Financial Markets Financial Instruments Risk & Return Questionnaire

The Investment Environment
Chapter 1: The Investment Environment
1
Real Assets versus Financial Assets
 Real Assets:
 Land, buildings, machines, …
 Contribute directly to …
 Financial Assets:
 Stocks, bonds,…
 Do not contribute directly to …
 Represent claims on …
 Investors income from financial assets …
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2
1
Financial Assets
 Three types of financial assets:
 Fixed Income Securities
 Equity
 Derivatives
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3
Financial Assets

Three types of financial assets:
 Fixed Income Securities
 Debt Securities
 Pay:
 Fixed …
 Or
 … income based on …
 Provide a wide range of maturities
 Money Market Securities
 Short term
 … marketable
 Usually, low …
 Example: …
 Capital Market Securities
 Long term
 Varying risk level
 Low default risk …
 High default risk like …
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2
Financial Assets
 Three types of financial assets:
 Equity
 common stocks
 … ownership …
 Shareholders are …
 … than debt securities
 Have … liabilities
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5
Financial Assets
 Three types of financial assets:
 Derivatives
 Contingent claims
 Options, futures contracts, …
 Hedging risks: … risks …
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3
Financial Markets and the Economy
 Financial Assets allow us to make the most of the economy’s
real assets
 The Informational Role of Financial Markets
 Stock prices reflect … of a firm’s current … and future …
 The higher the price the …
 The stock market encourages …
 Stock prices reflect …
 Is the market correct all the time?
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7
Financial Markets and the Economy
 Consumption timing
 If your income exceeds your expenses, ….
 If your expenses exceeds your income, ….
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4
Financial Markets and the Economy
 Allocation of Risk
 Real assets involve …
 Financial assets allow investors to … according to … risk …
 For example:
 Firm ABC is considering building a new plant that will sell EV
 … ABC plant
 … ABC stocks
 … ABC bonds
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9
Financial Markets and the Economy
 Separation of Ownership and Management
 Smaller business are owned and m.. by the same …
 In large public corporations, ownership and management are …
 Stocks holders … board of directors
 Board of directors … management
 Management objective is to ….
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5
Financial Markets and the Economy
 Separation of Ownership and Management
 Agency problems
 Conflict of interest between managers and owners
 Factors that might minimize agency problems:
 Compensation plan to management
 BoD monitoring the management team
 Outsiders (security analysts, large institution…) monitor the
firm
 Threat of takeover
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Financial Markets and the Economy
 Corporate Governance and Corporate Ethics
 Transparency in reporting!
 Auditors … the reporting ….
 In the …, Sarbanes-Oxley Act (in 2002) … the transparency of firms’
…
 Canadian provincial regulators …
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6
The Players

There are three main players in the financial markets:
 Firms
 Net demanders of …
 They raise capital to…
 The real asset income …
 Households
 Net suppliers of …
 They purchase …
 Governments
 Borrowers or lenders
 If the government has budget deficit, …
 If they the government has budget surplus, …
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13
The Players
 Financial intermediaries:
 Corporations and governments do not sell all their … directly to
individuals.
 Financial Intermediaries:
 Pension funds
 Mutual funds
 Insurance companies
 Banks
 Investment Bankers:
 Agents to market the securities to the investing …
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7
The Players
 Financial intermediaries:
 Match supplier of capital to demanders of capital


Who are the supplier of capital?
Who are the demanders of capital?
 Example of financial intermediaries:
 Investment companies
 Insurance companies
 Characteristics of financial intermediaries:
 Pool resources
 Lend to many borrowers
 Build expertise in assessing and monitoring risk
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15
The Players
 Financial intermediaries:
 Investment Companies:
 Diversification benefit!
 Specific portfolio creations
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8
The Players
 Financial intermediaries:
 Investment Bankers:
 Firms raise their capital by …
 This is not a daily activity and as such …
 Investment bankers help firm market new issues
 … underwriters
 Primary markets
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The Players
 Financial intermediaries:
 Venture Capital and Private Equity:
 Whereas large public corporations can raise funds by hiring … and
issuing …, younger, smaller, newly established companies …
 Smaller companies, rely on:
 Bank loans
 Investors
 The equity investment in these young companies is ….
 Sources of venture capital are:
 Venture capital funds…
 Angel investors…
 Pension funds…
 Venture capital investors … active role in … of a start-up firm.
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9
Financial Markets, Assets
Classes, and Financial
Instruments
Chapter 2: Financial Markets, Assets Classes,
and Financial Instruments
1
The Money Market
 The Money Market:
 Is a subsector of the …
 Consists of very short-term debt securities that are …
 … usually sold in …
 … for individual investors to invest in …
 Money market funds …
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2
1
The Money Market
 Treasury Bills:
 T-Bills are the … money market instruments
 Government raises money by …
 … at a discount
 At the T-bills …, the holder receives … face value
 The differences between the purchase price and ultimate maturity value …
 …maturities: 3, 6, and 12 months
 The sale is conducted in an …
 Highly liquid:
 They are easily converted …
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3
The Money Market
 Certificates of Deposit (CD):
 … time deposit with a chartered bank.
 Time deposits may not be …
 The bank pays interest and principal to the depositor only …
 CDs can be sold to another investors if cash is needed
 Marketable CDs
 In Canada … bearer deposit notes (BDNs)
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4
2
The Money Market

Commercial Paper:
 Short-term unsecured debt notes
 Issued by well-known …
 … issue commercial papers instead of … directly from banks!
 Unsecured
 It means they are not …
 However, they are often … a bank line of credit
 Longer maturity commercial papers require …
 Dominated in large amounts
 This makes it hard for …
 Individual investors can …
 Commercial papers are rated by rating agency
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5
The Money Market

Banker’s Acceptance (BA):
 … an order to a bank by a bank’s customer to pay a … at a …
 The bank endorse …
 Postdated check
 Very low risk
 Traded in the secondary market
 … widely used in commercial trades because…
 … sells at a discount
 Benchmark for the Canadian Dealer Offered Rate (CDOR)
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3
The Money Market
 Eurodollars Deposits:
 US dollar denominated deposits at foreign …
 Denominated in US currency
 Eurodollars CDs:
 Issued in US dollars by a foreign …
 The advantage of Eurodollar CDs over Eurodollar deposits …
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7
The Money Market

Repos and Reverses:
 Repurchase Agreements (Repos or RPs)
 Short-term borrowing
 Usually overnight
 Used by government securities dealers
 The government securities are used as collateral making the REPOs very
safe!
 Term Repo:
 Like Repo but with longer maturities
 Reverse Repo:
 A reverse transaction as a Repos
 Short-term lending while taking government securities as collateral
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4
The Money Market

The Bank of Canada Overnight Rate and the U.S. Federal Finds Rate:
 Policy Interest Rate
 Major Canadian financial institution borrow and lend overnight funds … at
a rate targeted by the Bank of Canada
 Policy Interest Rate
 This rate affects other key interest rates in Canada …
 Fed Funds Rate
 In the US federal funds market, banks borrow and lend overnight funds …
at a rate called the federal funds rate or Fed Funds Rate
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9
The Money Market

T-Bill Yields:
 T-Bills are quoted using the bond equivalent yield.
 The bond equivalent yield is estimated using the below formula:
???? ?????????? ????? = ???? =
1,000 − ? 365
×
?
?
 Where:
 rBEY: Bond Equivalent Yield
 P: T-Bill Price
 n: number of days to maturity
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5
The Money Market

T-Bill Yields:
 Consider a $1,000 par value T-bill sold at $960 with a 182 days maturity. What
is the bond equivalent yield on the T-bill (rBEY)?
1,000 − ? 365
×
?
?
1,000 − 960 365
???? ?????????? ????? = ???? =
×
960
182
= 0.083562 = 8.3562%
???? ?????????? ????? = ???? =
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11
The Money Market

T-Bill Yields:
 Consider a $1,000 par value T-bill sold at $960 with a 182 days maturity. What
is the bond equivalent yield on the T-bill (rBEY)?
???? ?????????? ????? = ???? =
1,000 − ? 365
×
?
?
 How did we obtain the bond equivalent yield formula?
 This is from the main simple interest formula
?? = ?? (1 + ??)
?ℎ??? ? =
182
365
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6
Financial Markets, Assets
Classes, and Financial
Instruments
Chapter 2: Financial Markets, Assets Classes,
and Financial Instruments
1
The Money Market

T-Bill Yields:
 T-Bills are quoted using the bond equivalent yield.
 The bond equivalent yield is estimated using the below formula:
???? ?????????? ????? = ???? =
1,000 − ? 365
×
?
?
 Where:
 rBEY: Bond Equivalent Yield
 P: T-Bill Price
 n: number of days to maturity
2
2
1
The Money Market

