Chapter 04 – Mutual Funds and Other Investment Companies
4-1
CHAPTER 4: MUTUAL FUNDS AND
OTHER INVESTMENT COMPANIES
PROBLEM SETS
1. The unit investment trust should have lower operating expenses. Because the investment
trust portfolio is fixed once the trust is established, it does not have to pay portfolio
2. a. Unit investment trusts: diversification from large-scale investing, lower transaction
b. Open-end mutual funds: diversification from large-scale investing, lower
transaction costs associated with large-scale trading, professional management that
c. Individual stocks and bonds: No management fee, realization of capital gains or
3. Open-end funds are obligated to redeem investor’s shares at net asset value, and thus
must keep cash or cash-equivalent securities on hand in order to meet potential
4. Balanced funds keep relatively stable proportions of funds invested in each asset class.
They are meant as convenient instruments to provide participation in a range of asset
classes. Life-cycle funds are balanced funds whose asset mix generally depends on the
Chapter 04 – Mutual Funds and Other Investment Companies
4-2
5. The offering price includes a 6% front-end load, or sales commission, meaning that
every dollar paid results in only $0.94 going toward purchase of shares. Therefore:
70.10$
NAV
7. Stock Value held by fund
A $ 7,000,000
B 12,000,000
000,000,4
8. Value of stocks sold and replaced = $15,000,000
000,000,42$
000,000,15$
9. a.
40.39$
000,000,5
000,000,3$000,000,200$
NAV =
−
=
NAVicePr −
40.39$36$−
10. Rate of return =
%8.8088.0
50.12$
50.1$50.12$10.12$
NAV
onsdistributi NAVNAV
0
01 ==
+−
=
+−
Chapter 04 – Mutual Funds and Other Investment Companies
4-3
11. a. Start-of-year price: P0 = $12.00 1.02 = $12.24
Although NAV increased by $0.10, the price of the fund decreased by: $0.99
24.12$
50.1$24.12$25.11$
P
onsDistributiPP
0
01 ==
+−
+−
b. An investor holding the same securities as the fund manager would have earned a
rate of return based on the increase in the NAV of the portfolio:
00.12$
NAV
0
12. a. Empirical research indicates that past performance of mutual funds is not highly
predictive of future performance, especially for better-performing funds. While
b. On the other hand, the evidence is more suggestive of a tendency for poor
13. NAV0 = $200,000,000/10,000,000 = $20
Dividends per share = $2,000,000/10,000,000 = $0.20
20$
14. The excess of purchases over sales must be due to new inflows into the fund. Therefore,
15. Fees paid to investment managers were: 0.007 $2.2 billion = $15.4 million
Since the total expense ratio was 1.1% and the management fee was 0.7%, we conclude
Chapter 04 – Mutual Funds and Other Investment Companies
4-4
16. As an initial approximation, your return equals the return on the shares minus the total
of the expense ratio and purchase costs: 12% − 1.2% − 4% = 6.8%
17. Suppose you have $1,000 to invest. The initial investment in Class A shares is $940 net
of the front-end load. After four 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
After paying the back-end load fee, your portfolio value will be:
Class B shares are the better choice if your horizon is four years.
With a fifteen-year horizon, the Class A shares will be worth:
For the Class B shares, there is no back-end load in this case since the horizon is greater
than five years. Therefore, the value of the Class B shares will be:
At this longer horizon, Class B shares are no longer the better choice. The effect of
18. 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 1.062
If the mutual fund is to be the better investment, then the portfolio return (r) must
satisfy:
0.96 (1 + r – 0.005)2 > 1.062
0.96 (1 + r – 0.005)2 > 1.1236
Chapter 04 – Mutual Funds and Other Investment Companies
b. If you invest for six years, then the portfolio return must satisfy:
0.96 (1 + r – 0.005)6 > 1.066 = 1.4185
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. With a 12b-1 fee instead of a front-end load, the portfolio must earn a rate of
return (r) that satisfies:
19. The turnover rate is 50%. This means that, on average, 50% of the portfolio is sold and
20. For the bond fund, the fraction of portfolio income given up to fees is:
%0.4
%6.0
= 0.150 = 15.0%
For the equity fund, the fraction of investment earnings given up to fees is:
%0.12
%6.0
= 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.
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21. 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