Chapter 1 The Process of Portfolio Management

Chapter 1 The Process of Portfolio Management

The Life of every man is a diary in which he means to write one story, and writes another; and his humblest hour is when he compares the volume as it is with what he vowed to make it. - J.M. Barrie

Outline Introduction Part one: Background, Basic Principles, and Investment Policy Part two: Portfolio construction Part three: Portfolio management Part four: Portfolio protection and contemporary issues

Introduction Investments Security analysis Portfolio management
Purpose of portfolio management Low risk vs. high risk investments The portfolio manager’s job The six steps of portfolio management

Investments Traditional investments covers: Security analysis
Involves estimating the merits of individual investments Portfolio management Deals with the construction and maintenance of a collection of investments

Security Analysis A three-step process
The analyst considers prospects for the economy, given the state of the business cycle The analyst determines which industries are likely to fare well in the forecasted economic conditions The analyst chooses particular companies within the favored industries EIC analysis (a top-down approach)

Portfolio Management Literature supports the efficient markets paradigm On a well-developed securities exchange, asset prices accurately reflect the tradeoff between relative risk and potential returns of a security Efforts to identify undervalued undervalued securities are fruitless Free lunches are difficult to find

Portfolio Management (cont’d)
Market efficiency and portfolio management A properly constructed portfolio achieves a given level of expected return with the least possible risk Portfolio managers have a duty to create the best possible collection of investments for each customer’s unique needs and circumstances

Purpose of Portfolio Management
Portfolio management primarily involves reducing risk rather than increasing return Consider two $10,000 investments: Earns 10% per year for each of ten years (low risk) Earns 9%, -11%, 10%, 8%, 12%, 46%, 8%, 20%, -12%, and 10% in the ten years, respectively (high risk)

Low Risk vs. High Risk Investments

Low Risk vs. High Risk Investments (cont’d)
Earns 10% per year for each of ten years (low risk) Terminal value is $25,937 Earns 9%, -11%, 10%, 8%, 12%, 46%, 8%, 20%, -12%, and 10% in the ten years, respectively (high risk) Terminal value is $23,642 The lower the dispersion of returns, the greater the terminal value of equal investments

The Portfolio Manager’s Job
Begins with a statement of investment policy, which outlines: Return requirements Investor’s risk tolerance Constraints under which the portfolio must operate

The Six Steps of Portfolio Management
Learn the basic principles of finance Set portfolio objectives Formulate an investment strategy Have a game plan for portfolio revision Evaluate performance Protect the portfolio when appropriate

The Six Steps of Portfolio Management (cont’d)
Learn the Basic Principles of Finance (Chapters 1 – 3) Set Portfolio Objectives (Chapters 4 – 5) Evaluate Performance (Chapters ) Protect the Portfolio When Appropriate (Chapters 21 – 25) Formulate an Investment Strategy (Chapters 6 – 14) Have a Game Plan for Portfolio Revision (Chapters 15 – 18)

Overview of the Text PART ONE: Background, Basic Principles, and Investment Policy PART TWO: Portfolio Construction PART THREE: Portfolio Management PART FOUR: Portfolio Protection and Contemporary Issues

PART ONE Background, Basic Principles, and Investment Policy
A person cannot be an effective portfolio manager without a solid grounding in the basic principles of finance Egos sometimes get involved Take time to review “simple” material Fluff and bluster have no place in the formation of investment policy or strategy

PART ONE Background, Basic Principles, and Investment Policy (cont’d)
There is a distinction between “good companies” and “good investments” The stock of a well-managed company may be too expensive The stock of a poorly-run company can be a great investment if it is cheap enough

The two key concepts in finance are: A dollar today is worth more than a dollar tomorrow A safe dollar is worth more than a risky dollar These two ideas form the basis for all aspects of financial management

Other important concepts The economic concept of utility Return maximization

Setting objectives It is difficult to accomplish your objectives until you know what they are Terms like growth or income may mean different things to different people

The separation of investment policy from investment management is a fundamental tenet of institutional money management Board of directors or investment policy committee establish policy Investment manager implements policy

