
Chapter 1: Investments: Background and Issues o 1.1: Real Assets vs Financial Assets
 real assets: assets used to produce goods and services
 financial assets: claims on real assets or the income generated by them
 financial assets simply define the allocation of income or wealth among investors o 1.2: Financial Assets
 three broad types of financial assets:
 debt o fixed income or debt securities promise either a fixed stream of income or a stream od income that is determined according to a specified formula o paid specified cash flow over a specific period o the investment performance of debt securities typically is leaast closely tied to the financial condition of the issuer
 equity o an ownership share in a corporation o not promised any particular payment

receive any dividends the firm may pay and have proated ownership in the real assets of the firm o equiy investments, therefore, is tied directly to the success of the firm and its real assets o tend to be riskier than investments in debt securities
 derivatives o such as options and futures contracts o provide payoffs that depend on the values of other assets o determined by the prices of OTHER assets such as bond or stock prices o hedge risks or transfer them to other parties

Investors also might invest directly in some real assets

Commodity and derivative markets allow firms to adjust their exposure to various business risks o 1.3: Financial Markets and the Economy
 real assets determine the wealth of an economy which financial assets merely represent claims on real assets
 financial assets allow us to makre the most of the economy’s real assets

The Informational Role of Financial Markets

Stock prices reflect investors collective assesment of a firms current performance and future prospects

Stock prices play a role in the allocation of capital in market economies, directing capital to the firms and applications with the greatest perceived potential

Consumption timing
1


You can shift your consumption over the course of your lifetime, thereby allocating your consumption to periods that provide the greatest satisfaction

Individuals can separate decisions concerning curent consumption from constraints that otherwise would be imposed by current earnings

Alloaction of Risk

Capital markets allow the risk that in inherent to all investments to be borne by the investors most willing to bear that risk

Also benefits the firms that do not need to raise capital to finance their investments

investors are able to select security types with the risk return characteristics that best suit their preferences

Seperation of Ownership and Management

Potential conflicts of interest are called agency problmes
 managers who are hired as agents of shareholders may pursue their own interests

Mechanisms have evolved to mitigate potential agency problems: 1. Compensation plans tie the income of the managers to the success of the firm. 2. Board of directors can force management out. 3. Outsider firms monitor the firm very closely

Corporate Governance and Corporate Ethics

In 2002, in response to the spate of ethics scandals, Congress passed the Sarbanes-Oxlry Act to tighten the rules of corporate governance o 1.4: The Investment Process

Investors make two types of decisions when constructing their portfolios

Asset allocation: allocation of an investment portfolio across broad asset classes

Security selection: choice of specific securities within each asset class

Security analysis invovles the valuation of particular securities that might be included in the portfolio
 “bottom up” strategy 
portfolio is constructed from the securities that seem attractively priced without as much concern for the resultant asset allocation o 1.5: Markets are Competitive

The Risk and Return Trade-off

Assets with higer expected returns entail greater risk

With higher risk assets priced to offer higher expected returns than lower risk assets

Diversification: many assets are held in the portfolio so that the exposure to any particular asset is limited

Efficient Markets
2


According to this hypothesis, as new information about a security becomes available, the price of the security quickly adjusts so that at any time, the security price equals the market consensus estimat of the value of the security

there would be neither underpriced nor overpriced securities

Passive management: buying and holding a diversified portfolio without attempting to identify mispriced securities

Active management: Attempting to identify mispriced securities or to forecast broad market trends o 1.6: The Players

1. Firms are net demanders of capital

2. Households typically are suppliers of capital

3. Governments can be borrowers or lenders, depending on the relationship between tax revenue and government expenditures

Corporations and governments do not sell all or even most of their securities directly to individuals
 Financial Intermediaries

Have evolved to bring together the suppliers of capital
(investors) with the demanders of capital (primarily corporations).

