Chapter 04 – Mutual Funds and Other Investment Companies
1. Mutual funds offer many benefits. Some of those benefits include: the ability to invest
with small amounts of money, diversification, professional management, low
2. Close-end funds trade on the open market and are thus subject to market pricing. Open-
3. 12b-1 fees are annual fees charged by a mutual fund to pay for marketing and
distribution costs.
4. A unit investment trust is an unmanaged mutual fund. Its portfolio is fixed and does not
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
6. Hedge funds have much less regulation since they are part of private partnerships and
free from most SEC regulation. They permit investors to take on many risks unavailable
7. An open-end fund will have higher fees since they are actively marketing and managing
8. Asset allocation funds may dramatically vary the proportions allocated to each market
4-1
10. Open-end funds must honor redemptions and receive deposits from investors. This flow
11. The offering price includes a 6% front-end load, or sales commission, meaning that
12. NAV = Offering price (1 – load) = $12.30 .95 = $11.69
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
Market v alue of assets － Market value of liabilities
S h ares outstanding
=
$42,000 ,000−$30 ,000
4, 000 ,000
= $10.49
14. The value of stocks sold and replaced = $15,000,000.
Turnover rate =
Value of stocks sold or replaced
Value of assets
15.
a. NAV =
Market v alue of assets － Market value of liabilities
S h ares outstanding
$200,000,000 － $3,000,000
5,000,000
b. Premium (or discount) =
=
$36−$39. 40
$39 . 40
= –0.0863 = –
8.63%
The fund sells at an 8.63% discount from NAV.
16. Given the NAV at the beginning and the end of the period, and the distributions during
the period, we can use the equation below to solve for the rate of return of the
8.80%
17. As the price of a close-end fund may deviate from its NAV, we instead use the price of
the net asset value when we calculate the rate of return:
a. Start of year price = $12.00 1.02 = $12.24
Δ(Price) － Distributions
S tart of year p rice
4.19%
b. An investor holding the same portfolio as the fund manager would have earned
a rate of return based on the increase in the NAV of the portfolio:
4-3
13.33%
18. Assume a hypothetical investment of $100. The end value of the investment will be
equal to I × (1 – front-end load) × (1 + r – true expense ratio)T
Loaded-Up
19.
a. NAV =
Market v alue of assets － Market value of liabilities
Shares outstanding
$450,000,000 － $10 ,000,000
44,000,000
b. Because 1 million shares are redeemed at NAV = $10, the value of the portfolio
decreases to:
Portfolio value = $450million – ($10 × 1million) = $440million
The number of shares outstanding will be the current shares outstanding minus
the number of shares redeemed: 44million – 1million = 43million.
Thus, net asset value after the redemption will be:
NAV =
Market v alue of assets － Market value of liabilities
Shares outstanding
=
$4 4 0,000,000 － $10 ,000,000
4 3 ,000,000
= $10
20.
a. Empirical research indicates that past performance of mutual funds is not highly
predictive of future performance, especially for better-performing funds. While
there may be some tendency for the fund to be an above average performer next
year, it is unlikely to once again be a top 10% performer.
4-4
Δ(NAV) － Distribution s
S tart of year NAV
21. Start of year NAV =
Market v alue of assets － Market value of liabilities
Shares outstanding
=
$200,000,000
10,000,000
= $20
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
Value of assets
$2,200,000,000
23. Fees paid to investment managers were: 0.7% × $2.2 billion = $15.4 million.
0.004 × $2.2 billion = $8.8 million.
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:
25. 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
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
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
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
27. The turnover rate is 50%. This means that, on average, 50% of the portfolio is sold and
28. For the bond fund, the fraction of portfolio income given up to fees is:
0 .6
4 . 0
= 0.150 = 15.0%
For the equity fund, the fraction of investment earnings given up to fees is:
0 . 6
12. 0
= 0.050 = 5.0%
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.
29. 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