PART TWO Portfolio Construction
Formulate an investment strategy based on the investment policy statement Portfolio managers must understand the basic elements of capital market theory Informed diversification Naïve diversification Beta

PART TWO Portfolio Construction (cont’d)
International investment Emerging markets carry special risk Emerging markets may not be informationally efficient

Stock categories and security analysis Preferred stock Blue chips, defensive stocks, cyclical stocks Security screening A screen is a logical protocol to reduce the total to a workable number for closer investigation

Debt securities Pricing Duration Enables the portfolio manager to alter the risk of the fixed-income portfolio component Bond diversification

Pension funds Significant holdings in gold and timberland (real assets) In many respects, timberland is an ideal investment for long-term investors with no liquidity problems

PART THREE Portfolio Management
Subsequent to portfolio construction: Conditions change Portfolios need maintenance

PART THREE Portfolio Management (cont’d)
Passive management has the following characteristics: Follow a predetermined investment strategy that is invariant to market conditions or Do nothing Let the chips fall where they may

Active management: Requires the periodic changing of the portfolio components as the manager’s outlook for the market changes

Options and option pricing Black-Scholes Option Pricing model Option overwriting A popular activity designed to increase the yield on a portfolio in a flat market Use of stock options under various portfolio scenarios

Performance evaluation Did the portfolio manager do what he or she was hired to do? Someone needs to verify that the firm followed directions Interpreting the numbers How much did the portfolio earn? How much risk did the portfolio bear? Must consider return in conjunction with risk

Performance evaluation (cont’d) More complicated when there are cash deposits and/or withdrawals More complicated when the manager uses options to enhance the portfolio yield Fiduciary duties Responsibilities for looking after someone else’s money and having some discretion in its investment

PART FOUR Portfolio Protection and Contemporary Issues
Called portfolio insurance prior to 1987 A managerial tool to reduce the likelihood that a portfolio will fall in value below a predetermined level

PART FOUR Portfolio Protection and Contemporary Issues (cont’d)
Futures Related to options Use of derivative assets to: Generate additional income Manage risk Interest rate risk Duration

PART FOUR Portfolio Protection and Contemporary Issues (cont’d)
Derivative securities Tactical asset allocation Program trading Stock lending CFA program

Chapter 2 The Two Key Concepts in Finance

It’s what we learn after we think we know it all that counts.
- Kin Hubbard

Outline Introduction Time value of money
Safe dollars and risky dollars Relationship between risk and return

Introduction The occasional reading of basic material in your chosen field is an excellent philosophical exercise Do not be tempted to include that you “know it all” E.g., what is the present value of a growing perpetuity that begins payments in five years

Time Value of Money Introduction Present and future values
Present and future value factors Compounding Growing income streams

Introduction Time has a value
If we owe, we would prefer to pay money later If we are owed, we would prefer to receive money sooner The longer the term of a single-payment loan, the higher the amount the borrower must repay

Present and Future Values
Basic time value of money relationships:

Present and Future Values (cont’d)
A present value is the discounted value of one or more future cash flows A future value is the compounded value of a present value The discount factor is the present value of a dollar invested in the future The compounding factor is the future value of a dollar invested today

Why is a dollar today worth more than a dollar tomorrow? The discount factor: Decreases as time increases The farther away a cash flow is, the more we discount it Decreases as interest rates increase When interest rates are high, a dollar today is worth much more than that same dollar will be in the future

Situations: Know the future value and the discount factor Like solving for the theoretical price of a bond Know the future value and present value Like finding the yield to maturity on a bond Know the present value and the discount rate Like solving for an account balance in the future

Present and Future Value Factors
Single sum factors How we get present and future value tables Ordinary annuities and annuities due

Single Sum Factors Present value interest factor and future value interest factor:

Single Sum Factors (cont’d)
Example You just invested $2,000 in a three-year bank certificate of deposit (CD) with a 9 percent interest rate. How much will you receive at maturity?

