Persistent Mispricing in Mutual Funds: The Case of Real Estate

Transcription

1 Persistent Mispricing in Mutual Funds: The Case of Real Estate Lee S. Redding University of Michigan Dearborn March 2005 Abstract When mutual funds and related investment companies are unable to compute an accurate net asset value, unintended wealth transfers will occur between buyers, sellers, and long-term investors in the funds. Previous research has found this effect to be limited to daily horizons. By focusing on an investment account involved with direct real estate ownership, we find evidence that this same phenomenon can occur on monthly frequencies as well. By comparing this situation to those analyzed previously, we are able to estimate the magnitudes of the asset mispricing and resulting wealth transfers. JEL Classifications: G23, G12, G14 Department of Accounting and Finance, University of Michigan Dearborn, Dearborn, MI Voice/fax

2 Persistent Mispricing in Mutual Funds: The Case of Real Estate March 2005 Abstract When mutual funds and related investment companies are unable to compute an accurate net asset value, unintended wealth transfers will occur between buyers, sellers, and long-term investors in the funds. Previous research has found this effect to be limited to daily horizons. By focusing on an investment account involved with direct real estate ownership, we find evidence that this same phenomenon can occur on monthly frequencies as well. By comparing this situation to those analyzed previously, we are able to estimate the magnitudes of the asset mispricing and resulting wealth transfers. JEL Classifications: G23, G12, G14 1 Introduction Open-end investment companies must compute a net asset value each business day. This serves as the basis for the price at which investors buy and sell shares. Since the counterparty for investor transactions in such a fund is the fund itself, inaccuracies in valuing the assets of the fund will result in unintended wealth transfers between trading fund investors and those investors who are more passively invested in the fund. Most U.S. fund assets are valued at the close of trading on the New York Stock Exchange, which occurs at 4:00 PM New York time. The standard method to value assets is to use the price at which the asset last traded. If some time has elapsed since the last trade, this presents the possibility for inaccuracies in the valuation of assets. For example, a stock trading only on the Tokyo Stock Exchange, which closes at 1:00 AM New York time, would not have traded for 15 hours. An investment company which does not address this issue leaves itself open to short-term traders profiting at the expense of the fund. News which occurs between 1:00AM and 4:00PM will not be reflected in the valuation of the Japanese stock. Investors who realize there has been positive news (for example, European and American stock prices increased that day) can buy the mutual fund at 1

3 an artificially low price and sell it the next day. This process generates a very high expected rate of return with relatively low risk, as documented by Boudoukh et al [2]. Authors including Bhargava, Bose, and Dubofsky [1] and Goetzmann, Ivković, and Rouwenhorst [6] have shown that implementing such strategies can generate high positive returns over time. Greene and Hodges [7] examine the effect of these strategies on more passive fund investors, and have found a potential loss of up to 100 basis points annually for some international funds. To alleviate these costs, fund managers have taken two main tactics. First, restrictions have been placed on short-term traders. However, as Chalmers, Edelen, and Kadlec [3] find, these restrictions are not always enforced. Second, fair value pricing values assets using information other than the last trade price, and thus can eliminate the short-term arbitrage opportunity. As Zitzewitz [11] and Redding [8] find, however, these fair value tactics are frequently not employed despite the low apparent cost of doing so. The previous research has focused on high-frequency (generally daily) data in which the mispricing is eliminated in expectation by the next valuation day. Here, we expand the scope of the research to a situation where the mispricing is persistent. We do this by examining a fund which has a large fraction of its assets invested directly in real estate. The frequency with which a given real estate property will trade in the market is given in years rather than hours. Therefore, the stale price phenomenon experienced for international stocks is potentially increased by orders of magnitude (along the time dimension) in the case of real estate. 2 The TIAA Real Estate Account The TIAA Real Estate Account is a variable annuity with assets of $7 billion open primarily for the retirement savings of participants in TIAA-CREF. It was established in 1995 and has the majority of its funds directly invested in real estate. The Account is very similar to an open-end mutual fund in that it must establish a unit value each business day to enable participants to buy or sell accumulation units in the Account. Eligible participants are currently able to buy or sell at this unit value without paying fees to the Account or to TIAA. It therefore faces a severe challenge in terms of determining high-frequency prices for assets which trade very infrequently. A primary difference between this Account and an open-end mutual fund is that this account is 2

