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The investment Environment ..................................................................................... 2
Asset Classes and Financial Instruments .................................................................... 5
How securities are traded ......................................................................................... 10
Mutual Funds and other investment companies ..................................................... 12
Learing About Return and Risk from the Historical Record...................................... 15
Risk and risk aversion ................................................................................................ 18
Optimal Risky Portfolios............................................................................................ 19
The Capital Asset Pricing Model ............................................................................... 22
Arbitrage Pricing Theory and multifactor models of risk and return ................... 25
Behavioral Finance and Technical Analysis........................................................... 28
Empirical evidence on security returns ................................................................ 30
Bond Prices and Yields .......................................................................................... 31
The Term Structure of Interest Rates ................................................................... 35
Managing Bond Portfolios .................................................................................... 37
Portfolio Performance Evaluation ........................................................................ 40
Portfolio performance evaluation ........................................................................ 43
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1
The investment Environment
1.1Investments and financial assets
Essential nature of an investment is to:
1: Reduce current consumption
2: Planned for later consumption
Real assets are assets to produce goods and services Generate net income to the economy
Financial assets are claims on real assets (such as stock and bonds)
Allocate income or wealth among investors.
Assets
Real Assets
Liabilities
Financial Assets
Examples:
- Patents:
- Lease obligations:
- Customers goodwill:
- A college education:
- A $10 bill:
Real
Financial
Real
Real
Financial
Financial assets
We distinguish among a broad type of financial assets common types are:
1: Fixed income
2: Equity
3: Derivatives
Fixed income promise either a fixed stream of income or a stream of income that is determined
according to a specified formula. Fixed income securities come in a tremendous variety of
maturities and payment provisions.
At one extreme the money market this refers to fixed income securities that are short, highly
marketable, low risk.
In contrast is the capital market includes long term securities (treasury bonds), bonds issued
federal agencies, state and local municipalities.
Equity or common stock this represent the ownership share in the corporation. Investments in
equity tend to be riskier than fixed income, because success depends on the success of the firm
Derivative securities. Such as options and futures contracts provide payoffs that are determined
by the prices of other assets such as bonds or stock prices (future swap contracts)
Financial markets
Informational role: investors in the stock market ultimately decide which companies will live
and die. Stock prices will reflect their collective judgment.
Consumption timing: financial markets allow individual to separate decisions concerning current
consumption from constraints that otherwise would be imposed by current earnings. Shift
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consumption by saving earnings in high earnings period to low low earnings period -> work life
to retirement.
Allocation of risk: capital markets allow the risk that is inherent to all investments to be borne
by the investors most willing to bear risk. E.G. Investment in Ford plant: low risk (bond) high risk
(shares), but both have a different reward system.
Separation ownership and management: this structure means that the owners and managers
of the firm are different parties. Agency problem (managers who are hires as agents of the
shareholders, may pursue their own interest.)
Mechanism to solve agency problem are:
1. Compensation plan tie the income of managers to the success of the firm.
2. The board of directors are not defenders of top management they can force out management
teams that are under performing.
3 Outsiders (pension funds, security analysts) monitor the firm closely and make the life of poor
performers at the least uncomfortable.
4. Bad performers are subject to the threat of a takeover. Shareholders can elect a different
board by (proxy contest)
Crisis in corporate governance
For markets to be efficient there must be enough transparency that allows investors to make
well-informed decisions.
Accounting scandals example Enron and WorldCom
Analyst scandals (overoptimistic research rapports) example City group Salamon Smith Barney
Initial public offering credit Swiss first Boston
The investments process
Asset allocation choosing among broad asset classes such as stocks and bonds
Security selection decision is to choice of which particular securities to hold within asset classes
Top down portfolio construction technique starts with the asset allocation decision-the
allocation of funds across broad asset classes-and the progress to more specific security
selection decision.
Security analysis involves the valuation of particular securities that might be included in the
portfolio
 Top down portfolio management
In contrast is the bottom-up strategy: this strategy does focus the portfolio on the assets that
seem to offer the most attractive investment opportunities.
Financial markets are highly competitive.
There are implications of the ‘free lunches’ (securities that are underpriced that they represent
obvious bargain.) This no-free lunch proposition has several implications:
Competition leads to a Risk return trade off, in which securities that offer higher expected
return also impose greater risk on investors. The presence of risk, however, implies that actual
returns can differ considerably from expected returns at the beginning of the investment period.
Completion among security analyst also promotes financial markets that are nearly
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informational efficient (Market efficiency) meaning that prices reflect all available information
concerning the value of the security. In the efficient market there is a choice between passive
and active management:
Active management
Finding undervalued securities
Timing the market
Passive management
No attempt to finding undervalued securities
No attempt to time
Holding diversified portfolio
Passive investments strategies make sense in nearly efficient markets.
Players in financial markets
Firms
net borrowers
Households
net savers
Government
net savers and borrowers
Financial intermediaries
Financial intermediaries pool investor funds and invest them. Their services are in demand
because small investors cannot efficiently gather information, diversity and monitor portfolios.
The financial intermediary sells his own securities to the small investors. The intermediary invest
the funds thus raised, uses the proceeds to pay back the small investors and profits from the
difference (spread)
Recent trends
Recent trends in financial markets include globalization, securitization, financial engineering of
assets, and growth of information and computer networks.
Globalization Tendency toward a worldwide investment environment, and the integration of
national capital markets
Securitization Pooling loans for various purposes into standardized securities backed by those
loans, which can then be traded like any other security
Financial engineering creating and designing securities with custom-tailored characteristics
The financial crisis showed the importance of systematic risk. The risk inherent to the entire
market or market segment. Also known as "un-diversifiable risk" or "market risk.
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Asset Classes and Financial Instruments
1) Fixed income market:
 Money market: a subsector of the fixed-income market. It consists of very shortterm debt securities that usually are highly marketable. Many of these securities
trade in large denominations, and so are out of the reach of individual investors.
Money market funds, however are easily accessible to small investors.
o Treasury Bills (T-bills, or just bills)  most marketable of all money
market instruments. Simplest form of borrowing: The government
raises money by selling bills to the public. At maturity the holder gets
the face value. T-bills have initial maturities of 28, 91 or 182 days. T-bills
are very liquid and sold at low transaction cost and with not much price
risk. The asked price is the price you would have to pay to buy a T-bill.
The bid price is the slightly lower price you would receive if you wanted
to sell a bill to a dealer. The bid-asked spread is the difference between
these prices.
o Certificates of Deposit (CD)  A time deposit with a bank. Time
deposits may not be withdrawn on demand. The bank pays interest and
principal to the depositor only at the end of the fixed term of the CD.
CEs issued in denominations greater than 100.000.
o Commercial Paper  Large, well-known companies often issue their
own short-term unsecured debt notes rather than borrow directly from
banks. These notes are called commercial papers. Commercial paper
maturities range up to 270 days. Usually it is issued in multiples of
100.000.
o Bankers’ Acceptances  starts as an order to a bank’s customer to pay
a sum of money at a future date, typically within 6 months. When the
bank endorses the order for payment as “accepted”, it assumes
responsibility for ultimate payment to the holder of the acceptance. At
this pint, the acceptance may be traded in secondary markets like any
other claim on the bank. Very safe assets.
o Eurodollars  are dollar-denominated deposits at foreign banks or
foreign branches of American banks. By locating outside the United
states, these banks escape regulation by the Federal Reserve.
o Repos and Reverses “repos” or “RPs”  The dealer sells government
securities to an investor on an overnight basis, with an agreement to
buy back those securities the next day at a slightly higher price. Term
repo  the same but loan can be 30 days or more. Reverse repo: is the
mirror image of a repo. Dealer finds an investor holding government
securities and buys them, agreeing to sell them back at a specified
higher price on a future date.
o Federal Funds.  banks maintain deposits of their own at a federal
reserve bank. Each member bank of the federal reserve system (Fed) is
required to maintain a minimum balance in a reserve account with the
Fed. Funds in the bank’s reserve account are called federal funds, or fed
funds. In the federal funds market, banks with excess funds lend to
those with a shortage. These loans, which are usually overnight
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
transactions, are arranged at a rate of interest called the federal funds
rate.
o Brokers’ Calls  Individuals who buy stocks on margin borrow part of
the funds to pay for the stocks from their broker. The broker in turn
may borrow the funds from a bank, agreeing to repay the bank
immediately (on call) if the bank requests it. The rate paid on such loans
is usually about 1% higher than the rate on short-term T-bills.
o The LIBOR Market. The London interbank Offered Rate (LIBOR) is the
rate at which large banks in London are willing to lend money among
themselves. EURIBOR (European Interbank Offered Rate) at which banks
in the euro zone are willing to lend euros among themselves.
o Yields on Money market instruments: Although most money market
securities are of low risk, they are not risk-free.
The bond market  is composed of longer-term borrowing or debt instruments
than those trade in the money market. This market includes:
o Treasury Notes and Bonds  The U.S. government borrows funds in
large part by selling Treasury notes and treasury bonds. T-note
maturities range up to 10 years, whereas bonds are issued with
maturities ranging from 10 to 30 years. Both make semiannual interest
payments called coupon payments. Although notes and bonds are sold
in denominations of 1000 par value, the prices are quoted as a
percentage of par value (a bid price of 98.5313 should be interpreted as
98.5313 % of par, or 985313 for the 1000 par value security.
o Inflation-Protected Treasury Bonds  Least risky. Government bonds
that are linked to an index of the cost of living in order to provide their
citizens with an effective way to hedge inflation risk. Inflation-protected
treasury bonds are called TIPS (Treasury Inflation Protected Securities).
The real interest rates you earn on these securities are risk-free if you
hold them to maturity.
o Federal Agency Dept  Some government agencies issue their own
securities to finance their activities. These agencies usually are formed
to channel credit to a particular sector of the economy that congress
believes might not receive adequate credit through normal private
sources. These securities are considered extremely safe assets, and their
yield spread above treasury securities is usually small.
o International bonds Many firms borrow abroad and many investors
buy bonds from foreign issuers. In addition to national capital markets,
there is a thriving international capital market, largely centered in
London. In contrast to bonds that are issued in foreign currencies, many
firms issue bonds in foreign counties but in the currency of the investor.
o Municipal Bonds  Are issued by state and local governments. They
are similar to Treasury and corporate bonds except that their interest
income is exempt from federal income taxation. Like treasury bond,
municipal bonds vary widely in maturity. Maturities range up to 30
years. The key feature of municipal bonds is their tax-exempt status.
Because investors pay neither federal nor state taxes on the interest
proceeds, they are willing to accept lower yields on these securities.
r(1-T)= after tax rate available.
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Corporate Bonds Corporate bonds are the means by which private
firms borrow money directly from the public. These bonds are similar in
structure to Treasury issues (they typically pay semi-annual coupons
over their lives and return the face value to the bondholder at maturity.
They differ most importantly from treasury bonds in the degree of risk.
 Secured bonds: which have specific collateral backing them in
the event of firm bankruptcy
 Debentures: unsecured bonds, which have no collateral
 Subordinated debentures, have a lower-priority claim to the
firm’s assets in the event of bankruptcy.
