CHAPTER 4: Mutual Funds and Other Investment Companies

2. What are some comparative advantages of investing in the following:

(a) Unit investment trusts. A Unit investment trust is a portfolio of assets fixed for the life of the fund. An advantage over an open-end mutual fund is there are no transaction or management costs. A disadvantage is that the portfolio is not re-allocated as perceived needs or opportunities change. An advantage over individual stocks and bonds is diversification. A disadvantage is that the sponsor, in order to earn a profit, will initially sell the “units” for a price above the NAV.

(b) Open-end mutual funds. An open-end mutual fund is a portfolio that is managed, either actively of passively, by the sponsor. Open-ended means the sponsor will issue new shares and redeem existing shares at the end of each trading day at the NAV.

An advantage over a Unit Investment Trust is that the shares are always sold or redeemed at the NAV and that the portfolio’s assets can be re-allocated as opportunities change. An advantage over individual stocks and bonds is diversification. A disadvantage is that an open-end mutual fund will charge a management fee. A passive fund (aka an index or indexed fund) fund will charge a small fee, but still charge a fee.

(c) Individual stocks and bonds that you choose for yourself. An advantage of individual stocks and bonds over is that there is no management fee (mutual fund) or premium paid for the assets (UIT) and realization of capital gains or losses can be coordinated with investor’s personal tax situation. Also the portfolio can be designed to meet investor’s specific risk, income or time-horizon needs.

A disadvantage is that it is harder to achieve diversification and trading costs might be higher. Also, an individual might not make good investment allocation decisions.

3. Open-end equity mutual funds find it necessary to keep a significant percentage of total investments, typically around 5% of the portfolio, in very liquid money market assets (cash equivalents). Closed-end funds do not have to maintain such a position in “cash equivalent” securities. What difference between open-end and closed-end funds might account for their differing policies?

Open-end funds are obligated to redeem investor's shares at the end of each trading day at the net asset value. So the shares of an open-ended mutual fund are, in theory, infinitely liquid at the NAV. In other words, investors do not incur the extra costs associated with a bid-ask spread. (Contrast this with an ETF or closed-end fund in which the shares must be sold to another investor.) Therefore, open-end funds must keep cash or cash-equivalent securities on hand in order to meet potential redemptions and so can’t be “fully invested” in stocks or bonds. Since closed-end funds do not redeem shares, closed-end funds do not need to hold cash reserves and can be fully invested. Investors in closed-end funds sell their shares (at the bid) on a stock exchange when they wish to liquidate. (See question #5.)

1 4. Balanced funds, life-cycle funds, and asset allocation funds all invest in both the stock and bond markets. What are the differences among these types of funds? A fund that holds both stocks and bonds is called a balanced fund. Life-Cycle funds and Allocation funds are types of balanced funds.

Regular Balanced funds keep a relatively stable proportion of money invested in each asset class. They are meant as convenient instruments to provide participation in a range of asset classes. They provide broad asset allocation services to their investors.

Life-Cycle Funds are balanced funds with a target sell date, such as 2050. The idea is that the fund will be held by those expecting to liquidate (due to retirement?) in 2050. The fund allocates money based on that sale date. When there is longer term to the sale date, the fund holds more risky assets (generally more equities) and when it is closer to the sale date, the fund holds more fixed-income securities. At the end, the fund holds all money-market securities.

Asset Allocation Funds try to earn superior returns by varying the asset class allocations and therefore engage in more aggressive market timing.

5. Why can closed-end funds sell at prices that differ from net asset value while open-end funds do not? Closed-end fund shares are not redeemed by the fund manager. They must be sold in the secondary market. Because of this, shares may trade at a substantial premium or discount to the NAV.

Discounts of 5% to NAV are commonly observed. Possible reasons for observed discounts include market reaction to poor past performance of the fund (and its managers), sentiment concerning the fund’s sector or maybe low awareness of the fund (bad marketing).

One line of reasoning goes that that large discounts should not persist since a well-capitalized arbitrageur could buy all the mutual fund shares and force the portfolio to liquidate at the NAV. But this ignores the need to buy all the mutual fund shares from the market (which would very likely cause the share price to rise) and then sell all the assets held by the fund (which might cause the price of the assets to fall). This would wipe-out the profits from the discount.