Banks, investment companies, insurance companies, and credit unions

issue their own securities to raise funds to purchase the securities of othercorporations

Financial intermediaries

both their assets and their liabilities are overwhelmingly financials

Primary social function of such intermediaries is to channel household savings to the business sector

Investment companies

firms managing funds for investors.
An investment company may manage several mutual funds

Hedge Funds: pool and invest the money of many clients but are open only to institutional investors such as pension funds, endowment funds, or wealthy individuals

they are more likely to pursue complex and higher risk strategies

Investment Bankers

Firm specializing in the sale of new securities to the public, typically by underwriting the issue

Can offer their services at a cost below that of maintaining an in-house security issuance division

Investment bankers advise in issuing corporation on the prices it can charge for the securities issued, appropriate interest rates, and so forth

Handles the marketing of the security in the primary market
 banks are called underwriters

Primary market: a market in which new issues of securities are offered to the public
3


Secondary market: previously issued securities are traded among investors

Venture Capital and Private Equity

Younger firms that have not yet issued securities to the public rely on venture capital

The equity investment in these young companies is called venture capital  money invested to finance a new firm

Set up as a limited partnership

Venture capital investors commonly take an active role in the management of a start-up firm

These investment in firms that do not trade on public stock exchanges are knowns as private equity investments
 Private equity: investments in companies that are not traded on a stock exchange o 1.7: The Financial Crisis of 2008

Anteccedents of the Crisis

Changes in Housing Finance

Fannie Mae and Freddie Mac  began buying large quantities of mortgage loans from originators and bundling them into pool that could be traded like any other financial asset

Mortgage backed securities

process was called securitization

Pass-through as that the investor in the private-label pool would bear the risk that homeowners might default on their loans.
Thus originating mortgage brokers had little incentive to perform due diligence on the loan as long as the loans could be sold to an investor

No documentation loans entailing little verification of a borrower’s ability to carry a loan soon emerged

Mortgage Derivatives

New risk shifting tools enabled investment banks to carve out
AAA rating securities from original issue junk loans

Collateralized debt obligations were among the most important and eventually damaging of these innovations

CDOs were designed to concentrate the credit (default) risk of a bundle of loans on one class of investors, leaving the other investors in the pool relatively protected from that risk

Credit Default Swaps

An insurance contract against the default of one or more borrowers

Purchaser of the sway pays an annual premium for the protection from credit risk

allowing investors to buy subprime loans and insure their safety

The Rise of Systematic Risk

Risk of breakdown in the financial system, particularly due to spill over effects from one market into others
4


Particularly devastating fallout of the Lehman Brothers bankruptcy was the money market for short term lending
 unsecured debt called commercial paper

The Shoe Drops

The Dodd-Frank Reform Act

Purpose is to mitigate systemic risk

Stricter rules for bank capital, liquidity, and risk management practices, mandates increases transparency o 1.8: Outline of Text

Chapter 2: Asset Classes and Financial Instruments o 2.1: The Money Market

Treasury Bills

Certificate of Deposit

Commercial Paper
 Bankers’ Acceptances

Eurodollars

Repos and Reverses
 Brokers’ Ca;;s

Federal Funds

The LIBOR Market

Yields onf Money Market Instruments o 2.2: The Bond Market

Treasury Notes and Bonds

Inflation-Protected Treasury Bonds
 Federal Agency Debt

International Bonds

Municipal Bonds
 Corporate Bonds

Mortgages and Mortgage-Backed Securities o 2.3: Equity Securities

Common Stock as Ownership Shares

Characterisitcs of Common Stock

Stock Market Listings

Preferred Stock

Depository Receipts o 2.4: Stock and Bond Market Indexes
 Stock Market Indexes

Dow Jones Averages

S&P Indexes
 Other U.S Market Value Indexes

Equally Weighted Indexes

Foreign and Internation Stock Market Indexes

Bond Market Indicators o 2.5: Derivative Markets

Options

Future Contracts
5


Chapter 3: Securities Markets o Investment bankers are generally hired to manage the sale of these securities in what is called the primary market for newly issued securities o Trades in existing securities take place in the secondary market o Primary marker: market for new issues of securities o Secondary market: market for already existing securities o 3.1: How Firms Issue Securities

Privately Held Firms

Private placement: Primary offering in which shares are sold directly to a small group of institutional or wealthy investors

Owned by a relatively small number of shareholder

Fewer obligations to release financial statement and other information to the public

