the stock exchange subsidiary, Oslo Børs Informasjon AS (OBI), all trades by each of the respective firm's insiders. The report provides the date of each insider's trade, the security traded, the trade amount, the direction of trade (purchase or sell), and the stock price per share of the transaction. The report also contains the end-of-quarter holdings of each insider in all of the firm's securities.

  OBI supplied us with a database that contains

1. the complete set of $18,301$ insider trade records in $247$ securities ($197$ companies) from January $1985$ through December $1992$, and
2. the last reported holding records for the population of $24,369$ insiders as of December $1992$.

As explained below, we use this information to reconstruct a monthly time series of each insider's holdings.

  Starting with the trade information, the average security has $96$ insiders trading a total of $80$ times over the sample period. Of the total number of registered insiders, $21$ percent traded at least once during the sample period. Thus, the $18,301$ trade records were produced by a total of $5003$ insiders trading an average of $3.7$ times. Of the $79$ percent of the insiders who never traded, $70$ percent never held any shares in the respective companies. The identity of these insiders was nevertheless recorded by the OBI and therefore included in our database as a matter of general disclosure requirements.

  Of the $18,301$ trades, $35$ percent are sales. Insider ownership averages $14$ percent of total firm equity, and fluctuates between $10$ percent and 18 percent over the sample period. The monthly change in the holdings includes a maximum net sale of approximately $1.5$ percent and a maximum net purchase of approximately $1.7$ percent of the company's stock. Over the sample period, insiders on average traded $26$ percent of the value of their total holdings per year, representing $14$ percent of the value of all trades on the OSE. In comparison, the turnover rate over the same period for the average OSE stock was $35$ percent.

  Turning to the OBI data on insider holdings, we recursively reconstruct from December $1992$ a monthly time series of each insider's holdings by subtracting each buy and adding each sale, adjusting for changes in the firms' total number of shares outstanding caused by new security issues and stock dividends. In creating this time series, three assumptions are made:

1. First, absent information to the contrary, we assume that insiders purchase their pro rata share of new equity issues.
2. Second, if a firm with positive insider holdings is delisted from the exchange, we assume that the insiders' holdings are brought to zero (sold) at the end-of-month price prevailing just prior to the month of delisting.
3. Third, at the time a shareholder becomes (or ceases to be) an insider, we do not treat the implied change in insider holdings as an insider buy (or sell).

  The individual insider shareholdings are used to form a portfolio of aggregate insider holdings, using the portfolio weight defined above in equations (1) and (2) in Section I. Given a vector of portfolio weights

$$w_{\textbf t}^{\textbf p} = \left[\begin{matrix} w_{t}^{1} \\ w_{t}^{2} \\ ... \\ w_{t}^{i} \\ ... \\ w_{t}^{N_{p}} \end{matrix}\right]_{N_{p} \times 1}$$

, we construct the monthly excess return on the insider portfolio as

$$r^{p}_{t+1} \equiv \sum_{i=1}^{N_{p}}w_{t}^{i} r_{t+1}^{i}$$

where $r_{t+1}^{i}$ is security $i$'s return over month $t + 1$ in excess of the risk-free rate. Monthly returns and prices are provided by OBI.

  The number of insider records used in the subsequent empirical analysis is slightly smaller than the population provided by the OBI. We discovered $95$ duplicate trade records, $18$ missing trade records, as well as missing holding records for $71$ insiders. Moreover, of the $247$ listed securities in the database, $17$ had zero insider holdings over the entire sample period. Thus, the total number of securities with insider trades is $230$. The total number of firms listed in our data set in a given month varies from a low of $99$ to a high of $131$ over the sample period, with an average of $116$.

B. Mutual Funds

  We select the seven largest mutual funds in Norway for which we could find complete data on portfolio weights between $1985$ and $1992.7$ The seven funds are Avanse (AVEM), Avanse Spar (SPIM), Kreditkassen K-Avkasting (KAGM), Kreditkassen K-Vekst (KVTM), G-Aksjefond (NAKM), UNI-finans (NOFM), and UNI-Pluss (NOPM).

  For each fund, we calculate the monthly change in the value of the fund including any dividend paid on the fund.

