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Syllabus for Course Finance 3000 Hawaii Pacific University. Professor : Dr. Gunter Meissner, Business: 544 0807, Office: FHT 5 th floor #1 E-mail: [email protected], Web: www.dersoft.com. Contents: The course focuses on three main issues: a) Basics of Finance

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slide1

Syllabus for Course Finance 3000

Hawaii Pacific University

  • Professor: Dr. Gunter Meissner, Business: 544 0807, Office: FHT 5th floor #1
  • E-mail: [email protected], Web: www.dersoft.com
  • Contents: The course focuses on three main issues:
      • a) Basics of Finance
      • b) Asset management
      • c) Debt Management

Goals: a) The student will be familiar with basic financial concepts

such as the Time value of money concept,Capital Budgeting (Investment decision process) and Working capital

management.

b) Asset management:

In the field of asset management every student will be a competent fund manager and financial adviser at the end of the semester. The student will learn about the two major investments: Bonds and stocks. The student will know how to apply the latest concepts and strategies of trading.

slide2

Syllabus for Course Finance 3000 cont.

  • c)Debt management:
  • In the field of debt management the student will be familiar with the classical types of liabilities of a company (stocks, bonds, loans). Also, the student will learn how to use financial innovations such as interest rate and currency swaps, caps, floors, dual-currency bonds and convertibles in order to reduce cost and the various types of risk.
  • Literature: 1) Slides on www.dersoft.com/hpu
  • 2) Essentials of Corporate Finance, Ross, Westerfield, Jordan
  • 3) Trading Financial Derivatives, Gunter Meissner
  • 4) Outperform the Dow: Using Options, Futures and Portfolio Strategies to Beat the Market, Gunter Meissner
  • 5) Credit Derivatives : Application, Pricing, and Risk Management,
  • Gunter Meissner(will be used for Risk Management)
  • 6) Dictionary of Finance and Investment Terms, Downes, Goodman
      • 7) RISK Magazine (available at Library desk)
slide3

Grading

  • Grading: Participation/Homework 10%
  • Trading game 10%
      • Financial paper 20%
      • Presentation of Financial Paper 10%
      • Mid-Term 25%
  • Final 25%

Point System

95.00 =< A =< 100

90.00 =< A- < 95.00

86.66 =< B+ < 90.00

83.33 =< B < 86.66

80.00 =< B- < 83.33

76.66 =< C+ < 80.00

73.33 =< C < 76.66

70.00 =< C- < 73.33

65.00 =< D+ < 70.00

60.00 =< D < 65.00

F < 60.00

slide4

Syllabus for Course Finance 3000 cont.

Permanent homework:

Read, listen to financial news!! Bring questions to class!

Financial paper: Each student will write a 10 page paper and present it leading a 30 minute discussion on his/her findings. The paper has to be handed in one week before presentation.

APA style, have a Table of Contents, have a Conclusion!

The paper has to show your own thought process !

Don’t cite too much, but analyze !

The quality of the argument is important, not the argument

itself !

slide5

Finance as a Science

Soft Sciences

• Marketing

• Management

• Communication

These sciences use Psychology, Sociology and common sense to solve problems; there is usually a “probably better” or “probably worse”

Hard Sciences

• Math/Statistics

• CS/IT

• Nature Sciences

(Physics, Chemistry, Astrophysics

Gene Technology)

These sciences use Math, Logic and Computers to solve problems; there is usually a “right “ or “wrong”

Finance

• Time Value of Money Concept

•Corporate Finance

• Stock/Bond Analysis

• Portfolio Theory (CAPM)

• Derivatives (Futures, Swaps,Options)

• Risk Management

•Accounting

• Behavioral Finance

• Investments

slide6

Should we learn Finance?

Of course!!!!

Why should we learn Finance??

slide7

Topics for financial paper

1)Analysis of the financial system of a certain country, especially the exchange

2) The American Bond Market: History (Junk Bonds in the 80’s to today),

Types of Bonds (Plain vanilla, floater…), Correlation of major Bond markets

3) Bond theory: Rate of return, Duration, Convexity, Bond stripping

4) The American stock market, History (1929 to today), Correlation to other major markets

Perspective, where does it go?

5)Stock analyses, P/E ratio, dividend yield, certificate, dividends, buybacks, stock splits,

6) World stock indices, Dow, Nasdaq, S&P, NYSE, Russel 2000, Dax , Nikkei, FTSE,

Hang-Seng, Indices of Emerging Markets, (B-share, Bolsa…), Correlation! Perspective

7) World commodity markets, Overview, indices (CRB), recent developments, Outlook - which one’s to buy

8) CAPM, Theory, Implication, Practical relevance today?

9) Monetary policy in the US, Instruments, Usage, Success

10) European Monetary Union, Too early?, too unprepared?

slide8

Topics for financial paper cont.

11) Balance sheet of a company, Structure and Contents, Valuable for a potential investor? How to improve it

12) Hong-Kong July 1, 1997, One country - Two systems, Status quo analyses - Outlook

13)Economic indicators: NAPM, CPI, PPI, initial jobless claims, employment cost index (ECI), non-farm payrolls, unemployment, GDP, consumer confidence, beige book

14) Mergermania – A threat to the capitalistic system?

15) Swaps – Theory and Practice

16)Convertibles – Types and Pricing

17) Dividend Policy – Effects on the stock price

18) The World bank and the IMF – Structure and Goals

19) Insider Trading

20) Technical Analysis – Trick or Treat

21) Capital gains tax in the USA

22) Mortgage backed securities in the USA

slide9

Topics for financial paper cont.

23) Mutual funds – Buy the one that has performed best?

25) Futures - Practical application and pricing

26) Options - Practical application and pricing

27) Programming the Black-Scholes model or binomial option pricing model

28) US Retirement Tools: IRA’s and 401K’s

29) The Asian financial crises part 2 – Impact on the US and world economy with a time lag?

30) Business cycles – Obsolete?

31) The Japanese economy: solutions to a 10-year recession

32) The Hawaiian economy: solutions to a 10-year ailing economy

33) Forecasting methodologies for stocks; an overview

34) Chapter 11 bankruptcy protection

35) Working capital management

36) Mergers and Aquisitions

slide10

Topics for financial paper cont.

37) Foreclosures, A sure bet?

38) Finance and Neural Networks

39) Finance and Fuzzy Logic

40) Finance and Chaos Theory

41) Derivatives: Curse or Blessing for Society ?