Corporate bonds sometimes come with options attached.
 Callable bonds give the firm the option to repurchase the bond
from the holder at a stipulated call price.
 Convertible bonds give the bondholder the option to convert
each bond into a stipulated number of shares of stock.
o Mortgages and Mortgage-backed securities  Until the 1970s almost
all home mortgages were written for a long term (15-30 year) with a fixed
interest rate over the life of the loan, with equal fixed monthly payments.
These so-called conventional mortgages are still the most popular, but a
diverse set of alternative mortgage designs has developed. Fixed-rate
mortgages have posed difficulties to lenders in years of increasing interest
rates. Adjustable rate mortgage: was a response to this interest rate risk.
Mortgage-backed security: is either an ownership claim in a pool of
mortgages or an obligation that is secured by such a pool. Mortgage lenders
originate loans and then sell packages of these loans in the secondary
market. For this reason, these mortgage-backed securities are called passtroughs.
o
2) Equity securities
 Common stock as ownership shares  also known as equity securities or equities,
represent ownership shares in a corporation. Each share of common stock entitles
its owner to one vote on any matter of corporate governance that are put to vote
at a annual meeting and to a share in the financial benefits of ownership. A board
of directors elected by the shareholders controls the corporation. The board
selects managers who run the corporation on a day-to-day basis. Managers have
the authority to make most business decisions without the board’s specific
approval. Vote by proxy = empowering another party to vote in their name. The
common stock of most large corporations can be bought or sold freely on one or
more stock exchanges. A corporation whose stock is not publicly traded is said to
be closely held. In most closely held corporations, the owners of the firm also take
an active role in its management. Therefore, takeovers are generally not an issue.
o Characteristics of Common stock:
 1) Residual Claim  stockholders are the last in line of all
those who have a claim on the assets and income of the
corporation.
 2) Limited liability  Unlike owners of unincorporated
businesses, whose creditors can lay claim to the personal
assets of the owner (house, car, furniture), corporate
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shareholders may at worst have worthless stock. They are
not personally liable for the firm’s obligations.
Stock market Listings: The NYSE is one of several markets in which investors
may buy or sell shares of stock. The dividend yield in only part of the retrun
on a stock investment. It ignores prospective capital gains (i.e., price
increases) or losses. Low dividend firms presumably offer greater prospects
for capital gains. The P/E ratio, or price-earnings ratio is the ratio of the
current stock price to last year’s earnings per share.
Preferred stock: has features similar to both equity and debt. Like a bond it
promises to pay to its holder a fixed amount of income each year. Instead
preferred dividends are usually cumulative; that is, unpaid dividends
cumulate and must be paid in full before any dividends may be paid to
holders of common stock. Preferred stock also differs from bonds in terms
of its tax treatment for the firm. Because preferred stock payments are
treated as dividends rather than interest, they are not tax deductible
expenses for the firm, this disadvantage is somewhat offset by the fact that
corporations may exclude 70% of dividends received from domestic
corporations in the computation of their taxable income. Individual investors
can not use the 70% tax exclusion. Even though preferred stock ranks after
bonds in terms of the priority of its claims to the assets of the firm in the
event of corporate bankruptcy, preferred stock often sells at lower yields
than do corporate bonds. Preferred stock may be callable by the issuing
firm, than they are called redeemable. It also may be convertible into
common stock at some specified conversion ratio.
Depository receipts  American Depository Receipts, or ADRs are
certificates traded in U.S. markets that represent ownership in shares of a
foreign company.
Stock and bond market indexes.
 Dow Jones Averages  30 large “blue-chip” corporations. Since 1896. Dow measures
the return (excluding dividentds) on a portfolio that holds one share of each stock, it is
called a price-weighted average (example page 41).
 Standard & Poor’s Indexes (S&P 500) represent an improvement over the Dow Jones
Average in two ways. (1) it is a more broadly based index of 500firms. (2) it is a market
value-weighted index. (example blz 45). Actually, most indexes these days use a
modified version of market-value weights. Rather than weighting by total market value,
they weight by the market value of free float, that is by the value of shares that are
freely tradable among investors. For example, this procedure does not count shares
held by founding families or governments. The distinction is more important in Japan
and Europe, where a higher fraction of shares are held in such nontraded portfolios.
 Investors today can easily buy market indexes for their portfolios. One way is to
purchase shares in mutual funds that hold shares in proportion to their representation
in the S&P or another index. These index funds yield a return equal to that index and so
provide a low-cost passive investment strategy for equity investors.
 Other U.S. market-value indexes 
o New York Stock Exchange (market-value weighted, all NYSE-listed stocks)
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National Association of Securities Dealers (more than 3000 over the counter
(OTC) firms traded on the Nasdaq market.
o Wilshire 5000 (ultimate U.S. equity index, market value of all NYSE and Amex
(American Stock Exchange) plus actively traded Nasdaq stocks. Over 6000
stocks.
Foreign and international stock market indexes:
o Nikki (japan)
o FTSE (UK)
o DAX (Germany)
o Hang Seng (Hong Kong)
o TSX (Canada)
A leader in constructing international indexes has been MSCI (Morgan Stanley
Capital International) which compute over 50 country indexes and several regional
indexes.
Bond Market Indicators: Merril Lynch, Lehman Brothers and Salomon Smith Barney are
the three well known bond indexes. The major problem with bond market indexes is
that true rates of return on many bonds are difficult to compute because the
infrequency with which the bonds trade make reliable up-to-date prices difficult to
obtain. The prices may differ from true market values.
o
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3) Derivative Markets
One of the most significant developments in financial markets in recent years has been the
growth of futures, options, and related derivatives. These instruments provide payoffs that
depend on the values of other assets such as commodity prices, bond and stock prices, or
market index values. For this reason these instruments sometimes are called derivative assets or
contingent claims.
 Options
o Call option  gives its holder the right to purchase an asset for a specified
price, called the exercise or strike price, on or before a specified expiration date.
Each option contract is for the purchase of 100 shares. However, quotations are
made on a per-share basis. The holder of the call need not exercise the option.
It will be profitable to exercise only if the market value of the asset that may be
purchased exceeds the exercise price.
o Put Option  Gives its holder the right to sell an asset for a specified exercise
price on or before a specified expiration date. Only exercised if its holder can
deliver an asset worth less than the exercise price in return for the exercise
price.
o Future contracts  is an obligation to buy or sell an asset at a stipulated futures
price on a maturity date. The long position, which commits to purchasing, gains
if the asset value increases while the short position, which mommits to
purchasing, loses.
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How securities are traded
Primary market: new issues marketed to public by investment bankers.
Secondary market: trading among private investors.
Two primary issues:
IPO – stocks issued by a formerly privately owned company selling stock to the public
for the first time.
Seasoned new issues – issues offered by companies that already have floated equity.
Public offering: to general investing public vs. Private placement: to few wealthy or institutional
investors (reduce liquidity).
Investment banker: underwriter, makes prospectus. Firms commitment: issuing firm sells
securities to underwriting syndicate for the public offering price less a spread, underwriter
assumes full risk vs. best-efforts agreement: bank agrees to help, but does not actually buy the
securities.
Shelf-registration: register securities and gradually sell them to the public for 2 years.
IPO: investors indicate their interest via a book, book building. Shares of IPOs are allocated to
investors in part based on the strength of each investor’s expressed interest in the offering. IPOs
are commonly underpriced (represent a cost of the issue). IPOs have been poor long-term
investments. Non-issuers show better relative performance.
Shares are trade on
1. National and local securities exchanges
NYSE, Amex: memberships (seats, majority owned by large full-service brokerage firms).
2. the over-the-counter market
No membership requirements, no listing requirements for securities, NASDAQ
Security dealers quote prices at which they are willing to buy/sell securities.
Bid price: price dealer willing to buy. Ask: price dealer willing to sell.
NASDAQ has 3 levels of subscribers: level 1: for firms dealing, may enter bid/ask prices. Level 2:
receive all bid/ask prices but cannot enter their own. Level 3: receive only median bid/ask
prices.
3. direct trading between two parties
Third market: refers to trading of exchange-listed securities on the OTC market.
The fourth market refers to direct trading between invesotrs in exchange-listed securities
without benefit of a broke (eliminates bid/ask spread, greater speed and anonymity).
Bond trading, NYSE Automated Bond System; majority trading in over-the counter market
among bond dealers.
Participants in trading on exchanges (read also pg 80):
Commission brokers: seat brokerage firm vs. floor brokers: independent members of the
exchange who handle their own seats and handle work for commission brokers.
Specialist: central to trading process, maintains a market in one or more listed securities.
Types of orders:
Market orders: immediately buy/sell at current market price.
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Limit buy order: execute when price falls below limit.
Limit sell order: sell as soon as price goes above limit.
Stop-loss order: sell of price falls below stipulated level.
Stop-buy order: buy when price rises above given limit. (These trades often accompany short
sales).
- Block houses: brokerage firms that help find potential buyers/sellers of large block trades.
- Since June ’95, an order executed on exchange must be settled within 3 working days.
Disadvantage of decentralized dealer market: investing public is vulnerable to trading through,
which refers to the practice of dealers to trade with the public at their quoted bid/ask prices
even if other customer have offered to trade at better prices.
Trading costs:
Full-service brokers - provide info and advice vs. discount brokers – no frills.
- minimum charge regardless of trade
- brokers commission
- Implicit cost: bid-ask spread
- Implicit cost: price concession investor may be forced to make for trading in quantity
that exceeds quantity dealer is willing to trade at posted bid/ask price.
Controversy: extent better execution (size effective bid-ask spread and amount impact in
market) on the NYSE offsets the generally lower explicit costs in other markets.
Paying for order flow: paying a broker for direct trade to particular dealer.
Buying on margin: act of taking on brokers’ call loans. Margin in account: portion of the
purchase price contributed by investor, remainder is borrowed from broker. The securities are
the collateral.
Percentage margin: ratio of the net worth (equity) to the market value of the securities.
Margin: equity in stock / value of stock.
Maintenance margin: P*nr shares – amount borrowed / P* nr shares (page 91)
Short sale: allows investors to profit from decline in security’s price. Short sales are only
permitted when last recorded change in stock price is positive. (margin calls on short sales – pg.
93)
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Mutual Funds and other investment companies
Benefits Investment companies
- record keeping
- diversification / divisibility (invest in many different securities  investment company
acts like one big investor)
- professional management (skills)
- lower transaction costs (large numbers)
Net Asset Value (NAV) = (market value of assets – liabilities) / # shares outstanding
2 types of Investment companies
(1) Unit investment trusts
- redeemable trust certificates
- pools of money invested in a portfolio (fixed for the life of a fund)
- unmanaged (= lower fees)
(2) Managed investment companies
(2a) Closed-end
When investor cashes out he/she sells
shares to other investors on organized
exchanges, through brokers, so price can
differ from NAV.