T-Bill Yields:
 Consider a $1,000 par value T-bill sold at $960 with a 182 days maturity. What
is the bond equivalent yield on the T-bill (rBEY)?
1,000 − ? 365
×
?
?
1,000 − 960 365
???? ?????????? ????? = ???? =
×
960
182
= 0.083562 = 8.3562%
???? ?????????? ????? = ???? =
3
3
The Money Market

T-Bill Yields:
 Consider a $1,000 par value T-bill sold at $960 with a 182 days maturity. What
is the bond equivalent yield on the T-bill (rBEY)?
1,000 − ? 365
???? ?????????? ????? = ???? =
×
?
?
 How did we obtain the bond equivalent yield formula?
 This is from the main simple interest formula
?? = ?? (1 + ??)
?ℎ??? ? =
182
365
 Solve for r:
??
⇒
− 1 = ??
?? − ??
??
⇒
= ??
??
?? − ??
1
⇒
× =?
??
?
1,000 − 960
365
⇒
×
=?
960
182
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4
2
The Money Market

T-Bill – Effect Annual Yields:
 The Bond Equivalent yield is not the effective annual rate of return on the T-bill
(effective annual yield)!!
 To illustrate the difference, calculate the effective annual rate of return on the
previously introduced T-Bill:
 Consider a $1,000 par value T-bill sold at $960 with a 182 days maturity. What is the equivalent
effective annual yield on the T-bill?
365
1,000 182
−1
960
= 1.085313 − 1 = 0.085313 = 8.5313%
?????????? ?????? ????? =
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5
The Money Market

T-Bill – Effect Annual Yields:
 Consider a $1,000 par value T-bill sold at $960 with a 182 days maturity. What is the equivalent
effective annual yield on the T-bill?
365
1,000 182
−1
960
= 1.085313 − 1 = 0.085313 = 8.5313%
?????????? ?????? ????? =
 How did we obtain the effective annual yield formula?
 This is from the main compounding formula:
?? = ?? (1 + ?)?
?ℎ??? ? =
 Solve for r:
??
⇒
= 1+?
??
⇒
??
??
182
365
= 1+?
⇒
??
??
− 1=?
⇒
??
??
− 1=?
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6
3
The Money Market

US T-Bill Yields:
 US T-Bills are also not quoted as effective annual rates of return.
 US T-Bills are quoted using the bank discount yield.
 The bank discount yield is estimated using the below formula:
???? ???????? ????? = ???? =
1,000 − ? 360
×
1,000
?
 Where:
 rBDY: Bank Discount Yield
 P: T-Bill Price
 n: number of days to maturity
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7
The Money Market

US T-Bill Yields:
 Consider a $1,000 par value US T-bill sold at $960 with a 182 days maturity.
What is the bank discount yield on the US T-bill (rBDY)?
???? ???????? ????? = ???? =
???? ???????? ????? = ???? =
1,000 − ? 360
×
1,000
?
1,000 − 960 360
×
1,000
182
1,000 − 960 360
×
1,000
182
= 0.079121 = 7.9121%
???? ???????? ????? = ???? =
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4
The Money Market

T-Bill Yields:
 Consider a $1,000 par value T-bill with a 91 days to maturity and a 0.99% Bond
Equivalent Yield. What is the T-Bill’s market price?
???? ?????????? ????? = ???? =
1,000 − ? 365
×
?
?
????? ??? ?:
365
?
365
⇒ ???? × ? = (1,000 − ?) ×
91
91
⇒ (0.0099 × ?) ×
= (1,000 − ?)
365
⇒ ???? × ? = (1,000 − ?) ×
⇒ 0.002468 × ? = 1,000 − ?
⇒ 1.002468 × ? = 1,000
⇒ ? = $997.538
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9
The Money Market

T-Bill Yields:
 Consider a $1,000 par value T-bill with a 91 days to maturity and a 0.99% Bond
Equivalent Yield. What is the T-Bill’s market price?
⇒ ? = $997.538
 What is the effective annual yield of the above T-Bill?
365
?
?????????? ?????? ????? =
??
?
?????????? ?????? ????? =
1,000
997.538
?????????? ?????? ????? =
1,000
997.538
−1
365
91
365
91
−1
− 1 = 0.009936
= 0.9936%
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5
The Bond Market

The Bond Market:
 Long-term debt instruments
 Includes:
 Government of Canada Bonds
 Provincial Bonds
 Municipal Bonds
 Corporate Bonds
 Mortgage Securities
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The Bond Market

Government of Canada Bonds:
 Canadas or Canada Bonds
 Issued by the …
 With less that three years to maturity, the bond is considered …
 Usually pay semi-annual coupon
 The yield to maturity (YTM) of the bond is a quoted rate (QR or APR)
compounded semi-annually (the bonds pays semi-annual coupons)
 YTM is the discount rate that will …
 The bond current yield is equal to the annual income divided by the bond price
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6
The Bond Market

Inflation-Protected Bonds:
 Bonds … linked to a proxy for the cost of living
 Treasury Inflation-Protected Securities (TIPS) in US
 Real Return Bonds (RRBs) in Canada
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13
The Bond Market
 Provincial Bonds:
 Like Government of Canada Bonds (in structure)
 Are they as safe as Canada bonds?
 Corporate Bonds:
 Issue by corporations
 Like Government of Canada Bonds (in structure)
 Are they as safe as Canada bonds?
 Secured bonds …
 Unsecured bonds …
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7
The Bond Market

Municipal Bonds:
 Munis
 … by city, municipality, county,..
 They fund capital expenditure; like …
 Fully taxable (in Canada)
 Exempt from tax (federal and) in US
 Pay attention to the after-tax returns on bonds when making your investment
decision!
 r1 (1-t) vs. r2
 Where:
 r1 : return on taxable bond
 t: Investors combined federal and provincial marginal tax rate
 r2 : return on non-taxable bond (like US Munis)
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The Bond Market

International Bonds:
 Canadian-Dollar Eurobond:
 Canadian dollar denominated bond sold outside Canada (in Britain for
example)
 Maple Bonds:
 Canadian dollar denominated sold in … by …
 Yankee Bonds:
 US dollar denominated bonds sold in … by …
 Samurai bonds:
 Yen denominated bonds sold in … by …
 Bulldog Bonds:
 British pound denominated bonds sold in … by …
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8
The Bond Market

Mortgages and Mortgage-Backed Securities:
 Mortgage lenders … loans, package them, and sell …
 A mortgage-backed security (MBS) …
 The mortgage originator continues to service the loan:
 Collect principal
 Collect Interest
 The mortgage originator passes all received payment to the new …
 MBS are called …
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9
Financial Markets, Assets
Classes, and Financial
Instruments
Chapter 2: Financial Markets, Assets Classes,
and Financial Instruments
1
Equity Securities

Common Stock – Ownership Shares:
 Common stocks represent … in a corporation
 … equity securities
 Shareholders elect …
 Board of Directors …
 Managers run …
 Board of Directors oversee …
2
2
1
Equity Securities

Common Stock – Ownership Shares:
 Restricted shares
 Usually, no voting rights
 Different in benefit to shareholders …
3
3
Equity Securities

Characteristics of Common Stock:
 Residual Claim:
 In case of bankruptcy, shareholders are paid …
 Claimants’ list includes:
 …
 Limited Liability
 The maximum shareholders can lose if the firm goes bankrupt …
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2
Equity Securities

Stock Market Listing:
 TSX is the major Canadian …
 Stock listing can be obtained from:
 TSX
 Major Canadian business newspapers like.
 For the United States, …
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5
Equity Securities

Stock Market Listing:
 On TSX securities are commonly traded in lots
 100 securities, , 500 securities, and 1000 securities … depending on the
stock market price

Investors wishing to trade in smaller lots, might need to pay … commission
fees.
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3
Equity Securities

Stock Market Listing:
 Divided Yield: Annual Dividend divided by the share price
 Dividend yields vary widely across firms
 Capital Gain:
 The appreciation in the value of a stock
 Total return to a stock investor comes from:
 Dividends
 Capital Gains
?(?1 ) =
 Where:




?(?1 ) + [?(?1 ) − ?0 ]
?0
r1: expected next year return
D1: expected dividend to be received during next year
P1: expected price by the end of year 1
P0: current price
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Equity Securities

Preferred Stock:
 Preferred stock is an … investment!
 Promises the holder a fixed amount …
 Usually has … life
 Usually does not have … power
 The lack of … and the promised … makes it similar to bonds!
 However, preferred shareholder cannot sue the company if …!
 Preferred dividend are not …
 Preferred dividends are cumulative:
 Unpaid dividends cumulate …
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4
Equity Securities

Preferred Stock:
 For the corporation issuing dividend, dividend is not …
 It is not like interest paid
 70% of dividend income received from domestic corporations …
 Preferred stocks sell at lower yields than corporate bonds!
 The advantage of excluding 70% of dividend overcome the fact that
preferred shares are … than bonds!
 Investors who cannot really benefit from the 70% tax …
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9
Stock and Bond Market Indexes