42) Internet IPO’s: A sure bet for professionals ?

43) Has the Fed done a good job lately?

44) Technical Analysis: An empirical test

45) US Retirement Plans (IRA’s and 401 K’s)

46) Do Stocks outperform Bonds in the long run?

47) Is the US sliding into a recession?

48) Day-trading – Only for Professionals?

49) E-Banking and E-Trading – Pros and Cons

50) Can international market correlations be exploited by traders?

51) Do Intra-day trends exist, that can be exploited by traders?

52) Collateralized Debt Obligations (CDO’s) – Pros and Cons

slide11

Topics for financial paper cont.

53) How to write a Business Plan – Write a detailed plan for your own company

54) Buy outs – Types, Pros Cons, Success rates

55) Are Bond Prices and Stock Prices positively or negatively correlated?

56) Are Stock Prices and Volatility negatively correlated?

57) Does an Increase in Volatility indicate an Market Reversal?

58) Does the Internet reduce company\'s cost of capital?

59) Will the Internet make Brokers obsolete?

60) Venture Capital: A Good Investment?

61) Malaysia’s Lesson from the Asian Financial Crisis: Should we ignore

help from the IMF?

62) Bush’s Anti Missile Shield: Technologically and financially ridiculous?

63) Credit Derivatives: What are they, what are they good for?

64) Where is the value in Behavioral Finance?

65) Investing in Hedge Funds – Too risky?

66) The Tobin tax – Can it decrease currency speculation and volatility?

67) Choose your own topic

slide12

Topics for financial paper cont.

68) The recent accounting scandals – What happened, what has to be done?

69) The Enron – Arthur Anderson saga – What went wrong? Lessons to learn

70) The WorldCom accounting scandal

71) The Value at Risk concept

72) Basel II – The BIS proposal to banking supervision

73) Corporate Risk Management: Market Risk, Credit Risk, Operational Risk

74) Credit Derivatives – An Overview

75) Credit Risk Management

76) A survey of credit risk vendors

77) Operational Risk – The next generation

78) Pricing Credit Derivatives (Chapter 5 in Meissner’s book)

79) Investing in ETFs – A good idea? What are the costs?

80) The Daimler-Chrysler Merger - A success story? The $275 million lawsuit

81) Dell’s direct sales strategy – The model of the future?

slide13

Topics for financial paper cont.

82) CEO and executive management compensation - Just a disgrace

or harmful for shareholder value? Should there be a cap?

83) Is the stock market crash over? Prediction for the future!

84) The US credit score - How is it derived, Is there to much emphasis on it?

85) The target Fed Funds rate – How does it exactly work?

86) The US bankruptcy law – Too lenient?

87) The Sarbanes-Oxley Compliance Solution – Pros and Cons

88) The US Double Deficit – A Danger for International Financial Markets?

89) Should China float its Yuan?

90) Hedge Funds – What are their main strategies? Should they be regulated?

91) Market Timing – How does it exactly work? Should it be restricted?

92) Reits – Invest now?

93) The US corporate tax law – Favoring the big?

94) Martha Stuart – Wrongfully Convicted?

slide14

Topics for financial paper cont.

95) Bondstripping – How does it work?

96) The weak dollar – Curse or Blessing for the US economy?

97) Nanotechnology stocks – A good investment?

98) The EU expansion to 25 states – Chaos in the making?

99) Robert Engle’s 2003 Nobel-Prize rewarded GARCH theory – Justified?

100) Volatility on Volatility – A good trading indicator?

101) “Mexifornia” - Should illegal immigrants receive the green card?

102) Microsoft – A falling giant?

103) A Model for a Fair Exchange Rate

104) A Fundamental Analysis Model to forecast stock prices

105) Fannie Mae and Freddy Mac – Too much profit, too little benefit for

mortgagors? Should they be privatized?

106) Should stock options be expensed?

107) Kmart – Sears, Another Failed Merger?

108) Hedgestreet – Derivatives for the small investor. A useful tool?

slide15

Topics for financial paper cont.

109) Stock market forecast for the next year

110) Fundamental and Technical Analysis of the Hawaii’s “Big Four”

111) High-Tech in Hawaii – An Analysis of Kamakura Corporation

www.kamakuraco.com

112) An Analysis and Improvement of Kamakura’s ‘Technical Report’

113) IBM selling its PC division to Lenovo – A good idea?

114) The Shareholder Value Concept – Outdated, Too shortsighted?

115) Is Management Compensation in the US too high? – Should there be a Cap?

116) Hyundai –Currently number 7, soon number 1?

117) Walmart, 2% of US GDP – Success by employee discrimination?

118) The Boeing –Airbus Battle, No chance for Boeing?

119) The IPO process – Unfair? Corrupt?

120) How are Stock prices and Bond prices correlated? An empirical Study

121) A Model for a Fair Stock Price – Combining fundamental and technical analysis

122) Are we in the middle of a housing bubble, which will pop soon?

slide16

Topics for financial paper cont.

123) Investible Hedge Fund Indexes – Where do we stand?

124) GM and Ford – What to do to fight Asia and Europe?

125) Do markets bottom and top on high volatility?

126) Private Equity Firms – Course or Blessing for the Economy?

127) Islamic Law (Shari’ah) – Opportunities and Challenges

128) Can we exploit the downturn during the earnings warning season?

129) Should GM merge with Nissan-Renault?

130) Ethics in Finance – Is there any?

Choose your own topic, preferably finance related!!

slide17

Jobs Jobs Jobs

MBA

FINANCE

Banking

(Trader, Marketer,

Manager, Sales, CFA)

CFP

Treasury

Department

of any

Company

(CFO, CRO, FRM)

Commercial

Bank

Investment

Bank /

Brokerage

House

Generally: Don’t study on easy street!!!

slide18

To be Successful

on the Job:

Stay single !!!

Experience

Emotional

Intelligence

Intelligence/

Knowledge

• Self-awareness (realize how you come across)

• Self-regulation (suspend a decision, analyze first)

• Sensitivity (cultural; sense emotional problems)

• Motivation / Ambition (work smart and work hard)

• Social Skills (Communication, Team-skill,

Persuasiveness)

slide19

Who manages Money???