(a load is a sales charge paid to seller)
Other investment organizations
(2b) Open-end (Mutual funds)
When investor cashes out he/she sells
shares back to fund at NAV
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-
Commingled funds
o Partnerships of investors that pool funds
o One management firm organizes partnerships for a fee
-
Real estate investment trusts (REITs)
o (1) equity trust; invests in real estate directly
o (2) mortgage trusts; invest in primarily mortage & construction loans
-
Hedge funds (features;)
o Private partnerships (only 1 SEC regulation)
o Lock-ups (periods that investments cannot be withdrawn
o Highly volatile
Mutual Funds (2b)
- investment policies (described in prospectus)
o money market funds
o equity funds
o bond funds
o international funds
o balanced funds
o asset allocation & flexible funds (stock & bonds  no particular risk, invest in
positive forecasts)
o index funds
Fees (cost of investments in mutual funds)
1. Front-end load (charge paid when buying shares  usually to broker; ≤ 8,5%)
2. Back-end load (charge paid when selling shares  also called contingent deffered sales
charges
3. Operating expenses (charge for operating portfolio)
4. 12 b-1 charges (funds charges these to pay brokers)
o Concerning 3 & 4  fees are deducted from assets, not billed
o Loads (1 & 2) are paid once, 12b-1 charges (4) are paid annually
o Fees (1 – 4) are commonly paid for advise
Rate of Return = (NAV1 – NAV0 + income & capital gain distribution) / NAV0
= Gross return (underlying portfolio in %) – total expense ratio (%)
-
ignores commission
is affected by fund’s expenses and 12 b-1 fees.
Soft dollars
- Stockbroker returns part of the trading commission to the fund; which is an advantage
to the mutual fund because;
- These purchases with soft dollars are not included in the fund expenses; therefore make
it hard for investors to compare fund expenses
Late trading
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Buy shares after closure of market (4.00 p.m.) at NAV if at 4.30 p.m. some positive news is
announced; next morning NAV will rises.
- ROR to most shareholders drops
- Late traders pay management fee to brokers and therefore they (the managers) allow it.
Market timing
U.S. & Japanese market close at different times. If U.S. market mumps significantly, the
Japanese will too the next morning
Changes to overcome these practices;
- 4.00 pm hard cutoff (no trading after 4.00)
- Fair value pricing (big changes in U.S. are adjusted in Japanese NAV)
- Edemption fees (rapid trading = buy & sell within 1 week cost > 2% fee)
Invest through a mutual fund  timing of sale is not in your hands, therefore no tax
management possible; if high turnover (ratio of trading activity / assets of portfolio)  capital
gains or losses are realized constantly and timing of tax obligation will be hard  tax inefficient.
Exchange – traded funds (ETFs)
Offshoots of mutual funds that allow investors to trade index-portfolios as shares of stock.
Advantages:
1. mutual funds can only be bought at end of the day (when NAV is calculated), ETFs the
entire day
2. can be sold short & on margins
3. tax advantage over mutual funds (sell shares to other traders p.110)
4. cheaper than mutual funds (buy from broker, not funds themselves, so funds don’t have
marketing fees  which are normally expensed as commissions)
Disadvantages:
1. prices can depart from NAV (more expensive)
2. ETFs must be purchased for a fee
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5
Learing About Return and Risk from the Historical Record
Determinants of the level of interest rates
Main factors that determine interest rates:
1. The supply of funds from savers, primarily households.
2. The demand for funds from businesses to be used to finance investments in plant,
equipment, and inventories (real assets or capital formation)
3. The government’s net supply of or demand for funds as modified by actions of the
Federal Reserve Bank.
Nominal interest rate (R), is the growth rate of the money and a real interest rate (r) is the
growth of the purchasing power; r ≈ R – i (i is inflation)
The exact relationship is given by 1+r = (1+R)/(1+i)  r = (R-1)/(1+i)
Three basic factors – supply, demand, and government actions – determine the real interest
rate. The nominal rate, which is the rate we actually observe, is the real rate plus the expected
rate of inflation.
With a higher expected inflation, the nominal rate ought to increase to maintain the same real
return. This is the so called Fisher equation: R = r + E(i)
Tax liabilities are based on nominal income and the tax rate determined by the investors’ tax
bracket. Given tax rate (t) and a nominal interest rate (R), the after tax rate is R(1-t). The real
after tax rate is: R(1-t) – i = (r+i)(1-t) – i = r(1-t) – it
Thus the after-tax real rate of return falls as the inflation rate rises.
Comparing rates of return for different holding periods
Zero-coupon bonds are bonds that are sold at a discount from par value and provide their entire
return from the difference between the purchase price and the ultimate repayment of par
value. Given the price, P(T), of a treasury bond with $100 par value and maturity of T years, we
calculate the total risk-free return as the percentage increase in the value of the investment
over the life of the bond: rf(T) = (100/P(T)) – 1
To compare returns on investments with different time horizons, we re-express each total
return as a rate of return for a common period. Typically this is expressed as an effective annual
rate (EAR), defined as the percentage increased in funds over a 1-year horizon.
For half-year investment: 1+EAR = (rf(0,5))2, and for a 25 year inv: (1+EAR)25 = rf(25)
 1+EAR = [1+rf(T)]1/T
For rates on short term investments use the annual percentage rate (ARP)
 APR = [(1+EAR)T-1]/T
To find rcc (continuously compounding rate) the EAR: ln(1+EAR) = rcc (simply put:exp(T*rcc)
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Risk and Risk Premiums
Holding period return (HPR) = (Ending price of a share – Beginning price +Cash dividend)/
Beginning price
The percent return from dividends is called the dividend yield, and so the dividend yield plus the
capital gains is the HPR.
Expected return is the sum of the probability of a scenario p(s) times the HPR r(s):
E(r) = ∑p(s)r(s) and σ2 = ∑p(s)[r(s)-E(r)]2
s
s
The expected reward is measured as the difference between the expected HPR and the risk-free
rate, the rate you can earn by leaving money in risk-free assets such as T-bills or the bank. This
difference is called the risk premium. The difference between the actual return and the risk-free
rate is called the excess return. The risk premium is the expected excess return and the
standard deviation of the excess return is an appropriate measure of its risk.
Time Series Analysis
When historical data is used, each observation is treated as an equally likely “scenario”. So with
n observation, we substitute equal probabilities of magnitude 1/n for each p(s) from the
expected return formula. The expected return, E(r), is then estimated by the arithmetic average
of the sample rates of return:
E(r) = ∑ns=1p(s)r(s) = 1/3∑ns=1r(s)
Variance = expected value of squared deviations
σ2 = ∑p(s)[r(s)-E(r)]2
_
1 n
Using historical data, the variance is estimated as:   [r ( s)  r ]2
n s 1
2
This equation is downward biased. The reason is that we have taken deviations from the
arithmetic average, instead of the unknown, true expected value, E(r), and have introduced a bit
of an estimation error. The bias can be eliminated by multiplying the arithmetic average of the
squared deviation by the factor n/(n-1):
_
_
1 n
 n  1 n
2
[ r ( s )  r ]2
 *  [r ( s)  r ] =

n  1 j 1
 n  1  n j 1
2 
σ=
_
1 n

[
(
)
]2
r
s
r

n  1 j 1
Reward-totVariability Ratio
The importance of the trade-off between reward and risk suggests that we measure the
attraction of an investment portfolio by the ratio of its risk premium to the SD of its excess
return  Sharpe Ratio (for portfolios) = Risk premium/SD of excess return.
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1. The Normal Distribution
 A smaller standard deviation means that possible outcomes cluster more
around the mea, while a higher SD implies more diffuse distribution.
 A measure of asymmetry called skew uses the ratio of the average cubed
deviations from the mean, called the third moment, to the cubed standard
deviation to measure any asymmetry of “skewness” of a distribution  Skew =
E[r(s) – E(r)]3/σ3
 When the distribution is positively skewed, the SD overestimates risk, because
extreme positive deviations from expectation nevertheless increase the
estimate volatility. Conversely, and more importantly, when the distribution is
negatively skewed, the SD will underestimate the risk.
 When the tails of a distribution are fat, there is more probability mass in the
tails of the distribution than predicted by the normal distribution. Kurtosis is a
measure if the degree of fat tails.  Kurtosis = (E[r(s) – E(r)]4/σ4) – 3
§5.8, page 144, is based on figure 5.6 and talks about historical data. §5.9 on long-term
investments is not mentioned in the slides and is not important in understanding following
chapters (see footnote page 151)
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6
Risk and risk aversion
Risk aversion and speculation are not consistent.
A prospect that has a zero risk premium is called a fair game. Investors, who are risk averse
reject investment portfolios that are fair game or worse. A risk-averse investor “penalizes” the
expected rate of return of a risky portfolio by a certain percentage to account for the risk
involved.
Utility, welfare – higher utility values are assigned to portfolios with more attractive risk-return
profiles.
Commonly employed utility function: U = E(r) – 0.005A2
A: index of investor’s risk aversion. The extent to which variance lowers utility depends on A.
The utility provided by risk-free portfolio is rate of return on that portfolio, no penalization for
risk.
Certainty equivalent rate of a portfolio is that rate that risk-free investments would need to
offer with certainty be considered equally attractive as the risky portfolio.
Risk-neutral investors judge risky prospects solely by their expected rate of return.
A risk-lover is willing to engage in fair games and gambles.
Mean-Variance Criterion: A dominates B if E(rA) E(rB) and A  B and at least one inequality is
strict.
Quadrant 2 and 3 (see pg. 172) desirability depends on exact nature of investor’s risk aversion.
Hedging: investing in an asset with a payoff pattern that offsets exposure to a particular source
of risk. It involved the purchase of a risky asset that is negatively correlated with the existing
portfolio.
Diversification: investments are made in a variety of assets to that exposure to risk of any
particular security is limited.
Portfolio mathematics:
Mean/expected return of asset is probability-weighted average of return in all scenarios.
E(r) =  Pr(s)r(s)
Variance:  Pr(s) * [r(s) – E(r)]2
Rate of return of portfolio is weighted average of rates of return of each asset
When risky asset is combined with risk-free asset, portfolio standard deviation equal risky
asset’s standard deviation multiplied by portfolios proportion invested in risky asset: portfolio =
e.g. 0.5*risky
Assets with returns that’ are inversely associated with the initial risky position are powerful
hedge assets. To quantify hedging potential of an asset: use the concept of covariance and
correlation. Covariance: measures how much the returns of 2 risky assets move in tandem.
Cov(rA,rB) =  Pr(s) [rA(s) – E(rA)] [rB(s) – E(rB)]
Correlation coefficient: scales the covariance to a value between –1 and +1.
 = cov(rA,rB) / (A*B)
Large negative correlation: move inversely.
When 2 risky assets with var A2 and B2 are combined into a portfolio with weights wA and wB:
portfolio variance =P2 = wA2 A2 + wB2 B2 + 2 wA * wB * Cov(rA,rB)
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7
Optimal Risky Portfolios
The investment decision can be viewed as a top-down process of three steps:
- Capital allocation between the risky portfolio and risk-free assets
- Asset allocation across broad asset classes
- Security selection of individual assets within each asset class
The ultimate goal of this investment process is to achieve the optimal capital allocation
according to the investors risk aversion and the expectations for the risk-return trade-off of the
optimal risky portfolio. The optimal risky portfolio is the combination of risky assets that
provides the best risk-return trade-off.
