Canadian Investors and the Discount on Closed-End Funds


We explore the role of the discount on closed-end funds (CEFD) in asset pricing and test its validity as a proxy for investor sentiment in the Canadian stock market. Results show that CEFD is not a priced factor. Both cross-sectional and time-series tests confirm that stocks with different exposures to CEFD do not have significantly different average returns. CEFD does not even provide incremental explanatory power after controlling for firm characteristics and risk factors. Furthermore, CEFD fails to be a proxy for investor sentiment with no correlation to either the consumer confidence index or flows to open-ended funds.

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Fig. 1


  1. 1.

    Gemmill and Thomas (2002) derived a similar formula.

  2. 2.

    The management fees and distribution policy cannot be changed without approval by the shareholders or unitholders.

  3. 3.

    Similar evidence is produced by Brauer (1993). He showed that only 7% of the variance of a standardized measure of weekly discount and premium changes can be explained by investor sentiment as defined by DeLong et al. (1990).

  4. 4.

    Other empirical tests rely on the correlation of fund discounts with other sentiment indicators, but evidence from this perspective is still conflicting. Malkiel (1977) and Lee et al. (1991) find positive correlations between open-end fund net redemptions and CEFD in the US market. Gemmill and Thomas (2002) identify a highly significant relationship between retail flow into open-end funds and CEFD in the U.K. They support the sentiment explanation.

  5. 5.

    Bers and Madura (2000) tested closed-end fund performance persistence using various fund characteristics such as discounts, expense ratios, and size.

  6. 6.

    Pontiff (1996) measured the unhedged risk of closed-end funds using residual standard deviation from regressing excess NAV returns on the excess returns of ten open-end mutual funds.

  7. 7.

    A higher dividend yield on the fund makes arbitrage less costly since it is easier to cover the dividend obligation on the short position in the underlying assets.

  8. 8.

    Dimson and Minio-Kozerski (1999) used Sharpe’s returns-based style analysis to infer the most effective asset mix for hedging underlying assets.

  9. 9.

    We compiled the list of missing closed-end funds in Fundata by checking the funds against the closed-end fund report in, which provides an updated list of all extant Canadian closed-end funds. We choose the funds that have disclosed NAV online for more than 1 year and for which the underlying assets value was over $100 million. The sample of missing funds in Fundata may be survivorship-biased since reports only extant closed-end funds.

  10. 10.

    Since Fundata doesn’t report funds’ trading identifiers (ticker symbol or CUSIP), we matched the data from Fundata with trading data in TSX-CFMRC via fund name.

  11. 11.

    Many Canadian funds hold income trusts. Since income trusts are exchange-traded securities similar to common stocks, we consider funds holding them as equity funds. We delete the funds that invest primarily in bonds or preferred stocks and keep equity and balanced funds that contain both equity and fixed-income securities. Discounts on country funds may reflect change in the domestic price of risk or a change in sentiment in foreign countries, even if the sentiment in Canada remains constant.

  12. 12.

    Canadian closed-end funds retained in our sample take various organizational structures and issue multiple securities. For reasons of brevity, we use the conventional term “common shares” to denote shares for traditional investment corporations, “capital shares” for split-share corporations, “units” for investment trusts, and “L.P. units” for limited partnerships.

  13. 13.

    The annual growth rate of closed-end funds in Canada since 1998 is over 30% (see the closed-end funds report of Investor Economics, 2006) and, as of May 2008, 239 closed-end funds are traded on the TSX (

  14. 14.

    This process may lead to biases since the NAVs of capital shares are reported as the NAV of the underlying portfolio less the par value, rather than the market value, of preferred shares. In a subsequent statistical analysis, we use a subsample with split-share funds excluded and find similar results.

  15. 15.

    The results are not tabulated but available from the authors upon request.

  16. 16.

    We also construct equal-weighted discount indices and indices based on the levels of discounts and find that the results are qualitatively similar.

  17. 17.

    The results of the FF3 alphas for Canadian closed-end funds are similar to those of FF3 plus momentum alpha and so are not reported.

  18. 18.

    We thank the referee for suggesting this approach.

  19. 19.

    All unreported results in this section are readily available from the authors upon request.

  20. 20.

    See Gompers and Metrick (2001), Pritsker (2002), Nagel (2005), and Agarwal (2009).

  21. 21.

    Many Canadian companies issue multiple classes of common shares, normally with different voting rights. Our definition of size and book-to-market implies that different classes of common shares of a company have the same size and book-to-market ratio.

  22. 22.

    This definition implies that different classes of common shares for a company might have different momentums. Furthermore, we use a 1-month lag to measure momentum because the bid-ask bounce can attenuate the continuation effect (Jegadeesh and Titman 1993, 1995; Moskowitz and Grinblatt 1999; Jegadeesh and Titman 2001).