Possible reasons for a closed-end fund’s shares to trade at a premium to NAV might be strong recent performance – investors will pay a premium to invest with a strong manager. Another reason might be that a fund invests in a market or sector with barriers to entry for retail (individual) investors. For example, the Morgan Stanley Eastern European fund (RNE) at one time traded at close to a 40% premium to NAV. One reason might be that investors were unable to gain access to these markets and paid the premium in order to gain access.

6. What are the advantages and disadvantages of exchange-traded funds versus mutual funds? Advantages of ETFs over mutual funds:  ETFs are traded on exchanges so can be sold or purchased at any time. Open-end mutual funds can only be bought or sold once per day at the close of trading (4:00 Eastern time).

 Since open-end mutual funds might have to sell assets held to finance redemptions, open-end mutual funds may trigger capital gains for the remaining shareholders. ETF shares are sold to new investors, so there is no capital gain trigger. 2  ETFs will allow large shareholders called “authorized participants” to redeem shares if the market sale would cause a difference in the market price and NAV. But these exiting ETF shareholders are given the assets underlying the ETF in exchange for the shares. This does not create a tax event for the remaining ETF shareholders.

Contrast this with an open-ended mutual fund. The fund sells assets and delivers cash in exchange for the fund shares. This can create a tax event.

Note that the ETF will also issue new shares if the purchase is large enough to cause the market price of the ETF shares to differ from the NAV. In this case, the buyer of the ETF shares purchases the assets underlying the ETF and delivers the assets to the ETF in exchange for ETF shares. Again, not a tax event for the other ETF shareholders.

 ETF shares are bought through stock brokers. This eliminates the cost to the sponsor of marketing the fund to individual small investors and can reduce fees.

Disadvantages of ETFs over mutual funds:  There is a brokerage commission charged when buying and selling ETF shares (unlike a no- load fund)

 There are both actively managed mutual funds and passively managed mutual funds. There are no (few?) actively managed ETFs.

7. An open-end fund has a net asset value of $10.70 per share. It is sold with a front-end load of 6%. What is the offering price? The offering price (P0) includes a 6% front-end load (FL), or sales commission, meaning that every dollar paid results in only $0.94 going toward purchase of shares.

P0 = NAV0/(1 – FL) = $10.70/(1 – 0.06) = $10.70/(0.94) = $11.38

8. If the offering price of an open-end fund is $12.30 per share and the fund is sold with a front-end load of 5%, what is its net asset value?

NAV0 = P0  (1 – FL) = $12.30  0.95 = $11.69

9. The composition of the Fingroup Fund portfolio is in the table below. The fund has not borrowed any funds, but its accrued management fee with the portfolio manager currently totals $30,000. There are 4 million shares outstanding. What is the net asset value of the fund? Value = Stock Shares Price Price x Shares A 200,000 $35 $7,000,000 B 300,000 $40 $12,000,000 C 400,000 $20 $8,000,000 D 600,000 $25 $15,000,000 Sum = $42,000,000 NAV = Equity/Shares Outstanding = (Assets – Liabilities)/Shares Outstanding = ($42,000,000 - $30,000)/4,000,000 = $10.49

3 10. Reconsider the Fingroup Fund in the previous problem. If during the year the portfolio manager sells all of the holdings of stock D and replaces it with 200,000 shares of stock E at $50 per share and 200,000 shares of stock F at $25 per share, what is the portfolio turnover rate?

Value of stocks sold and replaced = 600,000 x $25 = $15,000,000 Or Value of stocks sold and replaced = 200,000 x $50 + 200,000 x $25 = $15,000,000 Turnover rate = Value Sold and Replaced/Total Value = $15,000,000/$42,000,000 = 35.7%

11. The Closed Fund is a closed-end investment company with a portfolio currently worth $200 million. It has liabilities of $3 million and 5 million shares outstanding.

(a) What is the NAV of the fund? NAV = (Assets – Liabilities)/Shares Outstanding = ($200 – $3)/5 = $39.40

(b) If the fund sells for $36 per share, what is its premium or discount as a percent of net asset value? Premium (or discount) = (Price – NAV)/NAV = ($36 – $39.40)/$39.40 = -0.086 = -8.6% The fund sells at an 8.6% discount from NAV.

