Summary and Discussion – Chapter 9 – Investing in Investment Funds
Notes on The Intelligent Investor by Benjamin Graham
Notes by Jason Fernando
Created December 19th, 2013
Last updated January 6th, 2014
Reference document: Graham, Benjamin, and Jason Zweig. The Intelligent Investor. Rev. ed. New York: HarperBusiness Essentials, 2003.
- There are a wide variety of investment funds, each with unique advantages and disadvantages.
- Funds differ with respect to their goals, strategies, tax implications, and in other respects.
- Methods for assessing the value of a given fund will differ depending on the nature of the fund in question.
Thus far, Graham has focused on methods by which individual investors can best go about the process of selecting individual stock and bond investments for their personal portfolio. This hands-on approach is likely to appeal to those “enterprising” investors who have the time, temperament, or inclination to devote to developing the habits necessary to doing this well. There are, however, a whole classification of investors who have no such inclination. Is it necessary for such individuals to will themselves to manage their own portfolios?
The answer, as detailed in this chapter, is a qualified no. The investment funds industry, whereby individuals can invest in professionally managed portfolios (as well as some which are not actively managed), offers an alternative whereby the investor can participate in financial markets without needing to be solely responsible for the research and oversight of her portfolio. However, just as in the case of managing one’s own investments, it is necessary to weigh a variety of considerations in selecting the funds in which to invest. Let’s start, though, at the beginning.
What are investment funds?
Investment funds come in a variety of forms, so it is impossible to give a precise definition of the term “investment fund” which would apply accurately in all cases. At a basic level, however, an investment fund is an investment product which offers investors the ability to gain exposure to a variety of securities through one investment vehicle. For example, Investor A might invest $5,000 in a fund called Investment Fund B. This fund consists of 10 companies, and is actively managed. What this means in essence is that Investor A has now invested in each of those 10 companies which comprise Investment Fund B, but in doing so she has only had to make the one investment into Investment Fund B. If we assume that Fund B has invested equally in each of its 10 companies, then Investor A would end up with a $500 investment in each of the Fund’s 10 companies ($5,000 10 companies = $500 per company). The fact that the fund is “actively managed” means that a professional money manager is in charge of overseeing the fund, selecting the companies which it should include, and deciding when and in what quantity to buy and sell the shares in those companies.
By placing her money in this investment fund, Investor A has gained exposure to financial markets without having had to go through the trouble of researching and investing in a variety of individual companies. Moreover, in our example she has also invested in a fund with active management, meaning that she may have reason to believe that her funds are being well managed. Assuredly, this may not actually be the case, as fund managers routinely perform worse than the broad market (more on that later). Moreover, the assumption that having one’s funds managed by an external “professional manager” is an advantage is rational if and only if this manager has superior skill, time, experience, and/or temperament than yourself. History demonstrates that none of these qualities can necessarily be taken for granted.
The primary disadvantage of investing through investment funds is that there is a reasonably high probability of spending too much for too little. This is due to the fees charged by all funds, which consistently eat away at the fund’s returns. The following chart, derived from the US Financial Industry Regulatory Authority (FINRA)’s Fund Analyzer service, estimates the hypothetical returns on investment (ROIs) offered by three funds, each focusing on the US stock market. In this chart, the SPDR S&P 500 ETF, which is not actively managed and which strives only to reflect (rather than exceed) the performance of the S&P 500 index, noticeably outperforms its counterparts over the 20 years here observed. Due to the fact that it is not actively managed, the SPDR S&P 500 ETF charges a very low management fee of 0.09% per year as compared to the 1.5% fee of the Knowledge Leaders fund and the 1.28% fee of the Queens Road fund, respectively. This chart is but one hypothetical rendering of this phenomenon, based on a more-or-less random selection of funds. Readers can perform their own experiments using FINRA’s Fund Analyzer service online at http://apps.finra.org/fundanalyzer/1/fa.aspx.
