Seoul National University
Department of Economics
Stocks, Bonds & Derivatives 1
(212.338A Fall 2024)
Prof. Lee, Phil Sang
T, Th 09:30-10:45
Rm. 83-505
Office Hr : Tue. 11:00 – 12:00(101-514)
This course is the introductory course in modern theory of investments. It will provide you with b
ackground in the organization of various securities markets, and fundamental knowledge in
s
ecurities such as stocks, bond, or options and futures contracts. Emphasis is directed at valuation of
capital assets and risk management, and will introduce you to the principles of trades and
por
tfolio construction.
1
Textbook:
1. (textbook) Bodie, Kane & Marcus, Essentials of Investments, 12th ed. McGraw-Hill International
Edition
2. (reference) 이필상, 안동현, 손삼호, 최영민
- 주식의 이해, - 채권의 이해, - 파생상품의 이해, 홍문사 2022
3. (reference) 이필상, 정치가 망친 경제 경제로 살릴 나라, 비전브리지 2020.8
4. PPT Lecture Note (print out & Bring into class)
Exam: Midterm Oct. 29, Final Dec. 10, Essay Quiz Nov. 19
Gradings:
Exam
(100 points)
Final≥ Midterm
(70%)
(30%)
Final< Midterm
(50%)
(50%)
Essay Quiz
(5 points)
Essay Quiz on Current
Economic issues
2
Topics:
Part I. Elements of Investments
1. Economic Environment & Investment
2. Financial Instruments
3. Securities Markets
4. Mutual Funds and Hedge Funds
ch.1
ch.2
ch.3
ch.4,20
Part II. Portfolio Theory
1. Risk and Return
ch.5
2. Efficient Diversification
ch.6
3. CAMP and APT
ch.7
4. Behavioral Finance
ch.9
5. State Preference Theory and Portfolio Choice
Part III. Debt Securities
1. Bond Pricing
ch. 10
2. Term Structure
ch. 10
3. Duration
ch. 11
4. Immunization
ch. 11
Part IV. Derivative Markets
1. Futures and Options
2. Types of Trade
ch.15,17
ch.15,17
3. Futures Prices
ch.17
4. Options Prices
ch. 16
5. SWAP
ch.17
Part V. Security Analysis and Investment Management
1, Macroeconomic and Industry Analysis
ch.12
2. Equity Valuation
ch.13
3. Financial Statement Analysis
ch.14
4. Investment Management Process and Performance Evaluation
ch.22
4
Lecture Note
Stocks, Bonds & Derivatives
Prof. Lee, Phil Sang
Fall 2024
What to Learn?
I. Securities Markets
II. Portfolio Theory
III. Bond Prices and Yields
IV. Derivative Markets
V. Financial Analysis
Appendix. Black-Scholes Model of Option Pricing
6
I. Securities Markets
1. Financial Markets
2. Financial Instruments
3. Securities Trading
4. Mutual Funds and Hedge Funds
1. Financial Markets
(1) Consumption and Investment
C
E
Slope = -1.05
9
(2) Fisherian Separation
t=1
-(1+r)
P
C
E
0
t=0
10
(3) Assets
Real assets
: Assets used to produce goods and services
Financial assets
: Claims on real assets or the income generated by them.
11
(4) Financial Assets
Debt (fixed - income securities)
Equity
Derivative Securities
Venture Capital
Private Equity
Cryptocurrency
12
(5) Financial Markets
Valuation of financial assets
Allocation of resources and risk
Accumulation of national wealth
Information processing and surveillance
13
(6) Investment Process
Asset Allocation
Security analysis
Security selection
Rebalancing
Passive management (Diversified portfolio)
Active management (Attempt to identify mispriced securities)
14
The players
buyers
sellers
business firms
investors
business firms
non-profit
organizations
securities
markets &
intermediaries
governments
financial
institutions
15
(8) Financial intermediation
Primary market
Secondary market
Investment Bank
Investment Companies
Fintech and Financial Innovation
16
2. Financial Instruments
(1) Money Market vs Capital Market
Money markets : short-term, marketable, liquid, low-risk debt
securities
Capital markets : longer-term, riskier securities, i.e long-term debt,
equity, derivatives
18
Money Market Instruments
Treasury bills (TB, 0~1 year)
Certificate of deposits (CD)
Commercial paper (CP)
Banker’s acceptance (BA)
Euro dollars
Repos and Reverses
Federal Funds (Loans of banks with excess reserve to banks with
shortages)
LIBOR market
Money market funds (MMF)
19
Bond Market Instruments
Treasury notes (1~10 years) & Bonds (10~30 years)
International bonds
Municipal bonds (Muni’s)
Corporate bonds
Mortgage-Backed-Securities (MBS) etc.
Equity Securities
Common stocks
Preferred stocks
Depository receipts (DR)
21
(2) Risk-Return Trade-off
E(r)
futures
options
stocks
rf
warrants
bonds
0
22
(3) Market Indexes
DJIA 30 (price weighted)
S&P 500 (value weighted)
NASDAQ (National Association of Securities Dealers Automated Quotes System)
Nikkei
FTSE (UK)
DAX (Germany)
Hangseng (Hong Kong)
TSX (Toronto)
MSCI (Morgan Stanley capital international 50 country index)
EAFE(European, Australian, Far East index, Moragan Stanley)
KOSPI
KOSDAQ
Merrill Lynch bond index
Barclays bond index
Salomon Smith Barney bond index
23
(4) Derivatives
Call option
Put option
Futures contracts
Swaps
Warrants
CDO (Collateralized debt obligation)
CDS (Credit default swap)
24
(5) Exercise
The average rate of return on investments in large stocks has
outpaced that on investments in Treasury bills by about 7% since
1926. Why, then does anyone invest in Treasury bills?
→ Treasury bills serve a purpose for investors who prefer a low-risk
investment. The lower average rate of return compared to stocks
is the price investors pay for predictability of investment
performance and portfolio value . Also , they tend to be more
liquid, or at least more stable. So, if someone thought they might
need cash relatively quickly then they would prefer Treasury bills.
