Tutorial 2 - Solutions - Risky and complete portfolio PDF

Preview

Summary

Risky and complete portfolio...

Description

Investment and Portfolio Management

TOPIC 2 – TUTORIAL 2 1. Would you expect a typical open-end fixed-income mutual fund to have higher or lower operating expenses than a fixed-income unit investment trust? Why? Unit investment trust: - Fixed portfolio: once the trust is established => the portfolio will be fixed from then until the end of the life of the trust. - Fixed life: 5-7 years. At the end of the life of the trust, investors will vote whether they want to keep the trust going or not. ð Unmanaged investment vehicles ð Very low management fees

Investment vehicles

Unmanaged

Unit investment trust - very low management fee

Managed

Actively managed high management fee

Passively managed - low management fee

Mutual funds

Index fund

Hedge funds

ETF

2. Why can closed-end funds sell at prices that differ from net asset value while open-end funds do not? Open-end fund shares are traded between IC and investors - they are sold by the mutual funds directly to the investors ð the price is decided by NAV Closed-end fund shares are issued by the IC but after that are traded in the secondary market so the market price of fund share is decided by the supply and demand of the investors. ð the price may differ from NAV

Investment and Portfolio Management

3. The composition of the Fingroup Fund portfolio is as follows:

a. 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? b. 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? a. 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 Net asset value =

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

b. Value of stocks sold and replaced = $15,000,000 Turnover rate =

$15,000,000 = 0.357, or 35.7% $42,000,000

4. 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? b. If the fund sells for $36 per share, what is its premium or discount as a percent of net asset value? a. NAV =

b.

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

Pr ice - NAV $36 - $39.40 = = –0.086, or -8.6% NAV $39.40 The fund sells at an 8.6% discount from NAV

Premium (or discount) =

Investment and Portfolio Management

5. City Street Fund has a portfolio of $450 million and liabilities of $10 million. If 44 million shares are outstanding, what is net asset value? Net asset value =

$450, 000, 000 - $10, 000000 = $10 44, 000, 000

6. 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? NAV1 - NAV0 + Distributions $12.10 - $12.50 + $1.50 = = 0.088, or 8.8% NAV0 $12.50

7. 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? Turnover ratio = value of stock sold or replaced during the period / value of assets = $400m / $2.2 b = 18.18% 8. 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? Normally, offering price should be larger than NAV Because offering price = NAV + fee OP = NAV + fee OP = NAV + % of OP OP - % of OP = NAV ð OP = NAV / (1 - %) Per share: NAV0 = $20 (NAV at the beginning) ð P0 = NAV0 + fee = 20 / (1 – 4%) = 20.83 => actual initial investment Increase in value by 12%, expense ratio 1.2% - Percentage of NAV0 ð NAV1 = NAV0 x (1 + 12% - 1.2%) = 22.16 ð If you sell your shares at the end of the year: P1 = NAV1 ð RoR = (EV – BV) / BV = (P1 – P0) / P0 = (22.16 – 20.83) / 20.83 = 6.4% P0 = $20 (Price at the beginning) ð NAV0 = P0 – fee = 20 * (1 – 4%) = 19.2 ð NAV1 = 19.2 * (1 + 12% - 1.2%) = 21.3 ð If you sell your shares at the end of the year: P1 = NAV1 ð RoR = (EV – BV) / BV = (P1 – P0) / P0 = (21.3 – 20) / 20 = 6.4%

Investment and Portfolio Management

9. 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: a. 1 year? b. 3 years? c. 10 years? Assume $1,000 investment

Loaded-Up Fund

Economy Fund

Yearly growth (r is 6%)

(1 + r - .01 - .0075)

(.98) ´ (1 + r - .0025)

t = 3 years

$1,042.50 $1,133.00

$1,036.35 $1,158.96

t = 10 years

$1,516.21

$1,714.08

t = 1 year

In long term (long enough), the benefits of lower annual operating expense will outweight the disadvantages of high front-end load fee. Depends on your time horizon (how long do you want to invest?), you will choose a suitable fund with suitable fund fee.

Extra exercises: 1. What are some comparative advantages of investing in the following? a. Unit investment trusts. b. Open-end mutual funds. c. Individual stocks and bonds that you choose for yourself. a.

Unit investment trusts: Diversification from large-scale investing, lower transaction costs associated with large-scale trading, low management fees, predictable portfolio composition, guaranteed low portfolio turnover rate.

b.

Open-end mutual funds: Diversification from large-scale investing, lower transaction costs associated with large-scale trading, professional management that may be able to take advantage of buy or sell opportunities as they arise, record keeping. Individual stocks and bonds: No management fee; ability to coordinate realization of capital gains or losses with investors’ personal tax situations; capability of designing portfolio to investor’s specific risk and return profile.

c.

2. 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?

Investment and Portfolio Management

b. What would have been the rate of return to an investor who held the same securities as the fund manager during the year? a. Start-of-year price: P0 = $12.00 × 1.02 = $12.24 End-of-year price: P1 = $12.10 × 0.93 = $11.25 Although NAV increased by $0.10, the price of the fund decreased by $0.99. Rate of return =

P1 - P0 + Distributions $11.25 - $12.24 + $1.50 = = 0.042, or 4.2% P0 $12.24

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: NAV1 - NAV0 + Distributions $12.10 - $12.00 + $1.50 = = 0.133, or 13.3% NAV0 $12.00

3. Consider a mutual fund with $200 million in assets at the start of the year and 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 the fund’s 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 Rate of return =

$21.384 - $20 + $0.20 = 0.0792, or 7.92% $20...