CFA Review
Markets, participants, trading
computations, and indexes
Book chapters
• Chapter 1: Geometric and Arithmetic Mean
• Chapter 2: Tax effect on municipal/tax exempt
yields
• Chapter 3: p.79-90
• Chapter 4: markets, participants and trading
computations
• Chapter 5: indexes
• Chapter 25: mutual funds
• Check wikipedia.com and investopedia.com
Investment Vehicles
• Money markets (Treasury bills,CDs, Commercial
papers, Banker’s acceptances, Eurodollar deposits,
repo agreements, fed funds, broker call loans)
• Bond markets (Treasury notes and bonds, agency
bonds, non-US bonds, eurobonds, samurai bonds,
yankee bonds, Municipal bonds, corporate bonds,
Mortgage-backed)
• Equity markets (common stocks, preferred stocks)
• Derivatives (Options and futures)
• Mutual funds (NAV=[MVassets-MVliab]/#shares
outstanding)
• REITS
• ETFs
Security issuance
• Underwriters offer the following services:
origination, risk bearing, and distribution.
• Shelf registration falls under SEC rule 415: large
firms can register security issues and issue a
few at atime over the next 2 years.
• Private placements fall under SEC rule 144A
which allows firms to place securities privately
with large “sophisticated” institutional investors—
less red tape and cheaper.
• IPOs are 1st time issues by firms that do not
have share currently traded in the market place.
Organization of the Securities Market
• Primary Markets - new securities are sold through an
investment banker who takes care of the origination ( design of
the issue), the risk-bearing( assumption of risk of reselling to
the public), the distribution (process of selling the issue) and
facilitate the function of underwriting (negotiated or competitive
bid or best-efforts basis)
– Government bond issues
– Municipal bond issues
– Corporate issues
• Secondary Markets - where outstanding securities
are traded
– Securities exchanges (auction market: Commission brokers,
specialists, floor brokers, floor traders)
– Over-the-counter (OTC): National Association of Securities
Dealers Automated Quotation System (Electronic; Many
dealers); Three levels:
– Level 1 - Single Quote; Level 2 - All Quotes; Level 3 - Dealers Only
Example: Sample Trade On the
NASDAQ (Level 2)
• Sample quotes would show different bidask spreads from dealers.
Dealer
Bid
Ask
1
2
3
4
46 1/2
46 3/8
46 1/4
46 3/8
46 3/4
46 5/8
46 5/8
46 3/4
Other markets and stuff
• Third market: segment of OTC where stocks listed on
an exchange are also traded allows to trade the
security without having to go through the exchange
• Fourth market: it refers to the trading of securities
between investors without the services of a broker.
• ITS is the national market system, established to
centralize market price information and facilitate
transactions
• Block trading: large institutional investors making large
trades. SEC rule 113 prevents specialist from dealing
directly institutions block trading.
TYPES OF ORDERS
• Market Orders - buy or sell the stock at the
best price at that time.
• Limit Orders - customer specifies highest
purchase or lowest sell price. (Time specifications for order
may vary: Instantaneous - “fill or kill”, part of a day, a full day, several days,
a week, a month, or good until canceled “GTC”)
- limit buy: specifies the highest price investor is willing to pay.
- limit sell: specifies the lowest price investor is willing to
accept.
• Special orders
– Stop loss order: Implies that if the market price falls to or
below a specified price, the order becomes a market order
and the stock will be sold at the prevailing price.
– Stop buy order: Used by short sellers to minimize losses if
market price rises.
Example 1: Market Order
• You buy a round lot (multiple of 100) of ABC
stock at $20. Brokerage fees are 3% on each
transaction (3% for purchase and 3% for sale).
You receive a year later $0.5 per share in
dividends and sell the stock at $27. What is the
rate of return on investment?
Solution 1
R=Profit/investment
Return= Profit/initial investment
= (Ending value - Beginning Value + Dividends Transaction costs on purchasing and selling) / (initial
investment + transaction costs on purchasing)
• Beginning Value of Investment= $20n
• Ending Value of Investment = $27n
Dividends = $0.5n
Transaction Costs for purchase=3% x 20n=0.6n
Transaction Costs for sale=3% x 27n=0.81n
Profit = $27n - $20n + 0.5n-0.6n-0.81n = 6.09n
Initial investment = 20n+0.6n = 20.6n
R= $6.09n/$20.6n = $6.09/$20.6= 29.56%
Example 2: Stop loss orders
• Suppose you have 500 shares of ABC stock,
bought at $50 and priced at $60. You put a stop
loss order at $55. Why would you do that? If the
the price goes to $52, what would be your rate
of return with and without the stop loss order?
