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Lecture 1
Introduction
1
Outline
The Axioms of Finance
The Corporation
The Financial Manager
Real vs Financial Assets
The Stock Market
Roles of Financial Markets
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The Axioms of Finance
1. Investors prefer more to less (non-satiability)
•
•
A: $50 now for sure, or
B: $100 now for sure
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2. Money paid in the future is worth less than money
paid now
• B: $100 now for sure, or
• C: $100 in one year for sure
 How much are you willing to pay for asset B today?
Answer: $100
 How much are you willing to pay for asset C today?
Answer: less than $100
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2. Money paid in the future is worth less than money
paid now
• B: $100 now for sure, or
• C: $100 in one year for sure
 Suppose asset C trades for $96.1538 now.
 Your return from investing in asset C is:
𝐑𝐞𝐭𝐮𝐫𝐧 =
𝐆𝐚𝐢𝐧 𝐚𝐭 𝐄𝐧𝐝 𝐨𝐟 𝐘𝐞𝐚𝐫
100 − 96.1538
=
= 0.04 or 4%
𝐈𝐧𝐢𝐭𝐢𝐚𝐥 𝐏𝐫𝐢𝐜𝐞
96.1538
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𝐑𝐞𝐭𝐮𝐫𝐧 =
𝐆𝐚𝐢𝐧 𝐚𝐭 𝐄𝐧𝐝 𝐨𝐟 𝐘𝐞𝐚𝐫
100 − 96.1538
=
= 0.04 or 4%
𝐈𝐧𝐢𝐭𝐢𝐚𝐥 𝐏𝐫𝐢𝐜𝐞
96.1538
Note that:
100 − 96.1538
100
=
− 1 = 0.04 or 4%
96.1538
96.1538
𝐑𝐞𝐭𝐮𝐫𝐧 =
𝐆𝐚𝐢𝐧 𝐚𝐭 𝐄𝐧𝐝 𝐨𝐟 𝐘𝐞𝐚𝐫
𝐕𝐚𝐥𝐮𝐞 𝐚𝐭 𝐄𝐧𝐝 𝐨𝐟 𝐘𝐞𝐚𝐫
=
−𝟏
𝐈𝐧𝐢𝐭𝐢𝐚𝐥 𝐏𝐫𝐢𝐜𝐞
𝐈𝐧𝐢𝐭𝐢𝐚𝐥 𝐏𝐫𝐢𝐜𝐞
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2. Money paid in the future is worth less than money
paid now
• B: $100 now for sure, or
• C: $100 in one year for sure
 Suppose asset C trades for $96.1538 now.
 We say that the risk-free rate is 4%.
 Risk-free rate, 𝒓𝒇 : the rate at which money can be invested
without risk.
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3. Investors are risk-averse
• C: $100 in one year for sure, or
• D: $200 in one year with 50% chance, nothing otherwise
 The expected payoff of asset C is $100.
 The expected payoff of asset D is: 0.5 × 200 + 0.5 × 0 = $100
 Asset C is risk-free or riskless: it offers an expected payoff of $100
without risk
 Asset D is risky: it offers the same expected payoff of $100 with risk
 Which asset do you prefer?
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3. Investors are risk-averse
• C: $100 in one year for sure, or
• D: $200 in one year with 50% chance, nothing otherwise
 If for the same expected payoff (here $100), you prefer the safe
asset to the risky asset, we say that you are risk-averse.
 If for the same expected payoff (here $100), you prefer the risky
asset to the safe asset, we say that you are risk-lover.
 If you are indifferent between the two (so you care only about the
expected payoff, not about the risk of the payoff), we say that you
are risk-neutral.
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3. Investors are risk-averse
• C: $100 in one year for sure, or
• D: $200 in one year with 50% chance, nothing otherwise
 In finance, we assume that most investors are risk-averse, ie that
they prefer asset C to asset D in this case.
 This implies that investors are willing to pay a higher price for asset
C than for asset D.
 Suppose as before that asset C trades for $96.1538 now.
 How much are you willing to pay for asset D?
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 Suppose asset D trades for $90 now.