Economic Unions

EU, Nafta, Asean

Individuals

Companies

Countries

Reasons:

Debt

Reasons:

Assets

Recorded on a

slide20

Start of new Bear Market, March 2000

Bear Market

Bull Market

Bear Market

Bull Market

Bear

Black Monday

1987

1973 and 1978 OPEC

Crises

Post

War

Growth

Great

Depression

Conclusion:

slide23

Trading in the New Millenium

Broker versus Trader

What we trade

When we trade

Where we trade

How trades are executed

What we do

Criteria of good trader

How we trade

  • Fundamental analysis
  • Technical analyses
  • Seasons
  • Intuition

(Book chapter 2)

slide24

Broker versus Trader

What is a broker?

A broker is a person who invests your money until is gone (Woody Allan)

A broker is an

There are interbank brokers:

Trader at

Bank A

(Buyer)

Broker

Trader at

Bank B

(Seller)

There are “private investor” brokers

Private

Investor A

Broker

Exchange

Who takes price risk??

slide27

Investment Products

Mutual Funds are

About of all mutual fund managers underperform their benchmark!!!

Why????

slide28

General Reason:

Specific Reasons:

slide29

Investment Products

What about Hedge Fund or Fund of Funds performance??

Difficult to know..

Performance results suffer from ‘survivorship bias’ and ‘reporting bias’ (also

called backfill bias)

slide30

Investment Products

Considering the mutual fund performance disaster, what shall we do ?

Invest passively in

as QQQQ, SPY, DIA, etc

or

(Holding company depositary receipts) as

BBH (Biotech), Internet (HHH) or UTH

(Utilities) etc

slide31

Where we trade

  • on an exchange
  • OTC (over the counter)

(Book p.10,11)

slide32

How trades are executed

  • Open outcry
  • Electronically

(Book p.13,14)

slide33

On-line Trading

First step:

To trade:

Execution

of the trade:

The broker checks the order (in terms of size

and price) and puts it into the pit or computerized

trading system

The execution of the trade is displayed on your

computer screen

slide34

On-line Trading, cont.

Advantages of On-line trading:

Disadvantages of On-line trading:

slide35

Open Outcry

Exchange

Pit

Seat

Pit

Pit

Hawaii

Book p.13

slide36

Computerized Trading (as the NASDAQ)

AMZN

Bid

Size

Offer

Size

$ 99 300

$ 96 250

$ 94 50

$ 91 100

$ 90 200

$ 88 3000

Book p.13

slide37

Computerized Trading (as the NASDAQ)

AMZN

Bid

Size

Offer

Size

$ 99 300

$ 96 250

$ 94 50

$ 91 100

$ 90 200

$ 88 3000

Book p.13

slide38

Computerized Trading (as the NASDAQ)

“Level 2” trading allows an investor to see an

ECN (Electronic Communication Network) screen

slide39

What we do

  • Speculate
  • Arbitrage
  • Hedge

(Book p.5,6,9)

slide40

More on Speculation

Difference Gambling - Speculation - Investing

The chances of winning when gambling are

Example:

Exception:

The chances of winning when speculating are

In contrary to speculation,investing is

slide41

More on Speculation

These days, speculation is done ON MARGIN

This means

Example:

An investor wants to buy Yahoo, which trades at $100.

He buys it on margin, which is 40%, and only pays

The same logic applies to short selling.

Short selling is

Warning: Only speculate with money you can afford to lose

slide42

More on Arbitrage

Example:

Two traders quote the following prices for 1oz of Gold

Tokyo

Bid Offer

London

Bid Offer

Is arbitrage possible?

The term Arbitrage is often deliberately misused as

in “Risk-Arbitrage = Take-over Arbitrage” or

“Interest rate Arbitrage = Yield curve Arbitrage”

slide44

The Philosophy of Stock Price Forecasting

Forecast Possible:

No Forecast Possible:

The markets are “efficient”=

All information about a stock

is incorporated in the current

stock price. This is equivalent

to the

“Random Walk Hypothesis”=

• Fundamental Analysis

• Technical Analysis

• Seasonalities

• Times Series Analysis

• Neural Networks

• Chaos Theory

• Econometric Models

(“Outperform the Dow” Book chapter 2)

slide45

How we trade

trading are decisions based on

  • Fundamental analysis
  • Technical analyses
  • Seasons
  • Intuition

(Book p.16,17)

slide46

Fundamental analysis

Fundamental analysis is trying to forecast the movement of a stock price based on political, economical, sector-specific and company-specific data.

  • Political stability is essential
  • Macro-economicdata are to be analyzed
  • Sector is of importance
  • Company specific data are crucial

(Book p.16,17)

slide47

Financial Ratios

An Overview of Popular Financial Ratios

1) Earnings Ratios

PE Ratio = Market Price / Earnings per Share

(will be discussed)

PEG Ratio = Market Price / Earnings per Share / Growth Rate

(will be discussed)

(will be discussed)

Earnings per Share = Earnings / Number of Outstanding Stock

(will be discussed)

Dividend Yield = (Annual) Paid Dividend / Current Market Price

2) Liquidity Ratios

Current Ratio = Total Current Assets / Total Current Liabilities

Net Working Capital = Total Current Assets - Total Current Liabilities

Cash Flow = (Cash +Marketable Securities) / Total Current Liabilities

slide48

Financial Ratios

An Overview of Popular Financial Ratios

3) Profitability Ratios

(will be discussed)

Return On Equity = Earnings / Net Worth of Company1)

Operating Profit Margin = Operating Income / Net Sales

Net Profit Margin = Net Income / Net Sales

Book Value = Net worth of company1) / Number of outstanding stock

4) Capitalization Ratios

Debt-to-Equity Ratio (also called leverage) = (Bonds + Preferred Stock) / Net Worth of Company 1)

1) The Net Worth of a company = Shareholders Equity = Total Current Assets – Total Current Liabilities

slide49

Earnings ratios

One of the most important ratios is the price-earnings ratio, PE

The PE is the price of the stock divided by the earnings per

share of the company.

The earnings in the PE ratio can be trailing, current or expected.

If the company is healthy and earnings are growing, the trailing PE ratio is higher than the current PE ratio, which is again higher than the expected (also called forward) PE ratio.

The PE, which is published in newspapers and on screens, is

usually the expected PE.

As an example, if the stock of a company trades at $100 and

next years expected earnings per share is $5, then the

expected PE ratio is

Result:

slide50

Earnings ratios

A fairly new ratio is the Price Earnings Growth ratio, PEG

It is the PE ratio divided by next years expected growth rate:

Example: The price of IBM is $100, the earnings per share is $2,

And the next years expected growth rate is 50 (%).