4 Accumulation Units (000) Unit Value $ $ $ $ $ Increase in Units 95.04% 62.80% 33.29% 26.11% Holding Period Return 8.33% 10.07% 8.07% 8.17% Accumulation Units (000) Unit Value $ $ $ $ $ Increase in Units 23.90% 23.30% 9.75% 19.42% 21.76% Holding Period Return 10.66% 6.29% 3.41% 7.50% 12.57% Amounts are as of year-end except for the accumulation units value for 2004, which is September 30. Increase in accumulation units is as a percentage of the average of the levels at the beginning and end of the period. Table 1: TIAA Real Estate Account Accumulation Units a variable annuity open only to retirement accounts. Whereas a mutual fund pays distributions to its shareholders consisting largely of taxable income, the Real Estate Account pays no distributions. Income accrues to the investors in the form of a rise in the value of each Accumulation Unit. 1 The holding period return to an investor, which we have shown in Table 1, is therefore simply the percentage change in the value of a unit. Similarly, we can therefore look at changes in the number of Accumulation Units as the net result of buy and sell decisions of investors, without having to adjust for reinvested distributions. We will be interested in the potential dilutive effects of trades during period t on those investors already in the account at the beginning of period t. Partofthis dilutive effect is felt by investors who buy during period t. In Table 1, we therefore calculate the percentage change in accumulation units as the change relative to the approximate average level of units during period t: % AU t = AU t AU t 1 (AU t + AU t 1 )/2 (1) The Account was opened to investors in October Due to the time involved in finding suitable properties, as Table 2 shows, the Account was initially largely invested in cash equivalents. The Account s prospectus ([10], page 3) describes an investment strategy of investing between 70 and 95 percent of assets in real estate related investments. The principal strategy is direct 1 The capital structure of this Account includes an Annuity Fund in which those receiving payments in the form of an annuity experience the investment returns of the Account. The Fund is created so that owners of Accumulation Units and the annuity fund participate pro-rata in the investment results of the Account. 3

5 Asset Type Real Estate Properties $44 $132 $521 $820 $1313 REITs Other Real Estate Cash Equivalents Total Investments $118 $368 $801 $1211 $1687 Asset Type Real Estate Properties $1925 $2359 $3517 $4262 $5588 REITs Other Real Estate Cash Equivalents Total Investments $2389 $3226 $3800 $5058 $6855 Amounts are as of year-end except for 2004, which is September 30. Values are in millions of dollars. Real estate properties include joint ventures. Other Real Estate includes collateralized mortgage obligations and partnerships. Cash equivalents refers to short-term debt securities, some maturing in over one year. Table 2: TIAA Real Estate Account Assets ownership of real estate. Consistent with this mandate, the Fund s asset allocation fluctuates from year to year. Approximately 80% is held in direct property ownership, 5% in real estate investment trusts, and 15% in cash equivalents. The fund s direct property holdings are mostly unleveraged. Cash equivalents and other marketable securities can be valued fairly readily, but the direct property investment is a greater problem. The prospectus for the Account ([10], page 47) calls for each property to be appraised externally on an annual basis. The valuation of each property is reviewed internally on a quarterly basis to determine whether the most recent appraisal still represents a fair value for the property. Each property is normally carried at the amount of the last appraisal or review, although the Account reserves the right to conduct other revisions. As a result, a large portion of the Account s assets may have carrying values used to compute each day s unit value which are based on old market assessments. If this is the case, we should be able to derive a statistical test which will detect the resulting patterns in the reported unit values of the Account. 4

6 3 Testing for Valuation Inefficiency First, we develop a general model to enable us to test for pricing efficiency in a mutual fund with a substantial investment in illiquid assets. Consider a mutual fund which is invested in three sectors. A fraction α M of its capital is allocated to investments in marketable securities which generate (risky) returns M t in each period t. A further fraction α D of its capital is allocated to direct investments. Returns to these assets are not continuously observable due to the lack of an active market with current prices. However, the fund managers are able to value each asset in the portfolio on a rotating basis every k periods. The residual (1 α M α D ) is taken to be invested in a safe asset with return S t. These funds are reallocated each period to maintain the target portfolio shares. The allocation to direct investments is an investment in a large number n of individual illiquid investments. In each period, each direct investment i experiences a return D t + η it which is the combination of a common component D t and an idiosyncratic component η it,wheretheη it terms are independently and identically distributed normal variables with zero mean. Because there are a large number of investments, realizations of η it do not affect the aggregate portfolio return. However, the manager is required to value each asset according to its most recent valuation. In each period t, then, a fraction (k 1) k of the direct investments will experience zero observed return. The direct investments which are valued, however, were last valued in period t k andsowhenvalued in period t the cumulative 2 return is k 1 i=0 D t i. The observed return to the direct investments is therefore the fraction of direct investments valued in the period multiplied by the observed return to the newly valued assets. k 1 1 D t i (2) k i=0 The observed rate of return to the portfolio is therefore k 1 1 R t = α M M t + α D D t i +(1 α M α D )S t (3) k i=0 2 We adopt the first-order approximation that the total return is the additive sum of the period returns, given the relatively high frequency of the data. 5