Gives them more flexibility to pursue long term goals free of shareholder pressure

May only have up to 499 investors

Limits their ability to raise large amounts of capital

When private firms wish to raise funds, they sell shares directly to a small number of institutional or wealthy investors in a private placement

Publicly Traded Companies

Sell its securities to the general public and allow those investors to freely trade those shares in established securities markets

The first issue of shares to the general public is the firms initial public offereing, IPO

Seasonal equity offering: the sale of additional shares in firms that a;ready are publicly traded

Both stocks and bond typically are marketed by investment bankers who int his role are called underwriters

Underwriters: purchase securities from the issuing company and resell them to the public

Prospectus: a description of the firm and the security it is issuing that gets sent to the SEC

Issuing firm sells the secuurities to the underwriting syndicate for the public offereing price less a spread that serves as compensation to the underwriters

firm commitment

Investment banker also may receive shares of common stock

Shelf Registration

Rle 415 allows firms to register securities and gradually sell them to the public for two years following the initial registration

Initial Public Offerings

Road shows: generate interest among potential investors

Provide info to the issuing firm about pricing

Bookbuilding: process of polling potential investors

IPOs are commonly underpriced

IPO have been poor long term investments o 3.2: How Securities are Traded

Types of Markets

Direct sercha markets: least organized market

buyers and sellers must seek each other out directly o Craigslist

Brokered markets o
Next level of organization is brokered markets

where trading in a good is active, bokers find it profitable to offer such servicecs to buyers and sellers
6

o Real estate market o Brokers in particular markets decelop speacialized knowledge on valuing assets traded in that maket o Market is on the primary market

Dealer markets: markets in which traders specializing in particular assets buy and sell for their own accounts

Auction markets o A market where all traders meet at one place to buy or sell an asset o Most integrated in which all traders converge at one place to buy or sell an asset o
NYSE

Types of Orders

Market orders o Market orders are buy or sell orders that are to be executed immediately at current market prices o Bid price: the price at which a dealer or other trader is willing to purchase a security o Ask price: the price at which a dealer or other trader will sell a securitiy o Bid-ask spread: the difference between the bid and ask prices

Price contingent order o
Orders specifying prices at which they are willing to buy or sell a security o
Limit buy(sell) order: an order specifying a price at which an investor is willing to buy ir sell a security

Stop order: trade is not to be executed unless stock hits the price limit

Inside quotes: highest buy and lowest sell order

Trading Mechanisms

Dealer markets o An informal network of brokers and dealers who negotiate sales of securities o NASDAQ Stock market: the computer linked price quotations and trade execution system

Electronic communication networks o Computer networks that allow direct trading without the need for market makers o Orders can be corssed

matched up against one another automatically without a broker o Eliminates bid ask spread o Anonymity

Specialist makets o A trader who makes a market in the shares of one or more firms and who maintains a fair and oerderly market by dealing personally in the market o 3.3: The Rise of Electronic Trading
 when first established NASDAQ was primarily an over the counter dealer markets and the NYSE was a specalist market
 technology made it possible for traders to rapidly compare prices across markets and direect their trades to the markets with the best prices o 3.4: U.S Markets

NASDAQ

The New York Stock Exchange

Secondary markets where already issued securities are bought and sold by memebers

ECNs
7


Latency: the time it takes to acept process and deliver a trading order o 3.5: New Trading Strategies

Algorithmic Trading

DELIGATES TEADING DECISIONS TO COMPUTER PROGRAMS

The use of computer programs to make rapid trading decisions

High-Frequency Trading

A specialist class of algorithmic trading in which computer programs initiate orders in tiny fractions of a second, far faster than any human could process the information driving a trade

A subset of algorithmic trading that relies on computer programs to make very rapid trading decisions

Dark Pools

Trading venues that preserve anynymity but also affect market liquidity

Electronic trading netowrks where participants buy or sell large blocks of securities