What is the PEG ratio?

PEG ratios below 1 are considered fairly cheap, PEG’s of over 1

are considered fairly expensive

slide51

Earnings ratios

Of importance is also the earnings per share ratio.

It shows the allocation of the earnings to each share.

For example, if the earnings last year was $10 million and the number of outstanding stock is 10 million shares, the earnings per share is

This number is calculated after deducting taxes and dividends from the earnings.

slide52

Earnings/Profitability ratios

Closely related to the earnings per share is the return on equity

The return of equity shows how profitable each share is.

Return on equity is calculated as the return (= earnings) divided by the common stock at par (the original issue price of the stock) + capital surplus (difference between the current stock price and the par stock price) + retained earnings.

For example, if the yearly return of a company is $1,000,000, and the sum of common stock at par + capital surplus + retained earnings is $10,000,000, the return on equity is

slide53

Earnings ratios

Another important ratio is the dividend yield

It is the dividend divided by the current price of the

stock.

For example, if the dividend per year is $2 and the price of the stock is $100, then the dividend yield is

High tech stocks e.g. Yahoo often do not pay

a dividend.

slide54

Technical analysis

Technical analysis is trying to forecast the movement of a stock price from the pattern it has moved in the past.

The philosophy of technical analysis

  • Chart patterns reflect the fundamental data in an economy or a company
  • The markets move in trends
  • History repeats itself

(Book p.17,18)

slide55

Theories of Technical Analysis

a) Simple chart patterns

Trend, support resistance, double tops and bottoms,

triple tops bottoms, head and shoulders, flag

b) Moving average convergence-divergence (MACD)

c) Fibonacci Ratios and Elliot Wave principle

d) Relative strength index (RSI)

(Book p.17-33)

slide56

a) Simple chart patterns

The trend is your friend

An upward trend is a movement with consecutive higher lows and consecutive higher highs:

A downward trend is a movement with consecutive lower lows and consecutive lower highs.

A sideward trend is a movement which does not exceed a certain high and which does not fall below a certain low.

(Book p.18)

slide57

a) Simple chart patterns cont.

Support - Resistance

A support level is a level, where the market is expected to

from dropping, and possibly reverse to the upside. If however the support level is broken to the downside, a further significant is to be expected.

A resistance level is a level, where the market is expected to

from rising, and possibly reverse to the downside. If however the resistance is broken to the upside, a further significant is to be expected.

(Book p.22-25)

slide58

Support - Resistance cont.

Breaking of a resistance

(dashed line)

Resistance and support as the

previous low and high

(Book p.22-23)

slide59

Support - Resistance cont.

A support line, created by

connecting previous lows

False breakout

(Book p.23-25)

slide60

a) Simple chart patterns cont.

An ideal double top formation

Triple top formation

(Book p.25-26)

slide61

a) Simple chart patterns cont.

  • Ideal head and shoulders formation

Flag formation with an upward

breakout

(Book p.27-28)

slide62

b) Moving average convergence-divergence (MACD)

The MACD uses three exponentially smoothed averages to identify, like the concepts a) through c), a trend reversal or the continuation of a trend.

The MACD indicator reduces to two indicators:

The first, called the MACD1 indicator, is the difference between two exponential averages, usually a 26-day and a 12-day average.

The second, called Signal indicator, is the 9-day moving average of the MACD1 indicator.

The term convergence and divergence refers to a narrowing respectively widening of the MACD1 and the Signal indicator.

A buy signal is given, when the more volatile average, the MACD1 indicator, crosses the less volatile average, the Signal indicator, from beneath. If the MACD1 line crosses the Signal line from above, a sell signal is given.

(Book p.2-29)

slide64

b) Moving average convergence-divergence (MACD)

Calculation:

Example:

What is the EMAt for EMAt-1 = 10 and K = 0.2 (9 periods)

Pt = 12

EMAt =

Pt = 8

EMAt =

Pt = 4

EMAt =

So?

slide65

Fibonacci Ratios and Elliot Wave Principle

In the 13th century the mathematician Fibonacci discovered a number series with some quite astonishing results.

Adding two numbers to derive a result, then taking the last added number and adding it to the result, gives

1+1=2; 1+2=3; 2+3=5; 3+5=8 and so on, which gives the number series

Dividing consecutive numbers in this series by one another:

Dividing a number by the one following two places behind:

Technical analysts consider these numbers crucial.

(Book p.30)

slide66

Fibonacci Ratios and Elliot Wave Principle cont.

In 1946 the retired accountant Ralph Elliot wrote his book "Nature\'s law - The Secret of the Universe".

In this book he stated the “ElliotWave Principle”.

In its most basic form, the principle says, that markets move in a repetitive cycle of five waves to the upside, followed by three waves to the downside.

Elliot set certain rules for his principle, which are necessary for a certain pattern to qualify as an Elliot wave:

(Book p.30,31)

slide67

Fibonacci Ratios and Elliot Wave Principle cont.

Mandatory Elliot Wave rules:

1) correction wave 2 can never retrace more than 100% of wave 1

2) wave 3 can never be the shortest wave of waves 1, 3, or 5

3) the low of wave 4 is higher than the high of wave 1

(Book p.30,31)

slide68

Fibonacci Ratios and Elliot Wave Principle cont.

Voluntary Elliot Wave rules based on Fibonacci numbers:

  • The minimum length of wave 3 is the length of wave 1 plus 61.8% of wave 1
  • Wave 4 should reverse to the upside, after having retraced 38.2% of wave 3

• Highs and lows of the Elliot wave can be expected on day 13, 21, 34, 55,

and 89

The disadvantage of the Elliot Wave principle is the

(Book p.30,31)

slide69

Relative strength index (RSI)

The RSI was developed by Welles Wilder in 1978

It is based on the assumption, that after a strong rally the market is overbought and will enter into a downward correction phase.

Similarly, after a strong fall, the market is assumed to be oversold and it will enter into an upward correction phase.

The RSI tries to measure the degree of overboughtness respectively oversoldness and tries to identify, when the correction phase is likely to begin.

The RSI does not work well in markets that have a very

long and strong upward or downward trend.

(Book p.30,31)

slide70

Relative strength index (RSI) cont.

The RSI is calculated as

(2.2) RSI = 100 - (100 /( 1 + (Avg Up/Avg Dn)))

Avg Up=Sum of all changes for advancing periods divided by total of periods

Avg Dn = Sum of all changes for declining periods divided by total of periods

An example:

Given these data, Avg Up =

Avg Dn =

According to equation (2.2) RSI =

Due to equation (2.2), the RSI can take values between 0 and 100

(Book p.32)

slide71

Relative strength index (RSI) cont.