Types of Investment Funds
→ Open Funds
Open, or “open-ended” funds, are a type of investment fund whereby the fund manager can create new shares to sell to investors. Similarly, the fund manager can also buy back shares from investors in the event that they wish to sell their shares in the fund. In theory, there is no legal limit to the number of shares which an open-ended fund can issue. Therefore, an open-ended fund can have an indefinite number of investors. More information, courtesy of KhanAcademy.org.
→ Closed Funds
Closed, or “closed-end” funds are a type of investment fund whereby the total number of shares is pre-determined and cannot be increased beyond that pre-determined figure. Thus a closed fund with 100 shares can have no more than 100 shares in circulation. The second major characteristic of closed-end funds is that investors cannot sell their shares back to the fund manager; instead, they must sell their shares to other investors such that the total number of shares never changes. More information, courtesy of KhanAcademy.org.
→ “Passive” vs. “Active” Funds
A “passive” or “passively managed” fund is one which is not managed by a fund manager or team of managers. Instead, it simply tracks the performance of a given set of investments such as a group of stocks and/or bonds without changing the composition of this “set of investments” over time. Usually, this is achieved by tracking an index. For example, the SPDR S&P 500 ETF is a passive investment fund which tracks the performance of the S&P 500 index, which is a set of prominent US companies compiled by the credit rating agency Standard & Poore’s. An “active” or “actively managed” fund is—not surprisingly—one which is managed by a fund manager or team of managers. These managers extract a fee to compensate themselves for overseeing the fund, and in exchange they take responsibility for managing (i.e. buying, selling, researching) the money invested in the fund.
The core argument in favour of active management is that, at least in theory, skilled money managers can maximize the financial return of the fund while minimizing its risks. A passive fund, on the other hand, has no such human oversight and is therefore entirely at the mercy of the underlying market which it tracks, come boom or bust! The core argument against active management is that it is expensive, usually involving a 1 to 2% management fee per year. What this means is that a given active fund with, say, a 2% management fee must at least exceed the performance of the broad market by 2% in order to distinguish itself from a competing passive fund. Moreover, there is also the very real risk that the money manager in question may be tempted into taking on more risk than you are comfortable with in their efforts to produce these above-average returns. Consider the scenario from the fund manager’s perspective: Your financial compensation increases in line with the performance of the fund, meaning that generating high returns is your primary means of increasing your own bottom line through fees and bonuses. Some (though surprisingly, all too few) of your fund’s investors are aware of the fact that your 2% management fee is justified if and only if you can exceed the performance of the broad market by at least 2%. You, as fund manager, are therefore financially and socially encouraged to maximize returns beyond the level of the broad market. How is one to do this? Often, managers pursue above-average returns simply by betting on investments with above-average risk. This can work well in the short term—securing fees, praise, and bonuses for the manager—but it is disastrous in the long-term. A consistent policy of pursuing higher returns through systematic risk-taking is simply likely (in the strict probabilistic sense of the term) to fall apart in due time. Given the mathematics of losses, whereby a loss of 50% requires a subsequent gain of 100% simply to retrace the prior loss, this strategy is akin to that of a gambler who consistently pits himself against the odds of the house.