25
3. Securities Trading
(1) Public offering (IPO, SEO)
Underwriting
Syndicate
issuing firm
prospectus
lead underwriter
investment bank A
investment bank B
investors
→ investment banks bear the price risk
investment bank n
(2) Private Placement
Sell shares directly to a small number of institutional
or wealthy investors
28
(3) Types of markets
Direct search markets
Brokered markets
Dealers markets (markets in which traders specializing in particular
assets buy and sell for their own accounts)
Auction markets
29
Types of orders
Market orders
- bid price (the price at which a dealer or other trader is willing
to purchase a security)
- ask price (the price at which a dealer or other trader will sell a
security)
Price-contingent orders
- limit order(an order specifying a price at which an investor is
willing to buy or sell a security)
- stop order (trade is not to be executed unless stock hits a limit
price)
30
(4) Trading Mechanism
Dealer markets (OTC)
- Blocks (large number of shares of stocks are bought and sold)
Electronic communication networks (ECNs)
Specialist markets (e.g., NYSE, a trader who makes a market in the
shares of firms and who maintains a “fair and orderly market” by
dealing personally in the market)
T+1 settlement
Buying on margin (the act of taking advantage of broker’s call loans.
The margin is the net worth of investor’s account)
Short sales (The sale of shares not owned by the investor but
borrowed through a broker and later purchased to replace the
borrowed)
31
(5) New trading strategies
Algorithmic trading
High frequency trading
Dark pools
32
(6) Exercise
Firms raise capital from investors by issuing shares in the primary
markets. Does this imply that corporate financial managers can
ignore trading of previously issued shares in the secondary market?
→ Even if the firm does not need to issue stock in any particular
year, the stock market is still important to the financial manager.
The stock price provides important information about how the
market values the firm’s investment projects. For example, if the
stock price rises considerably, managers might conclude that the
market believes the firm’s future prospects are bright. This might
be a useful signal to the firm to proceed with an investment such
as an expansion of the firm’s business.
33
In addition , the fact that shares can be traded in the secondary
market makes the shares more attractive to investors since they
know that, when they wish to, they will be able to sell their shares.
This in turn makes investors more willing to buy shares in a
primary offering, and thus improves the terms on which firms can
raise money in the equity market.
34
4. Mutual Funds and Hedge Funds
(1) Investment Funds
Open-end funds (A fund that issues or redeems its shares at net
asset value)
Closed-end funds (shares may not be redeemed, instead are traded)
Commingled funds (partnership, similar to open-end)
Real estate investment trusts (REITs, closed-end)
36
(2) Mutual Funds
Money market funds
Equity funds
Specialized sector funds
Bond funds
International funds
Balanced funds (hold both stock & bond)
Asset allocation and flexible funds (market timing)
Index funds (performance matched to index)
Exchange traded funds (ETF)
37
(3) Hedge Funds
Private investment pool
Exempt from SEC regulation (private partnership)
Lock-up
More speculative than mutual funds
38
(4) Exercise
What are the benefits to small investors of investing via mutual
funds? What are the costs?
→ Professional fund managers perform advanced portfolio
managements by diversifying risk . However , they sometimes
charge too much fee . Also , fund managers might abuse their
authorities.
39
II. Portfolio Theory
1. Risk and Return
2. Efficient Diversification
3. CAPM and APT
4. Behavioral Finance
5. Technical Analysis
6. State Preference Theory and Portfolio Choice
1. Risk and Return
(1) Returns
1st
5%
2nd
12.5%
3rd
-10%
4th
12.5%
42
IRR
Cash Flow
(mil)
t=0
t=1
t=2
t=3
t=4
-1.0
-0.1
-0.5
+0.8
+1.0
43
Holding Period Return
44
(2) Measurement of Risk
Prob.
A
B
0.5
110
300
0.5
90
-100
mean
100
100
St. dev
10
200
standard deviation is a measure of risk.
45
(3) Calculation of Return and Risk
46
(4)VaR (Value at Risk)
Measure of downside risk. The worst loss that will be
suffered with a given probability, often 5% VaR can be derived
from mean and standard deviation of the distribution, i.e., a value
that is 1.64485(5th percentile of a normal distribution with a mean
of zero and a variance of 1) standard deviations below the mean
would correspond to a VaR of 5%
VaR=E(r)-1.64485σ
47
2. Efficient Diversification
(1) Return and Risk of Portfolio
Prob
Prob
0.5
0.5
0.03
0.025
0.10
0.5
0.03*0.7+0.1*0.3=0.051
0.05
0.5
0.025*0.7+0.05*0.3=0.0325
49
50
1.1
-0.1
2.25
4.31
1.0
0.0
2.5
4
0.9068
0.0932
2.73
3.901
0.9
0.1
2.75
3.902
0.8
0.7
0.2
3
4.03
0.3
3.25
4.37
0.6
0.5
0.4
3.5
4.88
0.5
3.75
5.51
0.4
0.6
4
6.22
0.3
0.7
4.25
6.99
0.2
0.8
4.5
7.79
0.1
0.9
4.75
8.63
0.0
1.0
5
9.5
-0.1
1.1
5.25
10.38
security2
5
2.73
MVP
security1
2.5
0
3.901 4
9.5
51
(2) Exercise
52
(3) Risk Diversification
Prob
Umbrella
Ice cream
Sun
0.5
-10%
+25%
Rain
0.5
+50%
+5%
E(r)
0.2
0.15
0.3
0.1
53
1.1
-0.1
2.25
5.35
4.501
4.31
4.01
1.0
0.0
2.5
4
4
4
4
3.45
4
0.9
0.1
2.75
2.65
3.723
3.902
4.15
4.55
0.8
0.2
3
1.3
3.721
4.03
4.46
5.1
0.7037
0.2963
3.24
0.00
3.96
4.36
4.86
5.63
0.6
0.4
3.5
1.4
4.49
4.88
5.41
6.2
0.4
0.6
4
4.1
5.92
6.22
6.64
7.3
0.2
0.8
4.5
6.8
7.64
7.79
8.03
8.4
0.0
1.0
5
9.5
9.5
9.5
9.5
9.5
-0.1
1.1
5.25
10.85
10.46
10.38
10.25
10.05
54
security2
security1
0
55
unique risk
market risk
56
(4) Exercise
57
58
(5) Exercise
59
60
(2) Prove that there always exists risk diversification effect if you make a portfolio
combining risky assets. If the short selling is undertaken, what happen to your
proof?