Blocks: large transactions in which at least 10,000 shares are bought or sold

Bond Trading o 3.6: Globalization of Stock Markets
 securities markets have come under increasing pressure in recent years to make international alliances or mergers-

pressure is due to the impact of electronic trading o 3.7: Trading Costs
 ful service brokers who provide a variety of services ften are refferd to as account executuce or fincial consultants
 brokers routinely provide information and advice relating to investment alternatives
 discretionary account: prescribe securities whenever deemed fit
 discount brokers provide no frills services

they buy and sell securities, hold them for safekeeping, offer marign loans, facilitate short sales o 3.8: Buying on Margin
 margin: describes securities purchased with money borrowed in part from a broker.
The margin is the net worth of the investors account
 do this so they can invest in a greater amount than their money allows
 broker call loans o 3.9: Short Sales
 the sale of shares not owned by the investors but borrowed through a broker and later purchased to replace the loan
 share canbe purchased later at a lower price than it initially sold for

seller gets profit
 profit from a decline in securities price o 3.10 Regulation of Securities Markets

Self-regulation

The Sarbanes Oxley Act

Create public company accounting oversigt to oversee auditing

Experts must serve on sudit committees

CEO and CFO must personally certify to fairly represent reports

Auditors can not provide other services

Board must be composed of independent directors

Insider Trading

Nonpublic knowledge about a corporation possessed by corporate officers, major owners, or other individuals with privleged access to info about the firm

Chapter 4: Mutual Funds and Other Investment Opportunities
8

o 4.1: Investment Companies o 4.2: Types of Investment Companies

Unit Investment Trusts

Managed Investment Companies
 Other Investment Organizations o 4.3: Mutual Funds

Investment Policies

How Funds are Sold o 4.4: Costs of Investing in Mutual Funds

Fee Structure
 Fees and Mutal Fund Returns o 4.5: Taxation of Mutual Fund Income o 4.6: Exchange-Traded Funds o 4.7: Mutual Fund Investment Performance: A First Look o 4.8: Information on Mutual Funds

Chapter 5: Risk and Return: Past and Prologue o 5.1: Rates of Return

Success is the rate at which their funds have grown during the investment period

Total HPR of a share depends on the increase/decrease in the price over the investment period as well as on any dividend income the share has provided

Rate of return is defined as dollar earned over the investment period

HPR assumes that the dividend is paid at the end of the holding period  when dividends are received earlier, the definition ignores reinvestment income between the receipt of the dividend and the end of the holding period

Percentage return from dividends, cash dividends/beginning price, is called the dividend yield, and so the dividend yield plus the capital gains yields equal the HPR

Holding period return: rate of return over a given investment period

HPR= [ending price-Beginning Price + cash dividend] / beginning price

Measuring Investment Returns over Multiple Periods

Characterize fund performance over the year, given that the fund experienced both cash inflows and outflows by the arithmetic mean, geometric mean, and dollar weighted return o Arithmetic average

Arithmetic average of quarterly return is just the sum of the quarterly returns dividend by the number of quarters

ignores compounding o Geometric average

Equal to the single per-period return that would give the same cumulative performance as the sequence of actual returns
9


Geometric return is also called the time weighted average return because it ignores the quarter to quarter variation in funds under management

an investor will obtain a larger cumulative return when high returns are earned in periods when larger sums have been invested and low returns are earned when less money is at risk o Dollar weighted return

To account for varying amounts under management, we treat the fund cash flows as we would a capital budgeting problem in corporate finance and compute the portfolio manager’s internal rate of return

Liquidation value of a portfolio is the final cash flow of the project

Dollar weighted average return is the internal rate of return of the project, which is the interest rate that sets the present value of the cash flows realized on the portfolio equal to the initial cost of establishing the portfolio

Conventions for Annualizing Rates of Return

Returns on assets with regular cash flows, such as mortgages with monthly payments and bonds with semi-annual coupons, usually are quoted as annual percentage rates, or APRs, which annualize per-period rates using a simple interest approach, ignoring compound interest

APR does not equal the rate at which our invested funds grow

this is called the effective annual rate

The EAR diverges by greater amounts from the APR as n becomes larger o APR = per period rate x periods per year o 1 +EAR = (1+ (APR/n))^n o APR=[(1+EAR)^1/n – 1] x n

With continuous compounding, the relationship between EAR and APR becomes o 1 + EAR = e^APR o 5.2: Risk and Risk Premiums