12. Corporate Fund started the year with a net asset value of $12.50. By year-end, its NAV equaled $12.10. The fund paid year-end distributions of income and capital gains of $1.50. What was the (pretax) rate of return to an investor in the fund? Return = (NAV1 + Distributions)/NAV0 – 1 = ($12.10 + $1.50)/$12.50 – 1 = 8.80%

13. A closed-end fund starts the year with a net asset value of $12.00. By year-end, NAV equals $12.10. At the beginning of the year, the fund was selling at a 2% premium to NAV. By the end of the year, the fund is selling at a 7% discount to NAV. The fund paid year- end distributions of income and capital gains of $1.50.

(a) What is the rate of return to an investor in the fund during the year?

P0 = NAV0 × (1 + Premium) = $12.00  1.02 = $12.24

P1 = NAV1 × (1 – Discount) = $12.10  0.93 = $11.25 The NAV increased by $0.10 but the price of the fund decreased by $0.99

Return = (P1 + Distributions)/P0 – 1 = ($11.25 + $1.50)/$12.24 – 1 = 4.17%

(b) What would have been the rate of return to an investor who held the same securities as the fund manager during the year? An investor holding the same securities as the fund manager would have earned a rate of return of the NAV and not been subject to the change from premium to discount.

Return = (NAV1 + Distributions)/NAV0 – 1 = ($12.10 + $1.50)/$12.00 – 1 = 13.33%

14. Mutual Fund Performance:

4 (a) Impressive Fund had excellent investment performance last year, with portfolio returns that placed it in the top 10% of all funds with the same investment policy. Do you expect it to be a top performer next year? Why or why not? See the discussion of Malkiel’s mutual fund return studies on the page 109 and in Table 4.4.

(b) Suppose instead that the fund was among the poorest performers in its comparison group. Would you be more or less likely to believe its relative performance will persist into the following year? Why? Again, see the discussion of Malkiel’s mutual fund return studies on the bottom of page 109 and in Table 4.4.

15. Consider a mutual fund with $200 million in assets at the start of the year and with 10 million shares outstanding. The fund invests in a portfolio of stocks that provides dividend income at the end of the year of $2 million. The stocks included in the fund's portfolio increase in price by 8%, but no securities are sold, and there are no capital gains distributions. The fund charges 12b-1 fees of 1%, which are deducted from portfolio assets at year-end. What is net asset value at the start and end of the year? What is the rate of return for an investor in the fund? NAV0 = $200,000,000/10,000,000 = $20 Dividends per share = $2,000,000/10,000,000 = $0.20 NAV1 is based on the 8% price gain, less the 1% 12b-1 fee:

NAV1 = $20  1.08  (1 – 0.01) = $21.384 Return = ($21.384 + $0.20)/$20 – 1 =7.92%

Note: In reality, mutual funds assess a portion of annual fees each day. Otherwise, if annual fees were assessed in their entirety on a single day, fund owners would just sell the fund the day before the fees were assessed and then buy it back the day after.

16. The New Fund had average daily assets of $2.2 billion last year. The fund sold $400 million worth of stock and purchased $500 million during the year. What was its turnover ratio? The excess of purchases over sales is most likely due to new inflows into the fund. Therefore only $400 million of stock held by the fund was replaced by new holdings. Turnover Ratio = $400/$2,200 = 18.2%

17. If New Fund's expense ratio (see the previous problem) was 1.1% and the management fee was 0.7%, what were the total fees paid to the fund's investment managers during the year? What were other administrative expenses? Fees paid to investment managers = 0.007  $2.2 billion = $15.4 million Total Expense Ratio = 1.1% Management Fees = 0.7%, Other Expenses = 1.1% - 0.7% = 0.4% Other Expenses = 0.004  $2.2 billion = $8.8 million

18. You purchased 1,000 shares of the New Fund at a (quoted) price of $20 per share (in other words, the NAV is $20) at the beginning of the year. You paid a front-end load of 4%. The securities in which the fund invests increase in value by 12% during the year. The fund's expense ratio is 1.2%. What is your rate of return on the fund if you sell your shares at the end of the year?