Index Definition:
 An index is …
 An index … a basket of securities
 … a portfolio of securities
 Example of some indices:










Dow Jones Industrial Average (United States)
S&P 500 (United States)
S&P/TSX Composite Index (Canada)
SSE Composite Index (China)
Nikkei 225 Index (Japan)
Dax Performance Index (Germany)
FTSE 100 Index (United Kingdom)
CAC 40 Index (France)
BSE Sensex Index (India)
FTSE MIB Index (Italy)
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5
Stock and Bond Market Indexes

Index Construction:
 Index is constructed by forming …
 How the securities are weighted in …
 Generally, securities are weighted in an index using three widely used
approaches:
 Weights are proportional to the stocks total market value
 Weights are proportional to the stocks price
 Weights are equal
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11
Stock and Bond Market Indexes

Index Construction:
 Generally, securities are weighted in an index using three widely used
approaches:
 Weights are proportional to the stocks’ total market value:
?? =
?? ??
∑?
? =1 ?? ??
 Where:
?? : ????ℎ? ?? ????? ? ? ?ℎ? ?????
?? : # ?? ?ℎ??? ???????????
?? : ????? ?? ??????? ?
?: ?????? ?? ?????????? ??????? ?ℎ? ?????
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6
Stock and Bond Market Indexes

Index Construction:
 Generally, securities are weighted in an index using three widely used
approaches:
 Weights are proportional to the stocks’ price:
?? =
??
∑?
? =1 ??
 Where:
?? : ????ℎ? ?? ????? ? ? ?ℎ? ?????
?? : ????? ?? ??????? ?
?: ?????? ?? ?????????? ??????? ?ℎ? ?????
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13
Stock and Bond Market Indexes

Index Construction:
 Generally, securities are weighted in an index using three widely used
approaches:
 Weights are equal:
1
?? =
?
 Where:
?? : ????ℎ? ?? ????? ? ?? ?ℎ? ?????
?: ?????? ?? ?????????? ??????? ?ℎ? ?????
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7
Stock and Bond Market Indexes

Index Return:
 Index return is estimated using the weighted average of the returns of the securities
…:
?
????? ?????? =
?? ??
?=1
?? : ????ℎ? ?? ???????? ? ?? ?ℎ? ????? ?? ?ℎ? ????????? ?? ?????? ?
?? : ?????? ??ℎ????? ?? ???????? ? ?? ?????? ?
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15
Stock and Bond Market Indexes

Index Construction:
 To illustrate in an example, suppose we have a hypothetical portfolio formed of two
stocks: ABC and XYZ with the below description:
Stock
Initial Price
# Shares
Return
ABC
$30
25 Millions
10%
XYZ
$60
5 Millions
5%
 The value of the index under the three previous scenarios:
 Market Value weighted Index:
25 × 30
= 0.7143 = 71.43%
(25 × 30) + (5 × 60)
5 × 60
=
= 0.2857 = 28.57%
(25 × 30) + (5 × 60)
???? =
????
????? ?????? = (???? × ???? ) + (???? × ???? )
????? ?????? = (0.7143 × 10%) + (0.2857 × 5%)
???? ?????? = (0.7143 × 10%) + (0.2857 × 5%)
= 8.5715%
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8
Stock and Bond Market Indexes

Index Construction:
 To illustrate in an example, suppose we have a hypothetical portfolio formed of two
stocks: ABC and XYZ with the below description:
Stock
Initial Price
# Shares
Return
ABC
$30
25 Millions
10%
XYZ
$60
5 Millions
5%
 The value of the index under the three previous scenarios:
 Price weighted Index:
???? =
???? =
30
= 0.3333 = 33.33%
30 + 60
60
= 0.6667 = 66.67%
30 + 60
????? ?????? = (???? × ???? ) + (???? × ???? )
????? ?????? = (0.3333 × 10%) + (0.6667 × 5%)
????? ?????? = (0.3333 × 10%) + (0.6667 × 5%)
= 6.6665%
17
17
Stock and Bond Market Indexes

Index Construction:
 To illustrate in an example, suppose we have a hypothetical portfolio formed of two
stocks: ABC and XYZ with the below description:
Stock
Initial Price
# Shares
Return
ABC
$30
25 Millions
10%
XYZ
$60
5 Millions
5%
 The value of the index under the three previous scenarios:
 Equal Weight:
???? = ???? =
????? ?????? = (????
1 1
= = 0.5
? 2
× ???? ) + (???? × ???? )
????? ?????? = (0.5 × 10%) + (0.5 × 5%)
????? ?????? = (0.5 × 10%) + (0.5 × 5%) = 7.50%
18
18
9
Stock and Bond Market Indexes

Price Return vs. Total Return:
 Index return is estimated using the weighted average of the returns of the securities
forming the index:
?
????? ?????? =
?? ??
?=1
 We can estimate individual securities returns as (Price Return):
?? =
??,? − ??,?−1
??,?−1
?? : ?????? ??ℎ????? ?? ???????? ? ?? ?????? ?
??,? : ????? ?? ???????? ? ?? ?ℎ? ??? ?? ?????? ?
??,?−1 : ????? ?? ???????? ? ?? ?ℎ? ??? ?? ?????? ? − 1
19
19
Stock and Bond Market Indexes

Price Return vs. Total Return:
 Index return is estimated using the weighted average of the returns of the securities
forming the index:
?
????? ?????? =
?? ??
?=1
 We can estimate individual securities returns as (Total Return):
?? =
??,? + (??,? − ??,?−1 )
??,?−1
?? : ?????? ??ℎ????? ?? ???????? ? ?? ?????? ?
??,? : ???????? ?????? ?? ???????? ? ?? ?????? ?
??,? : ????? ?? ???????? ? ?? ?ℎ? ??? ?? ?????? ?
??,?−1 : ????? ?? ???????? ? ?? ?ℎ? ??? ?? ?????? ? − 1
20
20
10
Stock and Bond Market Indexes

Toronto Stock Exchange Indexes:
 S&P/TSX Composite Index is Canada best-known …
 250 stocks
 Largest securities on TSX
 Market value-weighted
 The return on the index is price based
21
21
Stock and Bond Market Indexes

Dow Jones Averages:
 Dow Jones Industrial Average (DJIA)
 In the United States
 30 large corporation
 Since 1896
 Price weighted index
 The return on the index is price based
22
22
11
Stock and Bond Market Indexes

Standard and Poor’s U.S. Indexes:
 Standard & Poor’s Composite 500 (S&P 500) stock index
 500 firms
 Market value weighted index
 The return on the index is price based
23
23
Stock and Bond Market Indexes

Free float:
 In the weighting process:
 … the total shares outstanding
 Only … free float shares
 Free float shares:
 Shares freely …
24
24
12
Stock and Bond Market Indexes

Advantage of market-value-weighted and price-weighted index:
 Ease of replication:
 Market-value-weighted index:
 Price-weighted index:
 Equal-weighted index:
 Index Funds:
25
25
Stock and Bond Market Indexes
 Other US Indexes:
 New York Stock Exchange (NYSE)
 Market value weighted
 All NYSE …
 National Association of Securities Dealers (NASDAQ)
 3,000 securities
26
26
13
Stock and Bond Market Indexes
 Bond Market Indicators:
 Like stock indexes …
 Infrequent trading…
 Example of bond index in Canada:
 FTSE/TMX Bond Universe
 S&P Aggregate Canadian bond index
27
27
Derivative Markets
 Derivative Markets:
 Instruments that provide a payoff that depends on …
 Commodity prices, bonds, stocks, market index, …
 Also called contingent claims
28
28
14
Derivative Markets

Call Options:
 Give the holder the right but not the obligation to …

Put Options:
 Give the holder the right but not the obligation to …

LEAPS:
 Most traded call and put options are less … in maturity!
 LEAPS are options with longer maturities
 …
 Long-term Equity Anticipation Securities
29
29
Derivative Markets
 European Options
 American Options
 Option Terms:
 Price
 Maturity or expiration date
 Strike
 Who trades in options?
30
30
15
Derivative Markets

Futures Contract:
 An agreement to buy or sell ..
 Futures are traded at exchanges:
 Montreal Exchange (MX)
 CME Group
31
31
Derivative Markets
 Futures Contracts:
 Long Futures Position
 Short Futures Position
 Who uses Futures Contracts?
32
32
16
Derivative Markets
 A person long a futures contract has
the …
 A person long a call option contract
has the …
 It costs … to enter a futures contract
 It costs … to enter an option contract
33
33
Derivative Markets


Other Derivative Assets:
Warrants:
 Similar to Call options
 Longer maturities
 … the holder receive the shares from the firm itself …

Swaps:
 Agreement between two counterparties to exchange …
34
34
17
How Securities Are Traded
Chapter 3: How Securities Are Traded
1
How Firms Issue Securities