40-day price movement of a stock

Resulting 10-day RSI

An RSI of over 70 indicates an overbought market; an RSI of below 30 indicates an oversold market.

Result:

slide72

Critical appraisal of technical analysis

Technical analysis is not voodoo,

or is it?

Does technical analysis implicitly include fundamental data?

Not much empirical evidence!

Main justification of technical analysis:

(Book p.33)

slide73

Trading according to Seasons

Since 1950, 86.97% of the Dow gain occurred in the month from

November to April !!!

Sell in May and go away

(Data since 1968)

slide76

Trading according to Seasons cont.

From the former table we can see that in 8 out of 12 month, the increase in the first two weeks of the month was higher than in the second half of the month.

The increase in week 3 and 4 was only higher than the increase in week 1 and 2 in

If we look at the absolute changes and sum up all the increases in the first two weeks of each month, we get 73.68%.

Also, 12.53% + 13.94% = 26.47% of the Dow increase occurred in the

slide77

Trading according to Seasons cont.

What’s the “best” trading day of the week??

Results do depend on the time frame of data selection

slide79

Summary of Investing

  • Diversify! Diversify! Diversify! CAPM shows that

Diversification increases the ratio!

  • Mutual Funds are outdated! underperform

their benchmark!

  • What about Hedge Funds?
  • Hence, invest ‘passively’ in
  • Use the business cycles!
  • Use seasonal patterns if you invest shorter term
slide80

Summary of Investing cont.

Invest, don’t speculate; If you do speculate, watch the

market and only speculate with the money you can

afford to

lose

  • Growth stocks or value stocks ? Buy growth stocks,

small caps and junk bonds in an

Trend is your friend! Enjoy the ride;

don’t try to predict a trend-reversal

Buy beaten up-high tech stocks

Realize once a while!

Is patience is a virtue ?;

admit your are wrong!

slide81

What should we base our trading decision on ??

Fundamental analysis ?

Technical analysis ?

Seasons ?

Intuition ?

slide82

2) Bonds versus Stocks

Bonds

Definition:

A bond is a promissory note. The bond issuer promises to pay a specific sum of cash flows to the bond holder.

slide83

Bonds cont.

Types of bonds:

  • Debentures (unsecured debt obligation, i.e. savings account)
  • Short term bonds: Commercial paper (2 to 270 days, issued
  • by top banks and companies), Certificates of deposit (CD’s)
  • (several days to years, issued by banks)

• Savings Bonds: Issued by US Government for small investors,

Denomination from $50, usually local, state, and federal tax

exempt but lower yield than Treasuries

  • Treasuries:

Treasury bills: Maturity up to 1 year, auctions of 91 and 270 day

treasury bills take place weekly, minimum $5,000

Treasury notes: Maturity 1 year to 10 years, minimum $1,000

Treasury bonds: Maturity 10 years to 30 years, minimum $1,000

Treasury Bonds are local and state but not federal tax exempt

  • Mortgage bonds (secured by real estate)
  • Zero bonds (pay no coupon)
slide84

Bonds cont.

Types of bonds cont.

  • Junk bonds (credit rating of issuer is bad)
  • Eurobonds (An American company issues a bond outside the US and pays dollar interest and dollar principal)
  • Floating rate bonds

•Credit linked bonds

•Inflation linked bonds

  • Dual currency bonds

(Australian company, which invests in Japan and believes the Yen will devalue, issues a bond in yen, pays yen coupon and returns Australian Dollar at maturity (at maturity the issuer exchanges yen into Austral. $ at a fixed exchange rate, which is guaranteed by the underwriter))

slide85

Main differences between bonds and stocks

1) Bond prices return to their issue price (Fish-effect)

Stock prices are assumed normally or log-normally distributed

P

t

T

(Book p.203)

slide86

Main differences between bonds and stocks cont.

P

t

T

“Distribution function” of a bond and a stock

(Book p.203)

slide87

Main differences between bonds and stocks cont.

Normal versus log-normal distribution of a stock

Result:

(Book p.197)

slide89

Main differences between bonds and stocks cont.

Main criteria of stocks

  • Preferred stock
  • Convertible
  • IPO’s (going public)
  • Mergers / Spin-offs
  • Buy backs
  • Stock splits
  • Beta
  • Ratios: P/E ratio, earnings per share, return on equity, dividend yield
slide90

Bond pricing

The price of a bond B is the sum of all discounted future

cash flows.

The cash flows of a 5 year coupon bond with a principal

amount of $100 and a 3% annual coupon looks as follows:

1y

2y

3y

4y

5y

B?

slide91

Bond pricing cont.

Mathematically, the discounted sum of all future cash flows is

where

B : Bond price

n : number of coupon payments

ct : coupon at time t (known interest rate payments, paid every 6 months in the US)

y : yield to maturity

PA : principal amount

Treating the last coupon and tbe PA as one coupon cn, we get

(4.24)

(Book p.105,106)

slide92

Bond pricing cont.

Example 1: What is the price of 4 year 5% annual

coupon bond with a 3% yield and a principal amount of 100?

Example 2: What is the price of 4 year 5%-coupon bond

with a 5% yield and a principal amount of 100?

(Book p.105,106)

slide93

Bond pricing cont.

What is the Yield???

  • The yield (also called yield to maturity) is the of the bond
  • expressed as an annual percentage, if the bond is bought at the current
  • market price and held to maturity, assuming no default risk

b) The yield is the used in the discount factor df = 1 / (1+y)t

to derive the present value (the price of the bond). [FV x df = PV]

c) The yield curve (yield with respect to time) expresses

in an economy for AAA rated bonds

The higher the yield, the better to buy the bond????

slide94

Bond pricing cont.

Dirty versus Clean Price

The price found on screens and in newspapers usually the

Clean Price

If an investor buys a bond, he has to pay the clean price

Plus the ACCRUED INTEREST

The accrued interest is the interest that is calculated daily and has

accumulated since the last coupon date

The price that is actually paid when buying the bond is therefore the

Dirty Price =

Clean Price + Accrued Interest

(Book p.291)

slide95

Bond pricing cont.

Example: A bond trades at 103.00, has a coupon of 6% and

the last coupon date was 50 days ago. What does an investor

have to pay when he buys the bond?