𝐄𝐱𝐩𝐞𝐜𝐭𝐞𝐝 𝐑𝐞𝐭𝐮𝐫𝐧 =
=
𝐄𝐱𝐩𝐞𝐜𝐭𝐞𝐝 𝐆𝐚𝐢𝐧 𝐚𝐭 𝐄𝐧𝐝 𝐨𝐟 𝐘𝐞𝐚𝐫
𝐈𝐧𝐢𝐭𝐢𝐚𝐥 𝐏𝐫𝐢𝐜𝐞
0.5 × 200 + 0.5 × 0 − 90 100 − 90
=
= 0.1111 or 11.11%
90
90
or
=
0.5 × 200 + 0.5 × 0
100
−1=
− 1 = 0.1111 or 11.11%
90
90
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𝐄𝐱𝐩𝐞𝐜𝐭𝐞𝐝 𝐑𝐞𝐭𝐮𝐫𝐧 =
𝐄𝐱𝐩𝐞𝐜𝐭𝐞𝐝 𝐆𝐚𝐢𝐧 𝐚𝐭 𝐄𝐧𝐝 𝐨𝐟 𝐘𝐞𝐚𝐫
𝐈𝐧𝐢𝐭𝐢𝐚𝐥 𝐏𝐫𝐢𝐜𝐞
which is equivalent to:
𝐄𝐱𝐩𝐞𝐜𝐭𝐞𝐝 𝐑𝐞𝐭𝐮𝐫𝐧 =
𝐄𝐱𝐩𝐞𝐜𝐭𝐞𝐝 𝐕𝐚𝐥𝐮𝐞 𝐚𝐭 𝐄𝐧𝐝 𝐨𝐟 𝐘𝐞𝐚𝐫
−𝟏
𝐈𝐧𝐢𝐭𝐢𝐚𝐥 𝐏𝐫𝐢𝐜𝐞
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Equivalently, we can first calculate the return in each state:
Return in the up state =
200 − 90 200
=
− 1 = 1.2222 or 122.22%
90
90
Return in the down state =
0 − 90
0
=
− 1 = −1 or − 100%
90
90
Then:
Expected Return = 0.5 × 1.2222 + 0.5 × −1 = 0.1111 or 11.11%
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3. Investors are risk-averse
• C: $100 in one year for sure, or
• D: $200 in one year with 50% chance, nothing otherwise
 Asset D offers an expected return (11.11%) higher than the riskfree rate (4%), in order to compensate investors for bearing risk.
 Risk-return tradeoff:
Higher-risk assets are priced to offer higher expected returns than
lower-risk assets.
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 The difference between the expected return on a risky asset and
the risk-free rate is called the risk premium for that asset.
Expected return on a risky asset = 𝒓𝒇 + 𝐫𝐢𝐬𝐤 𝐩𝐫𝐞𝐦𝐢𝐮𝐦
 In our example, the risk premium for asset D is:
11.11% − 4% = 7.11%
 The risk premium is the investors’ compensation for bearing risk.
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The Axioms of Finance
1. Investors prefer more to less (non-satiability)
•
•
A: $50 now, or
B: $100 now
2. Money paid in the future is worth less than money
paid now (the time value of money)
• B: $100 now for sure, or
• C: $100 in one year for sure
3. Investors are risk-averse (the risk-return tradeoff)
• C: $100 in one year for sure, or
• D: $200 in one year with 50% chance, nothing otherwise
4. Markets are competitive (no free lunch)
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Markets are Competitive: No Free Lunch
Arbitrage
• A transaction where you buy an asset at a low price and
simultaneously sell the same asset (or an equivalent asset) at a
high price.
– Two assets are equivalent if they have the same same cashflows at every point in time and in every state of the world in
the future.
Arbitrage Opportunity ( = Free Lunch)
• Any situation in which it is possible to make a profit without
taking any risk and without making any investment.
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Markets are Competitive: No Free Lunch
Example of an arbitrage opportunity:
• A share of Google can be bought on both Nasdaq and NYSE
• The price is $1,730 on Nasdaq and $1,727 on NYSE
• Ignore trading costs!
• What do you do?
You buy the stock on the NYSE and sell it on Nasdaq. You make
$3 now, without any risk! A free lunch!
• You drive up the price on NYSE
• You drive down the price on Nasdaq
• Soon the price is the same in both places. No more free lunch!
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Markets are Competitive: No Free Lunch
Example of an arbitrage opportunity:
• A share of Google can be bought on both Nasdaq and NYSE
• The price is $1,730 on Nasdaq and $1,727 on NYSE
• Question: Can you sell the stock on Nasdaq without
previously buying it on NYSE?
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Short Sales
• Short-selling: selling an asset you don’t own
• Mechanics – 3 steps
1. Borrow the asset
2. Sell it and receive the current market price
3. Closing out the position: Buy the asset and return to the
party from which it was borrowed
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Long position: you
benefit if the price
goes up
*A negative cash flow implies a cash outflow.