How Firms Issue Securities:
 To raise money, firms can:
 Borrow money
 Sell shares in the firm
 Investment Bankers
 Primary Markets
 Secondary Markets
2
2
1
How Firms Issue Securities
 Privately Held Firms:
 Smaller number of shareholders
 Less obligation to publish financial statements
 Private placement
 Shares in a privately held firms:
 Do not trade on an exchange
 Lack Liquidity
 Equity Crowdfunding
3
3
How Firms Issue Securities
 Publicly Traded Companies:
 Initial Public Offering (IPO)
 Seasoned New Issue
 Investment dealer
 Role of investment dealer
4
4
2
How Firms Issue Securities

Initial Public Offering:
 Managed by investment bankers
 Preliminary prospectus
 Road shows
5
5
How Securities Are Traded


Types of Markets and Orders:
Types of Markets:
 Direct Search Markets
 Brokered Markets
 Dealer Markets
 Auction Markets
6
6
3
How Securities Are Traded


Types of Markets and Orders:
Type of Orders:
 Market Orders
 Price-Contingent Orders
 Limit buy order
 Limit sell order
 Limit order book
 Stop-loss order
 Stop-buy orders
7
7
How Securities Are Traded




Trading Mechanism:
Over-the-Counter Dealer Markets
Electronic Communication Networks (ECNs)
Specialist Markets
8
8
4
How Securities Are Traded
 The Execution of Trades:
 The registered trader:
 Asymmetric information
 The Rise of Electronic Trading:
9
9
How Securities Are Traded

Securities Markets:
 TMX Group:
 Toronto Stock Exchange (TSX):
 Venture Exchange
 Montreal Exchange
10
10
5
How Securities Are Traded

The Bond Markets:
 Over the Counter
 Candeal
 Liquidity
11
11
How Securities Are Traded
 The U.S. Markets:
 NASDAQ
 NYSE
 ECNs:
 Latency
12
12
6
How Securities Are Traded

New Trading Strategies:
 Algorithmic trading
 High frequency trading
 Dark pools
13
13
Trading Costs
 Trading Costs:
 Direct trading costs
 Commission to brokers
 Full-service brokers
 Discount brokers (basic service only)
 Indirect trading costs
 Bid-ask spread
14
14
7
Trading with Margin and Short Sales
 Trading with Margin:
 Trading with margin:
 Investors purchase securities without paying the full price!
 Investors engage in a short sale transaction
 Investors trade in derivatives
15
15
Trading with Margin and Short Sales

Buying on Margin:
 Investors purchasing stocks on margin, borrow …
 The margin account is the …
 The brokers charge the clients …
 All securities purchased on margin must be … collateral for the loan
 Regulations require a 30% margin
 i.e.: 70% of the purchase price might be borrowed
 Brokers will require higher margin!
 Typically, a 50% margin!
 The percentage margin (or Margin Ratio):
?????? ????? =
?????? ????? ?? ?????? − ???? ?????
?????? ????? ?? ??????
16
16
8
Trading with Margin and Short Sales

Buying on Margin – an example:
 Suppose an investor want to purchase 100 ABC stocks. Stock ABC is currently
traded at $150 per share. The investor has only $10,000 and want to borrow the
remaining amount from the broker (buying on Margin).
 What is the initial percentage margin?
 Total stock price = 100 x $150 = $15,000.
 Amount borrowed = $15,000 – $10,000 = $5,000.
?????? ????? =
?????? ????? ?? ?????? − ???? ?????
?????? ????? ?? ??????
?????? ????? =
$15,000 − $5,000 $10,000
=
= 66.67%
$15,000
$15,000
17
17
Trading with Margin and Short Sales

Buying on Margin – an example:
 Suppose an investor want to purchase 100 ABC stocks. Stock ABC is currently
traded at $150 per share. The investor has only $10,000 and want to borrow the
remaining amount from the broker (buying on Margin).
 If the stock price declines to $100, what will be the new margin ratio?
?????? ????? =
?????? ????? ?? ?????? − ???? ?????
?????? ????? ?? ??????
?????? ????? =
$10,000 − $5,000
$5,000
=
= 50%
$10,000
$10,000
18
18
9
Trading with Margin and Short Sales

Buying on Margin – an example:
 Suppose an investor want to purchase 100 ABC stocks. Stock ABC is currently
traded at $150 per share. The investor has only $10,000 and want to borrow the
remaining amount from the broker (buying on Margin).
 Given that the minimum margin requirement is a 30% margin ratio. What is the
maximum level that stock price can drop into without triggering a margin call?
?????? ????? =
?????? ????? ?? ?????? − ???? ?????
?????? ????? ?? ??????
?????? ????? =
(? × ?) − $5,000
= 30%
(? × ?)
(100 ?) − $5,000
= 30%
(100 ?)
????? ??? ?: 100 ? − $5,000 = 0.3 (100 ?)
?????? ????? =
100 ? = 30 ? + $5,000
70 ? = $5,000
? = $$71.4286
19
19
Trading with Margin and Short Sales

Buying on Margin – an example:
 Suppose an investor want to purchase 100 ABC stocks. Stock ABC is currently
traded at $150 per share. The investor has only $10,000 and want to borrow the
remaining amount from the broker (buying on Margin).
 Why do investors buy on margin?
 Calculate investors return if the stock price is $200 after one year. Assume the
broker will charge the investors 10% interest per year on the loan.
?????? ??ℎ?????
(?????? ????? ?? ???????=1 − ???????? ?????=1 − ???? ??????) − ??????? ?????? ????0
=
??????? ?????? ????0
?????? ??ℎ????? =
?????? ??ℎ????? =
( ? × ?1 − ? − ???? ??????) − $10,000
$10,000
( 100 × $200 − $5,000 × 0.1 − $5,000) − $10,000
$10,000
= 45%
20
20
10
Trading with Margin and Short Sales

Buying on Margin – an example:
 Suppose an investor want to purchase 100 ABC stocks. Stock ABC is currently
traded at $150 per share. The investor has only $10,000 and want to borrow the
remaining amount from the broker (buying on Margin).
 Why do investors buy on margin?
 Calculate investors return if the stock price is $200 after one year. Assume the
investor did not buy on margin and she manages to purchase with whatever
money she has?
?????? ??ℎ????? =
($13,333.33 − $10,000
= 33.33%
$10,000
21
21
Trading with Margin and Short Sales

Buying on Margin – an example:
 Suppose an investor want to purchase 100 ABC stocks. Stock ABC is currently
traded at $150 per share. The investor has only $10,000 and want to borrow the
remaining amount from the broker (buying on Margin).
 Why do investors buy on margin?
 Calculate investors return if the stock price is $100 after one year. Assume the
broker will charge the investors 10% interest per year on the loan.
?????? ??ℎ?????
(?????? ????? ?? ???????=1 − ???????? ?????=1 − ???? ??????) − ??????? ?????? ????0
=
??????? ?????? ????0
?????? ??ℎ????? =
?????? ??ℎ????? =
( ? × ?1 − ? − ???? ??????) − $10,000
$10,000
( 100 × $100 − $5,000 × 0.1 − $5,000) − $10,000
$10,000
= −55%
22
22
11
Trading with Margin and Short Sales

Buying on Margin – an example:
 Suppose an investor want to purchase 100 ABC stocks. Stock ABC is currently
traded at $150 per share. The investor has only $10,000 and want to borrow the
reamaining amount from the broker (buying on Margin).
 Why do investors buy on margin?
 Calculate investors return if the stock price is $100 after one year. Assume the
investor did not buy on margin and she manages to purchase with whatever
money she has?
?????? ??ℎ????? =
$6,666.67 − $10,000
= −33.33%
$10,000
23
23
Trading with Margin and Short Sales

Short Sales – an example:
 Suppose you tell your broker to sell short 1,000 stock ABC. Currently, ABC is
selling at $100. The broker requires a 40% initial margin.
 How much cash or cash equivalent, do you have to deposit with your broker?
?????? ????? ?? ??????
?????? ????? =
????? ?? ?????? ????
????? ?? ?????? ???? + ?????? ??????
?????? ????? =
????? ?? ?????? ????
?????? ????? =
????? ?? ?????? ???? + ?????? ??????
= 140%
????? ?? ?????? ????
?????? ????? =
????? ??? ?????? ??????:
1,000 × $100 + ?????? ??????
= 140%
1,000 × $100
$100,000 + ?????? ??????
= 140%
$100,000
$100,000 + ?????? ?????? = 1.4 × $100,000 = $140,000
?????? ?????? = $40,000
24
24
12
Trading with Margin and Short Sales