Single Sum Factors (cont’d)
Example (cont’d) Solution: Solve for the future value:

How We Get Present and Future Value Tables
Standard time value of money tables present factors for: Present value of a single sum Present value of an annuity Future value of a single sum Future value of an annuity

How We Get Present and Future Value Tables (cont’d)
Relationships: You can use the present value of a single sum to obtain: The present value of an annuity factor (a running total of the single sum factors) The future value of a single sum factor (the inverse of the present value of a single sum factor)

Ordinary Annuities and Annuities Due
An annuity is a series of payments at equal time intervals An ordinary annuity assumes the first payment occurs at the end of the first year An annuity due assumes the first payment occurs at the beginning of the first year

Ordinary Annuities and Annuities Due (cont’d)
Example You have just won the lottery! You will receive $1 million in ten installments of $100,000 each. You think you can invest the $1 million at an 8 percent interest rate. What is the present value of the $1 million if the first $100,000 payment occurs one year from today? What is the present value if the first payment occurs today?

Ordinary Annuities and Annuities Due (cont’d)
Example (cont’d) Solution: These questions treat the cash flows as an ordinary annuity and an annuity due, respectively:

Compounding Definition Discrete versus continuous intervals
Nominal versus effective yields

Definition Compounding refers to the frequency with which interest is computed and added to the principal balance The more frequent the compounding, the higher the interest earned

Discrete Versus Continuous Intervals
Discrete compounding means we can count the number of compounding periods per year E.g., once a year, twice a year, quarterly, monthly, or daily Continuous compounding results when there is an infinite number of compounding periods

Discrete Versus Continuous Intervals (cont’d)
Mathematical adjustment for discrete compounding:

Mathematical equation for continuous compounding:

Example Your bank pays you 3 percent per year on your savings account. You just deposited $ in your savings account. What is the future value of the $ in one year if interest is compounded quarterly? If interest is compounded continuously?

Example (cont’d) Solution: For quarterly compounding:

Example (cont’d) Solution (cont’d): For continuous compounding:

Nominal Versus Effective Yields
The stated rate of interest is the simple rate or nominal rate 3.00% in the example The interest rate that relates present and future values is the effective rate $3.03/$100 = 3.03% for quarterly compounding $3.05/$100 = 3.05% for continuous compounding

Growing Income Streams
Definition Growing annuity Growing perpetuity

Definition A growing stream is one in which each successive cash flow is larger than the previous one A common problem is one in which the cash flows grow by some fixed percentage

Growing Annuity A growing annuity is an annuity in which the cash flows grow at a constant rate g:

Growing Perpetuity A growing perpetuity is an annuity where the cash flows continue indefinitely:

Safe Dollars and Risky Dollars
Introduction Choosing among risky alternatives Defining risk

Introduction A safe dollar is worth more than a risky dollar
Investing in the stock market is exchanging bird-in-the-hand safe dollars for a chance at a higher number of dollars in the future

Introduction (cont’d)
Most investors are risk averse People will take a risk only if they expect to be adequately rewarded for taking it People have different degrees of risk aversion Some people are more willing to take a chance than others

Choosing Among Risky Alternatives
Example You have won the right to spin a lottery wheel one time. The wheel contains numbers 1 through 100, and a pointer selects one number when the wheel stops. The payoff alternatives are on the next slide. Which alternative would you choose?

Choosing Among Risky Alternatives (cont’d)
B C D [1-50] $110 $200 [1-90] $50 [1-99] $1,000 [51-100] $90 $0 [91-100] $500 [100] -$89,000 Avg. payoff $100

Example (cont’d) Solution: Most people would think Choice A is “safe.” Choice B has an opportunity cost of $90 relative to Choice A. People who get utility from playing a game pick Choice C. People who cannot tolerate the chance of any loss would avoid Choice D.

Example (cont’d) Solution (cont’d): Choice A is like buying shares of a utility stock. Choice B is like purchasing a stock option. Choice C is like a convertible bond. Choice D is like writing out-of-the-money call options.

