CHAPTER 04

5.
Exchange-traded funds can be traded during the day, just as the stocks they represent.
They are most tax effective, in that they do not have as many distributions. They have
much lower transaction costs. They also do not require load charges, management fees,
and minimum investment amounts. The disadvantages are that ETFs must be purchased
from brokers for a fee and investors may incur a bid-ask spread when purchasing an
ETF.

9.
a. A unit investment trust offers low costs and stable portfolios. Since they do not
change their portfolios, investors know exactly what they own. They are better suited to
sophisticated investors.
b. Open-end mutual funds offer higher levels of service to investors. The investors do
not have any administrative burdens and their money is actively managed. These are
better suited for less knowledgeable investors.
c. Individual securities offer the most sophisticated investors ultimate flexibility.
Investors can save money since they are only charged the expenses they incur. All
decisions are under the control of the investor.

10.
Open-end funds must honor redemptions and receive deposits from investors. This flow
of money necessitates retaining cash. Close-end funds no longer take and receive
money from investors. As such, they are free to be fully invested at all times.

13.
Given that net asset value equals assets minus liabilities expressed on a per-share basis,
we first add up the value of the shares to get the market value of the portfolio:

Stock Value Held by

Fund
A $ 7,000,000
B 12,000,000
C 8,000,000
D 15,000,000
Total $42,000,000

Knowing that the accrued management fee, which adjusts the value of the portfolio, totals
$30,000, and the number of the shares outstanding is 4,000,000, we can use the NAV
equation:
 Market value of assets － Market value of liabilities
Net asset value =
Shares outstanding

$42,000,000 − $30,000
= = $10.49
4,000,000

14.
The value of stocks sold and replaced = $15,000,000.
Value of stocks sold or replaced
Turnover rate =
Value of assets

$15,000,000
= = 0.3571 = 35.71%
$42,000,000

15.

Market value of assets － Market value of liabilities

a. NAV =
Shares outstanding

$200,000,000－ $3,000,000
= = $39.40
5,000,000

Pr ice − NAV $36 − $39.40

b. Premium (or discount) = = = –0.0863 = –8.63%
NAV $39.40
The fund sells at an 8.63% discount from NAV.

22.
The excess of purchases over sales must be due to new inflows into the fund.
Therefore, $400 million of stock previously held by the fund was replaced by new
holdings. So turnover is:
Value of stocks sold or replaced
Turnover rate =
Value of assets

$400,000,000
= = 0.1818 = 18.18%
$2,200,000,000
24.
Because the 4% load was paid up front and reduced the actual amount invested, only
96% (1.00 - .04) of the contribution was invested. Given the value of the portfolio
increased by 12% and the expense ratio was 1.2%, we can calculate the end value of the
investment against the initial contribution:
1 + r = 0.96 × (1 + 0.12 − 0.012) = 1.0637
Thus, the rate of return was: 1.0637 − 1 = 0.0637 = 6.37%
Or otherwise, you can calculate the rate of return by the actual amount invested and
value changes:
To purchase the shares, you would have had to invest: $20,000/(1 − 0.04) = $20,833
The shares increase in value from $20,000 to $20,000 × (1.12 − 0.012) = $22,160
The rate of return was: ($22,160 − $20,833)/$20,833 = 0.0637 or 6.37%

25.

a. Suppose you have $1000 to invest. The initial investment in Class A shares
is $940 net of the front-end load. After 4 years, your portfolio will be
worth:
$940 × (1.10)4 = $1,376.25
` Class B shares allow you to invest the full $1,000, but your investment
performance net of 12b-1 fees will be only 9.5%, and you will pay a 1% back-
end load fee if you sell after 4 years. Your portfolio value after 4 years will be:
$1,000 × (1.095)4 = $1,437.66
After paying the back-end load fee, your portfolio value will be:
$1,437.66 × 0.99 = $1,423.28
Class B shares are the better choice if your horizon is 4 years.

b. With a 15-year horizon, the Class A shares will be worth:

$940 × (1.10)15 = $3,926.61
For the Class B shares, there is no back-end load in this case since the horizon is
greater than 5 years. Therefore, the value of the Class B shares will be:
$1,000 × (1.095)15 = $3,901.32
At this longer horizon, Class B shares are no longer the better choice. The
effect of Class B's 0.5% 12b-1 fees cumulates over time and finally overwhelms
the 6% load charged to Class A investors.
26.

a. After two years, each dollar invested in a fund with a 4% load and a portfolio
return equal to r will grow to: $0.96 × (1 + r – 0.005)2
Each dollar invested in the bank CD will grow to: $1 × (1.06)2
If the mutual fund is to be the better investment, then the portfolio return, r,
must satisfy:
0.96 × (1 + r – 0.005)2 > (1.06)2
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
Therefore, r > 0.0869 = 8.69%

b. If you invest for six years, then the portfolio return must satisfy:
0.96 × (1 + r – 0.005)6 > (1.06)6 = 1.4185
(1 + r – 0.005)6 > 1.4776
1 + r – 0.005 > 1.0672
1 + r > 1.0722
r > 7.22%
The cutoff rate of return is lower for the six year investment because the "fixed
cost" (i.e., the one-time front-end load) is spread out over a greater number of
years.

c.
i. With a 12b-1 fee instead of a front-end load, the portfolio must earn a
rate of return (r) that satisfies:
1 + r – 0.005 – 0.0075 > 1.06
ii. In this case, r must exceed 7.25% regardless of the investment
horizon.

27.
The turnover rate is 50%. This means that, on average, 50% of the portfolio is sold and
replaced with other securities each year. Trading costs on the sell orders are 0.4%; the
buy orders to replace those securities entail another 0.4% in trading costs. Total trading
costs will reduce portfolio returns by: 2 × 0.004 × 0.50 = 0.004 or 0.4%
28.

a. For the bond fund, the fraction of portfolio income given up to fees is:
0.6%
= 0.150 = 15.0%
4.0%
b. For the equity fund, the fraction of investment earnings given up to fees is:
0.6%
= 0.050 = 5.0%
12.0%
c. Fees are a much higher fraction of expected earnings for the bond fund, and
therefore may be a more important factor in selecting the bond fund.
This may help to explain why unmanaged unit investment trusts are
concentrated in the fixed income market. The advantages of unit investment
trusts are low turnover and low trading costs and management fees. This is a
more important concern to bond-market investors.

30.
a. Using the Morningstar style box, we see that the fund invests primarily in small
growth stocks. This is entirely consistent with the fund name.

b. The Quartile Rank boxes show that the fund placed in the third quartile (thus below
median performance) in 2021.

c. The fund was in the top half of funds in its style group in 8 of 10 years, thus earning
it a four-star rating.

d. The expense ratio was 1.02%. This is not low-fee by comparison with the full
universe of equity funds, especially when asset-weighted fees are considered. But
this may not be the appropriate benchmark. The fund has a lower expense ratio than
other small-cap growth funds, and perhaps the appropriate benchmark should be
other funds with similar focus. If an investor wants exposure to this sector of the
market, higher expenses may be unavoidable.

e. Recent turnover was 107%. With trading fees of 0.25%, this turnover rate would
have reduced net return by 1.07 × 0.25% = 0.2675%.