→
61
62
(6) Optimal Portfolio with Risk-free Asset
CAL(Capital Allocation Line)
stock or portfolio of stocks
0
63
Optimal portfolio of risk-free asset and risky assets
CAL
optimal risky portfolio
0
64
(7) Efficient Frontier & CML
C
D
B
E
A
0
65
efficient frontier of risky assets
Portfolio
Stock
stock
MVP
Bond
0
66
CML(Capital Market Line)
M
MVP
0
Everybody holds the replica of market portfolio of risky assets.
(Portfolio separation)
Only systematic risk is rewarded.
Linear relationship between return and systematic risk.
67
(8) Calculation of Systematic Risk
68
69
(9) Exercise
70
71
72
(10) Exercise
73
74
3. CAPM and APT
(1) CAPM
SML(Security Market Line)
76
(2) Exercise
77
Multifactor Model
78
(3) Arbitrage Pricing Theory
79
(4) Efficient Market Hypothesis
3 versions of information set
strong form set
semi-strong form set
weak form set
Weak form – the history of past trading
Semi-strong form – all publicly available information
Strong form – all relevant information including inside information
80
(5) Exercise
Everybody holds the replica of market portfolio of risky assets. Why?
Is it always true?
→ Portfolios composed of market portfolio and riskless asset
guarantee lowest risk given any expected return. Therefore,
investors can minimize risk by investing in market portfolio
regardless of their preference structures. However, financial markets
are usually incomplete and some investors do not behave rationally,
therefore it may not hold in reality.
81
(6) Exercise
State
Probability
A
0.5
0.09
0.08
B
0.5
0.11
0.12
82
83
4. Behavioral Finance
(1) Behavioral Irrationalities
There are behavioral irrationalities that characterize investor
decision making. The behavioral shortcomings may be consistent
with market anomalies.
Issues :
- Errors in Information processing
- Behavioral Biases
- Limits to Arbitrages
85
(2) Errors in Information processing
The information processing errors can lead to misestimate the true
returns
➀ Forecasting errors
People tend to give too much weight to recent experience
➁ Overconfidence
People tend to overestimate the precision of their beliefs or forecasts,
and tend to overestimate their abilities
➂ Conservatism
Investors are too slow in updating their beliefs
➃ Representativeness Bias
People are prone to believe that a small sample is representative of a
broad population
86
(3) Behavioral Biases
Even if information processing were perfect, still the investors tend
to make irrational decision making.
➀ Framing
Decisions are affected by how choices are posed. For example, Trump vs Biden,
and Trump vs Harris.
➁ Mental Accounting
A specific form of framing, e.g., an investor may act risk seeking with his own
account but act risk averse with his child’s account
③ Disposition Effect
The reluctance of investors to sell shares that have fallen in price
87
➃ Regret Avoidance
People blame themselves more for unconventional choices that turn
out badly. So they avoid regret by making conventional decisions.
⑤ Prospect Theory
Investor utility function depends on gains or losses from investor’s
starting position, rather than on their levels of wealth.
Conventional
Prospect Theory
U
U
Risk Aversion
Risk Aversion
Risk Seeking
0
Wealth
∆ in Wealth
88
(4) Limits to Arbitrage
Behavioral biases would not matter if arbitrageurs could fully
exploit the mistakes of behavioral investors. But in practice, several
factors limit the ability to profit from mispricing.
➀ Fundamental Risk
Markets can remain irrational. The fundamental risk may limit the
activity of traders.
➁ Implementation Costs
Exploiting overpricing can be particularly difficult. For example,
short selling may not be free or entails costs.
89
➂ Model Risk
People may use a faulty model to value the security, which limits the
extent of arbitrage to which it will be pursued.
➃ Violation of Law of one price.
This may well limit the arbitrage.
90
(5) Exercise
What happens to the pricing of individual securities(CAPM) if
investors in the market have a tendency of framing?
→ CAPM hardly holds because the risk is not properly rewarded.
91
(6) Behavioral Irrationalities and
Stock Market Bubble
92
5. Technical Analysis
(1) Technical Analysis
Technical analysis is the search for recurring and predictable
patterns in stock prices. But the fundamental question is that the past
may not recur. They do not deny the value of fundamental
information but believe that prices only gradually close in an
intrinsic value
94
(2) Basic Findings
① Resistance level : a price level above which it is supposedly unlikely
for a stock or stock index to rise
② Support level : a price level below which it is supposedly unlikely for
a stock or stock index to fall
③ Momentum effect : the tendency of abnormal performance to continue
in following periods
④ Book-to-market effect : the tendency for investments with high ratios
of book value to market value to generate abnormal returns
⑤ P/E effect : portfolio of low P/E stocks have exhibited higher returns
⑥ Small - firm effect : stocks of small firms have earned abnormal
returns, primarily in the month of January
⑦
Anomalies : patterns of returns that seem to contradict the efficient market
hypothesis
95
(3) Trends and Corrections
➀ Moving Average
Average price over a given interval, e.g., 50 days which is updated
as time passes.
Stock
price
B
A
MA
day
Point A is a bullish signal because it signifies a shift from a falling
trend with prices below the moving average to a rising trend with
prices above the moving average. Vice versa point B.
96
➁ Point and Figure Chart
Simply traces significant upward or downward movements with a
designated width of price change.
Example
Price History
40
40.5
41
42*
41.5
42.5
43
43.75
44*
45
44
41.5*
41
40
39*
39.5
39.75
38
36*
37
39*
* Indicates an event that has resulted in an increase or decrease of at
least $2
Adv
+2
+1
0
-1
Dec
Adv
⨯
⨯
○
○
⨯
○
Sell signals are generated when stock prices penetrates previous
lows for those who want to sell and vice versa.
97
③ Breadth
The extent to which movement in a market index is reflected in
movements of individual stock prices. The most common measure
of breadth is spread between the number of stocks that advance and
decline in price. If advance outnumber declines the market may be
viewed as being stronger.