Short Sales – an example:
 Suppose you tell your broker to sell short 1,000 stock ABC. Currently, ABC is
selling at $100. The broker requires a 40% initial margin.
 If the minimum margin is 30%, up to what level the stock price should increase
before you receive a margin call?
?????? ????? =
????? ?? ?????? ???? + ?????? ??????
= 130%
????? ?? ?????? ????
1,000 × $? + $40,000
= 130%
1,000 × $?
????? ??? ?:
?????? ????? =
1,000 × $? + $40,000
= 130%
1,000 × $?
1,000 × $? + $40,000 = 1.3 × 1,000 × $?
1,000 × $? + $40,000 = 1,300 × $?
300 × $? = $40,000
? = $133.333
25
25
13
Risk, Return, and the
Historical Record
Chapter 5: Risk, Return, and the Historical
Record
1
Comparing Rates of Return for Different
Holding Periods
 Effective Rate per period:
???? =




???
1+
?
?
?
− 1
reff: effective rate for our period
APR: Quoted Rate (compounded rate)
m: number of compounding period per year
f: frequency of payments per year
??? = 1 +
 Effective Annual rate (f = 1):
???
?
?
− 1
2
2
1
Comparing Rates of Return for Different
Holding Periods
 Effective Rate per period:
???? =
???
1+
?
?
?
− 1
 What is the effective monthly rate of
5% compounded monthly?
 What is the effective semi-annual rate
of 5% compounded monthly?
3
3
Comparing Rates of Return for Different
Holding Periods
 Effective Annual Rate if the APR is
continuously compounded:
??? = ? ? ?? − 1
 e  2.71828
 Example: What is the effective annual rate
of 5% compounded continuously…
 EAR =
4
4
2
Comparing Rates of Return for Different
Holding Periods
 Effective Annual Rate if the APR is
continuously compounded:
??? = ? ? ?? − 1
 e  2.71828
 Example: What is the effective annual rate
of 5% compounded continuously…
 EAR = 5.1271%, or 6.4%?
5
5
Risk and Risk Premiums

Holding Period Return (HPR)
??????? ?????? ?????? = ???
?????? ????? ?? ? ?ℎ??? − ????????? ????? + ???ℎ ????????
=
????????? ?????
6
6
3
Risk and Risk Premiums

Holding Period Return (HPR)

Gross Return:
??+1 =
 Rt+1 … ; Pt+1 …; Pt …;

??+1 + ??+1
??
Net Return:
??+1 =
? ?+1 + (??+1 −?? )
??
=
? ?+1
??
+
(?? +1 −?? )
??
= ??+1 − 1
??+1 = Income Yield + Capital Gain/Loss
 Income Yield: Cash payout received by investors (dividend, coupon)
 Capital Gain/Loss: Change in security price
 Rt+1, rt+1 are also called realized return
7
7
Risk and Risk Premiums

Holding Period Return (HPR)

Example: Suppose you have bought a share for $100. At the end of the
year, it pays $3 dividend and sells for $105. Calculate the Gross Return and
Net Return, Income Yield and Capital Gains Yield….
8
8
4
Risk and Risk Premiums

Holding Period Return (HPR) (Expected Return)

For some instruments, we don’t know the income nor the price of the assets in the
future!

In such cases we use expected returns instead of realized returns!

Expected Gross Return:

Expectation are highly influenced by the information set available to investors!
?? (??+1 ) =

Expected Net Returns:
?? (??+1 ) + ?? (??+1 )
??
?? (??+1 ) =
(?? (??+1 ) − ?? )
?? (??+1 )
+
??
??
9
9
Risk and Risk Premiums

Holding Period Return (HPR) (Expected Return)

For some instruments, we don’t know the income nor the price of the assets in the
future!

In such cases we use expected returns instead of realized returns!

Expected Gross Return:

Expectation are highly influenced by the information set available to investors!
?? (??+1 ) =

Expected Net Returns:
?? (??+1 ) + ?? (??+1 )
??
(?? (??+1 ) − ?? )
?? (??+1 )
+
??
??
What are the factors affecting our expectations?
?? (??+1 ) =

10
10
5
Risk and Risk Premiums

Holding Period Return (HPR) (Expected Return)

For some instruments, we don’t know the income nor the price of the assets in the
future!

In such cases we use expected returns instead of realized returns!

Expected Gross Return:

Expectation are highly influenced by the information set available to investors!
?? (??+1 ) =

Expected Net Returns:
?? (??+1 ) + ?? (??+1 )
??
(?? (??+1 ) − ?? )
?? (??+1 )
+
??
??
What are the factors affecting our expectations?
?? (??+1 ) =


Past returns, past information, fluctuation in response to news and macroeconomic developments
11
11
Risk and Risk Premiums
 Gross return over two years:
 Case A: We invest the dividend in period 1
at zero rate (we don’t invest the dividend)
??+2 (??? ???????) =
??+1 + ??+2 + ??+2
??
12
12
6
Risk and Risk Premiums
 Gross return over two years:
 Case B: We reinvest the dividend in the same investment
instrument:
??+1
× (??+2 + ??+2 ) + ??+2 + ??+2
?
??+2 (??? ???????) = ?+1
??
??+1
+ 1 × (??+2 + ??+2 )
?
= ?+1
??
??+1 + ??+1
??+2 + ??+2
=
×
??+1
??
??+1 + ??+1
??+2 + ??+2
=
×
= ??+1 × ??+2
??
??+1
 Leading to the compounding formula!
(1 + ??+2 (??? ??????? ??????) = (1 + ??+1 ) × (1 + ??+2 )
13
13
Time Series Analysis of Past Rate of Returns
 Also Called Arithmetic Mean
????ℎ????? ??????? (??) =
∑??=1 ??
?
 ri: Individual Returns
 n: number of returns included in our
estimation (number of observations)
14
14
7
Time Series Analysis of Past Rate of Returns
 Also Called Arithmetic Mean
 What is the Arithmetic Mean of : 1%,
2%, 3%, 4%, and 5%:
????ℎ????? ??????? (??) =
∑??=1 ?? 1 + 2 + 3 + 4 + 5
=
=3
?
5
15
15
Time Series Analysis of Past Rate of Returns
1
????????? ???? (??) = [(1 + ?1 )(1 + ?2 )(1 + ?3 ) … (1 + ?? )]? − 1
 ri: Individual Returns
 n: number of returns included in our
estimation (number of observations)
16
16
8
Time Series Analysis of Past Rate of Returns
1
????????? ???? (??) = [(1 + ?1 )(1 + ?2 )(1 + ?3 ) … (1 + ?? )]? − 1
 What is the Geometric Mean of : 1%, 2%, 3%, 4%, and 5%:
17
17
Time Series Analysis of Past Rate of Returns
1
????????? ???? (??) = [(1 + ?1 )(1 + ?2 )(1 + ?3 ) … (1 + ?? )]? − 1
 What is the Geometric Mean of : 1%, 2%,
3%, 4%, and 5%:
????????? ???? (??)
1
= [(1 + 0.01)(1 + 0.02)(1 + 0.03)(1 + 0.04)(1 + 0.05)]5 − 1
= 2.99%
 N.B.: Note that the GM (2.99%) is less
than the AM (3%). The more the variation
in the returns the more the GM will differ
from the AM.
18
18
9
Time Series Analysis of Past Rate of Returns
 Geometric vs. Arithmetic Average (illustrative
example):
 Suppose you have observed the returns below for
Year
ABC Observed
stock ABC:
2005
2006
2007
2008
2009
2010
Arithmetic Average
Geometric Average
Value of $1 by end 2010 if
invested at the beginning of
2005
Return
10%
5%
15%
0%
-55%
-5%
-5%
-9.001%
$0.5678
?
19
19
Time Series Analysis of Past Rate of
Returns
 Geometric vs. Arithmetic Average:
 Arithmetic Average:
????ℎ????? ??????? (??) =
 Geometric Average:
1
?
?
????????? ??????? =
∑??=1 ??
?
(1 + ?(?) )
−1
?=1
 Geometric Vs. Arithmetic:
 Use Arithmetic Average if you want to predict future
expected next period return
 Use Geometric Average to estimate the average one period
return achieved on your investment
 Geometric Average is always less than Arithmetic Average
20
20
10
Time Series Analysis of Past Rate of
Returns