→ Broad Market vs. “Sector” Funds
A broad market fund is one which, as the name suggests, invests in a broad range of securities which are in aggregate representative of the market as a whole. For example, a stock mutual fund which invests in, say, 20 of the largest companies from the S&P 500 index can be considered a “broad market” fund, due to the fact that these 20 companies are almost assuredly involved in a broad cross-section of industries. The benefit of broad market funds is that they offer their investors a diversified portfolio, meaning that a downturn in any particular industry is unlikely to have a severe or sustained effect on the portfolio as a whole. A “sector” fund, by contrast, specializes in a particular sector such as insurance, energy, or technology companies. More specifically, it might invest in such sub-sectors as car insurance, offshore oil platforms, or social media companies. Sector funds can be exciting investments provided that the sector in which they invest is growing at a noticeably greater rate than that of other industries, but they can just as easily produce headaches for their investors in the event that their given sector sees a marked decline. Sector funds are generally more volatile investments than their broad market counterparts, due to the fact that sector funds are inherently undiversified. The following chart illustrates this phenomenon:
The red line here represents the SPDR S&P 500 ETF, which (as discussed previously) tracks the S&P 500 index and which is therefore a broad market investment fund. The blue line represents the Technology SPDR ETF, which tracks the Technology Select Sector Index. Whereas the S&P 500 consists of a diverse range of large companies across a variety of industries, the Technology Select Sector Index specializes in technology companies in sectors such as computer components, telecommunications, and defense systems. As we can see from the chart, the sector fund significantly outperformed the broad market between the years 1999 and 2000 while subsequently lagging the broad market thereafter.  During the late 1990s, speculators unquestionably poured money into technology companies based on a euphoric conviction in the perceived infallibility of businesses operating in the “technology sector”—a period known retrospectively as “the dot-com bubble” or simply “the technology bubble” of the late ‘90s. Consequently, sector funds which focused on these types of companies performed superbly during these brief years, only to collapse with equal severity once the bubble had run its course.
→ Hedge Funds
A hedge fund is an actively managed investment fund which is distinct from other classes of funds due to the following characteristics:
- Investment in hedge funds is restricted to high net-worth individuals (those with significant existing capital and/or large annual incomes).
- Hedge funds specialize in unusually “aggressive” techniques such as the use of leverage (meaning, the use of borrowed money), the trading of derivative products, investment in international markets, and the trading of otherwise illiquid securities. These are just a small handful of examples.
- Hedge fund investors are often required to refrain from withdrawing their investment in the fund until at least a pre-designated period of time (such as one year after purchase). Consequently, hedge funds are illiquid investments relative to most alternatives.
The purpose of a hedge fund is to allow its managers and investors access to a wider range of investment strategies than would be legally available to your average fund / fund manager(s). In theory, this flexibility can result in superior returns relative to more traditional investment funds. In practice, hedge funds often perform more poorly than the broad market. This is in part due to the significantly higher fees which hedge funds generally demand from their investors, but it is also due to the often risky strategies which hedge funds employ. As stated previously, strategies which involve consistently elevated levels of risk may pay off beautifully in the short-term, but they are unlikely to bear fruit over a sustained period of time due to the mathematics of losses (one bad day is equivalent to two “good” days; thus the minimization of bad days is of paramount importance). More information, courtesy of KhanAcademy.org.
→ Exchange Traded Funds (ETFs)
An “ETF” or “Exchange Traded Fund” functions similarly to a mutual fund. However, there are three important differences:
- As contained in its name, an ETF is an investment fund which trades on an exchange. This is distinct from a mutual fund in that mutual funds require investors to enroll in the fund directly through a participating institution such as a commercial bank or credit union. These institutions serve as sales facilities, processing the paperwork involved in receiving the customer’s investment. Accordingly, mutual funds receive extensive advertising in local bank branches; the branches are the sales team for these funds.
- ETFs are significantly less expensive than mutual funds. ETFs often feature management fees between 0.1 and 0.5%, whereas mutual funds’ fees range between 1 and 2%. This can have a significant cumulative effect on returns over a medium to long-term timeframe.
- ETFs are typically passive investments, whereas mutual funds are often actively managed.
Fund Valuations: Discount vs. Premium
Like individual stocks and bonds, investment funds can trade above or below their fair value. Consequently, investors can estimate whether a given fund is being undervalued or overvalued at a given time, and plan their purchase accordingly.  However, the extent to which investors can practically assess the valuation of a given investment fund is dependent on the type of fund which they are assessing. Let’s go over a few examples to illustrate what I mean.