When you only invest in one stock you are exposed to a lot of risk. By adding more stocks to
your portfolio, basic diversification, you can reduce the risk. When the firm-specific influences
on two stocks differ, diversification should reduce portfolio risk. By adding more and more
stocks to your portfolio, the volatility of the portfolio continues to decrease. Ultimately,
however, we cannot decrease risk any further because all firms are affected by common
macroeconomic factors. The risk that remains even after extensive diversification is called
market risk (or systematic risk or nondiversifiable risk). The risk that can be eliminated is called
unique risk, firm-specific risk, non-systematic risk or diversifiable risk.
The reduction of risk to very low levels in the case of independent risk sources is called the
insurance principle, because of the notion that an insurance company depends on the risk
reduction achieved through diversification.
Portfolios of two risky assets are relatively easy to analyze, and they illustrate the principles and
considerations that apply to portfolios of many assets. We consider a bond portfolio, denoted D,
and a stock fund, E. A proportion (wD) is invested in the bond fund, and the remainder is
invested in de stock fund (1 – wD or wE). The rate of return will be:
Rp = wDrD + wErE
The expected return on the portfolio is a weighted average of expected returns on the individual
securities:
E(rp) = wDE(rD) + wEE(rE)
The variance of the two-asset portfolio is:
σ2p = w2Dσ2D + w2Eσ2E + 2wDwE Cov(rD,rE)
where:
σ2D = Cov(rD,rD) and
σ2E = Cov(rE,rE)
This means that the variance of the portfolio is a weighted sum of covariances, and each weight
is the product of portfolio proportions of the pair of assets in the covariance term.
The goal of diversification is the reduction of risk, which means a lower standard deviation. Thus
with two assets, the portfolio standard deviation should be lower, unless the two assets are
perfectly correlated. To see this, notice that the covariance can be computed from the
correlation coefficient:
Cov(rD,rE) = ρDEσDσE
Therefore,
σ2p = w2Dσ2D + w2Eσ2E + 2wDwEσDσEρDE
Because the covariance is higher, portfolio variance is higher when ρDE is higher. In the case of
perfect positive correlation, ρDE = 1, the right hand side of the equation above simplifies to:
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σp = wDσD + wEσE
This explains that the standard deviation of the portfolio with perfect correlation is just the
weighted average of the component standard deviations. In all other cases, the correlation
coefficient is less than 1, making portfolio standard deviation less than the weighted average of
the component standard deviations. So portfolios of less than perfectly correlated assets always
offer better risk-return opportunities than the individual component securities on their own.
The lowest possible standard deviation is when the correlation coefficient is -1. This gives:
σ2p =( wDσD - wEσE)2
which solves for:
wD = σE / (σD + σE)
wE = σD / (σD + σE) = 1 – wD
A portfolio opportunity set shows all combinations of portfolio expected return and standard
deviation that can be constructed from the two available assets.
When you can also invest in risk-free T-bills the goal is to construct the portfolio with the highest
reward-to-variability (Sharpe) ratio. This can be done graphically by drawing a linear line from
the risk-free rate to the top of the portfolio opportunity set. The steepest possible line will yield
the highest reward-to-variability at the point of intersect.
Sp = [E(rp) – rf] / σp
In the case of two risky assets, the solution of the weights of the optimal risky portfolio, P, can
be shown to be as follows:
[E(rD) – rf]σ2E – [E(rE) – rf]Cov(rD,rE)
wD =
[E(rD) – rf] σ2E + [E(rE) – rf] σ2D – [E(rD) – rf + E(rE) – rf]Cov(rD,rE)
1 – wD
wE =
Now that we have the optimal risky portfolio we can construct the optimal complete portfolio
by using the individual investors risk aversion to find the percentage that should be invested in
the risky portfolio.
E(rp) – rf
y=
Aσ2P
When there are more than two risky assets we take a slightly different approach. Instead of
calculating all possibilities for all assets, we construct a minimum-variance frontier of risky
assets. This frontier is a graph of the lowest possible variance that can be attained for a given
portfolio expected return. The part of the frontier that lies above the global minimum-variance
portfolio is called the efficient frontier of risky assets.
Separation property refers to the fact that the portfolio choice problem may be separated into
two tasks. The first task is the determination of the optimal risky portfolio. This portfolio is the
same for all clients, regardless of risk aversion. The second task, allocation of the complete
portfolio to T-bills versus the risky portfolio, depends on personal preference.
Considering diversification and risk reduction, it is important to realise that the contribution to
portfolio risk of a particular security will depend on the covariance of that security’s return with
those of other assets, and not on the security’s variance.
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Diversification is based on spreading your wealth over multiple assets. The insurance industry
does this as well. They do not reduce risk by adding more of the same insurances but instead
they add different projects to reduce total risk. For large projects, the underwriters even engage
in risk sharing. This means that multiple underwriters will each take only a small part in a project
so that none of them bears all the risk. The bottom line is that portfolio risk management is
about the allocation of a fixed investment budget to assets that are not perfectly correlated.
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9
The Capital Asset Pricing Model
Het CAPM model is een belangrijk instrument van modern financial economics. Het model geeft
een precieze voorspelling van de relatie tussen het risico van een asset en de expected return.
Die relatie dient 2 funties:
- Het geeft een benchmark rate of return om mogelijke investeringen tegen elkaar af te
wegen.
- Het model helpt om een goede schatting te maken van de expected return on assets die
nog niet verhandeld zijn in de markt.
9.1 The CAPM
Het CAPM is 12 jaar na de foundation of modern portfolio management door Harry Markowitz
ontwikkeld. De grondleggers zijn Sharpe, Lintner en Mossin. Onderstaande punten tonen de
simplifying assumptions die tot het CAPM leiden.
-
Er zijn veel inversteerders, elk met een eigen wealth die klein is vergeleken bij die van
alle investeerders samen. Investeerders zijn price-takers.
Alle investeerders plannen voor één dezelfde holding period.
Er kan alleen geïnvesteerd worden in openbaar verhandelde assets zoals stocks en
bonds. Ook kunnen investeerders geld (uit)lenen tegen een vast, risk-free percentage.
Investeerders betalen geen taxes en transaction costs.
Alle investeerders zijn rational mean-variance optimizers, ze gebruiken allemaal de
Markowitz portfolio selection model.
Alle investeerders analyseren securities op dezelde manier en hebben hetzelfde
economische beeld van de wereld.
Bovenstaande aannames geven ons inzicht in het equilibrium in security markets. Hieronder
staat het equilibrium samengevat
-
-
-
Alle investeerders kiezen ervoor om een portfolio van risky assets te houden, in
proporties die overeenkomen met de representatie van de assets in de market portfolio
(M), die alle verhandeldbare assets bevat. Met risky assets worden stocks bedoeld. Dus:
de proportie van ieder stock in de market portfolio is gelijk aan de market value van dat
stock gedeeld door de totale market value van alle stocks.
M ligt niet alleen op de efficient frontier, it also will be the tangency portfolio to the
optimal capital allocation line, derived by each investor. Daardoor is de CML de beste
attainable capital allocation line. Alle investeerders houden M als hun optimal risky
portfolio, ze verschillen alleen in de hoeveelheid geinvesteerd kapitaal erin versus in de
risk-free asset.
De risk premium van M staat in verhouding met het risico en de risico aversie van de
investor: E(Rm) – Rf = Ā  ²m
De risk premium van individuele assets staat in verhouding met de risk premium van M,
en de Beta van het asset.
 i = Cov(Ri, Rm)
 ²m
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De risk premium van individuele assets is
E(Ri) – Rf = Cov(Ri, Rm) [E(Rm-Rf)] =  i [E(Rm)- Rf]
 ²m
De bijdrage van een stock aan het risico van de marktportfolio (M) kan het best gemeten
worden aan de hand van de covariantie met die portfolio. Zie hiervoor equation 9.3 op blz
299.
De reward to risk ratio voor investeren in M is market risk premium = E(Rm) - Rf
 ²m
Market variance
Dit wordt ook wel de market price of risk genoemd, omdat het de extra return weergeeft
die investeerders vragen voor de portfolio risk. Een basisprincipe van equilibrium is dat alle
investments dezelfde reward to risk ratio hebben. De reward to risk ratio van een stock en
van de market portfolio moeten dus overeen komen (equation 9.6).
De expected return beta relationship is de bekendste vergelijking van het CAPM.
E(Ri) = Rf +  i [E(Rm)- Rf]
Beta’s groter dan 1 worden gezien als agressieve stocks (de reactie op de markt is hoger
dan gemiddeld).
De expected return-beta relationship wordt grafisch weergegeven als de Security Market
Line (SML), zie figuur 9.2 op blz 302. De helling stelt de risk premium van de market portfolio
voor. De Capital Market Line (CML) graphs the risk premiums of efficient portfolios
(portfolios composed of the market and risk-free asset), as a function of portfolio standard
deviation. De SML graphs the risk premiums of individual assets as a function of asset risk.
De SML dient als benchmark voor de prestatie van de investeringen. Bij een gegeven risico
(in de vorm van de beta) toont de SML de required rate of return. Het verschil tussen de
verwachte rate of return en de fair rate of return (de rate of return bepaald door de SML) is
de Alpha (zie figuur 9.3).
9.2 CAPM and the index model
CAPM behandeld expected returns, maar ik werkelijkheid kunnen we alleen dingen zeggen
over de realized return. Om van expected returns naar realized returns te gaan wordt het
index model gebruikt: Ri =  i +  i Rm + ei (9.10 op blz 306).
Hierbij staat de Rm voor de realized return van de market portfolio, en niet voor de
expected return. De beta coëfficient van het index model is gelijk aan de beta van het
expected return model.
 i = Cov(Ri, Rm)
 ²m
De index model specification is E(Ri) – Rf =  i +  i [E(Rm)- Rf]. Als we deze vergelijken met
de expected return specification dan zien we dat bij dat model de factor Alpha is
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weggelaten. CAPM voorspelt namelijk dat Alpha 0 is voor alle assets (er is geen excess
return). CAPM stelt dat de verwachte waarde van Alpha nul is, voor alle securities. Het index
model van CAPM zegt dat de realized value van Alpha rond de nul ligt, bij een groep
historical observed returns. Het index model wordt ook wel het market model genoemd.
9.3 Is the CAPM practical?
Als het CAPM model valid is dat zou dit betekenen dat een index waarin alle verhandelbare
securities zitten ook valid is (punt 3, paragraaf 9.1). Alle alpha’s zouden in dat geval ook 0
moeten zijn, maar dat is niet te verwachten in real markets. CAPM kan beter worden gezien als
‘the best available model to explain rates of return on risky assets’. Een security is mispriced als
de alpha niet-nul is. Overpricing vindt plaats als alpha beneden nul is. Underpricing als alpha
boven nul is. In de veronderstelling dat CAPM het beste beschibare model is, moeten
investeerders een index vinden om mee te werken en macro analyse toepassen om mispriced
securities te identificeren (meer hierover in hoofdstuk 8).
