CHAPTER 4: MUTUAL FUNDS AND OTHER INVESTMENT COMPANIES

CHAPTER 4: Mutual Funds and Other Investment Companies

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

(a) Unit investment trusts.Unit investment trusts are pools 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 either actively or passively managed by the sponsor. Open-ended means the sponsor will issue new shares or 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 purchased at the NAV and that the portfolio can be re-allocated as perceived needs or 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 (or index) 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 (IUIT) and realization of capital gains or losses can be coordinated with investors personal tax situation and the portfolio can be designed to investors specific risk profile.

A disadvantage is that it is harder to achieve diversification.

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 net asset value. They are, in theory, infinitely liquid at the NAV. Investors do not incur the extra costs associated with a bid-ask spread. (Contrast this with an ETF or closed-end fund.) Therefore, open-end funds must keep cash or cash-equivalent securities on hand in order to meet potential redemptions.

Closed-end funds do not need the cash reserves because closed-end funds do not redeem shares. Investors in closed-end funds sell their shares (at the bid) when they wish to liquidate.

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 my 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 funds 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 funds 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 must sell shares to finance redemptions, these funds may trigger capital gains for the remaining shareholders. ETFs are sold to new investors so there is no capital gain trigger. ETFs also will allow large shareholders to redeem shares if the sale would cause a move in the price away from the NAV, but these shareholders are given the underlying stock, which does not create a tax event. (Note that the ETF will issue new shares if the purchase of ETF shares in the secondary market will cause a price move.) 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 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?StockSharesPriceValue = Price x Shares

A200,000$35 $7,000,000

B300,000$40 $12,000,000

C400,000$20 $8,000,000

D600,000$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

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 = $15,000,000Turnover 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 = $12.24P1 = NAV1 (1 Discount) = $12.10 0.93 = $11.25The 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:(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 Malkiels mutual fund return studies on the bottom of page 107 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 Malkiels mutual fund return studies on the bottom of page 107 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 = $20Dividends per share = $2,000,000/10,000,000 = $0.20NAV1 is based on the 8% price gain, less the 1% 12b-1 fee:NAV1 = $20 1.08 (1 0.01) = $21.384Return = ($21.384 + $0.20)/$20 1 =7.92%

Note that 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 sell the fund the day before the fees were assessed.

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 millionTotal 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 price of $20 per share 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) = $20,833NAV1 = NAV0(1 + Investment Return Expense Ratio) = $20(1 + 0.12 0.012) = $20(1.108) = $22.16Value of 1,000 shares at time 1 = $22,160

Note that due to the front-end load, P0 NAV0 but since there is no back-end load, P1 = NAV1Return 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 increases 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 + (1 + 0.06 0.0175)]N = (1.0425)N

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

Years (N)Loaded-UpEconomy

11.04251.0364

31.13301.1590

101.51621.7141

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 - 1For 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%

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-UpEconomy

14.25%3.64%

34.25%5.04%

104.25%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 ClassYearsFront LoadBack LoadReturn12b-1 FeesWealth Index

A46%0%10%0.0%1.3763

A156%0%10%0.0%3.9266

B40%1%10%0.5%1.4233

B150%0%10%0.5%3.9013

Four Year Holding Period: Choose Class BFifteen 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)NCD Wealth index after N years = (1 + rCD)N = (1.06)NThe 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 > 1.17041 + r 0.005 > 1.08191 + r > 1.0869r > 8.69% So if the mutual fund return exceeds 8.69%, it is better than the CD.

(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 > 1.066r > 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 > 1.06NNote that without the one-time fee, we can take each side to the 1/N power and get:(1 + r Expenses Fee) > 1.061 + r 0.005 0.0075 > 1.06r > 7.25% (regardless of the investment horizon)

23. Suppose that every time a fund manager trades stock, transaction costs such as commissions and bidasked 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 . Then the probability that any particular manager would finish in the top half of the sample five years in a row is ()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.

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