Arithmetic Average:
?
????ℎ????? ??????? =
?(?)?(?)
?=1
??
????ℎ????? ??????? =
1
?
?
?(?)
?=1
21
21
Time Series Analysis of Past Rate
of Returns
 The previous calculation of AM was based
on past data:
 We rely on past data to calculate the AM and
then rely on the obtained average to estimate
what should be next period(s) returns
 What if the past would not likely be
repeated in the future, like:
 Internet bubble
 The 2008 market crash
22
22
11
Time Series Analysis of Past Rate
of Returns
 To make our estimation more accurate we associate a
future expected probability for each past returns
 In case we have 10 historical returns. We need to associate
each return with a probability of future occurrence
 Since we have 10 returns, we need to estimate 10 expected
probabilities of occurrence
 The sum of the ten probabilities should add to one
 For example, we associate a low probability for the returns
achieved during the internet bubble knowing that it is
unlikely to have another internet bubble in the near future.
 The future expected returns obtained relying on this
method is simply called Expected Return (ER)
 We calculate expected return (ER) relying on the below
formula:
?
?? =
?=1
(?? × ????? )
E (r ) 

p (s)r (s)
s
23
23
Time Series Analysis of Past Rate
of Returns
State of the
Economy
Probability of
Occurrence
Expected
Return on
Stock A in this
State
High growth
0.1
50%
Medium growth
0.2
25%
No Growth
0.4
10%
Economic
slowdown
0.2
5%
Recession
0.1
-5%
ER=?
24
24
12
Risk, Return, and the
Historical Record
Chapter 5: Risk, Return, and the Historical
Record
1
Determinants of Interest Rates
 Interest rates are the most important
macroeconomic measure
 Forecasting interest rates determines
the expected return in the market
5-2
2
1
Determinants of Interest Rates:
Real and Nominal Rates of Returns
 HPR are nominal returns!
 To account for inflation (loss of purchasing
power of money) we need to work with real
returns
(1 + ???????? )
(1 + ????? ) =
(1 + ?)
→ ????? = ???????? − ?
 The returns we observe (achieve in case of
investing) are nominal returns
 These returns are affected by several factors:
3
3
Determinants of Interest Rates:
Real and Nominal Rates of Returns
 Nominal interest rate:


The promised rate of return over some period of
time in some unit of account
Growth rate of your money
 Real interest rate: growth rate of PP
rnom  Nominal Interest Rate
rreal  Real Interest Rate
i  Inflation Rate
rnom  i
1 i
Note : rreal  rnom  i
rreal 
5-4
4
2
Determinants of Interest Rates:
The Equilibrium Real Rate of Interest
Fundamental factors to determine level of IR:

Supply of funds from





Savers, primarily households
Demand of funds from
Businesses
Government’s Net Supply and/or Demand

Central Bank Actions (monetary actions) and Fiscal policy
The expected rate of inflation: uncertainty about measures of
purchasing power measured by CPI
5-5
5
Determinants of Interest Rates:
The Equilibrium Real Rate of Interest
Source: Chapter 5 – Bodie, Kane, Marcus, Switzer, Boyko, Panasian, and
Stapleton: Investments, 9th Canadian Edition, McGraw-Hill, 2019.
5-6
6
3
Determinants of Interest Rates:
The Equilibrium Nominal Rate of Interest
 As the inflation rate increases, investors
will demand higher nominal rates of
return
 If E(i) denotes current expectations of
inflation, then we get the Fisher Equation:
rnom  rreal  E i 
 If nominal rate = 7% and i=3% then real
rate =?
5-7
7
Determinants of Interest Rates:
Taxes and the Real Interest Rate
 Tax liabilities are based on nominal income
rnom  Nominal Interest Rate
rreal  Real Interest Rate
i  Inflation Rate
t  Tax Rate
rnom  1  t   i  r real  i   1  t   i  rreal 1  t   i  t
 The after-tax real rate falls as the inflation rises
and as tax rate rises!
5-8
8
4
Determinants of Interest Rates:
Taxes and the Real Interest Rate







An Example:
IR nom = Rnom = 0.12
Inf = i = 0.08
Then Rreal = ?
If no tax:

Rreal = Rnom – i = 0.12 – 0.08 = 0.04
If t=0.3:

After-tax Rnom = Before-tax Rnom x (1-Tax)

After-tax Rnom = 0.12 (1 – 0.3)= 8.4%

After-tax Rreal = After-tax Rnom – i

After-tax Rreal = 8.4%-8%=0.4%!
Investors are suffering with inflation! Because technically, After-Tax Real
return should have been:

After-Tax Rreal = Before-Tax Rreal x (1-Tax) = 0.04 (1-0.3) = 0.028 =
2.8%

The After-Tax Real Return has fallen by (i x t) (2.4%) because of
inflation!
5-9
9
Comparing Rates of Return for Different
Holding Periods
 Effective Rate per period:
???? =




???
1+
?
?
?
− 1
reff: effective rate for our period
APR: Quoted Rate (compounded rate)
m: number of compounding period per year
f: frequency of payments per year
??? = 1 +
 Effective Annual rate (f = 1):
???
?
?
− 1
10
10
5
Comparing Rates of Return for Different
Holding Periods
 Effective Rate per period:
???? =
???
1+
?
?
?
− 1
 What is the effective monthly rate of
5% compounded monthly?
 What is the effective semi-annual rate
of 5% compounded monthly?
11
11
Comparing Rates of Return for Different
Holding Periods
 Effective Annual Rate if the APR is
continuously compounded:
??? = ? ? ?? − 1
 e  2.71828
 Example: What is the effective annual rate
of 5% compounded continuously…
 EAR = 5.1271%, or 6.4%?
12
12
6
Risk and Risk Premiums

Holding Period Return (HPR)
??????? ?????? ?????? = ???
?????? ????? ?? ? ?ℎ??? − ????????? ????? + ???ℎ ????????
=
????????? ?????
13
13
Risk and Risk Premiums

Holding Period Return (HPR)

Gross Return:
??+1 =
 Rt+1 … ; Pt+1 …; Pt …;

??+1 + ??+1
??
Net Return:
??+1 =
? ?+1 + (??+1 −?? )
??
=
? ?+1
??
+
(?? +1 −?? )
??
= ??+1 − 1
??+1 = Income Yield + Capital Gain/Loss
 Income Yield: Cash payout received by investors (dividend, coupon)
 Capital Gain/Loss: Change in security price
 Rt+1, rt+1 are also called realized return
14
14
7
Risk and Risk Premiums

Holding Period Return (HPR)


Example: Suppose you have bought a share for $100. At the end of the
year, it pays $3 dividend and sells for $105. Calculate the Gross Return and
Net Return, Income Yield and Capital Gains Yield….
15
15
Risk and Risk Premiums

Holding Period Return (HPR) (Expected Return)

For some instruments, we don’t know the income nor the price of the assets in the
future!

In such cases we use expected returns instead of realized returns!

Expected Gross Return:

Expectation are highly influenced by the information set available to investors!
?? (??+1 ) =

Expected Net Returns:
?? (??+1 ) + ?? (??+1 )
??
(?? (??+1 ) − ?? )
?? (??+1 )
+
??
??
What are the factors affecting our expectations?
?? (??+1 ) =


Past returns, past information, fluctuation in response to news and macroeconomic developments
16
16
8
Risk and Risk Premiums
 Gross return over two years:
 Case A: We invest the dividend in period 1
at zero rate (we don’t invest the dividend)
??+2 (??? ???????) =
??+1 + ??+2 + ??+2
??
17
17
Risk and Risk Premiums
 Gross return over two years:
 Case B: We reinvest the dividend in the same investment
instrument:
??+1
× (??+2 + ??+2 ) + ??+2 + ??+2
?
??+2 (??? ???????) = ?+1
??
??+1
+ 1 × (??+2 + ??+2 )
?
= ?+1
??
??+1 + ??+1
??+2 + ??+2
=
×
??+1
??
??+1 + ??+1
??+2 + ??+2
=
×
= ??+1 × ??+2
??
??+1
 Leading to the compounding formula!
(1 + ??+2 (??? ??????? ??????) = (1 + ??+1 ) × (1 + ??+2 )
18
18
9
Time Series Analysis of Past Rate of Returns
 Also Called Arithmetic Mean
????ℎ????? ??????? (??) =
∑??=1 ??
?
 ri: Individual Returns
 n: number of returns included in our
estimation (number of observations)
19
19
Time Series Analysis of Past Rate of Returns
 Also Called Arithmetic Mean
 What is the Arithmetic Mean of : 1%,
2%, 3%, 4%, and 5%:
????ℎ????? ??????? (??) =
∑??=1 ?? 1 + 2 + 3 + 4 + 5
=
=3
?
5
20
20
10
Time Series Analysis of Past Rate of Returns
1
????????? ???? (??) = [(1 + ?1 )(1 + ?2 )(1 + ?3 ) … (1 + ?? )]? − 1
 ri: Individual Returns
 n: number of returns included in our
estimation (number of observations)
21
21
Time Series Analysis of Past Rate of Returns
1
????????? ???? (??) = [(1 + ?1 )(1 + ?2 )(1 + ?3 ) … (1 + ?? )]? − 1
 What is the Geometric Mean of : 1%, 2%,
3%, 4%, and 5%:
????????? ???? (??)
1
= [(1 + 0.01)(1 + 0.02)(1 + 0.03)(1 + 0.04)(1 + 0.05)]5 − 1
= 2.99%
 N.B.: Note that the GM (2.99%) is less
than the AM (3%). The more the variation
in the returns the more the GM will differ
from the AM.
22
22
11
Time Series Analysis of Past Rate of Returns
 Geometric vs. Arithmetic Average (illustrative
example):
 Suppose you have observed the returns below for
Year
ABC Observed
stock ABC:
2005
2006
2007
2008
2009
2010
Arithmetic Average
Geometric Average
Value of $1 by end 2010 if
invested at the beginning of
2005
Return
10%
5%
15%
0%
-55%
-5%
-5%
-9.001%
$0.5678
23
23
Time Series Analysis of Past Rate of
Returns
 Geometric vs. Arithmetic Average:
 Arithmetic Average:
????ℎ????? ??????? (??) =
 Geometric Average:
1
?
?
????????? ??????? =
∑??=1 ??
?
(1 + ?(?) )
−1
?=1
 Geometric Vs. Arithmetic:
 Use Arithmetic Average if you want to predict future
expected next period return
 Use Geometric Average to estimate the average one period
return achieved on your investment
 Geometric Average is always less than Arithmetic Average
24
24
12
Time Series Analysis of Past Rate of
Returns