→ Valuing open-end mutual funds
As mentioned earlier, an open-end mutual fund is one in which the fund managers can issue a theoretically unlimited quantity of shares. The value of each share is therefore dependent on two factors: 1) The net asset value of the securities owned by the fund; 2) the number of shares which the fund has issued (referred to commonly as the number of “shares outstanding”). When you divide the net asset value by the number of shares outstanding, you arrive at the Net Asset Value Per Share (“NAVPS”). To recap the above:
Net Asset Value per Share (“NAVPS”) = Net Asset Value (“NAV”) / Number of Shares Outstanding 
Let’s apply this calculation to the BMO Dividend Fund, a popular Canadian open-end mutual fund specializing in large dividend-paying companies listed on the Toronto Stock Exchange. As of writing, the Fund’s NAV is listed at $3,295,433,000,  while its number of shares outstanding is listed at 66,944.  Applying the above formula, we arrive at a net asset value per share of 49.23:
3,295,433 (net asset value) / 66,944 (number of shares outstanding)=49.23 (net asset value per share)
Now, what does this number tell you? On face value, this number (NAVPS) can be used to gauge the performance of the fund compared to prior years, in a manner which accounts for the creation of new shares by the fund. Accordingly, the most recent NAVPS—as with most other financial metrics—is listed in a column adjacent with NAVPS figures for previous years/quarters in the Fund’s annual report and in financial statements generally. This is done to facilitate year-to-year comparisons by investors.
On further analysis, however, it becomes clear that the NAVPS figure is at best an imperfect measure of a fund’s valuation. What the NAVPS tell you is only what the current market price is for the companies in which the fund is invested (in the BMO Dividend Fund’s case, large dividend-paying companies on the Toronto Stock Exchange). Note what it does not do:
- It does not tell you anything about whether the market price for those companies is a reasonable one.
- It does not tell you whether the fund itself (i.e. the management fee and other costs which constitute the price of the fund) is a worthwhile purchase.
Moreover, because open-end mutual funds are bought and sold at their net asset value, there is no means whereby an investor can wait to purchase shares in the fund when the fund itself is priced below the book value of its assets (in such situations, funds are said to be trading “at a discount” to its book value). Conversely, it is impossible to sell one’s shares in an open-end mutual fund when the fund priced above the book value of its assets (or, as it is commonly known, when it is trading “at a premium” to its book value).
In summary, open-end mutual fund investors who wish to buy low and sell high have few tools available to them in their efforts to do so. Measures of net asset value, including NAVPS, only go so far as indicating the price currently paid by the market for the individual companies of which the fund is comprised; they do not tell you whether those companies are being over or undervalued by the market, nor do they tell you whether the fund itself is a worthwhile purchase relative to alternative forms of investment. As we shall see in a moment, closed-end mutual funds differ from their open-ended counterparts in that their can purchase their shares at a discount to book value and sell them at a premium to book value.
→ Valuing closed-end mutual funds
As mentioned previously, closed-end mutual funds are created with a pre-determined number of shares beyond which the fund is unable to expand further. If a new investor wishes to buy shares in the fund, she must purchase them from a pre-existing investor, and vice-versa. The price at which shares are bought and sold is determined (or “discovered”) through the market actions of investors. Put simply, the selling price of a closed-end mutual fund share is whatever the seller is willing to sell it for. If a price offered by a buyer (called a “bid” in market jargon) matches a price offered by a seller (called an “ask”), then a sale is made and ownership of the share(s) changes hands. Because buyers and sellers can choose to sell the share(s) either above or below the cost at which it was previously purchased, the price of shares can fluctuate over time. At times, a closed-fund share can be trading for more than the net asset value of the fund. In such situations, the shares are said to trade “at a premium” to net asset value. Conversely, a closed-fund share is said to trade “at a discount” to net asset value when the price of the share is sold for less than the net asset value of the fund. For example, if Fund A has a NAV of $50 and is sold at a market price of $48, then Fund A is selling at a discount of $2 (or 4%). If, on the other hand, Fund A is sold at a market price of $52, then it is selling at a premium of $2 (or 4%).