• Solution 2:
• You are obviously satisfy with a profit of $5 per
share.
• With stop loss; R= (55-50)/50=10%
• Without stop loss; R= (52-50)/50=4%
Example 3: Limit orders
• Xyz stock is selling for $40. You have a limit buy order at $35.
During the year the stock goes to $30 then goes to $45.
(1)What is R? (2)What would have R been with a simple market
order? (3)What would R been is the limit buy order was at $25?
• Solution 3:
(1) When market declined to $30, your limit
order was executed $35 (buy), then the price
went to $45.
Rate of return = ($45 - $35)/$35 = 28.6%.
• (2)Assuming market order @ $40: Buy at $40,
price goes to $45
Rate of return = ($45 $40)/$40 = 12.5 %.
• (3) Limit order @ $25: Since the market did
not decline to $25 (lowest price was $30) the
limit order was never executed.
Margin Transactions
• An investor borrows part of the cost of an
investment and uses the securities as
collateral.
• Margin is the amount of money that the
investor must put into the investment.
• Investors using margin must pay an interest
rate to their broker (about 1.5% above the
lending bank’s call money rate)
Margin Semantic
If AM > IM: account is overmargined
If MM < AM < IM: account is restricted
If AM < MM: margin call
IM = Initial Margin
MM = Maintenance margin
AM = Actual margin
Example 1: Margin Transactions
Buy 200 shares at $50 = $10,000 position
Borrow 50%, investment of $5,000
If price increases to $60, position
–
–
–
–
–
–
Value is $12,000
Less
- $5,000 borrowed
Leaves $7,000 equity for a
$7,000/$12,000 = 58% equity position
Return on investment?
R=profit/initial investment=(12000-10000)/5000=40%
Example 2: Margin Transactions
Buy 200 shares at $50 = $10,000 position
Borrow 50%, investment of $5,000
If price decreases to $40, position
– Value is $8,000
– Less
- $5,000 borrowed
– Leaves $3,000 equity for a
– $3,000/$8,000 = 37.5% equity position
– Return on investment?
– R=profit/initial investment=(8000-10000)/5000=40%
Margin Transactions
• Initial margin requirement at least 50%
• Maintenance margin
–
–
–
–
–
•
•
•
•
Requirement proportion of equity to stock
Protects broker if stock price declines
Minimum requirement for maintenance margin is 25%
Margin call on undermargined account to meet margin requirement
If call not met, stock will be sold to pay off the loan
Example 3: Margin Transactions
In the previous example, how far can the stock price fall, before
you receive a margin call?
A call occurs when the proportion of equity = minimum
maintenance margin,i.e.
25%=(200P-5000)/200P
So P=5000/(200-25% x 200)= $33.33
Example 4: margin transactions
• You buy a round lot (multiple of 100) of
ABC stock at $20 on 55% margin. The
broker charges 10% on the borrowed
money Brokerage fees are 3% on each
transaction (3% for purchase and 3% for
sale). You receive a year later $0.5 per
share in dividends and sell the stock at
$27. What is the rate of return on
investment?
Solution 4
R=Profit/investment
Return= Profit/initial investment
= (Ending value - Beginning Value + Dividends - Transaction
costs on purchasing and selling - interests paid on borrowed
money) / (initial investment + transaction costs on purchasing)
• Beginning Value of Investment= $20n
• Ending Value of Investment = $27n
Dividends = $0.5n
Transaction Costs for purchase=3% x 20n=0.6n
Transaction Costs for sale=3% x 27n=0.81n
Interests on amount borrowed: 10% x 45% x 20n =0.9n
Profit = $27n - $20n + 0.5n-0.6n-0.81n-0.9n = 5.19n
Initial investment = 55% x 20n+0.6n = 11.6n
R= $5.19n/$11.6n = $5.19/$11.6= 44.74%
Short Sales
• Process: Borrow Stock -> Sell Stock -> Repurchase
Stock -> Replace Borrowed Stock
• Investors expect prices to fall.
– Proceeds are held by the broker.
– No set time limit.
– Short seller is liable for dividends.