④ Relative strength
Recent performance of a given stock or industry compared to that of
a broader market index.
98
(4) Sentiment Indicators
99
➂ Put/call ratio
Ratio of put options to call options outstanding on a stock.
Increase in the ratio signals bearish, as it indicates growing interest
in put options as a hedge against market decline. But the opposite
also may hold. The investors may believe that a good time to buy is
when the rest of the market is bearish.
➃ Short interest
The total number of stocks sold short.
Bullish signal in that all short sales must be covered. Bearish signal
in that short-sellers tend to be larger.
100
6. State Preference Theory
(1) Security as a Contingent Claim
Given (ya ,yb , ,ys;πa ,πb , ,π s),
choose (ca ,cb , ,cs;πa,πb, ,πs)
Fisher
Market
Opportunity
Max
Utility
↓
↓
SPT
102
Consider,
Sec1. x1=(x1a,x1b)=(10,20),ϕx1=15,W0=900
103
Consumption Choice
D
104
Spanning
105
(2) A-D (Arrow-Debreu)
Primitive Security
ca=(1,0) → ϕa=?
cb=(0,1) → ϕb=?
106
(3) Third Security Pricing
Third security pricing
107
a b c ⋯ S
Ca 1 0 0 ⋯ 0
Cb 0 1 0 ⋯
⋮ 0 0 1 ⋯
Cs 0 0 0 ⋯ 1
108
(4) Exercise
109
110
(5) Exercise
111
112
(6) Exercise
.
113
(7) CAPM vs SPT
114
1. Bond Pricing
(1) Variations in Bonds
① Callable bonds : Bonds that may be repurchased by the issuer at
a specified call price during the call period.
② Convertible bond : A bond with an option allowing the
bondholder to exchange the bond for a specified number of
shares of common stock in the firm.
③ Put bond : A bond that the holder may choose either to exchange
for par value at some date or to extend for a given number of
years.
④ Floating-rate bond : Bonds with coupon rates periodically reset
according to a specified market rate
⑤ Sinking Fund : A bond indenture that calls for the issuer to
periodically repurchase some proportion of the outstanding
bonds prior to maturity
⑥ Debenture : A bond not backed by specific collateral.
116
(2) Bond Management
① Substitution swap : Exchange of one bond for a bond with
similar attributes but more attractively priced.
② Intermarket spread swap : Switching from one segment of the
bond market to another
③ Rate anticipation swap : A switch made in response to forecasts
of interest rate changes.
④ Pure yield pickup swap : Moving to higher yield bonds, usually
with longer maturities
⑤ Tax swap : Swapping two similar bonds to receive a tax benefit
⑥ Horizon analysis : Forecast of bond returns based largely on a
prediction of the yield curve at the end of the investment horizon.
117
(3) Bond Pricing
P
P
Premium
Discount
0
r
T
time
118
(4) Exercise
As maturity nears, the bond price approaches to its face value. Is it always true? Why?
→ It is generally true. But in case of coupon bond the price may move above and below face
value depending on the interest rate movement in the market during the period before the
maturity.
119
(5) Exercise
What happens to the price of bonds if the national income falls due to
the slow economic growth. In this case what happens to the financial
cost of business firm.
→ If the national income decreases, the demand for bonds falls. Then
the price of bonds will fall, which will cause the financial cost of
business firms to rise.
120
2. Term Structure and Duration
(1) Bond Yields
122
123
(2) Exercise
124
(3) Exercise
125
(4) Exercise
Two bonds have identical times to maturity and coupon
rates . One is callable at 111 . The other at 106. Which
should have the higher yield to maturity? Why?
→ The bond callable at 106 requires the issuing firm to
pay bondholders 106% of the bond’s face value if the firm
decides to call the bond. The second bond should therefore
sell for a lower price because the call provision is more
valuable to the firm that issued it. Therefore, that bond’s
yield to maturity should be higher than that of the bond
callable at 111.
126
(5) Term Structure
YTM
ascending
flat
descending
0
Maturity date
127
(6) Macaulay’s Duration
128
129
130
(7) Exercise
Bond
Years to Maturity
Market Price
A
1
900
B
2
880
YTM
0.11
0.066
1
2
Maturity
131
b . If the term structure is descending , what happens to the
allocation of funds in the market?
→ Since bond with shorter maturity has higher YTM and
liquidity, the demand for short term bond increases, while the
demand for long term bond decreases. The long term trade of
funds decreases , thus discourages long term business
investments.
132
(8) Exercise
How can perpetuity, which has an infinite maturity have a
duration as short as 10 or 20 years?
→ Duration can be thought of as a weighted average of the
maturities of the cash flows paid to holders of the perpetuity,
where the weight for each cash flow is equal to the present
value of that cash flow divided by the total present value of
all cash flows. For cash flows in the distant future, present
value approaches zero(i.e., the weight becomes very small)
so that these distant cash flows have little impact , and
eventually, virtually no impact on the weighted average.
133
134
(9) Exercise
135
Midterm Exam Review (1)
136
137
138
Midterm Exam Review (2)
(1) Explain how the portfolio separation theorem holds. Under what conditions does
the theorem hold?
→ Refer to Slide
Conditions ① homogeneous expectations
② rational and risk averse investors
139
(2) Explain the relationship between CML and SML. How do you derive CAPM?
→ Refer to Slide
140
(3) What is the prospect theory? If the prospect theory holds, what happen to CAPM?
Explain.
→ Refer to Slide
CAPM assumes risk aversion and risk diversification. If the prospect theory holds, then
CAPM may not hold.
141
Midterm Exam Review (3)
142
(2) If the coupon rate is equal to bond yield, the price of bond is equal to face value
regardless of maturity. Provide a proof.
→ Refer to Slide
143
144
3. Immunization
(1) Immunization
A strategy to shield net worth from interest rate movements.