→ Valuing exchange traded funds
Like closed-end funds, shares in exchange-traded funds (ETFs) change hands between investors. This introduces a price discovery mechanism which can result in the market price for an ETF’s shares to be greater (at a premium) or lower (at a discount) than the ETF’s NAV. Unlike closed-end funds, however, ETFs can issue a theoretically unlimited number of shares, meaning that ETFs can trade on “primary” markets such as the NYSE, the NASDAQ, or the Toronto Stock Exchange. Consequently, it is possible for investors to purchase ETFs when they are trading at a discount to their NAV, and sell them at a premium to their NAV. However, the ETF market is structured in such a way as to minimize the significance of these pricing discrepancies.  Basing one’s investment strategy on the temporary discount or premium status of ETFs is therefore not advisable for the average investor; such discrepancies are generally unprofitable for all but the largest and most technologically sophisticated institutional investors. 
The main conclusion to be drawn from the above is that investors should not seek to profit from the discount or premium offered by ETFs. How, then, might the average investor go about assessing the quality of a given ETF over another? In my view, the most practical and informative question for the investor to ask himself when evaluating an ETF is the following: Does the price and composition of this fund offer me a cost-efficient means of investing in X, where X is the underlying sector/index in which the fund is specialized.
→ → Composition The latter of these criteria, composition, can be assessed by reviewing the Fund’s prospectus (the “prospectus” is the legally-mandated disclosure document which informs prospective investors as to the purpose, structure, and past performance of the investment fund). Specifically, investors should pay heed to the Fund’s holdings—meaning, those securities (such as companies or bonds) in which the fund is invested—and ask themselves whether these holdings are consistent with the sector/index which one wishes to access. For example, an investor wishing to invest in large Canadian dividend-paying companies would need to find such companies featured prominently in the holdings of a given ETF in order for that ETF to be an attractive investment vehicle. On a slightly more complex note, the investor would also be wise to ask herself (in this example) whether she is comfortable with the particular dividend-paying companies held by Fund. For instance, the BMO Dividend Fund which we addressed earlier is on face-value a perfect fit for “an investor wishing to invest in large Canadian dividend-paying companies”. However, such an investor may be uncomfortable with the fact that the grand majority of the BMO Dividend Fund’s holdings consist of large Canadian commercial banks. The point is that it is always worth looking “under the hood”, into the holdings of a fund, before concluding whether or not a Fund is a suitable investment. Just because a Fund’s name looks promising (such as a “Dividend Fund” for investors desiring dividend income) does not necessary mean that the particular structure of the fund is ideal for a given investor’s needs.
→ → Price By the “price” of the fund, I am referring to the fees/expenses associated with owning the fund. These include miscellaneous charges such as annual or quarterly fees, management fees which extract a fixed percentage from your investment return, and the commissions charged by your broker for buying and selling the Fund’s shares. Free services such as FINRA’s Funds Analyzer offer a convenient way of estimating the cumulative effects of these fees/expenses over time.
→ Valuing index funds
Index funds are unique among investment funds in that their objective is to match—not exceed—the performance of an underlying index. Before we go any further, it’s worth taking a moment to clarify what an index actually is. The popular financial education website Investopedia provides a succinct definition of the term “Index”. For our purposes, here are its key points:
- An index is an “imaginary portfolio of securities”.
- “Each index has its own calculation methodology”, meaning that two indexes which purport to represent, say, the Canadian oil and gas industry might go about doing so in markedly different ways.
- “Stock and bond market indexes are used to construct index mutual funds and exchange-traded funds (ETFs) whose portfolios mirror the components of the index.”
This third point is perhaps the most important of the three, because it leads us to the important issue of tracking errors. The term “tracking error” refers to the phenomenon whereby an index fund fails to accurately reflect/mirror/track its underlying index. What this means in practice is that a given index fund may under or overperform the index which it is intended to track. On face value, the idea of an index fund overperforming its index might not seem like such a bad thing, but given that it is the fundamental purpose of index funds to track their index, consistent overperformance may be indicative of fundamental problems in the structural design of the index fund. After all, an investor who chooses to use an index fund in order to access a given market/sector is ultimately interested in that market/sector; it is through that market that she will realize her investment returns. Being enticed by the “overperformance” of an index fund is to miss the point of the exercise; index funds are not so much investments in and of themselves as they are investment vehicles through which to invest in an underlying market/sector.