Cost of Shares = P0 = (NAV0 × Shares)/(1 – FL) = ($20 × 1,000)/(1  0.04) = $20,833 NAV1 = NAV0(1 + Investment Return – Expense Ratio) = $20(1 + 0.12 – 0.012) 5 = $20(1.108) = $22.16 Value of 1,000 shares at time 1 = $22,160

Note that the quoted “price per share” of $20 equals the NAV, but since you are paying a 4% front load, your effective price per share is $20/(1 – 0.04) = $20.833

Note that due to the front-end load, P0 ≠ NAV0 but since there is no back-end load, P1 = NAV1 Return is calculated from prices: Return = P1/P0 – 1 = $22,160/$20,833 = 6.37%

Note that Investment Return – Expenses – Load = 12%  1.2%  4% = 6.8% ≠ 6.37% This is because the load is paid at the beginning and changes the invested amount (P0).

19. Loaded-Up Fund charges a 12b-1 fee of 1.0% and maintains an expense ratio of .75%. Economy Fund charges a front-end load of 2% but has no 12b-1 fee and an expense ratio of .25%. Assume the rate of return on both funds' portfolios (before any fees) is 6% per year. How much will an investment in each fund grow to after 1 year, 3 years and 10 years?

Wealth Index at time N = (1 – Front Load)(1 + r – Fees)N

Loaded-Up: Front Load = 0% Fees = 0.01 + 0.0075 = 0.0175 (1 – 0)(1 + 0.06 – 0.0175)N = (1.0425)N

Economy: Front Load = 0.02 Fees = 0.0025 (1 – 0.02)(1 + 0.06 – 0.0025)N = 0.98(1.0575)N

Years (N) Loaded-Up Economy 1 1.0425 1.0364 3 1.1330 1.1590 10 1.5162 1.7141

Some notes on return measures: The Wealth Index is the value of a dollar invested in the fund. For example, $1 invested in Economy would be worth $1.7141 in 10 years.

The Holding Period Return (HPR) = Wealth Index - 1 For example, the 10 year HPR for Economy is 1.7141 – 1 = 0.7141 = 71.41%

The Annualized HPR = (1 + HPR)(1/N) – 1 For example, the Annualized HPR for Economy over the 10 year period is (1.7141)1/10 – 1 = 5.54%

6 The table below shows the Annualized HPR for each find and year. Note that the Annualized HPR for Loaded-Up is the same for each holding period but the Annualized HPR increases for Economy since the Front Load is charged only once.

Years (N) Loaded-Up Economy 1 4.25% 3.64% 3 4.25% 5.04% 10 4.25% 5.54%

21. The Investments Fund sells Class A shares with a front-end load of 6% and Class B shares with 12b-1 fees of .5% annually as well as back-end load fees that start at 5% and fall by 1% for each full year the investor holds the portfolio (until the fifth year). Assume the portfolio rate of return net of operating expenses is 10% annually. If you plan to sell the fund after 4 years, are Class A or Class B shares the better choice for you? What if you plan to sell after 15 years? Compute the Wealth Index, the HPR or the Annualized HPR for each class of shares and each holding period.

Wealth Index = (1 – Front Load)(1 + r – Fees)N(1 – Back Load)

For Class B shares and a four year holding period (Back Load is 1%): Wealth Index = (1 – 0)(1 + 0.10 – 0.005)4(1 – 0.01) = 1.4233

Share Year Front Back 12b-1 Wealth Class s Load Load Return Fees Index A 4 6% 0% 10% 0.0% 1.3763 A 15 6% 0% 10% 0.0% 3.9266 B 4 0% 1% 10% 0.5% 1.4233 B 15 0% 0% 10% 0.5% 3.9013

Four Year Holding Period: Choose Class B Fifteen Year Holding Period: Choose Class A

22. You are considering an investment in a mutual fund with a 4% load and expense ratio of . 5%. You can invest instead in a bank CD paying 6% interest.