Investment Strategy
à Duration of Investment = Duration of Assets
(Ex) An investor needs a fund (liability) of $10,898.23 in 2.91 years. In order to
meet the needs, the investor chooses to purchase a bond (asset) with F=$10,000,
coupon rate =3% per year, maturity = 3 years. The YTM is 3%.
t=0
t=1
t=2
Fund
Bond
t=3
10,898.23
300
300
10,300
Bond(net position)
Fund
Interest
Rate
FV
(t=2.91)
PV
FV
(t=2.91)
PV
2.5%
10,898.44(0.21)
10,142.80(0.19)
10,898.23
10,142.61
3.0%
10,898.23(0.00)
10,000.00(0.00)
10,898.23
10,000.00
3.5%
10,898.07(-0.16)
9,859.92(-0.14)
10,898.23
9,860.06
The fund will be fully provided if the rate
changes about at 3% by a small amount
146
Investment Strategy
→ Duration of assets = Duration of liabilities
PV
10,142.80
10,142.61
10,000.00
9,860.06
9,859.92
Fund(Single Payment)
Bond(Coupon)
0
2.5%
3%
3.5%
147
(2) Convexity
60
40
20
0
Not necessarily tangent
-3
-2
-1
0
+1
+2
+3
actual
-20
-40
duration approximation
-60
148
149
P
0
150
(3) Exercise
151
152
(4) Exercise
.
153
IV. Derivatives Markets
1. Futures and Options
2. Types of Trades
3. Futures Prices
4. Option Prices
5. Swap
1. Futures and Options
(1) Forwards and Futures
Forward
An agreement to buy or sell an asset at a certain future time for a certain price traded on OTC
(Over-The-Counter) markets
A Korean firm is to receive $1million in 3 months exposed to FX risk. To hedge the risk, short
FX forward at $1= \1,020, which means $1million= \1,020 million in 3 months (binding
commitment).
Payoff of
Long
Forward
1020
FX Rate
In 3 Months
Short
156
Futures
Standardized forward contract traded on an exchange. The exchange guarantees that the two
parties honor the contract by marking to the market (daily settlement).
Clearing
On Sept. 15, an investor takes a long position on one contract of Dec. futures on KOSPI 200 at
350 points where 1 point represents \ 500,000, then the initial margin should be \26,250,000
(= 350*500,000*0.15) and the maintenance margin should be \19,687,500 (= 26,250,000*0.75).
Then, the daily settlement procedure is as follows;
Date
Event
KOSPI 200 IN
DEC
Sep. 15
Long 1 contract
350
Sep. 16
Price changes
380
\15,000,000
((380-350)*\500,000)
\41,250,000
(\26,250,000+\15,000,000)
Sep. 17
Price changes
345
-\17,500,000
((345-380)*\500,000)
\23,750,000
(\41,250,000-\17,500,000)
330
-\7,500,000
((330-345)*\500,000)
\10,000,000
(\26,250,000 - \16,250,000)
\16,250,000
(\23,750,000-\7,500,000)
\15,000,000
((360-330)*\500,000)
\41,250,000
(\26,250,000+\15,000,000)
\0
Price changes
Sep. 18
Margin call
Sep. 19
Net Gain
Price changes
Counter trade
360
Gain./Loss
Margin Account
\26,250,000
\26,250,000
\41,250,000-\26,250,000-\10,000,000 = (360-350)*\500,000=\5,000,000
157
50,000,000
\ 41,250,000
\ 41,250,000
40,000,000
30,000,000
initial margin
26,250,000
= \ 26,250,000
maintenance margin
19,687,500
= \ 19,687,500
\ 16,250,000
Sept. 15
Sept. 16
Sept. 17
Sept. 18
Sept. 19
158
(2) Delivery vs Non-delivery
Consider a firm which needs raw materials in 3 months, of which price is expected to
rise. Long futures with the maturity of 3 months at a price F = 1,100.
(S = F)
t=0
t=1
t=2
t=3
Spot prices (S)
1,000
1,100
1,200
1,300
Future price (F)
1,100
1,150
1,250
1,300
Settlements and
delivery at t = 3
+ 50
+ 100
+50
-1,300
Settlements but no delivery,
buy spot at t = 3
+50
+ 100
+ 50
- 1,300
159
(3) Options
Option
A right to buy or sell an asset at a specified price on a specified day.
Call Option: A right to buy S at X in T
Put Option: A Right to sell S at X in T
Example
Call option for a stock issued by a company.
S0 = \ 500,000, C = \ 20,000, X = \ 500,000, T = 3 months.
profits
long call
+20,000
0
X = 500,000
ST
-20,000
short call
losses
Warrant : An option issued by the firm to purchase shares of the firm’s stock
160
Example
Put option for the KOSPI200 Index.
S0 = 350, P = 3.45, X = 355, T = 3 months.
profits
+3.45
short put
0
-3.45
ST
X = 355
long put
losses
161
(4) Combinations of Options
Covered Call
1. Sell call,
2. Buy futures.
Example
X=45, C=2.125,T=Dec. , f=45.75.
+F
2.125
combined
45.75
ST
-C
X=45
162
Protective Put
1.Buy stock,
2.Buy put.
Example
S=45.75, X=45, T=Dec., P=1.5
+S
combined
45.75
ST
+P
-2.25
X=45
163
Example
Collar : Options strategy that brackets the value of a portfolio between two bounds.
164
Bearish Spread
Example
1.Buy call X=50, T=Dec., C=1/2
2.Sell call X=45, T=Dec., C=2 1/8
+C
2+1/8
0
-1/2
ST
combined
-C
X=45
X=50
165
Butterfly Spread
Example
Bullish Spread +Bearish Spread.
Bullish
0
ST
Butterfly
Bearish
X=40
X=45
X=50
166
2. Types of Trades
(1) Futures - Hedge
Example
We have $ 1 million debt to pay in Dec. Given
Spot $ 1 = \1,350
Dec. Futures $ 1= \1,360
Long Dec. Futures at $ 1 = \ 1,360. Then,
1,350
1,360
0
Spot Rate (\/$)
in Dec.
Hedge
No Hedge
168
Example
We have $ 1 million debt to pay in Dec. Given
Spot $ 1 = \1,350
Mar. Futures $ 1= \1,400,
Long Mar. Futures
In Dec.
