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THE UNIVERSITY OF HONG KONG
The School of Economics and Finance
FINA2802_FINA2320_D– Investments and Portfolio Analysis
1st SEMESTER, 2017-2018
Teaching Assistant: Jason Tse
Contact Number: 2857 8308
Email: jasontch@hku.hk
Office Hours: Mon 09:30-11:20, 14:30-17:20
Wed 17:30-18:20
Thu 09:30-10:20, 13:30-16:20
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Chapter 1 The Investment Environment
1.1 Real Assets versus Financial Assets
Real Assets
Financial Assets
1.2 Financial Assets
Fixed-income/debt securities
Equity
Derivative securities
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Chapter 2 Asset Classes and Financial Instruments
2.0 The Financial Market
Money Markets
Capital Markets
2.1 The Money Market
Treasury Bills
Time Deposits
Commercial Paper
Bankers’ Acceptance
Eurocurrency
Repos and Reverses
Federal Funds
Brokers’ Calls
LIBOR
2.2 The Bond Market
Treasury Notes and Bonds
Inflation-Protected Treasury Bonds
Federal Agency Debt
International Bonds
Municipal Bonds
Corporate Bonds
Mortgages and Mortgage-Backed Securities
2.3 Equity Securities
Common Stock
Preferred Stock
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2.4 Stock and Bond Market Indexes
Price-Weighted Average Index
invest 1 share in each stock in an index portfolio, the investment in each stock in
that portfolio is proportional to the stock price.
∑𝐧𝐢=𝟏 𝐏𝐢
𝐏𝐖𝐀𝐈 =
𝐝
where Pi is the price of the stock that is included in the index
d is the divisor
High price stock dominates the price-weighted average index.
Value-Weighted Average Index
investment in each stock in the index portfolio is proportional to the market value of
each stock.
∑𝐧𝐢=𝟏 𝐏𝐢 × 𝐐𝐢
𝐕𝐖𝐀𝐈 =
𝐝
where Pi is the price of the stock that is included in the index
Qi is the quantity of shares outstanding related to the stock that is included in
the index
d is the divisor
High market value stock dominates the value-weighted average index.
Equally-Weighted Average Index
Invest equal amount in each stock in the index portfolio.
Market performance is measured by equally weighted average return of the returns
of each stock in the index.
To reset the portfolio to equal weights, periodic rebalance is required.
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PROBLEM (Stock Market Indexes)
Consider the three stocks in the following table. Pt represents price at time t, and Qt
represents shares outstanding at time t. Stock C splits two for one in the last period.
P0 Q0 P1 Q1 P2 Q2
A 90 100 95 100 100 100
B 50 200 45 200 45 200
C 100 200 110 200 55 400
a. Calculate the price-weighted index value of the three stocks at time 0 and time 1.
(90 + 50 + 100)
At t = 0, the value of the index = = 𝟖𝟎
3
(95 + 45 + 110)
At t = 1, the value of the index = = 𝟖𝟑. 𝟑𝟑
3
b. Calculate the rate of return on a price-weighted index of the three stocks from time 0 to
time 1.
(83.33 − 80)
The rate of return = = 𝟒. 𝟏𝟕%
80
c. What is the divisor for the price-weighted index in year 2 after the stock split?
(95 + 45 + 55)
= 83.33
d
d = 𝟐. 𝟑𝟒
d. Calculate the price-weighted index value of the three stocks at time 2.
(100 + 45 + 55)
At t = 2, the value of the index = = 𝟖𝟓. 𝟒𝟕
2.34
e. Calculate the rate of return of the price-weighted index from time 1 and time 2.
(85.47 − 83.33)
The rate of return = = 𝟐. 𝟓𝟕%
83.33
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f. If the starting value of the market value weighted index is 100, calculate the rates of
return from time 0 to time 1 and the index value at time 1.
At t=0, total market value
= $90 × 100 + $50 × 200 + $100 × 200 = $39,000
At t=1, total market value
= $95 × 100 + $45 × 200 + $110 × 200 = $40,500
($40,500 − $39,000)
The rate of return = = 𝟑. 𝟖𝟓%
$39,000
At t = 1, the value of the index = 100 (1 + 3.85%) = 𝟏𝟎𝟑. 𝟖𝟓
g. If the starting value of the equally weighted index is 100, calculate the rates of return
from time 0 to time 1 and the index value at time 1.