(a) If you plan to invest for 2 years, what annual rate of return must the fund portfolio earn for you to be better off in the fund than in the CD? Assume annual compounding of returns. Mutual Fund Wealth Index after N years = (1 – FL)  (1 + r – Expenses)N N N CD Wealth index after N years = (1 + rCD) = (1.06) The mutual fund is a better investment if its wealth index is greater: (1 – FL)(1 + r – Expenses)N > 1.06N (1 – 0.04)(1 + r – 0.005)2 > 1.062 (0.96)(1 + r – 0.005)2 > 1.1236 (1 + r – 0.005)2 > 1.1704 1 + r – 0.005 > 1.0819 1 + r > 1.0869 r > 8.69% So if the mutual fund return exceeds 8.69%, it is better than the CD. 7 (b) How does your answer change if you plan to invest for 6 years? Why does your answer change? (1 – FL)(1 + r – Expenses)6 > 1.066 (1 – 0.04)(1 + r – 0.005)6 > 1.066 r > 7.22% The cutoff rate of return is lower for the six-year holding period cost (i.e., the one-time front-end load) is spread out over a greater number of years.

(c) Now suppose that instead of a front-end load the fund assesses a 12b-1 fee of .75% per year. What annual rate of return must the fund portfolio earn for you to be better off in the fund than in the CD? Does your answer in this case depend on your time horizon? 12b-1 fee instead of a front-end load: (1 + r – Expenses – Fee)N > 1.06N Note that without the one-time fee, we can take each side to the 1/N power and get: (1 + r – Expenses – Fee) > 1.06 1 + r – 0.005 – 0.0075 > 1.06 r > 7.25% (regardless of the investment horizon)

23. Suppose that every time a fund manager trades stock, transaction costs such as commissions and bid–asked spreads amount to .4% of the value of the trade. If the portfolio turnover rate is 50%, by how much is the total return of the portfolio reduced by trading costs? A turnover rate of 50% means that, on average, 50% of the portfolio is sold and replaced each year. The trading costs of 0.4% are assessed on both the purchase and sales. Total trading costs will reduce portfolio returns by: 2  0.4%  50% = 0.4%

25. Suppose you observe the investment performance of 350 portfolio managers for 5 years and rank them by investment returns during each year. After 5 years, you find that 11 of the funds have investment returns that place the fund in the top half of the sample in each and every year of your sample. Such consistency of performance indicates to you that these must be the funds whose managers are in fact skilled, and you invest your money in these funds. Is your conclusion warranted? Suppose that finishing in the top half of all portfolio managers is purely luck, and that the probability of doing so in any year is exactly ½. Then the probability that any particular manager would finish in the top half of the sample five years in a row is (½)5 = 1/32. We would then expect to find that [350  (1/32)] = 11 managers finish in the top half for each of the five consecutive years. This is precisely what we found. Thus, we should not conclude that the consistent performance after five years is proof of skill. We would expect to find eleven managers exhibiting precisely this level of "consistency" even if performance is due solely to luck.

Extra Questions: 1. Consider four different investment alternatives:  Open-End actively managed mutual fund (Active OEF)  Open-End passively managed (or index) mutual fund (Passive OEF)  Closed-End active mutual fund (Active CEF)  A passive Exchange Traded Fund (Passive ETF)

(a) Describe how shares of each are traded. Can the shares be shorted? 8 All OEF shares (active and passive) are issued or redeemed by the fund sponsor once per day at 4:00pm New York time at the NAV. Since OEF shares are not available on a secondary market, the shares cannot be shorted.

CEF and ETF shares are traded like stocks on an exchange at the market price. CEF and ETF shares can be shorted.

(b) For each, will the NAV be equal or near the price? In other words, will the shares be sold a discount or premium? Since all OEF shares are issued or redeemed by the fund sponsor, they will always trade at the NAV.

Since CEF shares are exchange traded and there is no mechanism to buy shares from the sponsor or sell shares to the sponsor at the NAV, it might be the case the market price will differ from the NAV. The price for CEF shares rises and falls in response to investor demand.

A reasons why a CEF might trade at a premium to NAV is market participants desire to hold the fund because of expected strong manager performance. Another possible reason is that the fund holds assets that are difficult to buy or to value such as foreign stocks.

A reasons why a CEF might trade at a discount to NAV is the CEF shares are less liquid than the underlying shares held by the fund so CEF holders require a greater return than the holders of the underlying shares.