Scenario analysis and probability distributions

Scenario analysis: process of devising a list of possible economic scenarios and specifying the likelihood of each one, as well as the HPR that will be realized in each case

Probability distribution: list of possible outcomes with associated probabilities

List of possible HPRs with associated probabilities

Expected return: the mean value of the distribution of HPR
10


The probability distribution lets us derive measurements for both the reward and the risk of the investment

Expected return also is called the mean of the distribution of
HPRs

E[r]= weighted average of the returns of all possible scenarios

Variance: the expected value of the squared deviation from the mean

Standard deviation: the square root of the variance

The normal distribution

Probabilities are highest for outcomes near the mean and are significantly lower for outcomes far from the mean

We can transform any normally distributed return, r, into a standard deviation score, by first subtracting the mean return and the dividing by the standard deviation o Sr = r – E[r] / stdev o R = E[r] + sr x stdev

Standardized return, (Sr), is normally distributed with a mean of zero and a standard deviation of 1

When returns are normally distributed: o 1. The return of a portfolio comprising two or more assets whose returns are normally distributed also will be normally distributed o 2. The normal distribution is completely described by its mean and standard deviation. No other statistic is needed to learn about the behaviour of normally distributed means o 3. The standard deviation is the appropriate measure of risk for a portfolio of assets with normally distributed returns. In this case, not other statistic can improve the risk assessment conveyed by the standard deviation of a portfolio

Value at risk (VaR): can be derived from the mean and standard deviation of the distribution

Measure of the downside risk

the worse loss that will be suffered with a given probability, often 5%

Normality over time

Stdev is the appropriate risk measure for normally distributed portfolios

When returns over very short time periods are normally distributed, the HPRs up to holding periods as long as a month will be nearly normal

If we expressed those HPRs as continuously compounded rates, they will remain normally distributed. The practical implication is this: use continuously compounded rates in all work where normality plays a crucial role, as in estimated VaR from actual returns
11


Deviation from normality and value at risk

Longer left tail= larger losses

Shorter right tail = smaller gains

When and why the VaR is an important statistic

when returns are normal, knowing just the mean and stdev allows us to fully describe the entire distribution

When returns are not normal, the VaR conveys important additional information beyond mean and stdev

shows the shape of the distribution, skewness or risk of extreme negative outcomes

Two additional statistics are used to indicate whether a portfolio’s probability distribution differs significantly from normality with respect to potential extreme values o Kurtosis: measure of the fatness of the tails of a probability distribution. Indicates likelihood of extreme outcomes o Kurtosis of a normal distribution is 0, so positive values indicate higher frequency of extreme values than this benchmark o Skew: measure of the asymmetry of a probability distribution

Using time series of return

Scenario analysis postulates a probability distribution of future returns

Come from observing a sample history of returns

When you use a fixed probability, you obtain the simple average of the observations, often used to estimate the mean return

Variance is the expected value of the squared deviations of the mean return

Risk premiums and risk aversion

Risk free asset: the rate of return that can be earned with certainty

Risk premium: an expected return in excess of that on risk free securities
 “reward” as the difference between the expected HPR on the index fund and the risk free rate

Risk aversion: reluctance to accept risk
 By contrasting the risk premium on the investor’s entire wealth,
E(r) – rf, against the variance of the portfolio return

Individual assets in the complete wealth portfolio are of no concern to the investor here

Measure risk aversion by the risk premium offered by the complete portfolio per unit of variance  this ratio measures the compensation that an investor have apparently required per unit of variance to be induced to hold this portfolio
12

o A = E(r) – rf / stdev^2

Price of risk: the ratio of portfolio risk premium to variance

The price of risk of the marker index portfolio, which reflects the risk aversion of the average investor, is sometimes called the market price of risk
 The Sharpe Ratio

Ratio of portfolio risk premium to standard deviation

Commonly used to rank portfolios in terms of this risk return trade off

The reward to volatility ratio of a risk portfolio quantifies the incremental reward (increase in risk premium) for each increase of 1% in the portfolio standard deviation

A higher sharpe ratio indicates a better reward per unit of volatility

more efficient

Portfolio analysis in terms of mean and standard deviation of excess returns is called mean variance analysis

