Application Closedend funds and comovement

6.1. Closed-end funds

Closed-end funds differ from more familiar open-end funds in that they only issue a fixed number of shares. These shares are then traded on exchanges: an investor who wants to buy a share of a closed-end fund must go to the exchange and buy it from another investor at the prevailing price. By contrast, should he want to buy a share of an open-end fund, the fund would create a new share and sell it to him at its net asset value, or NAV, the per share market value of its asset holdings.

The central puzzle about closed-end funds is that fund share prices differ from NAV. The typical fund trades at a discount to NAV of about 10% on average, although the difference between price and NAV varies substantially over time. When closed-end funds are created, the share price is typically above NAV; when they are terminated, either through liquidation or open-ending, the gap between price and NAV closes.

A number of rational explanations for the average closed-end fund discount have been proposed. These include expenses, expectations about future fund manager performance, and tax liabilities. These factors can go some way to explaining certain aspects of the closed-end fund puzzle. However, none of them can satisfactorily explain all aspects of the evidence. For example, management fees can explain why funds usually sell at discounts, but not why they typically initially sell at a premium, nor why discounts tend to vary from week to week.

Lee, Shleifer and Thaler (1991), LST henceforth, propose a simple behavioral view of these closed-end fund puzzles. They argue that some of the individual investors who are the primary owners of closed-end funds are noise traders, exhibiting irrational swings in their expectations about future fund returns. Sometimes they are too optimistic, while at other times, they are too pessimistic. Changes in their sentiment affect fund share prices and hence also the difference between prices and net asset values.30

This view provides a clean explanation of all aspects of the closed-end fund puzzle. Owners of closed-end funds have to contend with two sources of risk: fluctuations

30 For the noise traders to affect the difference between price and NAV rather than just price, it must be that they are more active traders of closed-end fund shares than they are of assets owned by the funds. As evidence for this, LST point out that while funds are primarily owned by individual investors, the funds' assets are not.

in the value of the funds' assets, and fluctuations in noise trader sentiment. If this second risk is systematic - we return to this issue shortly - rational investors will demand compensation for it. In other words, they will require that the fund's shares trade at a discount to NAV

This also explains why new closed-end funds are often sold at a premium. Entrepreneurs will choose to create closed-end funds at times of investor exuberance, when they know that they can sell fund shares for more than they are worth. On the other hand, when a closed-end fund is liquidated, rational investors no longer have to worry about changes in noise trader sentiment because they know that at liquidation, the fund price will equal NAV They therefore no longer demand compensation for this risk, and the fund price rises towards NAV

An immediate prediction of the LST view is that prices of closed-end funds should comove strongly, even if the cash-flow fundamentals of the assets held by the funds do not: if noise traders become irrationally pessimistic, they will sell closed-end funds across the board, depressing their prices regardless of cash-flow news. LST confirm in the data that closed-end fund discounts are highly correlated.

The LST story depends on noise trader risk being systematic. There is good reason to think that it is. If the noise traders who hold closed-end funds also hold other assets, then negative changes in sentiment, say, will drive down the prices of closed-end funds and of their other holdings, making the noise trader risk systematic. To check this, LST compute the correlation of closed-end fund discounts with another group of assets primarily owned by individuals, small stocks. Consistent with the noise trader risk being systematic, they find a significant positive correlation.

6.2. Comovement

The LST model illustrates that behavioral models can make interesting predictions not only about the average level of returns, but also about patterns of comovement. In particular, it explains why the prices of closed-end funds comove so strongly, and also why closed-end funds as a class comove with small stocks. This raises the hope that behavioral models might be able to explain other puzzling instances of comovement as well.

Before studying this in more detail, it is worth setting out the traditional view of return comovement. This view, derived from economies without frictions and with rational investors, holds that comovement in prices reflects comovement in fundamental values. Since, in a frictionless economy with rational investors, price equals fundamental value - an asset's rationally forecasted cash flows discounted at a rate appropriate for their risk - any comovement in prices must be due to comovement in fundamentals. There is little doubt that many instances of return comovement can be explained by fundamentals: stocks in the automotive industry move together primarily because their earnings are correlated.