He has to pay the dirty price, which is the clean price

+ accrued interest:

Naturally, when you sell a bond, you sell it at the

Dirty price

(Book p.291)

slide96

Stocks Pricing

Bonds are priced by discounting all the (known) future cash flows back to

today.

The same logic can be applied for stocks.

However, the dividend of a stock is unknown, so we have to make

an assumption about future dividends.

Usually companies let their dividends grow with a constant rate g,

for example 3%.

Also, since stocks do not have a maturity date, we have to use

infinite time periods.

This leads us to the following equation for the price of a stock:

slide97

Stocks Pricing with the Constant-Growth Dividend Model

S = Stock price, D0 = last paid Dividend, g = dividend growth rate,

i = discount rate (also called required return of the stock)

Example:

A company\'s last paid dividend was $2. The growth rate of the dividend

is expected to be 3%. The discount rate is 6%.

What is the stock price using 5 future periods?

slide98

Stocks Pricing with the Constant-Growth Dividend Model

Critical Appraisal of the Constant Growth Dividend Model

The model shows the inverse relationship between interest rates and

Stock prices!

The model shows ONE factor that influences the price of a stock.

Other factors are expected revenue and earnings growth rate,

quality of management, market product, competitors, economy,

sector, psychology, legal battles, etc.

Many high-tech companies do not pay a dividend (such as Microsoft

or Yahoo). In this case the constant dividend growth model is of no value

slide99

Dividend Policy

As mentioned earlier, companies often have a long-term moderate growth rate of their dividend.

This policy is supposed to give confidence in the long term prospective of the company.

The share price of companies that have to reduce their dividends, usually suffer a severe decline in the share price.

(Emery p.476f)

slide100

Dividend Policy

The timeline of dividends

Dividend

declaration

date (Amount

and Ex-dividend

date are

announced)

Ex-dividend

date

(Stock price

drops by the

dividend

amount)

Holder of

Record date

(List of share-

holders

is established)

Dividend

payment

date

An investor has to own the stock BEFORE the ex-dividend date in order to

receive the dividend. That is why the stock drops at the dividend date.

slide101

Dividend Policy

Dividends Irrelevance Theorem

There is a school of thought lead by Miller and Modigliani, that the

payment of dividends is irrelevant for a company and that shareholders

should be indifferent to dividends.

The theorem says that the payment of dividends will equal the loss

of price appreciation of a stock. Thus, the share holder is indifferent

to receiving dividends or the stock price increase.

This theorem is correct if the following assumptions hold:

• No transaction costs when selling stocks (Otherwise dividends would

be preferable) or paying dividends (otherwise stock price increases are

preferred.

• Same tax treatment of dividends and share price increases

• The companies management is uninfluenced by dividends and

share price increases

Do theses assumptions hold in reality???

slide102

Dividend Policy

In most countries, like the US, dividends are treated less favorable

from a tax perspective than stock price increases.

One could argue that there is “double taxation” of dividends due

to the fact that they are taxed on a corporate level as income,

and as income for the individual investor.

That is why some countries, like Germany, have a lower tax rate

on dividends than on retained earnings of a company.

If dividends are taxed higher than stock price increases,

it follows, that it is in the companies and share holders interest

that no dividends should be paid!!

slide103

Dividend Policy

It can be argued that some investors simply like receiving dividends

(clientele effect)

This would make a company that pays dividends a popular choice

resulting in an increasing stock price. However, these days investors

behave fairly rational, and the clientele effect should be rater small.

Conclusion of dividend policy:

slide104

The Time Value of Money

One dollar today is worth more than one dollar tomorrow.

WHY???

slide105

The Time Value of Money cont.

How much less is a dollar worth in the future?

a) Without interest on interest:

$100 now are worth in three years with 10% pa:

FV : Future value

PV : Present value

i : interest rate pa

n : time in years

FV = PV (1 + i n)

Book p. 73

slide106

The Time Value of Money cont.

b) with discrete interest on interest

b1) annual interest on interest

FV = PV (1+i)n

100

1y

2y

3y

slide107

The Time Value of Money cont.

b2) semiannual interest on interest

withm = 2

FV = PV (1+i/m)nm

b3) monthly interest on interest

FV = PV (1+i/m)nm

withm = 12

(Book p. 74)

slide108

The Time Value of Money cont.

c) continuously compounded interest on interest

With m  infinity,

FV = PV (1+i/m)nm becomes

e = Eulers number = 2.7182...

(Book p. 74)

slide109

The Time Value of Money - Application

Guaranteed return on investment

GROI stand for

The investor invests $10,000 and is guaranteed at least $10,000 at maturity

How does that work???

The arranger takes a certain amount, invests it at the risk free rate and

takes the rest to invest in a risky trade.

Example: A Groi has an original investment of $10,000, 7 year maturity,

annual interest rate 6%. How much does the arranger invest

in the risk-free asset to guarantee the payback of $10,000?

=

(The $ grows to in 7 years, since

The rest,

slide110

The Groi graphically

may grow to

$3,349

invested in

risky asset

$6,651

Invested in

risk-free

asset

grows to

T

t0

slide111

Converting Interest Rates

a1) To convert a sub-annual rate into an annual rate, we use

(3.7) Eff = ((Nom / m) + 1) m -1

where

Eff : annual interest rate (effective rate)

Nom : sub-annual interest rate (nominal rate)

m : interest rate payment frequency per year

Thus, a semiannual rate of 9.84% equals an annual rate of

A quarterly rate of 9.84% equals an annual rate of

Book p.75

slide112

Converting Interest Rates cont.

a2) Converting an annual (effective) rate into a sub-annual

(nominal) rate, so solving equation (3.7) for Nom, gives

So an annual (effective) rate of 10.08% results in an semiannual (nominal) rate of

An annual (effective) rate of 0.1021 results in a

quarterly (nominal) rate of

Book p. 75

slide113

Converting Interest Rates cont.

b1)The conversion of an annual or sub-annual, also called discrete rate, into a continuously compounded rate, is done by equation

(3.9) ln (1 + Dis / m ) * m = cc

where

ln : natural logarithm

Dis : discrete interest rate (annual, sub-annual, etc.)

m : interest rate payment frequency per year

cc : continuously compounded interest rate

So an annual (discrete or effective) rate of 10.08% results in a continuously compounded rate of

A semiannual (discrete) rate of 9.84% results in a continuously compounded rate of

(Book p. 75,76)

slide114

Converting Interest Rates cont.

b2) Converting a continuously compounded rate into a discrete rate, so solving (3.9) for Dis, gives

(3.10) Dis = (ecc/m - 1) * m

where Dis, cc, and m are defined as in equation (3.9)

A continuously compounded rate of 10% is equal to an annual rate

of

A continuously compoundedrate of 9.61% is equal to a semiannual rate

of

(Book p. 75,76)

slide115

What is the APR (Annual Percentage Rate)?