Sharpe ratio is only valid for ranking portfolios, not individual assets o S = portfolio risk premium/ standard deviation of portfolio excess return o 5.3: The Historical Record

World and US Risky Stock and Bond Portfolios

The geometric average is always less than the arithmetic average

a normal distribution, the difference is exactly half the variance of the return

There is a greater discrepancy for small stocks, therefore, VaR will still ass important information about risk beyond standard deviation, at least for this asset class

Investors are concerned about their real (inflation adjusted) rates of return

Real geometric averages suggest that the real cost of equity capital for large corporation has been about 6%

Excess returns do not need to be adjusted for inflation because they are returns over and about the minimal risk free rate

Standard deviation divided by the square root of the number of observations

Testing for normality requires us to use continuously compounded rates

Measures are highly sensitive to rare but extreme outliers therefore, we can rely on these measures only in very large samples that allow for sufficient observations to be taken as exhibiting a representative number of such events o 5.4: Inflation of Real Rates of Return
 At any time, the prices of some goods may rise while the prices of other goods may fall, the general trend in prices is measured by examining changes in the consumer price index. The CPI measures the
13

cost of purchasing a representative bundle of goods, “the consumption basket”

Inflation rate: the rate at which prices are rising, measured as the rate of increase of the CPI
 Nominal interest rate: the interest rate in terms of nominal (not adjusted for purchasing power) dollars

Growth rate of money

Real interest rate: the excess of the interest rate over the inflation rate.
The growth rate of purchasing power derived from an investment

Growth rate of purchasing power

Real rate = (nom rate – inflation rate) / (1 + inflation rate)

The Equilibrium Normal Rate of Interest

Nominal rate ought to increase one for one with increases in the expected inflation rate o Nom rate = real rate + E(i)

US History of Interest Rates, Inflationm and Real Interest Rates o 5.5: Asset Allocation across Risky and Risk Free Portfolios
 Asset allocation: portfolio choice among broad investment classes

The most basic form of asset allocation envisions the portfolio as dichotomized into risky versus risk free assets

the fraction of the portfolio placed in risky assets is called the capital allocation to risky assets and speaks directly to investor risk aversion

Complete portfolio: the entire portfolio including risky and risk free assets

The Risk Free Asset

A default free, perfectly indexed bond offers a guaranteed real rate to an investor only if the maturity of the bond is identical to the investors desired holding period

A default free, perfectly indexed bond offers a guaranteed real rate to an investor only if the maturity of the bond is identical to the investors desired holding period

Money market mutual funds hold 3 types of securities: treasury bills, bank certificates of deposit (CDs), and commercial paper

Portfolio Expected Return and Risk

The risk premium of the complete portfolio will equal the risk premium of the risky asset time the fraction of the portfolio invested in the risky asset o E(rc) – rf = y[E(rp)-rf]

The stdev of the complete portfolio will equal the standard deviation of the risky asset times the fraction of the portfolio invested in the risky assets

Both the risk premium and the standard deviation of the complete portfolio increase in proportion to the investment in the risky portfolio
 The Capital Allocation Line
14


Depicts the risk return combinations available by varying capital allocation

The slope of the CAL equals the increase in expected return that an investor can obtain per unit of additional standard deviation or extra return per extra risk

You can construct complete portfolios to the right of point P by borrowing

borrow at the risk free rate

Risk Aversion and Capital Allocation

Individual investors with different levels of risk aversion, given an identical capital allocation line will choose different positions in the risky asset

Find the best allocation between the risky portfolio and risk free asset o [E(rp)-rf]/ A stdev^2 o 5.6: Passive Strategies and the Capital Market Line

Passive strategy: investment policy that avoids security analysis

Selected a diversified portfolio of common stocks that mirrors the corporate sector of the broad economy

Strategies are called indexing

the investor chooses a portfolio of all stocks in a broad market index such as the S&P 500
 We call the capital allocation line provided by one month t bills and the broad index of common stocks the capital market line

A passive strategy using the broad stock market index as the risky portfolio generates an investment opportunity set that is represented by the CML

Historical Evidence on the Capital Market Line

Costs and Benefits of Passive Investing

Factors that keep the active management industry going are 1.
The large potential of enrichment from successful investments- the same power of compounding working in your favour if you can add even a few basis points to total return 2. The difficulty in assessing performance and 3. Uninformed investors who are willing to pay for professional money management.