Short position: you
benefit if the price
goes down
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Markets are Competitive: No Free Lunch
Example of an arbitrage opportunity:
• A share of Google can be bought on both Nasdaq and NYSE
• The price is $1,730 on Nasdaq and $1,727 on NYSE
• Suppose you first short the stock and sell it on Nasdaq for
$1,730, and then you immediately buy it on NYSE for $1,727.
• Payoff at the end of the period:
– For the short position: you pay any dividend that the stock
pays, plus the ending price.
– For the long position: you receive any dividend that the
stock pays, plus the ending price.
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Markets are Competitive: No Free Lunch
• Your net future payoff from the long and the short positions
combined is exactly $0, no matter what the dividend and the
price will be at the end of the period.
• You receive a profit of $3 today, without any risk and payment
in the future – this is an arbitrage profit, aka a free lunch!
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Markets are Competitive: No Free Lunch
• In a well-functioning capital market, investors compete for
profits and trade to take advantage of any arbitrage
opportunities.
• So as investors sell the stock on Nasdaq, excess supply will
drive the price down.
• As investors buy the stock on NYSE, excess demand will drive
the price up.
• The only equilibrium is for the price to be equal on the two
markets.
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Markets are Competitive: No Free Lunch
• In other words, assuming a well-functioning capital market is
equivalent to assuming that there are no arbitrage
opportunities.
• The No Arbitrage condition is also called No Free Lunch or the
Law of One Price (LOOP):
– In competitive markets, assets with the same cash flows at
every point in time and in every state of the world must
have the same price today.
– Otherwise, there is an arbitrage opportunity.
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Duration of Arbitrage Opportunities
The duration of arbitrage opportunities resulting from differences in the price of the
S&P500 Futures Contract on the Chicago Mercantile Exchange and the price of the SPDR
S&P 500 ETF traded on the NYSE.
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Source: Budish et al, The High Frequency Trading Arms Race (…), QJE 2015
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Duration of Arbitrage Opportunities
The duration of arbitrage opportunities resulting from differences in the price of the
S&P500 Futures Contract on the Chicago Mercantile Exchange and the price of the SPDR
S&P 500 ETF traded on the NYSE.
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Source: Budish et al, The High Frequency Trading Arms Race (…), QJE 2015
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The Types of Firms
1.
2.
3.
4.
Sole Proprietorships
Partnerships
Limited Liability Companies
Corporations
Source: www.irs.gov
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The Corporation
 A legal entity (a person) separate from its owners
• Has many of the legal powers individuals have such as
the ability to enter into contracts, own assets, and
borrow money
• Limited liability: The corporation is solely responsible
for its own obligations. Its owners are not personally
liable for any obligation the corporation enters into.
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The Corporation
• Ownership
• Represented by shares of stock
• Sum of all ownership value is called equity.
• Owner of stock is called
– Shareholder
– Stockholder
– Equityholder
• Shareholders have:
– voting rights
– cash-flow rights (the right to receive dividends)
• Equity is a residual claim
– Shareholders have claim to what is left after paying all other
claimants, such as the tax authorities, employees, suppliers,
bondholders and other creditors
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The Corporation
• Double taxation of earnings and dividends
• Eg: Pre-tax earnings = $100; Corporate tax rate = 20% ;
Tax rate on dividend income = 20%
→ Net income = $100 x (1 – 0.20) = $80
→ A er-tax dividend = $80 x (1 – 0.20) =$64
• Exception: “S” Corporations
• Firm’s profits are not subject to corporate income tax,
but instead are allocated directly to the shareholders.
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Ownership Versus Control of Corporations
• Corporate Management Team
– In a corporation, ownership and direct control are typically
separate.
– Board of Directors
• Elected by shareholders
• Have ultimate decision-making authority
– Chief Executive Officer (CEO)
• Board typically delegates day-to-day decision making
to CEO.