  Mutual fund portfolio weights are collected from the periodic reports sent to fund customers. In Norway, fund companies are required to report portfolio weights three times a year: at the end of April, August, and December. Similarly to Grinblatt and Titman ($1993$), we assume that mutual fund managers revise their portfolios with the same frequency as the reporting requirement.

C. Risk Factors, Factor-Mimicking Portfolios, and Information Variables

  As listed in Table I, the empirical analysis employs three risk factors. The first is the excess (world) market return, dxmsci, represented by the with-dividend monthly change in the Morgan Stanley Capital Index (MSCI) (measured in Norwegian Kroner (NOK)) less the monthly yield on the three-month Norwegian Interbank Offer rate (NIBOR). The MSCI represents the value-weighted level of $19$ OECD stock markets plus Singapore/Malaysia and Hong Kong. Harvey ($1991$) shows that the MSCI return dominates many country proxies (including the U.S. New York Stock Exchange index) in the sense of having higher average historical returns per unit of variance.

  The second and third risk variables are the factor-mimicking portfolios for the changes in the term structure, dterm, and the real interest rate, nibor. These capture the effects on the discounted value of future cash flows of both the level of real short term rates and the term structure. Merton ($1973$) develops a model in which the interest rate level enters as a state pricing variable. Ferson and Harvey ($1991$, $1993$) use the real interest rate as a pricing variable in studies on U.S. and international data. Chen, Roll, and Ross ($1986$) find that changes in the term structure are priced in crosssectional tests of U.S. stock return portfolios.8

  The term structure variable dterm is measured as the change in the difference between the average monthly yield on Norwegian government longterm bonds and the average monthly yield on the three-month NIBOR.

$$dterm_{t} = \frac{average monthly yield on Norwegian government longterm bonds - the average monthly yield on the three-month NIBOR}{average monthly yield on Norwegian government longterm bonds - the average monthly yield on the three-month NIBOR} - 1$$

The real interest rate nibor is the level of the monthly NIBOR yield in excess of the change in the Norwegian CPI.

$$nibor = monthly NIBOR yield - the change in the Norwegian CPI$$

Because these two factors are not traded assets, one cannot strictly interpret the fitted values $\left( \hat{\gamma} \right)^{T} \textbf Z_{\textbf{t}}$ from equation (5) as estimates of the ex ante factor risk premia. These factors should be represented by portfolios of traded assets, or factor mimicking portfolios (see, e.g., Shanken ($1992$)). We form factor mimicking portfolios from linear combinations of size-based decile portfolios on the OSE using the procedure developed by Breeden, Gibbons, and Litzenberger ($1989$). This involves regressing the interest rate variables on the decile portfolio returns and the instruments in $\textbf Z_{\textbf{t}}$. The mimicking portfolio weights are then constructed to be the estimates of the slope coefficients on the decile portfolios, reweighted to sum to one.9

  The information variables in $\textbf Z_{\textbf{t}}$ are expected to capture predictable variation in the portfolio returns and factor risk premia. Our choice of information variables, as listed in Table I, include：

• the lagged values of the excess (world) market return, dxmsci（$-1$）,
• the excess (world) market dividend yield, xmsdiv（$-1$）,
• the real interest rate, nibor（$-1$）, and
• a January dummy variable, jdum, as predictor for changes in returns through time.

  Ferson and Harvey ($1993$), Harvey ($1991$), and Solnik ($1993$) use similar variables in international cross-country comparisons.

Table I

Definitions of (Factor-Mimicking) Risk Factors, Information Variables, Insider Portfolio Weights, and Insider Subportfolios Used in the Conditional Performance Analysis

This table defines the risk factors $\textbf F_{\textbf{t+1}}$ used to generate equilibrium risk premia in period $t + 1$, and the lagged information variables $\textbf Z_{\textbf{t}}$ that help predict next period's returns. Two of the three risk factors, rnibor and dterm, do not represent traded securities and are therefore replaced by factor-mimicking portfolios constructed from a linear combination of size-based decile portfolios on the OSE. The portfolio construction proceeds by regressing the nontraded factor on ten size-sorted decile portfolio returns and the instruments in $\textbf Z_{\textbf{t}}$. The factor-mimicking portfolio return is then computed as the product of the decile returns and their normalized (to sum to one) slope coefficients. The insider portfolio weights, $w^{p}_{t}$, are formed at the end of period $t$ and are used to form $r^{p}_{t+1}$, the insider portfolio return in period $t + 1$.