Chapter 6: Efficient Diversification o 6.1: Diversification and Portfolio Risk

Diversifying into many more securities continues to reduce exposure to firm specific factors

To the extent that virtually all securities are affected by common
(risky) macroeconomic factors, we cannot eliminate exposure to general economic risks

The reduction of risk to very low level because of independent risk sources is called the insurance principle
 Market/systematic/no diversifiable risk: risk factors common to the whole economy

Unique/firm-specific/non-systematic/diversifiable risk: risk that can be eliminated by diversification
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
International diversification may further reduce portfolio risk o 6.2: Asset Allocation with Two Risky Assets

Covariance and Correlation

A key determinant of portfolio risk is the extent to which the returns on the two assets vary either in tandem or in opposition.
Portfolio risk depends on the covariance between the returns of the assets in the portfolio

Bonds outperform stocks in both the mild and severe recession scenarios. In both normal growth and boom scenarios, stocks outperform bonds

The expected return on each fund equals the probability weighted average of the outcomes in the four scenarios

Then the portfolio return in each scenario is the weighted average of the returns on the two funds

Extreme events such as severe recession make for the large standard deviation of stocks

Portfolio risk is reduced most when the returns of the two assets most reliably offset each other

measure the tendency of the returns on two assets to vary either in tandem or in opposition to each other

covariance and the correlation coefficient

The sign of magnitude of this product are determined by whether deviations from the mean move together

The product of deviations is negative if one assets perform well of poorly in the same scenarios

The probability weighted average of the products is called the covariance and it measures the average tendency of the asset returns to vary in tandem, that it, to co vary

Correlation coefficient, which is the covariance divided by the product of the standard deviations of the returns on each fund

R-square is the square of the correlation coefficient and tells you the fraction of the variance of one return explained by the other return

See slides for equations

Using Historical Data

Alternative approach to scenario analysis is to use historical data to find covariance between the returns

Use realized returns to estimate variances and covariance’s

Means cannot be as precisely estimated from past returns

Divide the squared deviations by n-1 rather than by n. This is because we take deviations from an estimated average return rather than the true (but unknown) expected return; this is a procedure is said to be adjust for the “lost degree of freedom”
 The Three Rules of Two Risky Assets Portfolios
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
Properties of the portfolio are determined but the following 3 rules:

1. The rate of return on a portfolio is the weighted average of returns on the component securities, with the investment proportions as weights

2. The expected rate of return on a portfolio is the weighted average of the expected returned on the component securities, with the portfolio proportions as weights

3. The variance of the rate of return on a two risky asset portfolio is (see pg 156)

The variance of a portfolio is the sum of the combinations of the component security variances plus a term that involves the correlation coefficient between the returns on the component securities

The Risk Return Trade Off with Two Risky Asset Portfolios

Investment opportunity set: set of available portfolio risk-return combinations

The Mean-Variance Criterion

Dominate portfolio will be the case if it has higher mean return and lower variance or standard deviation

The portfolio standard deviation is a weighted average of the component security standard deviations only in the special case of perfect positive correlation

There are benefits to diversification whenever asset returns are less than perfectly positively correlated

See weight calculation *** o 6.3: The optimal Risky Portfolio with a Risk Free Asset

When we add the risk free asset to a stock plus bond risky portfolio, the resulting opportunity set is the straight line that was called the CAL

The slope of the CAL is the Sharpe ratio of the risky portfolio, that is, the ratio of excess return to standard deviation

Optimal risky portfolio: the best combination of risky assets to me mixed with safe assets to form the complete portfolio

resulting from the highest possible CAL

To find the composition of the optimal risky portfolio, we search for weights in the stock and bond funds that maximize the portfolios
Sharpe ratio

see book equation o 6.4: Efficient Diversification with Many Risky Assets

The Efficient Frontier of Risky Assets

Efficient frontier: graph representing a set of portfolios that maximizes expected return at each level of portfolio risk