CAPM is niet goed testable omdat de hypothetische market portfolio niet waar te nemen is. Zo
zijn bijvoorbeeld real estate en privately held businesses onderdeel van die market portfolio,
maar zeer slecht waar te nemen.
CAPM tests worden uitgevoerd rond de expected return – beta relationship (omdat de market
portfolio niet waar te nemen is) en laten zien dat de veronderstelling dat alpha 0 is, onjuist is. Er
wordt waargenomen dat low-beta securities hoge alphas hebben en high-beta securities lage
alphas hebben.
Het is wellicht verrassend dat het CAPM, ondanks zijn tekortkomingen, een veelgebruikte norm
in de US en andere ontwikkelde landen is. Er zijn twee oorzaken:
1. Er is geen betere methode voor het erkennen van systematic en firm specific risk.
2. De centrale uitkomst van CAPM (de efficiency van de market portfolio), is niet zo gek
want het aantal fondsen dat het beter doet dan de marktportfolio is niet groot.
9.5 Extensions of the CAPM
Het CAPM maakt gebruik van simplifying assumptions. Door die assumptions aan te passen kan
het CAPM uitgebreid worden. Zo ontstaat het Zero-Beta Model (blz 313), een model dat
aangepast is voor human capital en privately held businesses (blz 314) en een multiperiod
model (blz 316). Zie het boek voor meer diepgang.
9.5 Liquidity and the CAPM
De liquidity van een asset is het gemak en de snelheid waarmee het tegen een eerlijke market
value verkocht kan worden. Onderdeel van liquidity zijn de kosten van het aangaan van de
transactie (de bid-ask spread). Illiquidity wordt gemeten aan de hand van de discount op de
market value die de verkoper moet accepteren als het asset snel verkocht moet worden.
Dealers in over the counter markets geven prijzen aan waartegen zij een security willen kopen
(bid) of verkopen (ask), en bepalen dus ook de liquidity van een security. De bid-ask spread is de
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vergoeding die zij krijgen voor het verlenen van deze dienst. Met de electronische handel van
tegenwoordig moet nog steeds rekening worden gehouden met de bid-ask spread (denk maar
aan limit-orders). De discount in een security price door illiquidity kan aardig oplopen (zie blz
319 en 320 voor een rekenvoorbeeld).
Investeerders kunnen ook een compensatie vragen voor liquidity risk. Het kan namelijk
gebeuren dat een asset minder liquide wordt, op het moment dat men er vanaf wil. Equition
9.15 (blz 321) laat het model van Achara en Pedersen zien waarbij de expexted return van een
security afhangt van de kevel en risk of liquidity.
10 Arbitrage Pricing Theory and multifactor models of risk and
return
I recommend that you look at all the examples in the textbook for a better understanding of the
formulas and especially the arbitrage pricing method. You have to see the calculations to
understand the arbitrage opportunities. Pay special attention to figure 10.2, example 10.4 and
10.6.
10.1 Multifactor models: an overview
Factor models are tools that allow us to describe and quantify the different factors that affect
the rate of return on a security during any time period. As noted in chapter 8, uncertainty in
asset returns has two sources: a macroeconomic (common) factor and firm-specific events. The
common factor is constructed to have zero expected value, since we use is to measure new
information. The actual return on firm i will equal its initially expected return (E(Ri)) plus a (zero
expected) random amount attributable to economy wide events (βiF) plus another (zero
exoected value) attributable to firm-specific events (ei). F is the deviation of the common factor
from its expected value, βi is the sensitivity of the firm to that factor and ei is the firm-specific
disturbance.
Thus, the single factor model looks like:
Ri = E(Ri) + βiF + ei
A multifactor model allows for several factors to influence the return on a security. For example,
suppose that two important macroeconomic sources of risk are growth in GDP an Interest Rates.
The multifactor model then looks like:
Ri = E(Ri) + βigdp GDP + βiir IR + ei
The multifactor model is no more than a description of the factor that affect security returns.
The question left unanswered is where E(r) comes from. This is where the SML from the CAPM
comes in.
E(R) = Rf +  [E(Rm)- Rf] can be rewritten as E(r) = Rf + β RPm where RPm stand for the risk
premium of the market portfolio. As pointed in chapter 8, beta is the exposure of a stock or
portfolio to macroeconomic risk factors. Therefore, one interpretation of SML is that investors
are rewarded for their exposure to macro risk, but not for the exposure to firm specific risk ( the
ei in the equations above).
The expected rate of return in a two factor economy would be the sum of:
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1. The risk-free rate (Rf)
2. The sensitivity to GDP risk (βgdp) times the risk premium for GDP risk
3. The sensitivity to interest rate risk (βir) times the risk premium for interest rate risk
The multifactor SML can be written down as: (E)r = Rf + βgdp RPgdp + βir RPir
10.2 Arbitrage pricing theory
Just like CAPM, Arbitrage Pricing Theory (APT) predicts a SML linking expected returns to risk,
but the path it takes to the SML is different. APT relies on three propositions:
-
Security returns can be described by a factor model
There are sufficient securities to diversify away idiosyncratic risk
Well-functioning security markets do not allow for the persistence of arbitrage
opportunities.
An arbitrage opportunity would arise is shares of a stock sold for two different prices on two
different exchanges. Riskless profit could be made by buying a share of IBM on the NYSE for 50$
en selling it at the Nasdaq for 60$ at the same moment.
Now we look at the risk of a well diversified portfolio. De firm-specific risk becomes neglectible
so that only systematic risk remains. The rate of return of this portfolio is:
Rp = E(Rp) + βp F + ep
where βp = ∑Wi βi
ep = ∑Wi ei
is the weighted average of the βi of the n securities and
The systematic and nonsystematic variance of this portfolio can be seen at page 337 and 338.
The larger the amount of different stocks, the more the nonsystematic variance approaches to
zero and thus: the less nonsystematic risk. Because of this we can conclude that the return on a
well diversified portfolio equals:
Rp = E(Rp) + βp F
Because nonfactor (specific) risk can be diversified away, only factor (macroecnonomic) risk
should command a risk premium in market equilibrium. To fully understand this and to visualize
the arbitrage opportunity, you have te read pages 339 en 340. The one factor SML is the same
as the CAPM, as can be seen on page 341.
10.3 Individual asset and the APT
Read ‘the APT and the CAPM’ on page 343 of the book te see the differences between CAPM
and APT.
10.4 A multifactor APT
So far we have assumed there’s only one systematic factor affecting stock returns. This is to
simplistic. A two-factor APT woul look like:
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Ri = E(Ri) + βi1 F1 + βi2 F2 + ei
Factor 1 was the GDP growth and factor 3 was the interest rate decline. Each factor has zero
expected value because each measures the surprise in the systematic variable rather than the
level of the variable. Ei also has zero expected value.
A portfolio Q, can be formed by investing in other portfolio’s. For example P1 and P2. When one
decides to invest βp1 in one portfolio and βp2 in another and 1 - βp1 - βp2 in T-bills, portfolio Q
will haven an expected return of :
E(Rq) = Rf + βp1 [E(R1)-Rf] + βp2 [E(R2)-Rf]
10.5 Where should we look for factors?
One shortcoming of the APT is that it gives no guidance concerning the determination of the
relevant risk factors or their risk premiums. Two principles guide us when we specify a
reasonable list of factors. First, we want to limit ourselves to systematic factors with
considerable ability to explain security returns. Second, we wish to choose factors that seem
likely to be important risk factors (investors will demand meaningful risk-premiums to bear
exposure of those sources of risk). Chen, Roll and Ross composed a set of factors that might be
considered (see page 346). Also the Fama and French three factor model might be considered
(see page 347).
10.6 The multifactor CAPM and the APT
A multifactor extension of the single factor CAPM, the ICAPM, is a model of the risk-return
trade-off that predicts the same marketline as the APT.
E(Ri) = Rf + βim [E(Rm)-Rf] + βie [E(Re)-Rf]
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12
Behavioral Finance and Technical Analysis
The efficient market hypothesis makes two important predictions. First, it implies that security
prices properly reflect whatever information is available to investors. Second, it implies that
active traders will find it difficult to outperform passive strategies. To do so would require
differential insight which, in a highly competitive market, is hard to come by.
Behavioural finance looks at how real people make decisions, in contrast with conventional
theories that usually ignore this. Errors in information can lead investors to misestimate the true
probabilities of possible events or associated rates of return. These biases include:
- Forecasting errors (put too much weight in recent experience)
- Overconfidence (overestimation of precision of our own beliefs or forecasts)
- Conservatism (people are too slow in updating their beliefs in response to new
evidence)
- Sample size neglect and representativeness (people do not commonly take into account
the size of a sample)
Even if all the information is correct, individuals still make less-than-fully rational decisions using
that information. Some behavioural biases are:
- Framing (decisions are affected by how choices are framed)
- Mental accounting (specific form of framing, separate certain decision e.g. different
investment style for investment account and savings account)
- Regret avoidance (people have more regret (blame themselves more) for a wrong
decision when that decision was unconventional)
- Prospect theory (higher wealth provides higher satisfaction, but at a diminishing rate.
Therefore investors will reject risky prospects that don’t offer a risk premium)
Limits to arbitrage
- Fundamental risk (underpriced stocks are not certain to return to their ‘real’ value
within days. Managers may be judged on short-term performance)
- Implementation costs (short selling to exploit overpriced securities costs money and the
securities may have to be returned before the stock has dropped to its real value)
- Model risk (perhaps the model used to calculate the over or underpricing is faulty)
Technical analysis attempts to exploit recurring and predictable patterns in stock prices to
generate superior investment performance. For example, investors often hold on to losing
investments (disposition effect). This can lead to momentum in stock prices even if fundamental
values follow a random walk.
The Dow Theory is the grandfather of all trend analysis. It claims that three forces
simultaneously affect stock prices:
1. The primary trend is the long-term movement of prices, lasting from several months to
several years.
2. Secondary (or intermediate) trends are caused by short-term deviations of prices. These
are eliminated via corrections when prices revert back to trend values.
3. Tertiary (or minor) trends are daily fluctuations of little importance
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Moving averages are average levels of a stock or index over a given interval of time. It is
computed by adding the newest value every day (or week) and dropping the oldest value. When
the market breaks through the moving average line, it is taken as a bullish signal because it
signifies a shift from a falling trend to a rising trend. Alternatively, when prices fall below the
moving average it’s considered time to sell.
The breadth of the market is a measure of the extent to which movement in a market index is
reflected widely in the price movements of all the stocks in the market.
Market volume is also sometimes used to measure the strength of a market rise or fall.
Increased investor participation can be viewed as a measure of the significance of the
movement. The trin statistic is defined as:
Volume declining / Number declining
Trin =
Volume advancing / Number advancing
Trin, therefore, is the ratio of average volume in declining issues to average volume in advancing
issues. Ratios above 1.0 are considered bearish because the falling stocks would then have
higher average volume than the advancing stocks, indicating net selling pressure.