– Short seller is subject to the same margin
requirement as buyer
Short sale example 5
• You sell short 200 shares of ABC, which is
priced at $120. The margin requirement is 40%.
Commissions on sale are $113. During the
year, dividends of $2.9 are paid. At the end of
the year you repurchase the stock at $90 (you
close your position!) and you are charged $109
plus 10% on the money borrowed.
• What is you return on investment?
Solution 5
R=Profit/investment
*Profit on a Short Sale = Beginning Value
- Ending Value- Dividends - Transaction
Costs - Interest
• Beginning Value of Investment= 200 x
$120 shares= $24,000(which is sold under
a short sale arrangement)
•
Ending Value of Investment = 200 x $90
= $18,000 (Cost of closing out position)
Dividends = $2.9 x 200 shares = $580
Transaction Costs = $113 + $109 = $222
Interest = .1 x (.6 x 24000) = $1,440
Profit = $24,000 - $18,000 - $580 - $222 - $1440
= $3,758
Your investment = margin requirement + commission
Uses of Security-Market Indexes
• Benchmark to judge portfolio performance
– (be sure to analyze differential risk)
• Develop an index portfolio
– Index funds - match market performance
• Examine factors that influence aggregate
security price movement
• 3 types…
– Price weighted (DJIA)=average price
– Value weighted (S&P)=average market value
– Unweighted (Value line)= average (arithmetic or geometric)
return
Price weighted index: DowJones Industrial Average (DJIA)
30
DJIAt   Pit / Dadj
– Where:
i 1
• DJIAt = the value of the DJIA on day t
• pit = the closing price of stock i on day t
• Dadj = the adjusted divisor on day t
Example 6: Demonstration of the Impact of
Differently Priced Shares on a Price-Weighted
Indicator Series
PERIOD T+ 1
Period T
Case A
Case B
A
100
110
100
B
50
50
50
C
30
30
33
Sum
180
190
183
Divisor
3
3
3
Average
60
63.3
61
Percentage Change
5.5%
1.7%
.
Example 7: Change in DJIA Divisor
When a Sample Stock Splits
After one-for three
Before Split
Split by Stock A
Prices
Prices
A
30
10
B
20
20
C
10
10
60 3 = 20
40 X = 20
X = 2 (New Divisor)
Example 8: Price weighted--1 for 2 split effect on C
Stock
Price
A
10
B
15
C
20
Case 1: No change in price…
 Before the split: Index = 45/3=15
 After split (C goes to 10): Index=15, but divisor changes to
35/15=2.33; the index is still 15.
Case 2: change in price…
 Prior to the split a 10% increase in C (c goes to 22) would increase
the index from 15 to 15.67 (Index = 47 / 3 = 15.67).
 After a 2:1 split, and a 10 % increase in C (c goes to 11) would only
increase the index to 15.45 (Index = 36 / 2.33 = 15.45)
Criticism of the DJIA
• Sample used is limited
– 30 non-randomly selected blue-chip stocks are not
representative of the 1800 NYSE listed stocks
• Price-weighted series
– Stock split results in less weighting for sample
stock
– Introduces a downward bias in DJIA by reducing
weighting of fastest growing companies whose
stock splits
Value-Weighted Series
• Based on value, not just price.
Pt Q t

Index t 
x Beginning Index Value
 Pb Q b
Indext = index value on day t;
Pt = ending prices for stocks on day t;
Qt = number of outstanding shares of stock on day t;
Pb = ending price for stocks on base day;
Qb = number of outstanding shares on base day.
• Derive the initial total market value of all stocks used in the
series
– Market Value = Number of Shares Outstanding X Current
Market Price
• Assign an beginning index value (100) and new market values
are compared to the base index
• Automatic adjustment for splits
Example 9: Value-weighted: split effect (1 for 2)
Stock
A
B
C
Total
Index1999 
Stock
A
B
C
Total
Price
1998/99
20/22
40/ 50
60/80
# shares (millions)
2
2.5
1
Value (millions)
1998/99
40/44
100/125
60/80
200/249
249
 100  124.5
200
Price
1998/99
20/22
40/25
60/80
# shares (millions)
2
2.5/5
1
249
Index1999 
 100  124 .5
200
Value (millions)
1998/99
40/44
100/125
60/80
200/249
Unweighted (Equal Weighted) Price Indicator Series
• All stocks carry equal value.