Defining Risk Risk versus uncertainty Dispersion and chance of loss
Types of risk

Risk Versus Uncertainty
Uncertainty involves a doubtful outcome What you will get for your birthday If a particular horse will win at the track Risk involves the chance of loss If a particular horse will win at the track if you made a bet

Dispersion and Chance of Loss
There are two material factors we use in judging risk: The average outcome The scattering of the other possibilities around the average

Dispersion and Chance of Loss (cont’d)
Investment value Investment A Investment B Time

Dispersion and Chance of Loss (cont’d)
Investments A and B have the same arithmetic mean Investment B is riskier than Investment A

Types of Risk Total risk refers to the overall variability of the returns of financial assets Undiversifiable risk is risk that must be borne by virtue of being in the market Arises from systematic factors that affect all securities of a particular type

Types of Risk (cont’d) Diversifiable risk can be removed by proper portfolio diversification The ups and down of individual securities due to company-specific events will cancel each other out The only return variability that remains will be due to economic events affecting all stocks

Relationship Between Risk and Return
Direct relationship Concept of utility Diminishing marginal utility of money St. Petersburg paradox Fair bets The consumption decision Other considerations

Direct Relationship The more risk someone bears, the higher the expected return The appropriate discount rate depends on the risk level of the investment The risk-less rate of interest can be earned without bearing any risk

Direct Relationship (cont’d)
Expected return Rf Risk

Direct Relationship (cont’d)
The expected return is the weighted average of all possible returns The weights reflect the relative likelihood of each possible return The risk is undiversifiable risk A person is not rewarded for bearing risk that could have been diversified away

Concept of Utility Utility measures the satisfaction people get out of something Different individuals get different amounts of utility from the same source Casino gambling Pizza parties CDs Etc.

Diminishing Marginal Utility of Money
Rational people prefer more money to less Money provides utility Diminishing marginal utility of money The relationship between more money and added utility is not linear “I hate to lose more than I like to win”

Diminishing Marginal Utility of Money (cont’d)
$

St. Petersburg Paradox Assume the following game:
A coin is flipped until a head appears The payoff is based on the number of tails observed (n) before the first head The payoff is calculated as $2n What is the expected payoff?

St. Petersburg Paradox (cont’d)
Number of Tails Before First Head Probability Payoff x Payoff (1/2)1 = 1/2 $1 $0.50 1 (1/2)2 = 1/4 $2 2 (1/2)3 = 1/8 $4 3 (1/2)4 = 1/16 $8 4 (1/2)5 = 1/32 $16 n (1/2)n + 1 $2n Total 1.00 

St. Petersburg Paradox (cont’d)
In the limit, the expected payoff is infinite How much would you be willing to play the game? Most people would only pay a couple of dollars The marginal utility for each additional $0.50 declines

Fair Bets A fair bet is a lottery in which the expected payoff is equal to the cost of playing E.g., matching quarters E.g., matching serial numbers on $100 bills Most people will not take a fair bet unless the dollar amount involved is small Utility lost is greater than utility gained

The Consumption Decision
The consumption decision is the choice to save or to borrow If interest rates are high, we are inclined to save E.g., open a new savings account If interest rates are low, borrowing looks attractive E.g., a higher home mortgage

The Consumption Decision (cont’d)
The equilibrium interest rate causes savers to deposit a sufficient amount of money to satisfy the borrowing needs of the economy

Other Considerations Psychic return Price risk versus convenience risk

Psychic Return Psychic return comes from an individual disposition about something People get utility from more expensive things, even if the quality is not higher than cheaper alternatives E.g., Rolex watches, designer jeans

Price Risk Versus Convenience Risk
Price risk refers to the possibility of adverse changes in the value of an investment due to: A change in market conditions A change in the financial situation A change in public attitude E.g., rising interest rates and stock prices, a change in the price of gold and the value of the dollar

Price Risk Versus Convenience Risk (cont’d)
Convenience risk refers to a loss of managerial time rather than a loss of dollars E.g., a bond’s call provision Allows the issuer to call in the debt early, meaning the investor has to look for other investments

Chapter 3 A Review of Statistical Principles Useful in Finance

Statistical thinking will one day be as necessary for effective citizenship as the ability to read and write. - H.G. Wells

Outline Introduction The concept of return
Some statistical facts of life

Introduction Statistical principles are useful in:
The theory of finance Understanding how portfolios work Why diversifying portfolios is a good idea