The confidence index is the ratio of the average yield on 10 top-rated corporate bonds divided
by the average yield on 10 intermediate grade corporate bonds. When bond traders are
optimistic about the economy they require smaller default premiums on lower rated debt.
Hence the yield spread will narrow and the confidence index will approach 100%. Higher values
therefore, are bullish signals.
The Put/Call ratio is also a tool used to measure the market sentiment. Many technicians see an
increase in the ratio as bearish, as it indicates growing interest in put options as a hedge against
market declines.
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13
Empirical evidence on security returns
NB: Niet/nauwelijks behandeld in college!!!
In this chapter some empirical evidence of the CAPM and SML are presented.
Although the single factor expected return-beta relationship has not been confirmed by
scientific standards, its use is already commonplace in economic life. Early test of the single
factor CAPM rejected the SML, finding that nonsystematic risk did explain average security
returns. Later test controlling for the measurement error in beta found that nonsystematic risk
does not explain portfolio returns but also that the estimated SML is too flat compared with
that the CAPM would predict.
Roll’s critique implied that the usual CAPM test is a test only of the mean variance efficiency of a
prespecified market proxy and therefore that test of the linearity of the expected return beta
relationship do not bear on the validity of the model. Tests of the mean-variance efficiency of
professionally managed portfolios against the benchmark of a prespecified market index
conform with Roll’s critique in that they provide evidence on the efficiency of the prespecific
market index. Empirical evidence suggest that most professionally managed portfolios are
outperformed by market indexes, which lends weight to acceptance of the efficiency of those
indexes and hence the CAPM. Work with economic factors suggests that factors such as
unanticipated inflation do play a role in the expected return-beta relationship of security
returns.
Tests of the single-index model that account for human capital and cyclical variations in asset
betas are far more consistent with the single-index CAPM and APT. These tests suggest that
macro-economic variables are not necessary to explain expected returns. Moreover, anomalies
such as effects of size and book-to-market ratios disappear once these variables are accounted
for.
Volatility of stock returns is constantly changing. Empirical evidence on stock returns must
account for this phenomenon. Contemporary researchers use the variations of the ARCH
(autoregressive conditional heteroskedasticity model) algorithm to estimate the level of
volatility and its effect on mean returns.
Equity premium puzzle: originates from the observation that equity returns exceeded the riskfree rate to an extent that is inconsistent with reasonable levels of risk aversion – at least when
average rates of return are taken to represent expectations. Fama and French show that the
puzzle emerges primarily from excess returns of the past 50 years. Alternative estimates of
returns on stocks were high because of unexpected large capital gains. The study suggests that
future excess returns will be lower than realized in recent decades.
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14
Bond Prices and Yields
A bond is a security that is issued in connection with a borrowing arrangement. The borrower
issues a bond to the lender for some amount of cash. The arrangement obligates the issuer to
make specified payments to the bondholder on specified dates. When the bond matures, the
issuer repays the debt by paying the bondholder the bond’s par value (eq. it’s face value). The
coupon rate of the bond determines the interest payment: The annual payment is the coupon
rate times the bond’s par value. Zero-coupon bonds are issued without coupon payments.
These bonds are issued at prices considerably below par value, and the investor’s return comes
solely from the difference between issue price and the payment of par value at maturity.
If a bond is purchased between coupon payments, the buyer must pay the seller for accrued
interest, the prorated share of the upcoming semiannual coupon.
Accrued Interest 
Annualcoupon rate # days since last coupon payment

2
# days between coupon payments
Type of bonds:
• Callable (corporate) bond: An option in the bond that allows the issuer of the bond to
buy back the bond in the future at an in advance specified price. (reduces the value of
the bond). To compensate investors for this risk, callable bonds are issued with higher
coupons and promised yields to maturity than noncallable bonds.
• Convertible bond: gives the holder of the bond the right to convert bonds into company
stock at a pre-specified relative price of bonds per stock. (increases value of the bond).
• Puttable bond: allows the holder of the bond to extend the maturity of the bond beyond
the pre-agreed maturity. (Increases the value of the bond).
• Floating rate bond: specifies coupon rate as the time-varying short rate + a (fixed)
premium. The interesr payments are tied to some measure of current market rates.
• Preferred stock: stock with fixed dividends (perpetuity) with special rights. Like bonds,
preferred stock promises to pay a specified stream of dividends. Unlike bonds, the
failure to pay the promised dividends does not result incorporate bankruptcy. Instead,
the dividends cumulate, and the common stockholders may not receive any dividends
until the preferred stockholders have been paid in full. Unlike interest payments on
bonds, dividends on preferred stock are not considered tax-deductible expenses to the
firm. On the other hand, there is an offsetting tax advantage to preferred stock.
• International bonds: Foreign bonds are issued by a borrower from a country other than
the bond is sold. The bond is denominated in the currency in which it is marketed. Euro
bonds are bonds that are issued in the currency of one country, but are sold in other
national markets.
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Bond Pricing
To value a security, we discount its expected cash flow by the appropriate discount rate. The
cash flows form a bond consists of coupon payments until the maturity date plus the final
payment of par value. Therefore,
Bond value = Present value of coupons + Present value of par value
The bond value can be written as: Pbond ( t ) 
N

i 1
(R / 2)F
F

i
(1  r )
(1  r ) N
In which N is the number of half-years over which the bond runs, R denotes the coupon rate in
per annum terms and F denotes the face value of the bond.
1 
The price of the bond can be written as: Pbond ( t )  (R / 2)F 1 
r 
1 
1
 
F
N 
(1  r )  (1  r ) N
(annuity factor) + (PV factor)
Terminology in the equations is the same as used during lectures and not as written in the
book!!!!
At a higher interest rate, the present value of the payments to be received by the bondholder is
lower. When interest rates rise, bond prices must fall because the present value of the bond’s
payments is obtained by discounting at a higher interest rate.
A general rule in evaluating bond price risk is that, keeping all factors the same, the longer the
maturity of the bond, the greater the sensitivity of price to fluctuations in the interest rate. This
is why short term Treasury securities such as T-bills are considered to be safest. They are free
not only of default risk but also largely of price risk attributable to interest rate volatility.
Bond yields
 The yield to maturity is defined as the interest rate that makes the present value of the
bond’s payments equal to its price. The bond is held till maturity.
N
Pbond ( t )  
i 1


(R / 2)F
F

0
i
(1  r )
(1  r ) N
A callable bond may be retired prior to the maturity date. Bonds are typically called
when the market rates have decreased relative to the market rate used to price the
bond.
The Current yield measures the coming yield from holding the bond
current yield ( t ) 

R.F
Pbond ( t )
The Realized compound yield is the total average return on investment from holding
the bond till maturity. (Difference with yield to maturity is the fact that market interest
rates will change over time!). Can only be calculated at the end of the life of a bond.
Forecasting the realized compound yield over various holding periods or investment
horizons is called horizon analysis
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Yield to maturity depends only on the bond’s coupon, the current price, and par value at
maturity. All of these variables are observable today. In contrast, the HPR is the rate of return
over a particular investment period and depends on the market price of the bond at the end of
the holding period.
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Default Risk and Bond Pricing
Bond default risk, usually called credit risk, is measured by various firms (e.g. S&P, Moody’s) and
in which a top rating is AAA. Those rated BBB are considered investment-grade bonds, whereas
lower rated bonds are classified as speculative-grade or junk bonds.
Determinants of Bond Safty:
1. Coverage ratios – Ratios of company earnings to fixed costs
2. Leverage ratios – A too-high leverage ratio (debt-to-equity) indicates excessive
indebtedness.
3. Liquidity ratios – most common are the current ratio and the quick ratio, which measure
the firm’s ability to pay bills coming due with its most liquid assets.
4. Profitability ratios – Measures of rates of return on assets or equity.
5. Cash flow-to-debt ratio – This is the ratio of total cash flow to outstanding debt.
A bond is issued with an indenture which is the contract between the issuer and the bond
holder. Some restrictions in the indenture include:
 Sinking Funds – establishing a sinking fund, gives the issuer of the bond the option to
spread the burden of paying the bonds par value over several years.
 Subordination of Further Debt – To prevent firms from harming bondholders,
subordination clauses restrict the amount of additional borrowing.
 Dividend Restrictions – These limitations protect the bondholders because they force
the firm to retain assets rather than paying them out to shareholders.
 Collateral – Collateral can take several forms, but it represents a particular asset of the
firm that the bondholders receive if the firm defaults on the bond.
To compensate for the possibility of default, corporate bonds must offer a default premium.
The default premium is the difference between the promised yield on a corporate bond and the
yield of an otherwise-identical government bond that is riskless in terms of default.
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15
The Term Structure of Interest Rates
Term structure of interest rates: structure of interest rates for discounting cash flows of
different maturities.
Short interest rate: interest rate for a given time interval.
Yield curve: graph if yield to maturity as function of time to maturity.
Spot rate: yield to maturity on zero-coupon bonds that prevails today for a period corresponding
to maturity of the zero.
(Yields are averages of the interest rates in each period)
Bond stripping+ pricing! In world with certainty: yields to maturity can differ for bonds of the
same maturity if their coupon rates differ.
Pure yield curve: relationship yield to maturity & time to maturity for zero-coupon bonds. When
interest rate movements are known with certainty, and all bonds are properly priced, all will
provide equal 1-yr rates of return.
Forward interest rate: (1+fn) = (1+yn)n / (1+yn-1)n-1
The interest rate that actually will prevail in the future need not equal the forward rate. It is not
even necessarily the case that the forward rate equals the expected value of the future short
interest rate.
Forward rate: interest rate that would need to prevail in the second year to make the long- and
the short-term investments equally attractive, ignoring risk. When we account for risk: clear that
investor will shy away form long-term bond unless it offers expected return greater than that of
the 1-yr bond.
If individuals are short term investors, bonds must have prices that make f2 greater than E(r2).
Forward rate will embody premium: liquidity premium: compensates for the uncertainty about
price at which that will be able to sell long-term bonds at end of year. If all investors were longterm investors: now forward rate less than expected future spot rate. Whether forward rates
will equal expected future short rates depends on investors’ willingness to bear interest rate
risk, & willingness to hold bonds that do not correspond to their investment horizons.
Expectations hypothesis: forward rate equals market consensus expectation of the future short
interest rate, f2 = E(r2), liquidity premiums = 0. (upward sloping curve: evidence investors
anticipate increases in interest rates).
Liquidity preference theory of term structure: believe that short-term investors dominate the
market, so that forward rate exceeds the expected short rate, positive liquidity premium.
Direct relationship between yield on various maturities and forward interest rates:
1+yn = [(1+r1)*(1+f2)*(1+f3)…(1+fn)]1/n .
Yield curve is upward sloping, when forward rate for coming period is greater than yield at that
maturity.
To raise the yield to maturity, an above-average forward rate must be added to the other rates
in the averaging computation. What accounts for higher forward rate: (fn = E(rn) + liquidity
premium) expected rise in interest rates, or a higher required premium for holding longer-term
bonds.
The usually observed upward slope of yield curve, especially for short maturities, is the empirical
basis for the liquidity premium doctrine that long-term bonds offer a positive liquidity premium.