Suppose
Spot $1 = \ 1,170 → gain \ 180
Mar. Futures $1 = \ 1,220 → loss \ 180(counter trade)
(No basis risk)
169
(2) Futures - Speculation
Example
For two investors A and B with \1,000,000 respectively, suppose that the investor
A buys 10 shares of stock at \100,000 per share and that the investor B buys 200
contracts on the same stock at \100,000 per contract whose cash initial
margin(5%) is \1,000,000(=100,000x200x0.05). Then, as the price changes, the
profits for the two investors are as follows;
Price
Investor A
Investor B
\110,000 \10,000ⅹ10=\100,000
\10,000X200=\2,000,000
\90,000
-\10,000x200 =-\2,000,000
-\10,000x10=- \100,000
We can see the return and its variation for the investor B are larger. Such a trade
with a high risk and a high return is called a speculation trade.
170
(3) Futures - Arbitrage
Example
171
(4) Options - hedge
Example
1 Stock short
Hedge
1 Call long
Payoff
+Call
50,000
0
ST
-5,000
Hedged
-Stock
Hedge ratio( or delta) : The number of shares of stock required to hedge the price
risk
of holding one option
172
(5) Portfolio Insurance
Portfolio strategy that limit losses while maintaining upside
potentials
Example
1 stock long
1 put long
Payoff
+Stock
Combined
50,000
ST
+Put
173
(6) Options - Speculation
Example
For two investors A and B with \1,000,000 respectively, suppose that the investor
A buys 10 shares of stock at \100,000 per share and that the investor B buys
1,000 Dec. call options on the same stock at \1,000 per option with X=\100,000
and T=Dec. Then, on December, the profits for the two investors are as follows;
Price
Investor A
Investor B
\110,000
\(110,000 – 100,000)ⅹ10
=\100,000
\(110,000 - 100,000 -1,000)X1,000
=\9,000,000
\90,000
\(90,000 - 100,000)x10
=- \100,000
-\1,000x1,000 =-\1,000,000
We can see the return and its variation for the investor B are larger. Such a trade
with a high risk and a high return is called a speculation trade.
174
(7) Risk Free Portfolio
Example
t=T
Port.
t=0
ST≤50,000
+S
-50,000
+ST
+ST
-C
+7,000
0
-(ST-50)
-5,000
50,000-ST
0
-48,000
50,000
50,000
+P
ST>50,000
175
+S
+7,000
+2,000
-5,000
-P
-C
50,000
176
(8) Exercise
You establish a straddle on a stock using December call and put
options with a strike price of $70. The call premium is $5.25 and
the put premium is $6.
(1) What is the most you can lose on this position
→ Suppose long straddle, i.e., buying both call and put option for
Walmart stock
Net effect in both a call and a
put with the same strike price
and expiration date
Profit or Loss($)
Call Only
70
Stock Price($)
58.75
81.25
Strike Price
Put Only
The maximum possible loss = 5.25+6 = 11.25
177
(2) What will be your profit or loss if the stock is selling for $56 in
September?
→ -11.25+(70-56) = +2.75
(3) At what stock prices will you break even on the straddle?
→ -11.25+|70 – S|=0, S=81.25 or 58.75
178
(9) Exercise
An investor purchases a stock for $51 and a put for $.55 with a strike
price of $48. The investor sells a call for $.55 with a strike price of $56.
What is the maximum profit and loss for this position? Draw the profit
and loss diagram for this strategy as a function of the stock price at
expiration.
S
→
48
51
56
Long Put
Short Call
Maximum profit = $5, maximum loss=$3
179
(10) Exercise
You establish a straddle using March call and put options for a corporate stock with an exercise price of
$100. Current stock price is $100. The call premium is $5. If the stock price at maturity that breaks even is
$110. What will be the put premium? If you can make a risk free portfolio with the underlying stock, call
and put that earns 2% of interest rate, what will be the put premium?
Let put premium be P.
Break even on straddle: -5 - P + |100 – S| = 0
Plug S=110 => Put premium P=$5
180
t=T
Portfolio
t=0
+S
-100
-C
+5
+P
-P
0
0
-(95+P)
.
181
3. Futures Prices
(1) Cost of Carry Model
(Spot-Futures Parity Theorem)
F=P+C
1. F > P + C → Short F, Long P, and store.
2. F < P + C → Long F, Short P, and lend.
Example
Gold, Cash price \100 mill/kg. Interest rate 5% T-bill. Cost of storage and
insurance \100,000 per month. What is F with T = 3 months?
F=P+C
= \ 100,000,000 x(1 + 90/360 x 0.05) + 100,000 x 3
= \ 101,550,000
1. If F= \ 120,000,000, then the arbitrage profit is \ 18,450,000.
2. If F= \ 100,000,000, then the arbitrage profit is \ 1,550,000.
183
(2) Financial Futures
Financial Futures (No Physical Carrying Cost)
Example
184
185
(3) Exercise
→
.
186
→
.
187
(4) Exercise
.
188
.
189
4. Options Prices
(1) Factors Affecting Option Prices
Factors
European
Call
European
Put
American
Call
American
Put
S0
+
-
+
-
K
-
+
-
+
σ
+
+
+
+
r
+
-
+
-
d
-
+
-
+
T
+
?
+
+
Exercise price
- In the money
- At the money
- Out of the money
(2) Boundary of Option Prices
C≤S0
if C>S0
arbitrage profits by buying stock & selling call
t=0
+C-S0>0
t=T
ST≤K
ST>K
No ex
ex
ST>0
K>0
C≥S0-Ke-rT
<Proof >
Port A : one European Call + Investment
cash(Ke-rT) at rf
Port B : one share
t=T
Port
t=0
ST≤K
ST>K
A
C+Ke-rT
K
(ST-K)+K
B
S0
ST
ST
A=B
→ C≥max(0,S0-KerT)
193
Boundary of Call
Call
0
S
194
P≤Ke-rT
if P>Ke-rT,
arbitrage profits by selling put & investing Ke-rT in Bond
t=0
+P-Ke-rT>0
t=T
ST≤K
ST>K
ex
Pay K & buy stock
No ex
ST>0
K>0
195
P≥Ke-rT-S0
<Proof >
Port C : one European Put + one share
Port D : invest Ke-rT at rf
Port
t=0
C
D
t=T
ST≤K
ST>K
P+S0
K
ST
Ke-rT
K
K
C=D
C>D
P+S0≥Ke-rTor P≥Ke-rT-S0
→ P≥max(0,Ke-rT-S0)
196
Boundary of Put
Ke-rT
Put
0
S
Ke-rT-S0
197
Put-Call Parity
Port A : one European Call + Ke-rT in rf
Port B : one European Put + one share
t=T
Port
t=0
ST≤K
ST>K
A
C+Ke-rT
K
(ST-K)+K
B
P+S0
K
ST
A=B
A=B
→ C+Ke-rT = P+S0
.