Risk Factors ($\textbf F_{\textbf{t+1}}$)	Definition
dxmsci	Monthly change in the Morgan Stanley Capital Index in excess of the monthly yield of the three-month NIBOR (Norwegian Interbank Offer Rate).
rnibor	Factor-mimicking portfolio representation of nibor, the monthly yield on the three-month NIBOR net of the monthly change in the Norwegian CPI.
dterm	Factor-mimicking portfolio representation of the monthly change in the difference between average yields on Norwegian Long Term Government Bonds (six to ten years) and the three-month NIBOR.

Information Variables ($\textbf Z_{\textbf{t}}$)	Definition
dxmsci（$-1$）	dxmsci, lagged one period.
xmsdiv （$-1$）	Average monthly MSCI dividend yield, less the monthly NIBOR yield, lagged one period.
nibor （$-1$）	Monthly yield on three-month NIBOR net of the monthly change in the Norwegian CPI, lagged one period.
jdum	Dummy variable that equals one in the month of January and zero otherwise.

Insider Portfolio Weights (vpt)	Definition
dxmsci	Monthly change in the Morgan Stanley Capital Index in excess of the monthly yield of the three-month NIBOR (Norwegian Interbank Offer Rate).
rnibor	Factor-mimicking portfolio representation of nibor, the monthly yield on the three-month NIBOR net of the monthly change in the Norwegian CPI.

Insider Subportfolios (vpt)	Definition
Large, Medium, or Small weights only	Let ct [ ~ 1 3_ !@sup vit 2 inf vit#. The “Large” category contains all stocks that satisfy vit . sup vit 2 ct; The “Small” category contains all stocks satisfying vit , inf vit 1 ct (and thus includes vit 5 0!; and the “Medium” category contains all other stocks. Within each category, the securities are then reweighted to sum to one.
Large, Medium, or Small trades only	Let ct [ ~ 1 3_ !@supDvit6 2 inf Dvit6#, where Dvit [ vit 2 vi,t21 (the change in insider holdings in stock i from t 2 1 to t!. Stocks are placed in each of the three categories using an allocation rule analogous to the one shown above for the Large, Medium, and Small weights categories, with the additional constraint that stocks with no trade ~Dvit 5 0! are excluded.
Buys (sales) only	A portfolio that at each date t restricts Dvit [ vit 2 vi,t21 . 0 ~Dvit , 0 for “sales only”).

IV. The Performance of Insider Trades

  Our conditional performance measures presume that the instruments in $\textbf Z_{\textbf t}$ (described in Table I) to some extent are useful in predicting excess returns in period $t + 1$. To check this assumption, Table II reports ordinary least squares (OLS) regressions of monthly, value-weighted decile portfolio and value-weighted OSE index (TOTX) excess returns on $\textbf Z_{\textbf t}$. The size-sorted portfolios are constructed on a monthly basis by grouping stocks into one of $10$ deciles according to each stock's beginning-of-month market value. Use of size-sorted portfolios is motivated by the assumption that size (when measured by market value) may proxy for risk.10

  As shown in Table II, a significant amount of the variation in the valueweighted excess return can in fact be explained by the instruments in $\textbf Z_{\textbf t}$. The adjusted $R^{2}$ is $6.9$ percent and the p-value associated with the hypothesis that none of the return variation is explained by our instrument choice is well below $5$ percent. A similar pattern persists across the size decile excess returns, particularly for portfolios of larger-cap stocks: four of the ten portfolios have $p$-values well below $5$ percent. Across all portfolios, the lagged return on the MSCI world market index appears to be the most important explanatory variable. With this diagnostic check on the predictive power of $\textbf Z_{\textbf t}$, we now turn to the performance estimation.