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If term premiums, spread yield on long- and short-term bonds, generally are positive, then
anticipated declines in rates could account for a downward-sloping yield curve. Why might
interest rates fall: 2 factors: real rate and inflation premium.
Forward interest rate contract: construct a synthetic forward loan, sell (1+f2) 2-yr zeros for every
1-yr zero that you buy. This makes initial cash flow zero.
For coupon bonds: treat each coupon payment as a separate mini–zero–coupon bond.
Why do not all bond prices conform to a common discount function that sets price equal to
present value? Taxes, options investors have to sell early (also call provision).
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16
Managing Bond Portfolios
1. Bond prices and yield are inversely related: as yields increase, bond price will fall; as yields
fall, bond prices rise.
2. An increase in a bond’s yield to maturity results in a smaller price change than a decrease in
yield of equal magnitude.
3. Prices of long-term bonds tend to be more sensitive to interest rate changes than prices of
short-term bonds.
4. The sensitivity of bond prices to changes in yields increases at a decreasing rate as maturity
increases. In other words, interest rate risk is less than proportional to bond maturity.
5. Interest rate risk is inversely related to bond’s coupon rate. Prices of high-coupon bonds are
less sensitive to changes in interest rates than prices of low-coupon binds.
6. The sensitivity of a bond’s price to a change in its yield is inversely related to the yield to
maturity at which the bond is currently selling.
Explanation rule 5: In some sense a zero-coupon bond represents a longer-term bond than an
equal-time-to-maturity coupon bond. A coupon bond can be viewed as a “portfolio” of coupon
payments; hence the effective maturity of bond is some average of the maturities of all cash
flows paid out by bond.
Macaulay’s duration: (=average maturity measure of bond’s promised cash flows) computed as
weighted average of the times to each coupon or principal payment made by the bond.
Weight associated with each payment should be related to importance of payment to value of
bond. Weight wt = CFt / (1+y)t / bond price
Macaulay’s duration formula: D = Σ t * wt .
Duration is a key concept in fixed-income portfolio management – 3 reasons :
1. It is a simple summary statistic of the effective average maturity of portfolio
2. it turns out to be essential tool in immunizing portfolios from interest rate risk
3. duration is a measure of the interest rate sensitivity of portfolio.
When interest rates change, proportional bond’s price can be related to change in yield in
maturity: ΔP/P = – D * [Δ(1+y) / 1+y]
Practioners use: modified duration D*= D/(1+Y) and say ΔP/P = – D* Δy.
What determines duration: (3 key factors: time to maturity, coupon rate, yield to maturity)
1. The duration of a zero-coupon bond equals its time to maturity.
2. Holding maturity constant, a bond’s duration is higher when the coupon rate is lower.
3. Holding the coupon rate constant, a bond’s duration generally increases with its time to
maturity. Duration always increases with time to maturity for bonds selling at par or at a
premium to par.
4. Holding other factors constant, the duration of a coupon bond is higher when the bon’s
yield to maturity is lower.
5. The duration of a level perpetuity is: duration perpetuity = (1+y) / y.
6. The duration of a level annuity is: duration annuity = (1+y)/y – (T/(1+y)T-1)
7. Duration of a coupon bond = (1+y)/y – ((1+y) +T(c-y)) / (c [1+y]T -1) + y)
8. For coupon bonds selling at par value, 7. simplifies to: (1+y)/y [1- (1/(1+y)T)]
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Duration implies linear relationship between bond prices and yields, however this is not the
case. The duration approximation always understates the value of the bond; it underestimates
the increase in bond price when the yield falls, and it overestimates the decline in price when
the yield rises. Curvature o the price-yield curve: convexity.
Accounting for convexity: ΔP/P = – D* Δy + ½ *convexity * (Δy)2.
Convexity is a desirable trait. Bonds with greater convexity gain more in price when yields fall
than they lose when yield rise. Costs for investors: they will have to pay more and accept lower
yield on bonds with greater convexity.
Callable bonds: also region of negative convexity (price-yield curve is below tangency line):
unattractive asymmetry: interest rates increases result in larger price decline than the price gain
to an interest rate decrease of equal magnitude.
Convention on Wall Street is to compute effective duration of bonds with embedded options:
Effective duration = – ΔP/P / Δr, Δr=assumed increase in rates – assumed decrease in rates and
ΔP = price at increase – price at decrease.
Passive bond management:
-indexing strategy: replicate performance of given bond index. Problems: index is very broad
based (more than 5000 securities), rebalancing problems (bonds drop from index when
maturity,1yr), bonds generate interest income –must be reinvested. Use stratified/cellular
approach (bonds in cell considered homogenous)
-immunization techniques: seek to establish a zero-risk profile: strategies used by investors to
shield their overall financial status from exposure to interest rate fluctuations. Idea behind
immunization is that duration-matched assets and liabilities let the asset portfolio meet the
firm’s obligations despite interest rate movements.
Fixed-income investors face 2 offsetting types of interest rate risk: price risk and reinvestment
risk. For a horizon equal to the portfolio’s duration, price risk and reinvestment risk exactly
cancel out.
Duration matching balances the differences between the accumulated value of the coupon
payments (reinvestment risk) and the sale value of the bond (price risk). Hence: when interest
rates fall, the coupons grow less than in the base case, but the gain on the sale of the bonds
offsets this and vice versa.
However for greater changes in the interest rate, pv curves diverge. This reflects fact that fund
actually shows a small surplus. If obligation was immunized, why surplus in fund? Convexity!
Coupon bond has greater convexity than the obligation it funds. Hence: important to rebalance
immunized portfolios. Even if interest rates do not change, asset durations will change solely
because of passage of time.
Construction immunized portfolio: 1. Calculate duration of liability. 2. Calculate duration of asset
portfolio. 3. Find asset mix that sets durations equal. 4. Fully fund the obligation (difference PV
and FV zero-coupon bond!!). 5. Rebalance!
Dedication strategy: Cash flow matching on a multiperiod basis. CF matching: automatically
immunize portfolio from interest rate movements because CF from bond and obligation exactly
offset each other. No need for rebalancing.
Problems immunization: duration is strictly valid only for flat yield curve (all payments
discounted at common interest rate), not flat: replace CF/(1+y)t by pv of CF (pv=discounted at
rate from yield curve corresponding to date of particular CF).
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Moreover, duration matching will only immunize portfolios for parallel shifts in yield curve and
immunization can be inappropriate goal in an inflationary environment.
Two sources of potential value in active bond management: forecasting interest rate,
identification relative mispricing. Active bond portfolio strategies:
1. Substitution swap: exchange of 1 bond for a nearly identical substitute (temporarily
mispricing – discrepancy – profit opportunity: mind equality of credit risk!)
2. Intermarket spread swap: when investors believes yield spread between 2 sectors of bond
market is temporarily out of line. (spread high – eventually narrows)
3. Rate anticipation swap: pegged to interest rate forecasting. If investors believe rates will fall,
they will swap into bonds of longer duration.
4. Pure yield pickup swap: pursued as a means of increasing return by holding higher-yield
bonds. When yield curve is upward sloping, yield pickup swap entails moving into longerterm bonds (5. Tax swap: exploit some tax advantage)
Horizon analysis: interest rate forecasting: see example pg. 549.
Contingent immunization: mixed passive-active strategy: see example pg. 549. Minimum
acceptable terminal value X/(1+r)T : trigger point. Then active strategy is ceased: immunization
strategy is initiated.
Interest rate swap: contract 2 parties: exchange a series of CF
Financial engineering: Inverse floaters, Po & IO strips (pg 553-555)
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24
Portfolio Performance Evaluation
The arithmetic average of a portfolio is estimated for the expected rate of return of a portfolio
for the next quarter. This value is also called the internal rate of return.
The geometric average of a portfolio, which can differ substantially from the arithmetic, is the
constant quarterly return over the quarters that would yield the same total or cumulative
return. Each return has an equal weight in the geometric average. For this reason, the
geometric average is referred to as a time-weighted average.
(example page 852!!!)
Adjusting return for risk
Evaluating performance based on average return alone is not very useful. Returns must be
adjusted for risk. The simplest way to adjust returns for portfolio risk is to compare rates of
return with those of other investment funds with similar risk characteristics. However, such
rankings can be misleading. For example if the portfolio characteristics are not truly comparable.
Methods of risk-adjusted performance evaluation using mean-variance criteria came on stage
simultaneously with the capital asset pricing model (CAPM). Jack Treynor, William Sharpe and
Michael Jensen recognized immediately the implications of the CAPM for rating the
performance of managers. Two reasons that the risk-adjusted performance measures are not so
popular are (1) Generally negative cast to the performance statistics. (2) Mean-variance may
have suffered relates to intrinsic problems in the measures.
For now however, we can catalog some possible risk-adjusted performance measures for a
portfolio, P, and examine the circumstances in which each measure might be most relevant.
1) Sharpe measure divides average portfolio excess return over the sample period by the
standard deviation of returns over that period. It measures the reward to (total)
volatility trade-off.
2) Treynor’s measure (like sharpe’s) gives excess return per unit of risk, but it uses
systematic risk instead of total risk.
3) Jensen’s measure is the average return on the portfolio over and above that predicted
by the CAPM, given the portfolio’s beta and the average market return. Jensens’s
measure is the portfolio’s alpha value.
4) The information ratio divides the alpha of the portfolio by the nonsystematic risk of the
portfolio called “tracking error” in the industry. It measures abnormal return per unit of
risk that in principle could be diversified away by holding a market index portfolio.
Each measure has some appeal, but each does not necessarily provide consistent assessments
of performance, since the risk measures used to adjust returns differ substantially.
A variant of Sharpe’s measure was proposed by graham and Harvey. Their approach has been
dubbed the M^2 measure (for Modigliani-Squared). Like Sharpe ratio, the M2 measure focuses
on total volatility as a measure of risk, but its risk-adjusted measure of performance has the
easy interpretation of a differential return relative to the benchmark index. To compute the M2
we imagine that a managed portfolio, P, is mixed with a position in T-bills so that the “adjusted”
portfolio matches the volatility of a market index such as the S&P 500. The adjusted portfolio,
we call P*, would than have the same standard deviation as the index. We now may compare
their performance simply by comparing returns. (To compute the M2 see example blz
855,formula is there as well.)
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The appropriate performance measure depends on the role of the portfolio to be evaluated.
Appropriate performance measures are as follows:
a) Sharpe: when the portfolio represents the entire investment fund.
b) Information ratio: when the portfolio represents the active portfolio to be optimally
mixed with the passive portfolio.
c) Treynor or Jensen: when the portfolio represents one sub-portfolio of many. (Treynor’s
performance measure is appealing because when an asset is part of a large investment
portfolio, one should weigh its mean excess return against its systematic risk rather than
against total risk to evaluate contribution to performance)
Formules en uitleg staan op blz 858.
Performance measurement for hedge funds
It’s quite clear that a hedge fund should never serve as a sole investment vehicle for any
individual investor. Instead, we must treat a hedge fund as an active portfolio that is added to a
baseline well-diversified portfolio. We will tread the equity portfolio as the baseline component
of the investor’s portfolio to which we may consider adding hedge funds in the search for
additional alpha, sometimes called portable alpha. This framework is widely adopted in the
investment industry.