7 Lagging this one period gives R t 1 = α M M t 1 + α D 1 k k D t i +(1 α M α D )S t 1 (4) i=1 Note that the correlation between R t and R t 1 derives from the fact that they have k 1 realizations of the D term in common. Direct investments valued in periods t and t 1each experience as part of their observed returns the unobservable components D t 1 through D t k+1. Given the high expected correlation between the returns of the two periods, we will likely find stronger empirical results by focusing on the innovation to the reported returns. Finding the difference between the previous two equations gives: R t R t 1 = 1 α M (M t M t 1 )+α D k (D t D t k )+(1 α M α D )(S t S t 1 ) (5) R t = 1 R t 1 + α M (M t M t 1 )+α D k (D t D t k )+(1 α M α D )(S t S t 1 ) (6) In equation (6), the terms D t and D t k are not directly observable. Restricting equation (6) to its observable components gives: R t = R t 1 + α M (M t M t 1 )+(1 α M α D )(S t S t 1 ) (7) It is quite likely that an investment fund has a certain focus. As a result, we would expect the underlying return D t +η it to each direct investment to be correlated with the return M t on marketable assets. Therefore including M t in an empirical test without including D t creates the possibility of omitted variable bias. We will therefore sometimes choose to restate the right side of equation (7) with market values observable at time t 1. Returns on the safe asset S t, on the other hand, are unlikely to face the same correlation problem and can more safely be included. Another equation which can therefore be estimated to test the proposal that the fund is not valuing its assets in a timely way is therefore R t = β 0 + β R R t 1 + β M M t 1 + β S (S t S t 1 ) (8) where we would expect β M = α M < 0 based on equation (6). We further expect β R > 0 due 6

8 to the common components of each period s observed return, as described above. Further, we expect β S =(1 α M α D ) > 0, providing that the returns on safe assets are uncorrelated with other assets in the portfolio. Alternatively, if returns on the fund s other investments are positively (negatively) correlated with innovations in the short-term interest rate, we would expect a lower (greater) coefficient on β S. Alternatively, if we take the view that using the contemporaneous return S t is problematic, we can regress R t purely on lagged values: R t = β 0 + β R R t 1 + β M M t 1 + β S S t 1 (9) Here, we would still likely expect coefficient β R to be positive reflecting the lagged assessment values of the illiquid assets, and β M = α M. The likelihood that short-term interest rates are strongly autocorrelated at reasonably high frequencies, however, will mean that the estimate β S will suffer from some omitted variable bias. β S will here represent the general level of short-term interest rates, rather than the innovations to short-term interest rates called for in equation (6). 4 Empirical Results To test equation (8) in the context of the TIAA Real Estate account, we have gathered data for the monthly returns from July 1996 through January We do not have continuous data on the shares on each type of asset, but we note that taking a simple average of the percentage holdings for each report shown in Table 2 suggests a 5.43% holding in REITs. Equation (8) suggests that if the TIAA Real Estate unit values are being determined using stale pricing, their returns should be positively autocorrelated, but also negatively correlated with the lag of the accurately-priced portion of their portfolio and positively correlated with changes in the yield on their cash-equivalent holdings. Since most of the marketable securities held by the Account are real estate investment trusts, we use the Vanguard REIT Index Fund monthly total returns as a proxy for returns on these assets. The Vanguard REIT Index Fund, as its name implies, is not actively managed, and provides a good representation of the returns to REITs. For the returns on safe assets we use returns on CREF s own money market fund. All returns are computed from the end of one calendar month to the end 7