$95 − $90
rA = = 5.56%
$90
$45 − $50
rB = = −10%
$50
$110 − $100
rC = = 10%
$100
5.56% + (−10%) + 10%
The rate of return = = 𝟏. 𝟖𝟓%
3
At t = 1, the value of the index = 100 (1 + 1.85%) = 𝟏𝟎𝟏. 𝟖𝟓
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Chapter 3 How Securities are Traded
3.1 How Firms Issue Securities
Primary Market vs. Secondary Market
Investment Banking
Shelf Registration
Initial Public Offerings
3.2 How Securities are Traded
Types of Markets
Direct Search Markets
Brokered Markets
Dealer Markets
Auction Markets
Trading Mechanisms
Dealer Markets
Electronic Communication Networks (ECNs)
Specialist Markets
3.3 & 3.4 U.S. Securities Markets and Market Structure in Other Countries
NASDAQ
The New York Stock Exchange
Electronic Communication Networks
3.5 Trading Costs
Brokerage Commission
Bid-Ask Spread
3.6 Buying on Margin
Purchasing stocks on margin means the investor borrows part of the purchase price of
the stock from a broker.
The margin in the account is the portion of the purchase price contributed by the
investor; the remainder is borrowed from the broker.
If the stock value keeps falling after the margin account is set up, there is a possibility
that the net worth/equity will become negative. In other words, the stock value is
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insufficient to cover the loan from the broker.
To guard against the risk, broker sets a maintenance margin.
If the percentage margin falls below the maintenance level, the broker will issue a
margin call, which requires the investor to add extra asset (cash or liquid securities) to
the margin account.
Buying on margin can achieve greater upside potential as well as exposing to greater
downside risk.
𝐄𝐪𝐮𝐢𝐭𝐲 𝐢𝐧 𝐚𝐜𝐜𝐨𝐮𝐧𝐭 𝐀𝐬𝐬𝐞𝐭𝐬 − 𝐋𝐢𝐚𝐛𝐢𝐥𝐢𝐭𝐢𝐞𝐬
𝐌𝐚𝐫𝐠𝐢𝐧 = =
𝐌𝐚𝐫𝐤𝐞𝐭 𝐕𝐚𝐥𝐮𝐞 𝐨𝐟 𝐒𝐭𝐨𝐜𝐤 𝐌𝐚𝐫𝐤𝐞𝐭 𝐕𝐚𝐥𝐮𝐞 𝐨𝐟 𝐒𝐭𝐨𝐜𝐤
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PROBLEM (Buying on Margin)
Dée Trader opens a brokerage account and purchases 300 shares of Internet Dreams at $40
per share. She borrows $4,000 from her broker to help pay for the purchase. The interest
rate on the loan is 8% p.a. and any interest incurred will be included in the liabilities.
a. What is the initial margin in Dée’s account when she first purchases the stock?
Dee Trader
Assets Liabilities
Internet Dreams
Loan $4,000
300 x $40 = $12,000
Owner's Equity
Equity
$12,000-$4,000= $8,000
$8,000
Initial Margin = = 𝟔𝟔. 𝟔𝟕%
$12,000
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b. If the share price falls to $30 per share by the end of the year, what is the remaining
percentage margin in her account? Please explain whether the investor will receive a
margin call if the maintenance margin requirement is 30%.
Dee Trader
Assets Liabilities
Internet Dreams
Loan $4,000
300 x $30 = $9,000
Interest Incurred
$4,000 x 8% = $320
Owner's Equity
Equity
$9,000-$4,000-$320= $4,680
The remaining percentage margin is now: $4,680/$9,000 = 52%
Since the remaining margin is 52% > 30%. Therefore, the investor will not receive
a margin call.
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c. What is the rate of return on her investment?
(Ending equity in the account Initial equity)
Initial equity
($4,680 $8,000)
=
$8,000
= −𝟒𝟏. 𝟓%
d. How low can the price of Internet Dreams fall in order to get a margin call before any
interest incurred?
Asset − Liabilities
Maintenance Margin = = 30%
Value of Stock
300P − $4,000
= 30%
300P
P = $𝟏𝟗. 𝟎𝟓
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