According to the formulas on page 863, you should use the information ratio to measure
performance of hedge funds.
However, it is well to pause to consider several problems in evaluating investments
performance of hedge funds.
1) They seem to have substantially nonlinear factor exposures not captured by standard
linear index models. This implies that risk is not constant and that estimated alphas will
be biased if we use a standard, linear index model. The betas typically differ by
substantial margins and down-market betas tend to be higher than up-market betas.
This is precisely what investors presumably do not want: higher market sensitivity when
the market is weak.
2) Hedge funds also pose problems because they tend to hold less-liquid assets for which
market prices are less readily available. When assets are not actively traded, the hedge
fund must estimate its value in order to calculate rates of return. Such procedures result
in serial correlation. Serial correlation is evidence of liquidity problems.
3) Santa Claus effect, hedge funds report average returns in December that are more than
double their average returns in other months. This is because than the performance
incentive fees kick in. If funds take advantage of illiquid markets to manage returns,
then performance measurement becomes almost impossible.
4) Hedge funds tend to hold more illiquid assets than other institutional investors such as
mutual funds. They can do so because of share restrictions such as lock-up provisions
that commit investors to keep their investment in the fund for some period of time. It is
important to control for liquidity when evaluating performance. If it is ignored, what
may be no more than fair compensation for illiquidity may appear to be true “alpha”
that is, risk-adjusted abnormal returns.
Market timing: In this pure form, market timing involves shifting funds between a market-index
portfolio and a safe assets, such as T-bills or a money market fund, depending on whether the
market as a whole is expected to outperform the safe asset. To simplify, suppose that an
investor holds only the market-index portfolio and T-bills.
 No market timing: beta is constant
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
Market timing: beta increases with expected market excess return
Main point: The shifting mean and variance of actively managed portfolios make it even harder
to assess performance. A typical example is the attempt of portfolio managers to time the
market, resulting in ever-changing portfolio betas.
Style Analysis was introduced by William Sharpe. A well-known study concluded that 91.5% of
the variation in returns of 82 mutual funds could be explained by the funds’ asset allocation to
bills, bonds, and stocks. The R-square of the regression would measure the percentage of return
variability attributable to style or asset allocation, while the remainder of return variability
would be attributable either to security selection or to market timing by periodic changes in the
asset-class weights.
Morning Star Rating Mehtod: compares each fund to a peer group represented by a style
portfolio within four asset classes. Risk-adjusted ratings (RAR) are based on fund returns relative
to the peer group and used to award each fund one to five stars based on the rank of its RAR.
Morningstar INC. is the premier source of information on mutual funds. Stars are given
according to the funds percentile.
Performance evaluation has two very basic problems:
1) Many observations are needed for significant results even when portfolio mean and
variance are constant.
2) Shifting parameters when portfolios are actively managed makes accurate performance
evaluation all the more elusive.
We can not overcome these difficulties completely, bus we need to do the following:
1) Maximize the number of observations by taking more frequent return readings.
2) Specify the exact makeup of the portfolio to obtain better estimates of the risk
parameters at each observation period.
Still even with more data, an insidious problem that will continue to complicate performance
evaluation is survivorship bias. Since poorly performing mutual funds are regularly closed down,
sample data will include only surviving funds. Survivorship bias also affects broad-market
indexes used as bogey portfolios and generates upward biased returns that are harder to beat.
Performance attribution procedures:
Rather than focus on risk-adjusted returns, practioners often want simply to ascertain which
decisions resulted in superior or inferior performance. Superior investment performance
depends on an ability to be in the right securities at the right time. Attribution studies start from
the broadest asset allocation choices and progressively focus on ever-finer details of portfolio
choice.
Common attribution procedures partition performance improvements to asset allocation, sector
selection and security selection. Performance is assessed by calculating departures of portfolio
composition from a benchmark or neutral portfolio.
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25
Portfolio performance evaluation
Handig om zelf naar alle grafieken te kijken het hoofdstuk interpreteerd grafieken en tabellen je
hebt het zo doorgelezen.
Global markets
( dit is vooral in grafieken af te lezen)
Us markets are only a part of the world portfolio. International capital markets offer important
opportunities for portfolio diversification with enhanced risk-return characteristics.
Us markets is 39.2 % of all markets in 2005
Us market share is down from 49% in 2000.
For a passive strategy one could argue that a portfolio of equities of just the six countries with
the largest capitalization would make up 71.5 % in 2005 of the world portfolio and may be
sufficiently diversified. This argument will not hold for an active portfolio that seeks to tilt
investments toward promising assets. Active portfolio will naturally include many stock or even
indexes of emerging markets. Countries with larger relative capitalization of equities will tend to
be richer. The graph shows (page 901) that a 1 procent increase in the ratio of market
capitalization to GDP is associated with an increase in per capita GDP of 0.91. Countries below
this regression line such as Indonesia and Pakistan suffered from deterioration of the business
environment due to political strife and or government policies that restricted the private sector.
Home country bias
Home country bias is the excess weight of your country relative to its weight in the otherwise
efficient portfolio.
People would expect that investor would be aware of the opportunities offered by international
investing. Yet in practice investor portfolios notoriously overweight home country stock
compared to a neutral indexing strategy and underweight or even completely ignore foreign
securities
Issues
What is the risk of investing in foreign securities?
How do you measure benchmark return on foreign investments?
Are there benefits to diversification in foreign securities?
Risk factors
Opportunities in international markets do not come free with risk. Risk factors that are unique
to international investments are: exchange rate risk and country specific risk
1 Foreign Exchange rate risk is variation in the return relative to changes in the relative value of
domestic and foreign currency. The total return is the return investment return and return on
foreign exchange. It is not possible to completely hedge a foreign investment. But in the context
international portfolios exchange rate risk may be partly diversifiable. (The evidence comes from
correlation coefficient). An investor could hedge an exchange rate risk using a forward or future
contract in foreign exchange. Future and forward markets are used to eliminate the risk of
holding another asset. But a perfect hedge in not possible unless the foreign currency rate of
return is known.
Return in the US is a function of two factors:
1 return in the foreign market
2 return on the foreign exchange
2 Country specific risk
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In principle security analysis at the macroeconomic industry and firm specific level is similar in
all countries. Such analysis aims to provide estimates of expected returns and risk of individual
assets and portfolios. To achieve the same quality of information about assets in a foreign
country is by nature more difficult and hence more expensive. However the risk of coming by
false or misleading information is greater. Consider example American investors in Indonesia or
an Indonesia investor investing in America. For the American investor it is more difficult,
because the US investment environment is more transparent than that of Indonesia.
Political risk services group ratings PRS’s
Rank countries with respect to financial, economic and political risk. They assign composite
rating from very high risk to very low risk based on the above elements. They are divided into
five categories: very low risk (100-80) low risk (79.9-70) moderate risk (69.9-60), high risk (59.950) very high risk (less than 50). The composite risk rating is a weighted average of the three
measures (financial, economic, political risk). Political is measured at a scale of 100-0 en
financial and economic on scale of 50-0. The three measures are added and divided by two to
obtain the composite ratings.
Investment in emerging markets riskier
The graph shows 25.3 that investment in emerging markets is largely riskier than in developed
countries, at least as measured by volatility of returns.
Graph 25.5 shows that investing in emerging markets provided higher average return than
investing in developed countries. This data is far from conclusive since five-year averages are
subject to considerable impression. Also a higher standard deviation is not a good measure of
risk. The risk of a single market can be measured by the covariance of the overall portfolio.
Diversification benefits
A correlation coefficient of the hedged (local currency) and unhedged (us dollar) returns are
very similar, confirming that hedging currencies is not a significant issue in internationally welldiversified portfolios.
The correlation coefficients between stock indexes of one country and bond portfolios of
another are very low, suggesting that income portfolios that are balanced between stock and
bonds would greatly benefit from international diversification.
Figure 25.7 suggests that international diversification can reduce the standard deviation of a
single stock to about 12%.
The baseline technique for constructing efficient portfolios is the efficient frontier. A useful
efficient frontier is constructed from expected returns and an estimate of the covariance matrix
of returns. The benefit from this efficient diversification is reflected in the curvature of the
efficient frontier. Other things equal the lower the covariance across stocks, the greater the
curvature of the efficient frontier and the greater the risk reduction for any desired expected
return.
Recent realized returns could be highly misleading estimates of expected future returns; they
are more useful for measuring prospective risk. There are two reasons for this.
1 market efficiency implies that stock prices will be difficult to predict with any accuracy, but no
such implication applies to risk measures.
2 it is a statistical fact that errors in estimates of standard deviation and correlation from
realized data are of a lower order of magnitude than estimates of expected return. For these
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reasons, using risk estimates from realized returns does not exaggerate as much the potential
benefits from diversification. Figure 25.9 shows a realistic assessment that reveals modest but
significant benefits from international diversification using only developed countries.
The model of Roll predicts that a macroeconomic shock would affect all countries and that
diversification can only mitigate country specific events. Our best guess therefore is that the
diversification benefits shown by the world CAMP model are realistic.
In conclusion from the graphs:
1 Evidence shows diversification is beneficial.
2 It is possible to expand the efficient frontier oboes the domestic market frontier.
3 It is possible to reduce the systematic risk level below the domestic only level
Performance attribution
If we focus on an investor with a passive portfolio. Their objective is to maximize diversification
with limited expense and effort. It appears that for a passive investor, the benefits of
international diversification are not what they are commonly purported to be. Perhaps the
notorious home bias isn’t a bias at all, just a commonsense response to these sorts of results.
For active investors international investing offers greater opportunities. International investing
calls for specialization in additional fields of analysis: currency, country and worldwide industry,
as well as greater universe for stock selection.
Active and international investing as well as passive requires benchmark portfolio. One widely
used index of non-US stock is the European, Australian, Far East index computed by Morgan
Stanley Capital international.
An issue that sometimes arises in that international context is the appropriateness off marketcapitalization weighted schemes in the construction of international indexes. Capitalization
weighting is far and away the most common approach. Some argue that is might not the best
weighing scheme in an international context. This is in part because different countries have
differing proportions of their corporate sector organized at publicly trade firms.
Some argue that is would be more appropriate to weight international indexes by GDP rather
than market capitalization. The justification for this view is that an internationally diversified
portfolio should purchase shares in proportion to the broad asset base of each country, and GDP
might be a better measure of the importance of a country in the international economy that the
value of its outstanding stock
Several world market indexes can form a basis for passive international investing. Active
international investing management can be partitioned into the following:
Currency selection Asset allocation in which the investor chooses among investments
denominated in different currencies.
Country selection type of active international management that measures the contribution to
performance attributable to investing in the better-performing stock markets of the world.
Stock selection An active portfolio management technique that focuses on advantageous
selection of particular stocks rather than on broad asset allocation choices.
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Cash and bond selection Asset allocation in which the choice is between short-term cash
equivalents and longer-term bonds.
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