9 of the next calendar month. We can then rewrite the generic form (8) as: TIAA t = β 0 + β 1 TIAA t 1 + β 2 REIT t 1 + β 3 (MMKT t MMKT t 1 )+ɛ t (10) The results of this regression are shown in Table 3. Note that in equation (10) we have suppressed those variables not observable at time t 1, with the exception of the return on a money market fund. This latter element is likely to be largely predictable one month ahead. This is due to both the short-term predictability of Federal Reserve policy and also due to accounting rules for money market funds. Under these rules, short-term debt securities are valued by money market funds (including the CREF Money Market Fund) at amortized cost rather than market value. Posted returns are therefore partially a lagged function of market returns. Column 6 of Table 3 shows the estimation of equation (10). Our expectations were for a positive sign on TIAA t 1 reflecting the delays in assessing the values of direct investments, a negative sign with a magnitude approximating the portfolio share of REITs for the coefficient on REIT t 1 and a positive coefficient on the money market term. Indeed, the estimated coefficient on REIT t 1 (0.0453) is very near to the portfolio share (0.0543) derived from Table 2. The relatively high value of the coefficient on innovations to the interest rate may be due to other interest-sensitive components of the portfolio. As an example, the fund stands to gain from a rise in interest rates to the (limited) extent that its real estate holdings are financed with fixed rate mortgages. Other columns of Table 3 provide alternative specifications of the relationship specified in equation (10). In each specification where the investment performance of REITs is controlled for, the coefficients both on the lagged return of the Account itself and the lagged return on REITs are remarkably stable across specifications and statistically significant. Comparing column 1 to the later columns, we can see that it is indeed necessary to control for the performance of the marketable REITs in order to bring out the autocorrelation in the direct property investments. This autocorrelation is the result of the fact that innovations to the actual property values in one month are only gradually incorporated into the valuations of all of the properties held by the Accounts, as each property comes up in turn for its annual appraisal. To control for any possibility that some other feature of real estate investment would generate 8

10 TIAA t ** ** ** ** ** (0.1003) (0.1242) (0.1302) (0.1311) (0.1282) (0.1216) REIT t ** ** ** ** ** (0.0122) (0.0126) (0.0127) (0.0125) (0.0120) MMKT t * (0.2234) (0.9332) MMKT t * (0.2257) (0.9400) MMKT t MMKT t * (0.9258) Constant ** ** ** ** ** ** (0.0008) (0.0008) (0.0010) (0.0010) (0.0009) (0.0008) Adj. R DW Notes: The dependent variable is the period t monthly return on the TIAA Real Estate account. Independent variables include the lagged return on this Account, the lagged return on the REIT index fund, and returns on the money market fund. Standard errors are in parentheses. Single asterisk denotes significance at the 5% level, double asterisk denotes significance at the 1% level. DW is the Durbin-Watson statistic. Table 3: TIAA Real Estate Monthly Returns these results spuriously, we have run regressions for each specification in Table 3 with the roles of the REIT Index fund and the TIAA Real Estate Account reversed. Since the calculated asset value of the REIT Index fund is based entirely on daily market trades, it is subject to all the risks of real estate investing but not to the phenomenon of outdated assessments. These alternative regressions (not shown) provide no statistically significant results, and thereby validate the reported results in Table 3 as being economically meaningful. Table 4 includes contemporaneous returns of the REIT Index Fund, and thereby brings our equation closer to that presented in equation (7). Specifically, we are now testing TIAA t = β 0 + β 1 TIAA t 1 + β 2 (REIT t REIT t 1 )+β 3 (MMKT t MMKT t 1 )+ɛ t (11) This is as close to equation (6) as can be estimated without access to the unobservable innovations D t to the true value of the direct investments. Our prediction is still that β 2 will have a value approximating the share of REITs in the portfolio but now with a positive sign. Column 6 in Table 4 shows the test of equation (11). The coefficient on REIT returns is even closer than in the 9