A. Conditional Event Study Approach

  Given the importance of event studies in the empirical literature on insider trades, we begin our performance analysis using the event-study approach. Table III reports average abnormal return estimates for a seven-month event window ~W 5 7! estimated using equation (4). As described in Section I.B, the estimation procedure yields a total of E vectors m[ e p , p 5 1,..., E, each containing the seven monthly abnormal return estimates for the respective portfolios. Portfolio p is formed using all firms in calendar month ep that have nonzero net insider trades in that month. We follow Seyhun ($1986$) and define a firm with nonzero net trades as one where the number of insiders buying the firm’s shares is different from the number of insiders selling. Portfolio abnormal returns are then estimated for month e p (event month $0$) through month ep 1 6 (event month $6$) always using T 5 48 monthly return observations ending in month ep 1 6. The table reports the average value of
m[ e
p
, as well as the p-value for this average. To illustrate, let m[ e
p,0 denote the first element of the vector m[ e
p
, that is, the estimated abnormal return over

V. A Comparison with the Performance of Mutual Funds

  As indicated in the introduction, it is interesting to compare the performance of insiders to that of managed mutual funds. While neither the insider portfolio nor the mutual fund portfolios are by themselves necessarily optimal portfolios from the individual investor’s point of view, their relative performance sheds light on the likelihood that the aggregate insider portfolio weights in fact reflect private information. Given the potential presence of corporate control benefits from insider holdings (which increase the costs of insider sales), as well as the decentralized nature of the insider portfolio (which prevents optimal asset allocation across individual insider holdings), it follows that for insiders to receive a higher average risk-adjusted return than mutual funds they must trade on inside information.

  Table VIII presents conditional Jensen's alpha estimates for the seven mutual funds in the data base. Moreover, the table shows the alpha estimates for an equal-weighted portfolio of the seven funds, as well as for two selffinancing “difference portfolios.” Each difference portfolio consists of a long position in the average mutual fund portfolio and a short position in the portfolio of insider holdings (both value-weighted and ownership-weighted). Thus, the difference portfolios allow us to directly test for differences in abnormal performance between insiders and mutual funds.

  As reported for insider trades in Table VI, the goodness-of-fit test statistic fails to support the hypothesis that betas are time-varying, which also explains why the alpha estimates in the table are not particularly sensitive to whether or not we assume time-varying betas. Focusing first on the average mutual fund, the hypothesis of zero abnormal performance cannot be rejected at conventional levels of significance using either ap or ap*. The values of these parameters are $0.007$ and $0.006$ with $p$-values of $0.114$ and $0.169$, respectively. Note that these parameter values are indistinguishable from the corresponding alpha-values for the OSE index shown earlier in Table IV ($0.007$ and $0.005$), which are also found to be insignificant. Because the alpha estimates most likely reflect a survivorship bias resulting from our mutual fund sample selection procedure, these estimates are, if anything, overstated. In sum, we conclude that the average mutual fund on the OSE does not exhibit abnormal performance over the sample period. This conclusion is also supported by an examination of the individual mutual fund performance estimates: only one fund of seven shows a Jensen's alpha that is significant at the $5$ percent level or better.

  Our findings for OSE mutual funds are consistent with the thrust of the evidence on U.S. mutual fund performance whether based on unconditional estimates (e.g., as surveyed by Grinblatt and Titman ($1995$) or conditional Jensen's alpha as in the study of $67$ open-end mutual funds by Ferson and Schadt ($1996$). Interestingly, Ferson and Schadt also report that going from an unconditional to a conditional portfolio benchmark approach causes the distribution of Jensen's alpha to shift to the right and to be centered near zero, possibly reflecting a negative bias in unconditional alpha estimates.

  Table VIII also provides evidence that the average mutual fund outperforms the portfolio of insider holdings. In the two last rows of the table, although the alpha-estimates based on time-varying betas are both insignificant, the estimate of ap* is 0.013 ~ p-value of 0.008) and 0.020 ~ p-value of 0.038) when using the value-weighted and ownership-weighted insider portfolios, respectively. Because positive values of alpha means that the average mutual fund outperforms the aggregate insider portfolio, this finding further undermines the view that insiders tend to trade on private, inside information.