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The Financial Functions Within a Corporation
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The Role of the Financial Manager
(2)
(1)
Financial
manager
Firm's
operations
(4a)
(a bundle of
real assets)
(4b)
(3)
Financial
markets
(investors
holding financial
assets)
(1) Cash raised from investors
(2) Cash invested in firm
(3) Cash generated by operations
(4a) Cash reinvested
(4b) Cash returned to investors
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The Balance Sheet
Assets
Equity
Debt
Uses of funds
Sources of funds
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The Role of the Financial Manager
• The financial manager has three main tasks:
– Make investment decisions
o What projects should the firm invest in?
o Also called capital budgeting decisions
– Make financing decisions
o The mix of debt and equity is called the capital structure
decision
o The payout decision
• How much cash to distribute to the shareholders, and
• How to distribute the cash: dividends vs share repurchases (stock
buybacks)
– Manage working capital
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Real vs Financial Assets
Real
Assets
Financial Assets:
Claims on income generated
by real assets
Do not directly contribute to
the productive capacity of
the economy
Productive
Capacity
Land, buildings,
machines,
intellectual
property, human
capital, etc.
Financial assets traded on the
capital market are called
securities.
- Eg publicly traded stocks,
publicly traded bonds
- Bank loans are financial
assets, but they are not
securities
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Financial Assets – Asset Classes
Financial Assets: Claims on Real Assets
Fixed-Income Securities:
Equity:
Promises a fixed stream of income or
a stream of income determined by a
specified formula; debt
eg money market instruments,
bonds, preferred stock
Represents ownership share in a
corporation; common stock; residual
claim
Derivatives:
Provide payoffs that are determined by
the prices of other assets
eg call options, put options, forward,
futures contracts
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Other Types of Investment
• Investment in currency
• Commodities, eg corn, wheat, natural gas
• Real estate
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Balance Sheet, U.S. Households, 2019
Source: Flow of Funds Accounts of the United States, Board of Governors of the Federal Reserve System,
June 2019; reproduced in Bodie, Kane, Marcus, Essentials of Investments, 12th edition
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Financial Assets = Financial Liabilities
• Financial assets and liabilities must balance.
Financial Assets
(Owner of the claim)
Financial Liability
(Issuer of the Claim)
• Thus, when all balance sheets are aggregated, only real assets
remain.
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Real vs Financial Assets
`
Firm
Household
Assets
House $250,000
Car - $30,000
Stock in Firm $120,000
Bank Deposit $150,000
Liabilities
Stock
Market
Mortgage $70,000
Assets
Liabilities
Building $160,000
Equipment $40,000
Stock $120,000
Bank Debt $80,000
Bank
Assets
Liabilities
Mortgage $70,000
Firm Loan $80,000
Deposits $150,000
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If we aggregate the three balance sheets, the financial assets cancel out.
Total wealth in the economy = value of real assets
= 250,000 + 30,000 + 160,000 + 40,000 = 480,000
`
Firm
Household
Assets
Liabilities
House $250,000
Car - $30,000
Stock in Firm $120,000
Bank Deposit $150,000
Stock
Market
Mortgage $70,000
Assets
Liabilities
Building $160,000
Equipment $40,000
Stock $120,000
Bank Debt $80,000
Bank
Assets
Liabilities
Mortgage $70,000
Firm Loan $80,000
Deposits $150,000
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The Stock Market
• Corporations can be private or public
– A private company has a limited number of owners and
there is no organized market for its shares
– A public company has many owners and its shares trade on
an organized market, called a stock market
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The Biggest Stock Markets in the World
Source: www.world-exchanges.org
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Market Share of Trading in NYSE-Listed Shares
Source: James J. Angel, Lawrence E. Harris, and Chester Spatt, “Equity Trading in the 21st Century,” Quarterly
Journal of Finance 1 (2011), pp. 1-53
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The S&P500
As of 07/15/2020; Source: CapitalIQ
Size by: Market Capitalization
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The Stock Market
• Primary Markets
– When a corporation itself issues new shares of stock and
sells them to investors, they do so on the primary market.
• IPO (Initial Public Offering): the first time that a private firm offers
its stock to the public
• SEO (Seasoned or Secondary Equity Offering): a new equity offering
by an already public company
• Secondary Markets
– After the initial transaction in the primary market, the
shares continue to trade in the secondary market between
investors.
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Roles of Financial Markets
1. Efficient allocation of capital
– Financing of large projects
– Informational role
2. Efficient allocation of risk
– Investors can select securities consistent with their tastes
for risk
– Diversification
– Hedging
• For example, an American company that exports goods
to Europe and is paid in euros, but has to pay its
workers wages in dollars is exposed to fluctuations in
the euro-dollar exchange rate.
• The company can hedge (i.e insure against) this risk by
selling euros forward
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Roles of Financial Markets
3. Consumption Smoothing
– When current basic needs are met, use securities to
store wealth and transfer consumption to the future
Dollars
– Investing and borrowing
Consumption
Savings
Dissavings
Dissavings
Income
Age
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