11 TIAA t ** ** ** ** ** (0.0787) (0.0801) (0.0806) (0.0765) (0.0748) REIT t REIT t ** ** ** ** ** (0.0052) (0.0052) (0.0053) (0.0050) (0.0050) MMKT t ** (0.1539) (0.6416) MMKT t ** (0.1551) (0.6420) MMKT t MMKT t ** (0.6370) Constant ** ** ** ** ** (0.0006) (0.0007) (0.0007) (0.0007) (0.0006) Adj. R DW Notes: Column numbering done to be consistent with Tables 3 and 5 The dependent variable is the period t monthly return on the TIAA Real Estate account. Independent variables include the lagged return on this Account, returns on the REIT index fund, and returns on the money market fund. Standard errors are in parentheses. Single asterisk denotes significance at the 5% level, double asterisk denotes significance at the 1% level. DW is the Durbin-Watson statistic, and in each case fails to reject no serial correlation of the errors using both 5% critical values. Table 4: TIAA Real Estate Monthly Returns and Innovations to REIT Returns previous table to the predicted value of , and the coefficients on lagged returns of the Real Estate Account are still in the area of one-half. Durbin-Watson tests have again been conducted to test for serial correlation. As is well known, the Durbin-Watson tests have an expected value of 2 under the null hypothesis of no serial correlation. There are two sets of critical values to test this hypothesis. Using the stricter condition of the inner critical values, we still do not reject of the null hypothesis of serial correlation at the 5% level. The relevant critical values for Table 4 range from 2.24 to To address a slight concern with serial correlation in Table 4, we remove the restriction that the coefficients on contemporaneous and lagged REIT returns must be the same magnitude. We therefore estimate TIAA t = β 0 + β 1 TIAA t 1 + β 20 REIT t + β 21 REIT t 1 + β 3 (MMKT t MMKT t 1 )+ɛ t (12) Contemporaneous REIT returns may be correlated with the unobservable contemporaneous innovation D t to the underlying values of Real Estate Account directly held property. Since this effect 10

12 TIAA t ** ** ** ** ** ** (0.0755) (0.0876) (0.0905) (0.0918) (0.0874) (0.0839) REIT t ** ** ** ** ** ** ** (0.0072) (0.0064) (0.0063) (0.0064) (0.0061) (0.0061) (0.0073) REIT t ** ** ** ** ** (0.0085) (0.0087) (0.0089) (0.0085) (0.0082) MMKT t ** (0.1553) (0.6352) MMKT t ** (0.1581) (0.6400) MMKT t MMKT t ** (0.6358) Constant ** ** ** ** ** ** ** (0.0006) (0.0006) (0.0007) (0.0007) (0.0007) (0.0006) (0.0003) Adj. R DW Notes: The dependent variable is the period t monthly return on the TIAA Real Estate account. Independent variables include the lagged return on this Account, the returns on the REIT index fund, and returns on the money market fund. Standard errors are in parentheses. Single asterisk denotes significance at the 5% level, double asterisk denotes significance at the 1% level. DW is the Durbin-Watson statistic, and fails to reject no serial correlation at the 5% level for specifications 2 through 6. Table 5: TIAA Real Estate Monthly Returns and Contemporaneous REIT Returns was not incorporated into the derivation of equations (6) and (11), we may expect to estimate β 20 > β 21. In table 5, we see that indeed the parameter estimates are substantially the same as in Table 4. As we expected, the coefficients on contemporaneous REIT returns are indeed greater in magnitude than the coefficients on lagged REIT returns. The parameter estimates, however, are each still in the expected area. The parsimonious specifications in columns 1 and 7 show strong evidence of positive serial correlations. The other columns, however, have very comforting Durbin-Watson statistics. In particular, column 6, which estimates equation (12) directly, has a statistic of Magnitude of the Mispricing We can get an approximate idea of the magnitude of the mispricing caused by these periodic appraisals by looking at a similar problem studied in the literature involving a property index. The index in question is maintained by the National Council of Real Estate Investment Fiduciaries 11

13 (NCREIF). This NCREIF Property Index (NPI) is a cumulative total return index for direct, unleveraged investment in commercial property in the United States. Construction of the NPI therefore involves the same problem we have confronted here determining the value of commercial real estate which is generally assessed only annually. Geltner and Goetzmann [5] use property-level data to develop an estimate of the current values. Fu [4] shows that the resulting Current Value Index (CVI) has less autocorrelation than the uncorrected NPI. In short, the NPI acts as a moving average of recent returns, just as we found in equation (3). The NPI is therefore smoother than the underlying values, has added autocorrelation in returns, and is a lagged indicator of actual market values. Using Geltner and Goetzmann s sample period of 1977 through 1997 and equating the sample means of the NPI and the CVI, we find that the mean absolute difference between the two indices is on the order of 1.5%. We take this as a rough estimate of the mean error resulting from valuing U.S. commercial real estate using the periodic assessment method common to the NPI and the TIAA Real Estate Account. We must multiply this by the fraction of the Account invested directly in real estate. Table 2 shows that in the early years a relatively small fraction of the Account was invested, but has been stable at around 80% since (The mean percentage since 1999 is 81.64%). Multiplying these two gives an average pricing error to the Account of approximately 120 basis points. 6 Arbitrage Opportunities The literature on mutual fund mispricing discussed earlier focused on daily frequencies. In these studies, delays of hours between the last trade of the fund assets and the 4:00 pricing of the mutual fund created a trading opportunity. Since in expectation this mispricing would be entirely eliminated by the next trading day, this created an opportunity for investors to profit at the expense of the passive fund shareholders by trading on a daily basis. The effect of delayed assessed values in the TIAA Real Estate Fund is less subject to such shortterm trade. Summers [9] points out that even if a major financial market is mispriced, if the rate of mean reversion is sufficiently slow it is difficult for analysts to identify the mispricing and even more would-be speculators to take advantage of this information. In our case, we have seen that 12