  23. 23.

    We also construct the three factors by orthogonalizing each term with the others for the purpose of better disentangling the effects of these factors, and we find similar results.

  24. 24.

    The companies that report their asset values as market values (e.g., ETFs, closed-end funds, etc.) are excluded because their book-to-market ratios are not available or, if available, they do not reflect the same information as those of ordinary companies.

  25. 25.

    The monthly returns of the ten intersectional portfolios and three mimicking portfolios related to size, book-to-market, and momentum factor in Canada over July 1999 to December 2007 are not presented but are available from the authors.


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Correspondence to Mohamed A. Ayadi.

Appendix A: Pricing factors construction

Appendix A: Pricing factors construction

Following prior studies, we define or calculate the firm characteristics as follows: market value of common equity (ME) or firm size is defined as the aggregate market value of all classes of common equities issued by a company; book value of common equity (BE) is calculated as the Compustat North America book value of stockholders’ equity, plus balance-sheet deferred taxes and investment tax credit (if available), less the book value of preferred stockFootnote 21; and momentum (prior performance) is gauged by compounding the return over prior 6 months with a 1-month lag.Footnote 22 Our sample consists of 1074 Canadian common stocks with the required characteristics at each month, so it provides a reliable and comprehensive dataset with which to construct mimicking portfolios.

Our procedure for developing the mimicking portfolios related to ME, BE/ME, and momentum is based on three independent sorts, followed by an orthogonalization of BE/ME and momentum with ME.Footnote 23 Along the lines of FF (1993), we construct portfolios that mimic the underlying risk factors in returns related to ME and BE/ME. For each June of year y, we rank all eligible common stocks in the TSX by ME to calculate a 50% breakpoint for ME and also independently rank positive BE/ME (companies that report their asset values as market value are excluded)Footnote 24 to extract 30% and 70% breakpoints for BE/ME. The common shares above the 50% firm size breakpoint are designated by B (Big), and the remaining 50% are designated by S (Small). Independently, the firms above the 70% BE/ME breakpoint are designated by H (High), the middle 40% are designated by M (Medium), and the firms below the 30% BE/ME breakpoint are designated by L (Low). Based on these attributes, the common shares in the TSX are assigned into one of the six intersectional portfolios: S/L, S/M, S/H, B/L, B/M and B/H. Using these component common shares, we calculate monthly value-weighted returns of these six intersectional portfolios from July of year y to June of year y+1 and then rebalance the portfolios. As in FF (1993), the BE/ME of a company at June of year y is the ratio of BE at the end of fiscal year y-1 to ME at the end of calendar year y-1.

The momentum factor is constructed using the approach in Kenneth French’s website. At the beginning of month t, we identify the common shares in TSX with poor prior performance (Down) and with good prior performance (Up) based on the breakpoints for the bottom and top 30% of the ranked values of the prior compounding return from month t-7 to month t-2. We also independently split the common shares in the TSX into big and small ME groups using the 50% breakpoint for ME. Using these attributes, we assign the common shares in TSX to one of the four intersectional portfolios-S/D, S/U, B/D, and B/U-to calculate value-weighted returns at month t for these portfolios, and the mimicking portfolios are rebalanced monthly.

Using the monthly returns of these ten intersectional portfolios, we calculate the monthly returns of three mimicking portfolios for the underlying risk factors with the following formulasFootnote 25:

$$ {\text{SMB}} = \frac{{{\text{(S/H}} - {\text{B/H)}} + {\text{(S/M}} - {\text{B/M)}} + {\text{(S/L}} - {\text{B/L)}}}}{3} $$
$$ {\text{HML}} = \frac{{{\text{(S/H}} - {\text{S/L)}} + {\text{(B/H}} - {\text{B/L)}}}}{{2}} $$
$$ {\text{UMD}} = \frac{{{\text{(S/U}} - {\text{S/D)}} + {\text{(B/U}} - {\text{B/D)}}}}{{2}} $$

where SMB (small minus big) denotes the return of a zero-investment portfolio in which small-size stocks are bought and big-size stocks are shorted; HML (high minus low) is the return of a zero-investment portfolio in which stocks with high book-to-market ratio are bought and stocks with low book-to-market are shorted; And UMD (up minus down) represents the return of a zero-investment portfolio in which stocks with good prior performance are bought and stocks with poor prior performance are shorted.

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Ayadi, M.A., Ben-Ameur, H., Lazrak, S. et al. Canadian Investors and the Discount on Closed-End Funds. J Financ Serv Res 43, 69–98 (2013).

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  • Closed-end funds
  • Investor sentiment
  • Cross-sectional regressions

JEL classification

  • G11
  • G12
  • G15