Greater than zero
0
0
199
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
.
�ℎ�
�
�
�
�
� (�
�+ �
0)
�
�
�
� �
�
� (�+
� ��−�
)
�
�= 0
+(�
�+ �
0)
�
�
�
-(�+ ��−�
)
�
�
�
(�
)
(�+
)
�+ �
−
��−�
0
> (�
�+ �
0 ) − (�+ �) = 0
�
�
=�
�� ≤ �
−�
+�
0
�� > �
− ��
+ ��
0
200
(4) Binomial Model of Option Pricing
One-Step Binomial
Example
Call Option with X=21, T=0.25, rf=12%
S0=20
ST=22 → CT=1
ST=18 → CT=0
Consider a port, risk free
ΔStock Long
→
1 Call Short
t=0
20Δ-C
22Δ-1=18Δ
Δ=0.25
t=T
22*0.25-1=4.5
18*0.25-0=4.5
20*0.25-C=4.5e-0.12*3/12 → C=0.633
In general
S0,C0
S0u, Cu
S0d, Cd
→ Iong Δshares, short 1 call
S0dΔ-Cd=S0uΔ-Cu
t=0
t=T
S0Δ-C0 → S0uΔ-Cu → C0=S0Δ-(S0uΔ-Cu)e-rT
⇒ C=e-rT[PCu+(1-P)Cd] where
where
Example
u=1.1, d=0.9, r=0.12, T=0.25, Cu=1, Cd=0
→ P=0.6523, C=0.633
⇒ Prob of up&down does not matter. The prob are already incorporated into
the price of stock(Random Walk i.e. nobody knows the future distribution, still
Binomial model works)
(Risk-Neutral Valuation)
C0=e-rT[PCu+(1-P)Cd]
P can be interpreted as a prob of as upward movement in stock price. Why?
E(ST)=PS0u+(1-P)S0d=PS0(u-d)+S0d=S0erT
22
Above ex. 20
18
Call
(Plug in
)
X=21, rf=12%. Then P must satisfy 22P+18(1-P)=20e+0.12*3/12 → P=0.6523
1, P=0.6523
0, (1-P)=0.3477
→ expd value
(0.6523*1+0.3477*0=0.6523)
In a risk-neutral world 0.6523e-0.12*3/12 =0.633 (same result)
Two-Step Binomial
Consider Call with X=21
22 (2.0257)
20 (1.2823)
18 (0.0)
24.2 (3.2)
19.8 (0.0)
19.8 (0.0)
16.2 (0.0)
u=1.1, d=0.9, r=0.12, T=0.25⨯2, P=0.6523
→ e-0.12*3/12 (0.6523*3.2+0.3477*0)=2.0257
→ e-0.12*3/12 (0.6523*2.0257+0.3477*0)=1.2823
In general
Cu=e-rδT[PCuu+(1-P)Cud]
Cd=e-rδT[PCud+(1-P)Cdd]
or
C=e-rδT[PCu+(1-P)Cd]
C=e-2rδT[P2Cuu+2P(1-P)Cud+(1-P)2Cdd]
Example
The above procedure can be used to price any derivative dependent on
a stock whose price changes are binomial
50 (5.2244)
ⓐ
60 (1.6455)
40 (10.4637)
ⓑ
ⓒ
72 (0)
48 (4)
48 (4)
32 (20)
If above put is American,
At ⓑ Value of option = 1.6455, Payoff from early ex -8 → No ex
At ⓒ Value of option = 10.4637, Payoff from early exercise=12 → Early ex
At ⓐ e-0.03*1(0.5761*1.6455+0.4239*12.0=5.8564)
Payoff from early ex +2 → No ex
(5) Exercise
206
1464.1
1331
1197.9
1210
1197.9
1089
980.1
1100
1197.9
1089
980.1
990
980.1
891
801.9
1000
1197.9
1089
980.1
990
.
980.1
891
801.9
900
980.1
891
801.9
810
801.9
729
656.1
207
208
(6) Exercise
.
209
(7) Exercise
.
210
t=0
t=T
.
211
(8) Exercise
.
212
.
213
(9) Black-Scholes Model*
214
215
216
Binomial
vs
BS
217
218
219
(10) Exercise
220
Hence, if the option is a European call, its value c is given by
c = 42N(0.7693)-38.049N(0.6278)
If the option is a European put, its value p is given by
p = 38.049N(-0.6278)-42N(-0.7693)
While,
N(0.7693)=0.7791,
N(-0.7693)=0.2209
N(0.6278)=0.7349,
N(-0.6278)=0.2651
So that
c = 4.76,
p=0.81
Ignoring the time value of money, the stock price has to rise by
$2.76 for the purchaser of the call to break even. Similarly, the
stock price has to fall by $2.81 for the purchase of the put to
break even
221
(11) Exercise
In what aspects, the binomial option pricing model and BS option
pricing model are similar?
→ They both assume risk neutral valuation. Also, binomial model is
a discrete approximation of the continuous Brownian motion of
Black-Scholes model.