An APR is a nominal interest rate!, thus it ignores interest

on interest.

The APR is calculated as the sub-annual rate (Nom)

times the number payments in a year (m).

APR = Nom * m

Example 1:

An entrepreneur pays 2% interest every 3 months. What

is the APR?

Thus, interest on interest is ignored

slide116

What is the APR (Annual Percentage Rate) cont.

Example 2:

A car dealer tells you the APR, which has to be paid

twice a year is 4%. What do you have to pay and when?

Thus, interest on interest is ignored.

slide117

What is the APR (Annual Percentage Rate) cont.

Example 2 cont:

The car dealer tells you to pay 2% every 6 months, thus the

nominal interest rate is 4%.

What is the effective (= annual and “real”, ) interest rate?

We use equation:

Therefore the effective (=annual) interest rate is

Result:

slide118

More on Corporate Finance

  • Capital Budgeting
  • Dividend policy (already discussed)
  • Working Capital Management
  • Budgeting and financial forecasting
slide119

Capital Budgeting

Capital budgeting is another term for the

Investment decision process

When should a company do a certain investment???

Also, an investment can be done because of strategic reasons:

  • Increase market share
  • Hurt a competitor
  • Improve customer relations

(Emery p.298f)

slide120

Criteria for the Investment Decision

(How can we tell, if a an investment will be good or bad)

Net present value criteria:

Do the investment if the net present value of all future cash flows is >0.

NPV : net present value

CFt :outgoing and incoming cash flow at time t (after tax)

k : discount rate (=required rate of return)

IO : Initial cash outlay

slide121

Net present value criteria cont.

Example:

Volkswagen is considering investing in a new 3-Liter car.

The company expects an initial investment in R&D

(research and development) of $10,000,000.

It expects negative outflows in year 1 and 2 of $2,000,000

and $1,000,000 resp.. It expects profits in year 3 and 4 of

$4,000,000 and $5,000,000 resp. and $8,000,000 for the

years 5. The discount factor is 4%.

Should Volkswagen build the 3-Liter car?

NPV =

Result:

slide122

Capital Budgeting cont.

Closely related to the NPV criteria is the

Profitability Index or Benefit/Cost ratio

According to the profitability index, should Volkswagen do the

investment?

PI=

Result:

slide123

Comparing the NPV criteria and the PI Index

If the NPV is positive, it follows that the PI will be

Thus, the NPV criteria and the PI index are basically identical.

Advantage of NPV and PI:

Disadvantage of NPV and PI:

slide124

Capital Budgeting cont.

Internal rate of return (IRR)

The internal rate of return measures the return or profit of

the investment.

It is equivalent to the yield of a bond!!

Mathematically, the IRR is the discount rate, that guarantees

the future cash flows of the investment (CF) equal the initial

outflow (IO):

slide125

Features of the Internal rate of return (IRR)

Unfortunately, we can’t solve the equation

easily for IRR (we have to use search

procedures) like Newton-Raphson)

Usually , a company has a target IRR. If the calculated

IRR is higher than the target IRR, so investment is

done, vice versa.

As the yield of the bond, the IRR concept (and the NPV

and the PI assume), that all cash flows are reinvested at

the discount = IRR rate. This is obviously a disadvantage.

slide126

The modified IRR (MIRR)

The drawback, that in the IRR model the cash flows are reinvested

at the IRR rate, is solved in the MIRR model.

In the MIRR model the cash flows are reinvested at the MIRR rate.

The MIRR rate can be calculated in 2 steps:

1) Calculate the future value of the cash flows using

2) Calculate the MIRR using

(is derived from )

slide127

The modified IRR (MIRR)

Example:

A company has an IO of $1,000, and expects inflows of $300 at the end

of year 1, $400 at the end of year 2, $500 at the end of year 3 and $600 at

the end of year 4. The cash flows are expected to be reinvested at 15%.

What is the MIRR rate?

1) The future value of the cash flows is, following

FV =

slide128

The modified IRR (MIRR)

the MIRR is

2) Using

As a comparison, the standard IRR of the above example is

24.89% (see ECXEL file NPV IRR comparison)

slide129

Comparing the NPV and IRR Method

Question:

If the NPV and IRR model return different results, what model

should we trust???

Example:

(see EXCEL file

“NPV IRR comparison”)

Solution:

Compare the NPV and IRR of the differencein cash flows

slide131

Working Capital Management

Firstly, the Yield Curve (= Interest rate curve) in an economy

is usually steep

Yield curves of the US, Germany and Japan on July 15, 1998

Result: Investing money short term results in a lower return

(Emery p.579f)

slide132

Working Capital Management cont.

Liquidity is

the ability to pay off debt

Profitability is

the ability to make profits

Working capital and liquidity are often used as synonyms and

consist of cash and short term assets.

Short Term assets consist of treasury bills, commercial paper

(issued by banks and corporations) and CD’s (issued by banks)

Net working capital is the difference between short term assets

and short term liabilities.

Net working capital has to be positive, otherwise you are

slide133

Working Capital Management cont.

The working capital trade off is

the trade-off between liquidity and profitability

The higher the liquidity (=cash and short term assets) the

the risk of defaulting on debt , but

The lower the liquidity (=cash and short term assets) the

the profitability (long term assets and investment in the firm’s

business), but

slide134

Working Capital Management cont.

How can we solve the liquidity - profitability trade-off??

We can reduce the trade-off by the

Maturity Matching Principle

Match long term investments (real estate, trucks, machinery) with

Short term assets (computers, software) can be matched with

slide135

Financial Forecasting and Budgeting

Forecasting in financial management is necessary to determine

a companies financial need.

Financial Forecasting is principally done in 3 steps:

1. Forecasting of the companies sales revenues and other income

over the planing period.

2. Forecasting of the level of necessary investments and other

expenses

3. Use 1. and 2 to determine the financial need

((Emery p.648f))

slide136

Financial Forecasting and Budgeting cont.

Important for a company is the forecast of Sales.