The Concept of Return Measurable return Expected return
Return on investment

Measurable Return Definition Holding period return
Arithmetic mean return Geometric mean return Comparison of arithmetic and geometric mean returns

Definition A general definition of return is the benefit associated with an investment In most cases, return is measurable E.g., a $100 investment at 8%, compounded continuously is worth $ after one year The return is $8.33, or 8.33%

Holding Period Return The calculation of a holding period return is independent of the passage of time E.g., you buy a bond for $950, receive $80 in interest, and later sell the bond for $980 The return is ($80 + $30)/$950 = 11.58% The 11.58% could have been earned over one year or one week

Arithmetic Mean Return
The arithmetic mean return is the arithmetic average of several holding period returns measured over the same holding period:

Arithmetic Mean Return (cont’d)
Arithmetic means are a useful proxy for expected returns Arithmetic means are not especially useful for describing historical returns It is unclear what the number means once it is determined

Geometric Mean Return The geometric mean return is the nth root of the product of n values:

Arithmetic and Geometric Mean Returns
Example Assume the following sample of weekly stock returns: Week Return Return Relative 1 0.0084 1.0084 2 0.9955 3 0.0021 1.0021 4 0.0000 1.000

Arithmetic and Geometric Mean Returns (cont’d)
Example (cont’d) What is the arithmetic mean return? Solution:

Arithmetic and Geometric Mean Returns (cont’d)
Example (cont’d) What is the geometric mean return? Solution:

Comparison of Arithmetic & Geometric Mean Returns
The geometric mean reduces the likelihood of nonsense answers Assume a $100 investment falls by 50% in period 1 and rises by 50% in period 2 The investor has $75 at the end of period 2 Arithmetic mean = (-50% + 50%)/2 = 0% Geometric mean = (0.50 x 1.50)1/2 –1 = %

Comparison of Arithmetic & Geometric Mean Returns
The geometric mean must be used to determine the rate of return that equates a present value with a series of future values The greater the dispersion in a series of numbers, the wider the gap between the arithmetic and geometric mean

Expected Return Expected return refers to the future
In finance, what happened in the past is not as important as what happens in the future We can use past information to make estimates about the future

Return on Investment (ROI)
Definition Measuring total risk

Definition Return on investment (ROI) is a term that must be clearly defined Return on assets (ROA) Return on equity (ROE) ROE is a leveraged version of ROA

Measuring Total Risk Standard deviation and variance Semi-variance

Standard Deviation and Variance
Standard deviation and variance are the most common measures of total risk They measure the dispersion of a set of observations around the mean observation

Standard Deviation and Variance (cont’d)
General equation for variance: If all outcomes are equally likely:

Standard Deviation and Variance (cont’d)
Equation for standard deviation:

Semi-Variance Semi-variance considers the dispersion only on the adverse side Ignores all observations greater than the mean Calculates variance using only “bad” returns that are less than average Since risk means “chance of loss” positive dispersion can distort the variance or standard deviation statistic as a measure of risk

Some Statistical Facts of Life
Definitions Properties of random variables Linear regression R squared and standard errors

Definitions Constants Variables Populations Samples Sample statistics

Constants A constant is a value that does not change
E.g., the number of sides of a cube E.g., the sum of the interior angles of a triangle A constant can be represented by a numeral or by a symbol

Variables A variable has no fixed value
It is useful only when it is considered in the context of other possible values it might assume In finance, variables are called random variables Designated by a tilde E.g.,

Variables (cont’d) Discrete random variables are countable
E.g., the number of trout you catch Continuous random variables are measurable E.g., the length of a trout

Variables (cont’d) Quantitative variables are measured by real numbers
E.g., numerical measurement Qualitative variables are categorical E.g., hair color

Variables (cont’d) Independent variables are measured directly
E.g., the height of a box Dependent variables can only be measured once other independent variables are measured E.g., the volume of a box (requires length, width, and height)

Populations A population is the entire collection of a particular set of random variables The nature of a population is described by its distribution The median of a distribution is the point where half the observations lie on either side The mode is the value in a distribution that occurs most frequently