222
5. Swap
(1) Coupon Swap
prefer float
pay fixed 3.475%
firm A
prefer fixed
firm B
pay LIBOR
borrow
fixed 3.7%
pay
fixed 3.7%
fixed rate 3.7%
float rate LIBOR+0.25%
gain
0.025%
pay float
LIBOR+0.75%
borrow float
LIBOR+0.75%
fixed rate 4.25%
float rate LIBOR+0.75%
gain
0.025%
224
CMS
Generic
ST Floating
Swap
Rate
(6m LIBOR 91day CD)
(Constant Maturity Swap)
Fixed Rate
LT Floating
Rate
(5yr, 10yr(Treasury)
rate, Reset
periodically)
225
(3) Basic Rate Swap
pay CP rate
firm A
firm B
pay LIBOR rate
borrow
pay LIBOR rate
LIBOR Market
pay CP
rate
borrow
CP Market
226
(4) DLS(Derivative Linked Securities)
Investor
Bank
227
(5) Coupon Swap Reversals
initial swap
reversal
pay LIBOR
firm A
pay LIBOR
bank
pay fixed 3%
firm B
pay fixed 4%
bank earns 1%
228
(6) Cocktail Swap
firm A
firm B
firm C
prefers
$ fixed
possible
$ float
$ fixed
\fixed
$ float
\fixed
market
borrow $ float
pay $ float
firm A
$ fixed
\ fixed
$ float
bank
\ fixed
borrow $ fixed
borrow \ fixed
firm B
market
pay $ fixed
firm C
$ fixed
$ float
market
pay \ fixed
229
(7) Parallel Loan
Korea
USA
ROK parent
loan
\
pay \
US subsidiary
contact
US parent
loan $
pay $
ROK subsidiary
230
(8) Back to Back Loan
(no subsidiary involved)
Korea
$
Korea Co
step 1
step 2
step 3
\ loan
bank
Korea Co
USA
US Co
$ loan
\
bank
US Co
\ interest
$ interest
bank
bank
Korea Co
US Co
\ principal
bank
$ principal
bank
231
(9) Bond Swaps
① Substitution Swap
Exchange of one bond for a bond with similar attributes but more actively priced.
② Intermarket Spread Swap
Switching from one segment of the bond market to another.
③ Rate Anticipation Swap
A switch made in response to forecasts of interest rate changes.
④ Pure Yield Pickup Swap
Moving to higher-yield bonds, usually with longer maturities.
⑤ Tax Swap
Swapping two similar bonds, motivated by a reduction in total tax obligations.
⑥ Horizon Analysis
Forecasts of bond returns based on a prediction of the yield curve at the end of the
investment horizon as well as the interest rate on reinvested coupon income.
232
V. Financial Analysis
1. Macroeconomics & Industry Analysis
2. Equity Valuation
3. Financial Statement Analysis
4. Investment Management & Performance Evaluation
1. Macroeconomic
& Industry Analysis
(1) Fundamental Analysis
The Analysis of determinants of firm value, such as prospects for
earnings and dividends.
The fundamental analysis is performed based on macroeconomic
& industry analysis
235
(2) Macroeconomic Analysis
① Predict the effect of economic policies in and out of the country
on key macroeconomic variables, i.e., GDP, interest rate,
inflation rate and the exchange rate.
② Use economic indicators to describe and predict the economy’s
path through the business cycle.
Peak : The transition from the end of an expansion to the start of a
contraction
Trough: The transition point between recession and recovery
Leading economic indicators : Economic series that tend to rise or fall
in advance of the rest of the economy.
236
(3) Industry Analysis
① Predict which industries will be more or less sensitive to business
cycle.
② Analyze the effect of industry life cycles and structure on the
firms’ earnings prospects over time.
Cyclical industries : Industries with above-average sensitivity to the state
of the economy
Defensive industries : Industries with below-average sensitivity to the
state of the economy
Industry life cycle : Stages through which firms typically pass as they mature
Sector rotation : An investment strategy that entails shifting portfolio into industry
sectors that are expected to outperform others based on
macroeconomic forecasts
237
2. Equity Valuation
(1)Limitations of Book Value
① Liquidation value : Net amount that can be realized by selling
the assets of a firm and paying off the debt.
② Replacement cost : Cost to replace a firm’s assets.
③ Tobin’s q : Ratio of market value of the firm to replacement cost.
④ Intrinsic value : The present value of a firm’s expected future net
cash flows discounted by the required rate of return.
⑤ Market capitalization rate : The market-consensus estimate of the
appropriate discount rate for a firm’s cash flows.
239
(2) Dividend Discount Models (DDM)
240
241
(3) Investment Opportunities
242
243
.
244
3. Financial Statement Analysis
(1) Financial Statements
Income Statement
Balance Sheet
The Statement of Cash Flows
246
(2) Statement of Cash Flows
247
(3) Profitability Ratio
248
Ex. For a firm with no debt, ROA=10%, t=0.4
What is ROE?
What if the firm maintains D/E=2/3, r=8%?
249
(4) Decomposition of ROE
(Dupont System)
EBIT
-I
EBT(Pretax profits)
-T
NI
250
Ex.
Margin
=
ROA
Firm A
2%
5.0
10%
Firm B
20%
0.5
10%
Firm A : Low Margin, High Turnover
Firm B: High Margin, Low Turnover
251
(5) Exercise
252
(6) EVA(Economic Value Added)
253
(7) Utilization Ratios
254
(8) Liquidity Ratios
255
(9) Market Price Ratios
256
257
(10) PE and GO
① Price-earning multiple : The ratio of a stock’s price to its
earnings per share
② PEG ratio : Ratio of P/E multiple to earnings growth rate.
258
4. Investment Management &
Performance Evaluation
(1) Investment Management Process
planning
object
execution
feedback
strategy
economic
market
environment
expectation
portfolio
performance
construction
measurement
monitoring
260
(2) Passive Management
vs Active Management
Passive - Holding a well-diversified portfolio without attempting to
reach out security mispricing.
Active – Attempts to achieve to realize excess returns, whether by
forecasting markets or by identifying mispriced securities.
261
(3) Performance Evaluation
262
Final Exam Review (1)
.
263
.
264
(3) The bonds with greater curvature have higher value than otherwise. How
does it hold?
→ Refer to Slide
.
265
Final Exam Review (2)
.
266
267
268
.
269
Cash Flow
Portfolio
Buy Call
Lend K
.
Sell Put
Short Stock
Greater
Greater
Greater
than zero
than zero
than zero
270
Final Exam Review (3)
.
271
144 (44)
120
(24.599)
96 (0)
100
96 (0)
.
80
(0)
64 (0)
272
273
.
274
3
4
5
6
7
8
10
11
12
(3) Risk-Neutral Valuation
13
S
S
S
S
S
14
15
The End