Three ways to draw the efficient frontier are 1. Maximize the risk premium for any level of SD 2. Minimize the SD for any level of risk premium and 3. Maximize the Sharpe ratio for any level of SD (or risk premium)
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
One way to see whether the short sale constraint actually matters is to find the efficient portfolio without it. If one or more of the weights in the optimal portfolio turn out negative, we know the short sale restriction will result in a different efficient frontier with a less attractive risk-return trade off

Choosing the Optimal Risky Portfolio

The CAL formed from the optimal risky portfolio will be tangent to the efficient frontier of risky assets

Global maximum Sharpe ratio portfolio is the optimal portfolio

The Preferred Complete Portfolio and the Separation of Property

Separation property: the property that implies portfolio choice can be separated into two independent tasks: 1. Determination of the optimal risky portfolio, which is a technical problem and
2. The personal choice of the best mix of the risk portfolio and the risk free asset

Optimal risky portfolios for different clients may vary because of constraints on short sales dividend yield, tax considerations, or other client preferences


Constructing the Optimal Risky Portfolio: An Illustration o 6.5: A Single Index Stock Market

Index Models: model that relates stock returns on both a broad market index and firm specific factors

Designed to estimate these two components of risk for a particular security or portfolio

Excess return: rate of return in excess of the risk free rate

can express the distinction between macroeconomic factors and firm specific factors by decomposing this excess return in some holding period into three components (regression equation)
 Beta: the sensitivity of a security’s returns to the market factor

A beta greater than 1= cyclical stocks

A beta less than 1= defensive stocks
 Firm specific/ residual risk: component of return variance that is independent of the market factor

Alpha: a stocks expected return beyond that induced by the market index, its expected excess return when the markets excess return is zero

Positive alpha suggests an under-priced security
 The index model separates the realized rate of return on a security into macro and micro components. The excess rate on each security is the sum of the 3 components

The component of return due to movements in the overall market; beta is the security’s responsiveness to the market
(beta*Rm)

The component attributable to unexpected events that are relevant only to this security (e)
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 The stock’s expected excess return if the market factor is neutral, that is, if the market index excess return is 0 (alpha)

Variance of the excess return of the stock

alpha + beta*return +firm specific risk

The total variance of the rate of return of each security is a sum of two components

1. The variance attributable to the uncertainty of the entire market

2. The variance of the firm specific return, which is independent from market performance

Statistical and Graphical; Representation of the Single-Index Model

Regression equation of Ri on the market excess return Rm
 the excess return on the security is the dependent variable that is to be explained by the regression
 Security characteristic line: plot of a security’s predicted excess returns from the excess return on the market

The slope=beta

Beta measures the systematic risk since it predicts the response of the security to each extra 1% return on the market index

Actual return also include a residual e

The greater the beta of a security, that is the greater the slope of the regression, the greater the systematic risk and total variance

A negative beta security provides a hedge against systematic risk

Dispersion of the scatter of actual returns about the regression line is determined by the residual variance

Measure the ratio of systematic variance to total variance

A large correlation coefficient means systematic variance dominates the total variance that is, firm specific variance is relatively unimportant

Diversification in a Single Index Security Market

What are the systematic and non-systematic variances of this portfolio o Non-systematic: w*e o Systematic: w^2 * stdev^2

Using Security Analysis with the Index Model

Information ratio: ratio of alpha to the standard deviation of the residual

Active portfolio: the portfolio formed by optimally combining analysed stocks
 Residual variance is the weighted sum of each stock’s residual variance, using the squared portfolio weights o 6.6: Risk of Long-Term Investments

Risk and Retun with Alternative Long-Tem investments
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
A common misconception is that long term investors should allocate a greater proportion of wealth into stock because in some sense stocks are less risky over long term horizons

Both the mean and the variance of continuously compounded, serially uncorrelated returns (excess returns) grow in proportion to the length of the holding period

Risk grows proportionally over time

Why the Unending Confusion?

Time diversification seems to offer a better risk-return trade off if you compare the All-In to the “one in” strategy that invests all in one year and nothing later
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