There are many forecasting methods is finance:

Linear regression analysis, Non-linear regression analysis,

Multi-variate regression analysis, Time series analysis,

Econometric models, Stochastic processes, Monte-Carlo

simulation and more

Lets look at a linear regression-analysis to forecast sales:

slide137

Financial Forecasting and Budgeting cont.

One form of regression analysis is time series analysis.

In time series analysis time t is on the x-axis.

Example:

Let’s assume the sales of Turbodyne (TRBD) are:

In January $30,000, in February $34,000, in March $35,000

and in April 39,000.

What are the expected sales in May, calculated on a linear

time series analysis?

slide138

Financial Forecasting and Budgeting cont.

Sales

r

$40,000

$30,000

time t

1

2

3

4

5

Jan

Feb

Mar

Apr

May

The goal is to find a linear regression function r, which minimizes

the differences between the observed points and r.

We then extrapolate r to find the sales for May.

slide139

Financial Forecasting and Budgeting cont.

Sales

r

$40,000

S

b =

$30,000

t

a

time t

1

2

3

4

5

Jan

Feb

Mar

Apr

May

In order to find the regression function r, we have to find a and b.

slide140

Financial Forecasting and Budgeting cont.

a =

b =

where

n:

number of observations

average of times t;

average of times S;

slide141

Financial Forecasting and Budgeting cont.

With

t = 1,2,3,4 and

S= 30,000; 34,000; 35,000; 39,000

b =

a =

slide142

Financial Forecasting and Budgeting cont.

It follows that the estimated Sales at time t =5,

so in May, are

S = a +b t =

This forecast is based on the assumption, that the sales

will increase linearly on the basis of historical data.

slide143

Financial Forecasting and Budgeting cont.

The Sales forecast is often used as a basis to plan other

financial items, such as inventories.

The Percent of sales method for Financial Forecasting uses a

linear forecasting:

Inventories

30,000

20,000

Forecasted

Sales

30,000

70,000

slide144

Financial Forecasting and Budgeting cont.

Creating a budget

A budget tells you what you can’t afford, but it doesn’t keep

you from buying it (William Feather)

A budget is an estimate of revenues and expenditures.

Revenue =

Number of sales * price per sales unit

Example:

Dell sells 1 million PC’s in the year 2000 for $500 each.

What is Dell’s revenue for 2000?

A Cash-budget estimates a company’s necessary financial needs

based on expected revenues and expenditures.

((Emery p.648f))

slide145

Financial Forecasting and Budgeting cont.

A Cash budget consists of

  • Estimated Cash receipts
  • Estimated Cash payments
  • Expected monthly cash balance
  • Financial need
slide148

Practice Exam

  • Task 1 (25 points)
  • 1)If the market rises and breaks an important resistance line,
  • technical analysis recommends buying
  • True False
        • 
  • 2) If the market falls and breaks an important support line,
  • technical analysis recommends selling.
  • True False
        • 
  • 3) Speculation means trying to exploit the movement of an asset.
  • True False
        • 
  • 4) Traders take risks, brokers don’t
  • True False
        • 
slide149

5) In the long run, stocks tend to outperform bonds

  • True False
        • 
  • 6) Arbitrage is another word for risk-less profit
  • True False
        • 
  • 7) The yield curve of an economy is usually down-ward sloping
  • True False
        • 
  • 8) When buying on margin, you trade with borrowed money
  • True False
        • 
  • 9) The Nasdaq has outperformed the Dow in the last half year
      • True False
  • 10) The unemployment rate in the USA is close to 7.2%
  • True False
        • 
slide150

Task 2 (25 points)

a) The annual market interest rate is 10%. An investor wants to

invest $1000 for 5 years.

The banker offers the client to pay back $1000 + $1000 * 0.1 * 5

= $1,500. Is the banker trying to rip off the client?

b) If you were the banker, what would you pay back to the

client after 5 years?

      • c)A client wants to invest $1000 for 5 years. The banker offers
      • to pay 5% quarterly or 5.2% annually. The client decides
      • to take 5% quarterly. Did he do the right thing?
  • Use (Eff = ((Nom / m) + 1) m –1) Eff and Nom in %!
slide151

Task 3 (25 points)

a)The annual coupon of a bond is 5%. The annual yield is

also 5%. What is the price of the bond with a principal of $1000?

b) What is the 20 day accrued interest of the bond?

c) What is the difference between the coupon of a bond and

the dividend of a stock?

slide152

Task 4 (25 points)

a) After attending the Fin300 class at HPU, you have become a

successful financial advisor. One of your clients wants to invest

$100,000 dollars. What are the two questions you ask him first?

b) Your client wants to open up a savings account. What is your

reply

c)What do you suggest to the client as investment alternatives?

slide153

Learning e and ln

The number e -Eulers number- is an irrational number (a

number that cannot be divided by tow integers (an integer is

a number without decimals, so -3 and 4 are integers,

-3.1 or 4.55 are not)

The value of e = 2.71828182…. The decimals of e are indefinite

Mathematically e = 1+ 1/1! + 1/2! + 1/3! =… = (1 + 1/m) m

with m to infinity

e has nice features such as if y = e x then y’ = e x

y = e f(x) then y’ = f’(x) e f(x)

slide154

Logarithm

The logarithm of the number N to the base a is the exponent to

which x has to raised to yield N. Thus

Loga N = x if and only if ax = N

Examples:

Log 10 1 = 0 since 100 = 1

Log 10 10 = 1

Log 10 100 = 2

Log 10 1000 = 3

Log 4 16 =

Log 10 (0.001) =

slide155

If the base of the logarithm is e, the logarithm is called

natural logarithm.

Log e = ln

Examples:

ln 1 = 0 since 2.71830 = 1

ln 10 = 2.326 since 2.71832.3026 = 10

ln 100 = 4.6052 since 2.71834.6052 = 100

ln -3

slide156

Three important rules apply to logarithms:

a) ln (a * b) = ln a + ln b

b) ln (a / b) = ln a - ln b

c) ln ab = b * ln a

Rule c) comes in handy for solving equations:

Solve for x, when 10x = 7, using rule c)

Mathematically logarithms have nice features such as

If y = ln x then y’ = 1/x

If y = ax then y’ = ax ln a

slide157

Graphically ln x and e are reflected across the y = x line

y

y = ex

y = x

y = ln x

1

x

1

Logarithmic functions are often used in psychology to

explain human behavior.

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