Based on the above, we can conclude that, when it comes to “valuing” an index fund, investors benefit from choosing funds with a good record of low tracking error relative to their peers. In addition to this, choosing a fund with low expenses is critical to the long-term performance of the fund (as discussed previously). A more technical explanation of tracking error is provided by Vanguard.
→ Valuing hedge funds
Hedge funds are the most difficult investment fund to describe, due to the fact that they are legally designed to be capable of investing in a wide variety of styles. Because of this, no single definition of what a hedge fund does can hope to be accurate universally. Similarly, the inherent diversity of hedge funds makes “valuing” them—meaning, inferring the extent to which a given hedge fund is overpriced or underpriced relative to its underlying value—even more challenging. Perhaps the best advice that can be given on this point is to employ a healthy degree of skepticism when dealing with hedge funds.  After all, hedge funds are notoriously expensive investment vehicles, with the industry standard fee structure (the infamous “Two and Twenty” compensation structure) demanding a hefty 2% upfront fee of total assets plus an ongoing 20% of all investment returns. This means that if you invested $2,000,000 (often close to a minimum sum for investment in a hedge fund) and made a 10% return on investment, $40,000 (2%) would be taken right off the top and an additional $39,200 would be subtracted from your 10% return (20% of $196,000, where $196,000 consists of the 10% return gained on the $1,960,000 which, subject to the initial 2% fee, was actually invested in the fund). Of course, in this scenario you would still be left with a sizeable $156,800 return. This may seem to provide ample justification for the hedge fund’s fees, but one must always compare such results to the behaviour of the stock market as a whole. What, in other words, would a passive index fund have returned during the same timeframe? Research has shown that the majority of hedge funds underperform the broad market once fees are subtracted from their investment return. This has proven especially true since the 2008-’09 financial crisis, since which time the HFRI Fund Weighted Composite Index—which tracks the average performance of hedge funds—has returned 9.7% over the last 12 months and an average of 7.62% over the last 60 months (5 years).  This performance seems impressive when taken on its own, but it must be viewed in its proper context: during the last 12 months, the SPDR S&P 500 ETF—which passively tracks the performance of the S&P 500 index—has returned 30.01%, while over the past 60 months it has returned an average of 17.43% per year.  These figures are intended only to provide a cautionary example as to how it should never be simply assumed that hedge funds outperform the broad market; once fees are taken into consideration, the opposite often occurs. There is, however, an important argument to be raised at this juncture, which is that outperforming the market is not the fundamental objective of a hedge fund. Rather, the objective of a hedge fund is to outperform the market per unit of risk. The logic here is that a passive (and, consequently, low-cost) investment vehicle such as the SPDR S&P 500 ETF is no less and no more than a mirror for the broad market index which it tracks. Consequently, while index funds may offer spectacular returns under certain conditions (such as the bull-market in stocks which has existed since 2009), they do so without offering any degree of protection against similarly spectacular movements in the opposite direction (such as the disastrous crisis which preceded the current bull-market). Another way of phrasing this is that index funds do not “hedge” against risk; they do not take precautions against (ultimately inevitable) market declines. Hedge funds, so the argument goes, do hedge, as their name suggests. Therefore, investors should be willing to tolerate lower returns by a given hedge fund provided that that fund is providing a greater degree of protection against potential losses.
This argument makes sense in theory, but less so in practice. The problem here is that hedge funds, despite their name, are often more genuinely concerned with maximizing financial returns than with preserving capital through the conservative hedging of risks. Thus while the above argument may well be valid in certain cases, it cannot be accurately applied in defense of the hedge fund industry in any general sense. For the most part, hedge funds have been trying to “beat the market”, and they have failed. Thus most can be justly accused of having lost at their own game. Ultimately, however, the critical evaluation of any given hedge fund—along with all manner of other investments—is the sole responsibility of the investor.