Arithmetic Average:
?
????ℎ????? ??????? =
?(?)?(?)
?=1
??
????ℎ????? ??????? =
1
?
?
?(?)
?=1
25
25
Time Series Analysis of Past Rate
of Returns
 Both AM and GM are based on past data:
 We rely on past data to calculate the AM and
then we rely on the obtained average to
estimate what should be next period(s)
returns
 What if the past would not likely be
repeated in the future
 Like the internet bubble
 The 2008 market crash
26
26
13
Time Series Analysis of Past Rate
of Returns
 To make our estimation more accurate we associate a
future expected probability for each past returns
 In case we have 10 historical returns. We need to associate
each return with a probability of future occurrence
 Since we have 10 returns, we need to estimate 10 expected
probabilities of occurrence
 The sum of the ten probabilities should add to one
 For example, we associate a low probability for the returns
achieved during the internet bubble knowing that it is
unlikely to have another internet bubble in the near future.
 The future expected returns obtained relying on this
method is simply called Expected Return (ER)
 We calculate expected return (ER) relying on the below
formula:
?
?? =
?=1
(?? × ????? )
E (r ) 

p (s)r (s)
s
27
27
Time Series Analysis of Past Rate
of Returns
State of the
Economy
Probability of
Occurrence
Expected
Return on
Stock A in this
State
High growth
0.1
50%
Medium growth
0.2
25%
No Growth
0.4
10%
Economic
slowdown
0.2
5%
Recession
0.1
-5%
ER=?
?
?? =
?=1
(?? × ????? )
= 0.1 × 50% + 0.2 × 25% + 0.4 × 10% + 0.2 × 5% + 0.1 × (−5%)
= 14.5%
28
28
14
Time Series Analysis of Past Rate of Returns
 Measuring Risk (SD):
 Risk is defined as the probability of not achieving the desired
return!
 Standard Deviation is a measure of the variation of the returns
 The more the standard deviation the bigger is the returns’
variation
 The bigger the returns’ variation, the bigger the returns vary,
the larger are the chances that the realized returns are below
what you desire. Hence the bigger the risk!
 That is why Standard deviation is considered as a quick
measure of RISK.
 The larger the standard deviation the larger the risk
29
29
Time Series Analysis of Past Rate of Returns
 Measuring Risk (SD):


Standard Deviation may be expressed as: SD or  or Volatility or
Vol or Sigma
Standard deviation is calculated relying on the following formula:
Observation
‘i’ Return
??? −???? = ? =
Standard
Deviation

∑??=1(?? − ?̅ )2
?−1
Average of
the returns
in your
sample
number of
observations
We call the above Standard deviation ex-post because we are not
associating probability with each ‘i’ return observation
30
30
15
Measuring Risk (SD)

Ex-ante Standard deviation is calculated relying on the following formula:
number of
observations
Standard
Deviation
?
(????? )(?? − ?̅ )2
??? −???? =
?=1
Average of
the returns in
your sample
Observation
‘i’ Return

We call the above Standard deviation ex-ante because we are associating an
expected future probability of occurrence with each return ‘i’
31
31
Time Series Analysis of Past Rate of Returns
 Measuring Risk (SD, example):
 Calculate the SD of the below returns: 1%,
2%, 3%, 4%, and 5%?
 The AM was found to be 3
??? −???? = ? =
∑??=1(?? − ?̅ )2
?−1
??? −???? = ?
=
(0.01 − 0.03)2 + (0.02 − 0.03)2 + (0.03 − 0.03)2 + (0.04 − 0.03)2 + (0.05 − 0.03)2
5−1
= 1.583%
32
32
16
Time Series Analysis of Past Rate of Returns

Measuring Risk (SD, example):Calculate the ex-ante SD of the below returns:
State of the
Economy
Probability of
Occurrence
Expected Return on
Stock A in this State
High growth
0.1
50%
Medium growth
0.2
25%
No Growth
0.4
10%
Economic slowdown
0.2
5%
Recession
0.1
-5%
?
(????? )(?? − ?̅ )2
??? −???? =
?=1
 The Average was found to be 14.5%
??? −????
=
(?1 )(?1 − ?̅ )2 + (?2 )(?2 − ?̅ )2 + (?3 )(?3 − ?̅ )2 + (?4 )(?4 − ?̅ )2 + (?5 )(?5 − ?̅ )2
=
(0.1)(0.5 − 0.145)2 + (0.2)(0.25 − 0.145)2 + (0.4)(0.1 − 0.15)2 + (0.2)(0.05 − 0.145)2
+(0.1)(−0.05 − 0.145)2
??? −???? = 14.569%
33
33
Time Series Analysis of Past Rate of
Returns
 Excess Returns and Risk Premiums:
 Excess return: is usually measured as the difference between
the actual rate of return on a risky asset and the risk free rate.
 Risk Premium: is measured as the difference between the
expected HPR on the index stock fund (like S&P500) and the
risk-free rate.
 Considering that risk free investments bear zero risk relative to
other (risky) investments, then to induce investors to invest in
the risky investment, investors should earn a return above the
risk free rate
 This type of investor is called Risk Averse Investor!
 They are risk averse because they are not keen to bear more risk if this risk
is not justified by higher expected returns!
34
34
17
Time Series Analysis of Past Rate of
Returns
 Risk:
 Risk is usually associated with the likelihood
(possibility) that our future returns are less
than the respective expected ones!
 One of the widely used statistical measure to
proxy risk is standard deviation (volatility)
 Skewness and Kurtosis affect the level in which
we can rely on volatility as an adequate proxy
for risk! Let us see why!
35
35
The Normal Distribution
Source: Chapter 5 – Bodie, Kane, Marcus, Switzer, Boyko, Panasian, and
Stapleton: Investments, 9th Canadian Edition, McGraw-Hill, 2019.
 What are the characteristics of a normal
distribution?
36
36
18
The Normal Distribution
Skewed – Distribution
Source: Chapter 5 – Bodie, Kane, Marcus, Switzer, Boyko, Panasian, and
Stapleton: Investments, 9th Canadian Edition, McGraw-Hill, 2019.
37
37
The Normal Distribution
Fat tail – Distribution
Source: Chapter 5 – Bodie, Kane, Marcus, Switzer, Boyko, Panasian, and
Stapleton: Investments, 9th Canadian Edition, McGraw-Hill, 2019.
38
38
19
Deviation from Normality and Alternative Risk Measures
 We can define a distribution through its moments
 The number of moments needed to define a
distribution depends on how well it behaves!
1. Mean:
 Mean (arithmetic Average): is the first moment of
the distribution.
 Mode is the point where we observe the highest
number of observations
 Probability weighted mean:
?
?(?) =
?(?)?(?)
 Sample mean:
?=1
1
?
?̅ =
?
??
?
39
39
Deviation from Normality and Alternative Risk Measures
2. Volatility:
 Volatility () is the square root of the Variance (2)!
 Variance: is the second moment of the distribution
 Variance measures dispersion of the distribution:
 It measures the expected value of the squared deviations from expected
return
 Variance (volatility) measure the uncertainty of the outcome.
 Probability weighted Variance: ?
?2 =
?(?)[?(?) − ?(?)]2
?=1

Historical Population Variance:
?
1
[?? − ?]2
?2 =
?