Populations (cont’d) A distribution can have skewness
There is more dispersion on one side of the distribution Positive skewness means the mean is greater than the median Stock returns are positively skewed Negative skewness means the mean is less than the median

Populations (cont’d) Positive Skewness Negative Skewness

Populations (cont’d) A binomial distribution contains only two random variables E.g., the toss of a die A finite population is one in which each possible outcome is known E.g., a card drawn from a deck of cards

Populations (cont’d) An infinite population is one where not all observations can be counted E.g., the microorganisms in a cubic mile of ocean water A univariate population has one variable of interest

Populations (cont’d) A bivariate population has two variables of interest E.g., weight and size A multivariate population has more than two variables of interest E.g., weight, size, and color

Samples A sample is any subset of a population
E.g., a sample of past monthly stock returns of a particular stock

Sample Statistics Sample statistics are characteristics of samples
A true population statistic is usually unobservable and must be estimated with a sample statistic Expensive Statistically unnecessary

Properties of Random Variables
Example Central tendency Dispersion Logarithms Expectations Correlation and covariance

Example Assume the following monthly stock returns for Stocks A and B:
Stock A Stock B 1 2% 3% 2 -1% 0% 3 4% 5% 4 1%

Central Tendency Central tendency is what a random variable looks like, on average The usual measure of central tendency is the population’s expected value (the mean) The average value of all elements of the population

Example (cont’d) The expected returns for Stocks A and B are:

Dispersion Investors are interest in the best and the worst in addition to the average A common measure of dispersion is the variance or standard deviation

Example (cont’d) The variance ad standard deviation for Stock A are:

Example (cont’d) The variance ad standard deviation for Stock B are:

Logarithms Logarithms reduce the impact of extreme values
E.g., takeover rumors may cause huge price swings A logreturn is the logarithm of a return Logarithms make other statistical tools more appropriate E.g., linear regression

Logarithms (cont’d) Using logreturns on stock return distributions:
Take the raw returns Convert the raw returns to return relatives Take the natural logarithm of the return relatives

Expectations The expected value of a constant is a constant:
The expected value of a constant times a random variable is the constant times the expected value of the random variable:

Expectations (cont’d)
The expected value of a combination of random variables is equal to the sum of the expected value of each element of the combination:

Correlations and Covariance
Correlation is the degree of association between two variables Covariance is the product moment of two random variables about their means Correlation and covariance are related and generally measure the same phenomenon

Correlations and Covariance (cont’d)

Example (cont’d) The covariance and correlation for Stocks A and B are:

Correlations and Covariance
Correlation ranges from –1.0 to +1.0. Two random variables that are perfectly positively correlated have a correlation coefficient of +1.0 Two random variables that are perfectly negatively correlated have a correlation coefficient of –1.0

Linear Regression Linear regression is a mathematical technique used to predict the value of one variable from a series of values of other variables E.g., predict the return of an individual stock using a stock market index Regression finds the equation of a line through the points that gives the best possible fit

Linear Regression (cont’d)
Example Assume the following sample of weekly stock and stock index returns: Week Stock Return Index Return 1 0.0084 0.0088 2 3 0.0021 0.0019 4 0.0000 0.0005

Linear Regression (cont’d)
Example (cont’d) Intercept = 0 Slope = 0.96 R squared = 0.99

R Squared and Standard Errors
Application R squared Standard Errors

Application R-squared and the standard error are used to assess the accuracy of calculated statistics

R Squared R squared is a measure of how good a fit we get with the regression line If every data point lies exactly on the line, R squared is 100% R squared is the square of the correlation coefficient between the security returns and the market returns It measures the portion of a security’s variability that is due to the market variability

Standard Errors The standard error is the standard deviation divided by the square root of the number of observations:

Standard Errors (cont’d)
The standard error enables us to determine the likelihood that the coefficient is statistically different from zero About 68% of the elements of the distribution lie within one standard error of the mean About 95% lie within 1.96 standard errors About 99% lie within 3.00 standard errors

Chapter 1 The Process of Portfolio Management

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