CFA ReviewCFA Review

Markets, participants, trading Markets, participants, trading computations, and indexescomputations, and indexes

Book chaptersBook 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 VehiclesInvestment 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 issuanceSecurity 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 MarketOrganization 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 Example: Sample Trade On the NASDAQ (Level 2)NASDAQ (Level 2)

• Sample quotes would show different bid-ask spreads from dealers.

Dealer Bid Ask1 46 1/2 46 3/4

2 46 3/8 46 5/8

3 46 1/4 46 5/8

4 46 3/8 46 3/4

Other markets and stuffOther 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 ORDERSTYPES 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 OrderExample 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 1Solution 1R=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 = $27nDividends = $0.5nTransaction Costs for purchase=3% x 20n=0.6nTransaction Costs for sale=3% x 27n=0.81n Profit = $27n - $20n + 0.5n-0.6n-0.81n = 6.09nInitial investment = 20n+0.6n = 20.6n

R= $6.09n/$20.6n = $6.09/$20.6= 29.56%

Example 2: Stop loss ordersExample 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 ordersExample 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 TransactionsMargin 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 SemanticMargin 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 TransactionsExample 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 TransactionsExample 2: Margin Transactions

Buy 200 shares at $50 = $10,000 positionBorrow 50%, investment of $5,000If 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 TransactionsMargin 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 transactionsExample 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 4Solution 4R=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 = $27nDividends = $0.5nTransaction Costs for purchase=3% x 20n=0.6nTransaction Costs for sale=3% x 27n=0.81n Interests on amount borrowed: 10% x 45% x 20n =0.9nProfit = $27n - $20n + 0.5n-0.6n-0.81n-0.9n = 5.19nInitial investment = 55% x 20n+0.6n = 11.6n

R= $5.19n/$11.6n = $5.19/$11.6= 44.74%

Short SalesShort 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 5Short 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 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 = $580Transaction Costs = $113 + $109 = $222Interest = .1 x (.6 x 24000) = $1,440Profit = $24,000 - $18,000 - $580 - $222 - $1440 = $3,758Your investment = margin requirement + commission= (.40 x $24,000) + $113= $9600 + $113= $9,713

R= $3,758/$9,713 = 38.69%

Uses of Security-Market IndexesUses 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: Dow-Price weighted index: Dow-Jones Industrial Average (DJIA)Jones Industrial Average (DJIA)

– Where:• 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

DJIA P Dt iti

adj

1

30

/

Example 6: Demonstration of the Impact of Example 6: Demonstration of the Impact of Differently Priced Shares on a Price-Weighted Differently Priced Shares on a Price-Weighted

Indicator SeriesIndicator 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 Example 7: Change in DJIA Divisor When a Sample Stock SplitsWhen 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 CExample 8: Price weighted--1 for 2 split effect on CStock 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 DJIACriticism 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 SeriesValue-Weighted Series• Based on value, not just price.

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• Weighting depends on market value

Index Beginning Index Valuet

PQ

PQxt t

b b

Example 9: Value-weighted: split effect (1 for 2)Example 9: Value-weighted: split effect (1 for 2)

  Price # shares (millions) Value (millions)Stock 1998/99   1998/99

A 20/22 2 40/44B 40/ 50 2.5 100/125C 60/80 1 60/80

Total     200/249

5.124100200

249Index1999

  Price # shares (millions) Value (millions)

Stock 1998/99   1998/99

A 20/22 2 40/44

B 40/25 2.5/5 100/125

C 60/80 1 60/80

Total     200/249

5124100200

2491999 .Index

Unweighted (Equal Weighted) Price Indicator SeriesUnweighted (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.– Base = 100 (6/30/61).

100rn

1Index Arithmetic

1001)r1(Index Geometric

n

1ii

n

1ni

1ii

Example 10: Unweighted IndexExample 10: Unweighted Index

• 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

  Price # shares (millions) %changeStock 1998/99   1998 to 1999

A 20/22 2 =(44-40)/40=10%25%B 40/50 2.5

C 60/80 1   

33.3%

Example 11: summaryExample 11: summary

• Calculate the index values at days 1,2 and 3 for a price weighted, value weighted and unweighted index.

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

Solution11: price weighted indexSolution11: 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 indexExample: value weighted index

• 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

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

Example: unweighted indexExample: unweighted index

• 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

PA x QA

PB xQB

PC x QC

% % % Avg%

Day 1 1000 1250 400

Day 2 800 1200 440 -20% -4% 10% -4.67%

Day 3 1100 1250 400 37.5% 4.17% -9.09% 10.86%

Index usesIndex uses• Passive strategy: Follow the index…• Benchmark: another way to look at

risk/return (cap, growth matrix)

Value

PB<1.75

Core

1.75<PB<2.25

Growth

PB>2.5

Large

(Top 5%)

Dow

Ru1000

SP500

Ru1000

SP500

Ru1000

Mid:

(5% to 15%)

RU3000 SP400

Nasdaq

RU3000

SP400

Nasdaq

Small

(Bottom 80%)

RU2000 SP600

RU2000

SP600

Nasdaq

Facts: Correlations Among Daily Equity Price Facts: Correlations Among Daily Equity Price ChangesChanges

• 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 indicesBond indices• Benchmark for bond portfolio• Series are difficult to obtain, Mutual funds (bond fund)

can be used as proxy .

Short<4y 4y<X<7y Long Duration>7y

High qualityAAA, AA

LB, ML, SSB (sub families)

LB, ML SSB

Medium A,BBA LB, ML, SSB (sub families)

LB, ML SSB

LowBBB or less LB, ML, SSB (sub families)

LB, ML SSB

Facts: Mixed indexesFacts: 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