14 the time scale of the mispricing is short enough that we can detect it statistically. However, it does not lend itself to the sort of day-trading tactics such as that described by Goetzmann, Ivković, and Rouwenhorst [6] since the mispricing is not undone in a short period. Further, TIAA does place strong restrictions on short term trading from this Account. The Account is therefore unlikely to suffer the substantial losses to short-term speculators that some international mutual funds have evidently suffered. However, this mispricing still has real effects. In any given period, the mispricing will involve transfers first between those buyers and sellers of units whose trades match, and second transfers between the net buyers or sellers of units and the long-term investors in the Account. Even after the rapid percentage growth after the inception of the Account, the Account has shown strong net purchases of Accumulation Units. Between 1999 and 2003, Table 2 shows that on average accumulation units have grown at an arithmetic average of 20.5% per period. Since Account returns have been positive in recent years, the wealth transfers mentioned above will be from sellers to buyers, and from long-term investors to net buyers. The 120 basis point mispricing is an estimate of the transfer from buyers to sellers. Annually selling 20% of units at a 120 basis point discount means that long-term investors suffer an annual dilution loss of 24 basis points. This cost to long-term investors is substantial. However, it is significantly less than the losses suffered by international mutual funds as a result of short-term arbitrage. Enhanced use of fair value pricing, involving updating the valuations of all properties based on the information contained in each partial monthly set of assessed values, could substantially reduce these transfers. 7 Conclusion By exploring the TIAA Real Estate Account, we have been able to expand the literature on mutual fund mispricing. With direct real estate investments, mispricing is persistent over a period of months rather than simply overnight. This mispricing has real effects, as it causes unintended wealth transfers between buyers, sellers, and long-term holders of units in the Account. Over the period studied long-term shareholders may have lost approximately 24 basis points in annual return through the dilutive effect of selling underpriced units to new investors. 13

15 References [1] Bhargava, Rahul, Anne Bose, and David A. Dubofsky, Exploiting International Stock Market Correlations With Open-End International Mutual Funds, Journal of Business, Finance, and Accounting, 25, 1998, pp [2] Boudoukh, Jacob, Matthew P. Richardson, Marti Subrahmanyam, and Robert F. Whitelaw, Stale Prices and Strategies for Trading Mutual Funds, Financial Analysts Journal, 58, 2002, pp [3] Chalmers, John, Roger Edelen, and Gregory Kadlec, On the Perils of Security Pricing by Financial Intermediaries: The Wildcard Option in Transacting Mutual-fund Shares, Journal of Finance, 56, 2001, pp [4] Fu, Yuming, Estimating the Lagging Error in Real Estate Price Indices, Real Estate Economics, 31, 2003, pp [5] Geltner, David, and William Goetzmann, Two Decades of Commercial Property Returns: A Repeated-Measures Regression-Based Version of the NCREIF Index, Journal of Real Estate Finance and Economics, 21, 2000, pp [6] Goetzmann, William N., Zoran Ivković, and K. Geert Rouwenhorst, Day Trading International Mutual Funds: Evidence and Policy Solutions, Journal of Financial and Quantitative Analysis, 36, 2001, pp [7] Greene, Jason T. and Charles W. Hodges, The Dilution Impact of Daily Fund Flows on Open-end Mutual Funds, Journal of Financial Economics, 65, 2002, pp [8] Redding, Lee S. The Stale Price Toolbox, Finance Letters, 2, 2004 [9] Summers, Lawrence H., Does the Stock Market Rationally Reflect Fundamental Values?, The Journal of Finance, 41, 1986, pp [10] Teachers Insurance and Annuity Association, TIAA Real Estate Account Prospectus, 2004 [11] Zitzewitz, Eric, Who Cares About Shareholders? Arbitrage-Proofing Mutual Funds, Journal of Law, Economics, and Organization, 19, 2003, pp