– On discount/vs premium: http://www.schwab.com/public/schwab/resource_center/expert_insight/investing_strategies/exchange_traded_funds/etf_premiums_and_discounts_friend_or_foe.html
– A good primer on closed-end funds, by BlackRock: http://www2.blackrock.com/us/individual-investors/insight-education/investing-basics/understanding-discounts-and-premiums
– The “market pricing” of closed-end mutual funds is discussed by the Closed- End Fund Center at: http://www.cefa.com/Learn/Content/CEFBasics/netassets.fs
– More information on tracking error: http://www.vanguard.com/jumppage/international/web/pdfs/INTUTE.pdf.
At the time of publication, Jason Fernando had no positions in any of the securities mentioned in this article. He does not intend to trade any of the securities mentioned in this article within 48 hours of publication.
 The technology sector’s dramatic rise during the late 1990s was driven by distinctly unintelligent speculation by unsophisticated “investors”; this drove an immense bubble in stock prices which ultimately collapsed in the early 2000s. Some small handful of speculators no doubt profited immensely from this period, but the vast majority suffered equally immense fiscal devastation.
 There is, however, an important difference between valuing investment funds and valuing individual investments. In valuing an individual company, the investor can research the financial statements of the company and perform an in-depth quantitative and qualitative assessment of its past and present business operations. In the case of a fund, however, this becomes practically impossible due to the large number of companies of which the fund (assuming it is a stock fund) is comprised. In theory, an investor would need to investigate every one of the constituent companies of the fund in order to arrive at a thorough understanding of the fund’s overall value. Even if one had the patience to do so, this practice may not yield workable conclusions because the fund may be invested in a range of companies with radically different business operations, meaning that “apples to oranges” comparisons would be all but inevitable. Because of this, the process of valuing investment funds is generally less thorough than that of individual companies. Investors should therefore not place too much confidence in their ability to accurately infer the valuation of investment funds.
 I must note that I have simplified this formula for ease of communication. In actuality, in calculating a fund’s NAV per share one also subtracts liabilities such as management fees and other expenses from the NAV before dividing by the number of shares outstanding. Moreover, the NAV itself is a “weighted average” of the market price for the underlying securities held by the fund. A creative explanation of how weighted averages are calculated is provided by Investopedia: http://www.investopedia.com/video/play/weighted-average/.
 This figure is provided in the “Statement of Net Assets” section of the Fund’s September 30th 2013 Annual Report, under the heading Net assets representing unitholders’ equity. It can be accessed at http://www.bmo.com/pdf/mf/prospectus/en/bmo146_annirpt-Eng.pdf. Note that this figure refers only to the Fund’s “Series A” shares, which are its most widely distributed variety. For more information on the various share types issued by the fund, read Note 7(a) of the Annual Report, under the section Notes to the financial statements.
 Here again, this figure refers to the Fund’s “Series A” shares. This information can be found under Note 7(b) of the September 30th 2013 Annual Report, under Notes to the financial statements.
 The ETF provider Horizons provides a well-written explanation of the role played by “market makers” in ensuring that the market price of ETFs remains close to their NAV over the medium-to-long term: http://us.horizonsetfs.com/pdf/factsheets/Understanding%20ETF%20Premiums%20and%20Discounts.pdf.
 The practice of profiting from the minute discrepancies between the market price and the NAV of ETFs is a form of “arbitrage”. In today’s networked market, in which the majority of trades (by size and volume) are conducted by supercomputers trading on behalf of large institutional firms, consistent successful arbitrage operations by the average investor are almost entirely impossible.
 Skepticism is among the investor’s most valuable assets, and should be employed as much as possible in one’s research and decision-making. However, hedge funds are arguably more requiring of skepticism than most, for reasons discussed below.
 See: https://www.hedgefundresearch.com/mon_register/index.php?fuse=login&hi
 See: https://www.spdrs.com/product/fund.seam?ticker=SPY.