An ETF’s authorized participants (APs) have the ability to exchange the underlying assets for fund shares or vice versa. This means the APs can essential buy or sell ETF shares at the NAV. If the market price deviates too much from the NAV, the APs will engage in this arbitrage activity until the market price is close or equal to the NAV.

(c) Describe the fees and loads. Management Fees All four will have management fees charged as a percentage of assets under management (AUM). Active OEFs and CEFs will have higher management fees than passive OEFs and ETFs.

Front Loads and Back Loads Active OEFs may charge a front-end load. This is percentage of the money invested that is used to pay a sales commission to the broker selling the fund.

Some Active OEFs charge a back load. This is percentage of the sale price kept by the fund upon liquidation. Usually the percentage decreases to zero over a period of a few years. Back loads encourage investors to hold the fund for a longer period of time.

Passive OEFs shouldn’t charge a front load or a back load, but some do. (This is why the “No” is “starred” in the table below.)

9 Because they are exchange-traded and trade like stocks, CEFs and ETFs don’t charge front loads or back loads, but you will have to pay a brokerage commission and the bid-ask spread (as you would for any stock trade).

12b-1 Fees 12b-1 Fees are charged like regular management fees, but the SEC rule allows funds to separate the disclosure of these fees. 12b-1 fees are used to pay for a mutual fund’s costs not associated with managing the portfolio of assets such as distribution costs and costs associated with communicating with shareholders. 12b-1 fees, like front loads, are also often used as to pay a commission to brokers for selling the fund. The amount of the 12b-1 fee, which can be as high as 75 basis points for commissions and 25 basis points for service fees, is charged as a percentage of assets under management (AUM), that same as regular management fees.

(d) Describe trading of fund assets and the associated trading costs and capital gain taxes.

Managers of active OEFs and active CEFs will attempt to beat their benchmark index by buying and selling stocks. The fund incurs a commission for each transaction and must also “pay” the bid- ask spread each time it trades.

In addition, since assets sold for more than the purchase price are realized capital gains, these tax liabilities are passed on the fund’s shareholders.

Passive OEFs and ETFs do not frequently trade stocks. However, large quantities of redemptions might cause a passive OEF to sell assets to fund redemptions.

Exchang Short Management Front Back 12b-1 Assets e Traded Position NAV vs Price Fee Load Load Fee Traded Active OEF No No Equal Higher Maybe Maybe Maybe Yes Passive OEF No No Equal Lower No* No* No* No Active CEF Yes Yes Premium or Discount Higher No No No Yes ETF Yes Yes Equal or Close Lower No No No No

2. An actively managed mutual fund that holds large-cap stocks  Charges annual management fee of 3.00% of assets under management.  Charges a 1.00% 12b-1 fee.  Charges 5.00% sales commission

ETF that tracks the S&P500 charges an annual management fee of 0.25%.

The expected annualized holding period return of the S&P 500 is 10%. You have a 15-year holding period.

(a) Calculate the expected wealth index for a 10-year investment in the S&P500 ETF.

WI = (1 – FL)[1 + r(1 – Perform Fees) – Man Fees – 12b-1 Fees]N(1 – BL) WI = (1 – 0)[1 + r(1 – 0) – 0.0025 – 0]N(1 – 0) WI = [1 + r – 0.0025]N WI = [1 + 0.10 – 0.0025]15 WI = [1 + 0.0975]15 WI = 4.0371

10 (b) Calculate the necessary annualized holding period return for the active mutual fund gross of fees or “before fees” so that an investor net of fees or “after fees” is indifferent between the ETF and the active fund. In other words, what must the average annual holding period return of the active fund over this time period for wealth indices for the two alternatives to be equal?

WI = (1 – FL)[1 + r(1 – Perform Fees) – Man Fees – 12b-1 Fees]N(1 – BL) WI = (1 – 0.05)[1 + r(1 – 0) – 0.03 – 0.01]15(1 – 0) WI = (0.95)[1 + r – 0.04]15

Solve for the r that equates the WIs:

WI = (0.95)[1 + r – 0.04]15 = 4.0371 [1 + r – 0.04]15 = 4.0371/0.95 [1 + r – 0.04]15 = 4.2496 [1 + r – 0.04] = 4.24961/15 [1 + r – 0.04] = 1.1013 r = 1.1013 + 0.04 – 1 = 14.13%

11