• Value Line Averages
– Bases on geometric average of price returns for the
1700 stocks.
– Adjusted to reflect stock splits and dividends.
1


– Base = 100 (6/30/61). 

i  n
n
Geom etricIndex     ( 1  ri )  1  100
  i 1






1 n 
Arithm eticIndex    ri   100
n

 i 1 
Example 10: Unweighted Index
Stock
A
B
C
Price
1998/99
20/22
40/50
60/80
# shares (millions)
2
2.5
1
%change
1998 to 1999
=(44-40)/40=10%
25%
33.3%
• Arithmetic average =
(10%+25%+33.3%)/3=22.77%
– Arithmetic Index=100*(1+22.77%)=122.77
• geometric average =
[(1+10%) x (1+25%) x (1+33.3%)]1/3 - 1 =
22.39%
– Geometric Index=100*(1+22.39)=122.39
Example 11: summary
PA
PB
PC
QA
QB
QC
Day 1
10
25
10
100
50
40
Day 2
8
24
11
100
50
40
Day 3
11
50
10
100
25
40
• Calculate the index values at days 1,2 and 3 for a
price weighted, value weighted and unweighted index.
Solution11: price weighted index
•
•
•
•
•
Day 1: Index=(10 +25+10)/3=15
Day 2: Index=(8+24+11)/3= 14.33
Day 3:
Find the new divisor: (2 for 1 split);
Before change in price Index =14.33. Yet, after
split total value = (8+48+11)=67; new
divisor=67/14.33=4.68
• After change in
price,Index=(11+50+10)/4.68=15.18 2 x 24
Example: value weighted index
PA
PB
PC
QA
QB
QC
ΣPxQ
Day 1
10
25
10
100
50
40
2650
Day 2
8
24
11
100
50
40
2440
Day 3
11
50
10
100
25
40
2750
• Index day 1= 100 (or whatever you want)
• Index day 2=(2440/2650) x 100=92.08
• Index day 3 =(2750/2650) x 100=103.77
Example: unweighted index
PA x
QA
PB
xQB
PC x %
QC
%
%
Avg%
Day 1
Day 2
1000
800
1250
1200
400
440
-20%
-4%
10%
-4.67%
Day 3
1100
1250
400
37.5% 4.17% -9.09% 10.86%
• Index day 1= 100 (or whatever you want)
• Index day 2= (1-4.67%)*100=95.33
• Index day 3 =95.33 x (1+10.86%)=105.68
Index uses
• Passive strategy: Follow the index…
• Benchmark: another way to look at
risk/return (cap, growth matrix)
Large
(Top 5%)
Mid:
(5% to
15%)
Small
(Bottom
80%)
Value
PB<1.75
Dow
Ru1000
RU3000
Core
1.75<PB<2.25
SP500
Ru1000
SP400
Nasdaq
RU3000
Growth
PB>2.5
SP500
Ru1000
SP400
Nasdaq
RU2000
SP600
RU2000
SP600
Nasdaq
Facts: Correlations Among Daily Equity Price
Changes
• Alternative NYSE series have high positive
correlations.
• NYSE, AMEX, and NASDAQ have lower
positive correlation.
• Correlations between U.S., U.K. and Japan
support the case for global investment.
Bond indices
• Benchmark for bond portfolio
• Series are difficult to obtain, Mutual funds
(bond fund) can be used as proxy .
High
qualityAAA, AA
Medium A,BBA
Short<4y
LB, ML,
SSB (sub
families)
LB, ML,
SSB (sub
families)
LowBBB or less LB, ML,
SSB (sub
families)
4y<X<7y
LB, ML
Long Duration>7y
SSB
LB, ML
SSB
LB, ML
SSB
Facts: Mixed indexes
• Merrill Lynch-Willshire U.S. Capital Markets Index
(ML-WCMI) Market-value weighted index measures
total return performance of the combined U.S. taxable
fixed income (Merrill-Lynch) and equity markets
(Wilshire 5000)
– Tracks over 10,000 stocks and bonds
• Brinson Partners Global Security Market Index (GSMI)
Includes:
–
–
–
–
U.S. stocks and bonds
Non-U.S. equities
Non-dollar bonds
Allocation to cash
• Matches a typical U.S. pension fund allocation policy
• Close to the theoretical “market portfolio of risky
assets” in CAPM