The closed-end fund evidence shows that the fundamentals-based view of comovement is at best, incomplete: in that case, the prices of closed-end funds comove even though their fundamentals do not.31 Other evidence is just as puzzling. Froot and Dabora (1999) study "twin stocks", which are claims to the same cash-flow stream, but are traded in different locations. The Royal Dutch/Shell pair, discussed in Section 2, is perhaps the best known example. If return comovement is simply a reflection of comovement in fundamentals, these two stocks should be perfectly correlated. In fact, as Froot and Dabora show, Royal Dutch comoves strongly with the S&P 500 index of U.S. stocks, while Shell comoves with the FTSE index of UK stocks.

Fama and French (1993) uncover salient common factors in the returns of small stocks, as well as in the returns of value stocks. In order to test the rational view of comovement, Fama and French (1995) investigate whether these strong common factors can be traced to common factors in news about the earnings of these stocks. While they do uncover a common factor in the earnings news of small stocks, as well as in the earnings news of value stocks, these cash-flow factors are weaker than the factors in returns and there is little evidence that the return factors are driven by the cash-flow factors. Once again, there appears to be comovement in returns that has little to do with fundamentals-based comovement.32

In response to this evidence, researchers have begun to posit behavioral theories of comovement. LST is one such theory. To state their argument more generally, they start by observing that many investors choose to trade only a subset of all available securities. As these investors' risk aversion or sentiment changes, they alter their exposure to the particular securities they hold, thereby inducing a common factor in the returns of these securities. Put differently, this "habitat" view of comovement predicts that there will be a common factor in the returns of securities that are the primary holdings of a specific subset of investors, such as individual investors. This story seems particularly appropriate for thinking about closed-end funds, and also for Froot and Dabora's evidence.

A second behavioral view of comovement was recently proposed by Barberis and Shleifer (2003). They argue that to simplify the portfolio allocation process, many investors first group stocks into categories such as small-cap stocks or automotive industry stocks, and then allocate funds across these various categories. If these categories are also adopted by noise traders, then as these traders move funds from

31 Bodurtha et al. (1993) and Hardouvelis et al. (1994) provide further interesting examples of a delinking between fundamentals-based comovement and return comovement in the closed-end fund market. They study closed-end country funds, whose assets trade in a different location from the funds themselves and find that the funds comove as much with the national stock market in the country where they are traded as with the national stock market in the country where their assets are traded. For example, a closed-end fund invested in German equities but traded in the USA typically comoves as much with the U.S. stock market as with the German stock market.

32 In principle, comovement can also be rationally generated through changes in discount rates. However, changes in interest rates or risk aversion induce a common factor in the returns on all stocks, and do not explain why a particular group of stocks comoves. A common factor in news about the risk of certain assets may also be a source of comovement for those assets, but there is little direct evidence to support such a mechanism in the case of small stocks or value stocks.

one category to another, the price pressure from their coordinated demand will induce common factors in the returns of stocks that happen to be classified into the same category, even if those stocks' cash flows are largely uncorrelated. In particular, this view predicts that when an asset is added to a category, it should begin to comove more with that category than before.

Barberis, Shleifer and Wurgler (2001) test this "category" view of comovement by taking a sample of stocks that have been added to the S&P 500, and computing the betas of these stocks with the S&P 500 both before and after inclusion. Based on both univariate and multivariate regressions, they show that upon inclusion, a stock's beta with the S&P 500 rises significantly, as does the fraction of its variance that is explained by the S&P 500, while its beta with stocks outside the index falls.33 This result does not sit well with the cash-flow view of comovement - addition to the S&P 500 is not intended to carry any information about the covariance of a stock's cash flows with other stocks' cash flows - but emerges naturally from a model where prices are affected by category-level demand shocks.

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