  Finally, turning to the conditional portfolio weight measure of performance, Table IX reports estimates of Fp for each of the seven mutual funds. Due to the data reporting constraints in the sample of mutual funds explained in Section II, this table constrains portfolio weights to be revised three times a year only. That is, we measure the covariance between the reported portfolio weights and the subsequent four-month holding period return residual (thus using nonoverlapping data). The return residuals are obtained by regressing the holding period return from month t to t 1 3 on the instruments Zt. Thus, the portfolio weights are assumed to be chosen using information available only at the beginning of the four-month period. None of the estimates of F p in Table IX are statistically significant at the 5 percent level.13 In sum, jointly with Table VI, we find no evidence, using the conditional covariance measure, that either the aggregate insider portfolio or the managed mutual funds earn superior returns.

VI. Conclusion

  This paper evaluates the performance of the population of insider holdings and trades on the Oslo Stock Exchange during a period with relatively lax insider regulations and enforcement. The evaluation proceeds by forming portfolios of monthly aggregate insider holdings, which reflect the insiders' actual holding periods in their respective stocks, and then subjecting these portfolios to modern techniques of performance measurement. Moreover, we compare the performance estimates for the aggregate insider portfolios to the performance of managed mutual fund portfolios on the OSE over the same time period.

  Our empirical methodology incorporates and extends recent developments
in the literature on mutual funds and our study is the first to apply these techniques to insider trades. Thus, we employ the conditional portfolio benchmark approach of Ferson and Schadt ($1996$) to produce estimates of Jensen's alpha in a world with time-varying expected excess returns. Moreover, we extend the portfolio weight approach of Cornell ($1979$) and Grinblatt and Titman ($1993$) and estimate the conditional covariance between monthly insider holdings and subsequent portfolio returns. For comparison purposes, we also perform a conditional version of the traditional event-study technique that has produced much of the important stylized facts often referred to in the public debate on insider trading regulations.

  Overall, the performance analysis rejects the hypothesis of positive abnormal performance by insiders. This conclusion appears robust to the weighting scheme and to a variety of trade characteristics, including the size and direction of the trade. Portfolio weights based on the level of insider holdings (measured using either dollar value invested or by the fraction of the firms' shares held), or sorted based on the change in insider holdings (which excludes periods of nontrading), produce statistically insignificant or negative abnormal performance.

  At first sight, this conclusion appears to contradict the findings of several empirical studies on insider trades in other markets, such as those by Seyhun ($1986$) on U.S. firms, Fowler and Rorke (1984) on Canadian firms, and Pope et al. ($1990$) in the United Kingdom. Using classical event study techniques, these studies generally find significant evidence of insiders purchases before abnormal price increases and sales before abnormal price decreases. In fact, when we apply this classical technique to our data, we find some evidence of abnormal returns over a four-month period following insider trades, primarily from sale transactions. However, it appears that this abnormal return is driven by the methodology itself: The abnormal return largely disappears in a conditional multifactor setting and when the portfolio weights are constructed to more closely mimic relative trade size. Finally, our more general performance measures also allow portfolio weights to vary through time reflecting actual insider holding periods, which appears to further eliminate evidence of abnormal performance produced by the classical event-study approach.

  Relative to the administratively centralized asset allocation decisions of mutual fund managers, the performance of the insider portfolio “suffers” from the decentralized nature of individual insiders' trading decisions. Moreover, insiders enjoying corporate control benefits from their ownership positions may optimally decide not to sell even in situations where publicly available information used by mutual fund managers dictates that such sales will increase expected returns. Thus, for insiders to receive a higher average risk-adjusted return than mutual funds, they must trade on inside information, making the comparison with mutual fund performance particularly interesting. Our results indicate that insiders on average do not outperform the average mutual fund in our sample.

  Given the extensive sensitivity analysis performed throughout this paper, our finding of statistically insignificant abnormal performance of the aggregate insider portfolio appears robust. Perhaps insiders, in a market like the OSE, only rarely possess inside information, or perhaps the value of maintaining corporate control benefits tends to offset the value of trading on such information. A further discrimination between these two alternative explanations for our finding is left for future research.