Historical Sample Variance:
?=1
?2 =

1
?−1
?
[?? − ?]2
?=1
N.B.: Estimates of SD can be more reliable by sampling more frequently
40
40
20
Deviation from Normality and Alternative Risk Measures
2. Skewness:
 Skewness: is the third moment of the distribution
 Skewness measures asymmetry of the distribution
 If skewness is positive, the distribution is skewed to
the right!
 The Standard Deviation (Volatility) Overestimate the risk!
 If skewness is negative, the distribution is skewed to
the left!
 The Standard Deviation underestimate the risk! Why!
 Skewness is the ratio of the average cubed deviation
from the mean to the cubed standard deviation:
???????? =
?[?(?) − ?(?)]3
?3
41
41
Deviation from Normality and Alternative Risk Measures
3. Kurtosis:
 Kurtosis: is the fourth moment of the
distribution
 Kurtosis measures the degree of fat tails in the
distribution
 The higher the kurtosis, the fatter the tails of
the distribution
 The more the standard deviation will underestimate
the risk
 Kurtosis is the ratio of the average fourth power
deviation from the mean to the fourth power
standard deviation: ???????? = ?[?(?) − ?(?)]4 − 3
?4
42
42
21
Deviation from Normality and Alternative Risk Measures
 The Normal Distribution:
 The normal distribution can be defined by its first
two moments (mean and variance)
 The skewness of a normal distribution is zero
 The kurtosis of a normal distribution is zero
 Normal distribution is widely used in Empirical
Analysis
 Normal distribution is Symmetric
 Normal Distribution is Stable
43
43
Deviation from Normality and Alternative Risk Measures
 Sharpe Ratio
 Investments instruments that are more risky than the
risk free should earn higher return than the risk free
(positive excess return and positive risk premium)
 Considering Standard Deviation (SD) as a good proxy
for risk, than instruments with higher SD are expected
to have higher Risk Premium (RP)
 Based on the above point, professor William Sharpe
devised the Sharpe Ratio – Reward to Volatility
Measure to evaluate performance of investment
managers:
 The ratio of Risk Premium to SD of Excess Return
?ℎ???? ????? =
???? ???????
?? ?? ?????? ??????
44
44
22
Deviation from Normality and Alternative Risk Measures
 Other Measures of Risk (VAR, CTE,
LPSD):
 Value at Risk (VaR):
 Is the quintile of a distribution
 Usually we define VaR by the 1% or
quintile
 A 1% VaR means that there is a
probability that our loss will be below the
value
 However we have no idea about
magnitude of our loss
5%
1%
VaR
the
45
45
Deviation from Normality and Alternative Risk Measures
 Other Measures of Risk (VAR, CTE, LPSD):
 Lower Conditional Tale Expectation (LCTE) or
Expected Shortfall (ES):
 LCTE answer the question that VaR does not
answer
 LCTE add to VaR
 LCTE gives us a rough idea about what should be
the expected magnitude of our loss
 If VaR tell us that there is a 5% probability that
our loss be equal or below the VaR value then
LCTE continues and say that the expected
(average) loss would be of …
46
46
23
Deviation from Normality and Alternative Risk Measures
 Other Measures of Risk (VAR, CTE, LPSD):
 Lower Partial Standard Deviation (LPSD)
 Similar to usual standard deviation
 Uses only negative deviations from the risk-free
return
 Addresses the asymmetry in returns issue
???? =
∑??=1 ?? − ??
?−1
2
; ?? ????????? ?? < ??
 Sortino Ratio
 The ratio of average excess returns to LPSD
47
47
Historical Records
 Some Remarks:
 Stocks offer the highest returns but have
the highest SD
 This supports the idea that investors demand a
risk premium to bear risk!
48
48
24
2022-02-16
FINA 4466
Ch. 6
Capital Allocation to Risky Assets
1
1
Introduction
 Portfolio construction is compromised of two tasks
 Allocation of overall portfolio to safe assets or risky assets
 Determination of composition of the risky portion of the portfolio
 Portfolio theory starts with the capital allocation decision
 Constructing an optimal risky portfolio may be a challenging task
 Depends on the risk-return trade-off
 Know (Risk Premium) RP and Volatility
 Delegate it to a professional – hence fund managers’ importance
 Choosing the amount of money you need to allocate to a risky
portfolio is a personal decision that depends mainly on one’s
preferences – attitude towards risk
2
2
1
2022-02-16
Risk and Risk Aversion
 We will assume that investors are rational!
 Rational investors will avoid investing in a risky asset unless they are
compensated for the risk they are taking by additional expected return
 Risk Averse
 Hence, rational investors will invest in risky assets only if they anticipate
higher returns that is commensurate to the risk they are accepting!
 Expected return on risky investments should be an increasing function of
the risk involved by such investments!
 Does every investor require the same compensation (additional
return) for the risk taken?
 Investors’ tolerance for risk is a function of their Risk Aversion (RA)
3
3
Risk and Risk Aversion – Risk, Speculation and Gambling
 Speculation involves taking a risk with the expectation of being compensated
for it by appropriate returns
 Speculation is taken in spite of the risk involved, only when there is perceived
favourable risk-return trade-off
 Considerable investment risk sufficient to affect the decision
 Commensurate gain means positive risk premium (Expected Return > Rf )
 A Gamble involves taking up risk for the sake of enjoyment
 No perceived expectation of risk-return trade-off
 A Thin line differentiates speculations from gambling:
 Personal expectations! Expected payoff could be zero in gambling.
 Heterogeneous expectations:
 Expectations are only based on information
 Do all investors have access to the same set of information?
4
4
2
2022-02-16
Risk and Risk Aversion – Risk Aversion and Utility Values
 The higher the risk, the more the expected returns should be
in order to lure in rational risk averse investors
 Similarly, the more risk averse the investor is, the more
compensation she/he requires in order to take a risky
project!
 Note:
 A Risk Averse investor does not necessarily shy away from risk
into a riskless investment! She/he simply needs to be
commensurately compensated for the risk they are taking by the
appropriate expected returns!
5
5
Risk and Risk Aversion – Risk Aversion and Utility Values
 Intuitively, more attractive portfolio gives more expected
return for lower risk
6
6
3
2022-02-16
Risk and Risk Aversion – Risk Aversion and Utility Values
 We need to be able to rank the attractiveness of risky
investments (different risk and different returns) to
different investors (with differing Risk Aversion)
 This ranking function is called a Utility function.
 This ranking procedure or function should depend on three
main factors:
 Risk (measured by volatility)
 Reward or compensation (measured by expected returns)
 Personal preference (measured by Risk Aversion Coefficient)
7
7
Risk and Risk Aversion – Risk Aversion and Utility Values
 There are different forms of Utility functions
 We will cover Quadratic Utility functions in this course:
? = ?(?) −
1
?? 2
2
 U: Utility Value obtained from a particular investment
 E(r): expected return on the investment (a proxy for compensation)
 A: Risk Aversion Coefficient of the Investor
 2: Variance of the portfolio (a proxy for risk)
 You can think of U as a score assigned to competing portfolios
 As compensation (E(r)) increases, utility increases, and the investment
becomes more attractive
 As risk increases (2), utility decreases, and the investment becomes
less attractive
 As the Risk Aversion increases, the utility decreases, and the investment
will loose some of its lure to investors!
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Risk and Risk Aversion – Risk Aversion and Utility Values
 Remarks on the Utility functions:
? = ?(?) −
1
?? 2
2
 For risk free investments, utility directly maps to expected return as
risk is assumed to be zero (2 =0)
 In selecting risky portfolios, investors choose the investment that
delivers the highest utility.
 Any risky portfolio should generate enough utility (equal to or
greater than the utility generated by the available risk free rate) to be
chosen by a rational risk averse investor
 The certainty equivalent rate of a portfolio is the rate that
risk-free investments would need to offer with certainty to
be considered equally attractive to the risky portfolio.
 The utility generated by the risky portfolio equal to the utility generated by
the risk free investment 
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Risk and Risk Aversion – Risk Aversion and Utility Values
Example – what is U for these 3 portfolios
Compounding
Period
Risk
Premium
Expected
Return
Risk (SD)
2%
7%
5%
M (medium risk)
4
9
10
H (high risk)
8
13
20
L (low risk)
Table 6.1
Available risky portfolios (risk-free rate = 5%)
Each portfolio receives a utility score to assess the
investor’s risk/return trade off, rf=0.05.
Three investors with A= 2 , 3.5 and 5
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Risk and Risk Aversion – Risk Aversion and Utility Values
Varying Degrees of Risk Aversion
Investor
Risk
Aversion
(A)
2
3.5
5
Utility Score of Portfolio L
[E(r) = 0.07; σ = 0.05]
Utility Score of Portfolio M
[E(r) = 0.09; σ = 0.10]
Utility Score of Portfolio H
[E(r) = 0.13; σ = 0.20]
0.07 − ½ × 2 × 0.052 = 0.0675
0.09 − ½ × 2 × 0.12 = 0.0800
0.13 − ½ × 2 × 0.22 = 0.09
2
2
0.07 − ½ × 3.5 × 0.05 = 0.0656 0.09 − ½ × 3.5 × 0.1 = 0.0725
2
0.07 − ½ × 5 × 0.05 = 0.0638
2
0.09 − ½ × 5 × 0.1 = 0.0650
0.13 − ½ × 3.5 × 0.22 = 0.06
0.13 − ½ × 5 × 0.22 = 0.03
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Risk and Risk Aversion – Risk Aversion and Utility Values
 Risk Neutral Investors: A=0
 Judge investment opportunities by their returns only
 Risk is irrelevant
 They don’t penalize for the risk
 Risk Loving Investors: A
Purchase answer to see full
attachment