Foundations of Finance
Week 1 – Overview of Financial Markets
Why do Financial Markets exist?
People with excess capital
Gains from trade !
↵
People with Ideas/Opportunities
2
Overview of Financial Markets
↵
Most (all ?) transactions fit into this framework
Demand for capital
Entrepreneurs
Students
Some countries
Firms




Supply of capital



Households
(bank accounts)
Pension plans
Some other countries
Provides for
1. Consumption smoothing
2. Optimal use of capital
3
Overview of Financial Markets
Core concepts
4
TODAY: A bird’s eye
perspective
Overview of Financial Markets
Financial Markets
The role of markets in our economy and how they function
A Closer Look
Question: How does a firm obtain financing?

SUPPLIERS OF
CAPITAL
CAPITAL
MARKETS
CONSUMERS OF
CAPITAL
Part of the answer: It must issue financial assets

6
Overview of Financial Markets
What is a Financial Asset?
Real Assets are used to produce goods and services:
land, equipment, buildings, knowledge
Financial Assets are claims on real assets or the
income generated by them
INVESTORS
FINANCIAL ASSETS
CLAIM
CLAIM
7
Overview of Financial Markets
REAL ASSETS
Large Firm
Start-up
Financial and Real Assets
Financial Assets



One parties asset is another’s liability
Thus the value of all financial assets in the economy
sums to zero
Real Assets


8
The value of all real assets determines the true value of
the economy
Overview of Financial Markets
Real and Financial Assets
Households
Liabilities
Assets
Mortgage - $2 M Shares of Stock - $5M
Bank Loan - $1M Bank Deposit – $3 M
House - $3 M
Firms
Liabilities
Assets
Equity - $4 M
Bank Debt – $1 M
Human Capital - $3M
Computers - $ 1M
Patents $1 M
Banks
Liabilities
Assets
Deposits – $3 M
Equity - $1M
Mortgage - $2 M
Loans – $2 M
9
Overview of Financial Markets
Common Types of Financial
Assets
Features of Debt and Equity claims
Basic Financial Assets
Debt





Equity (Ownership)


11
Bank Loan
Corporate Bond
Treasuries
Pensions
Stocks
Overview of Financial Markets
A (hopefully) intuitive example

You want to start a lemonade stand



You anticipate that it will earn $20
You have $10, but you need $15
Your parents lend you $5

How is this “firm” financed?

You make $12 in revenues

12
how do you split the proceeds?
Overview of Financial Markets
Debt vs. Equity

Seniority



Debt holders paid first
Equity holders paid once debt holders have received all
claims
Cash Flows


Debt holders receive a fixed amount
Equity holders have a claim on firm value which exceeds
liabilities to debt holders
What does this structure imply for the relative riskiness
(variance) of these payoffs?
13
Overview of Financial Markets
Debt vs. Equity - Graphically
20
15
Value of Equity
Value of Debt
Firm Value
10
5
0
0

5
10
15
20
What if the firm can’t pay back debt holders?


14
Renegotiation
Bankruptcy
Overview of Financial Markets
Fixed Income Securities

Some examples:






Two types of cash flows


15
Treasury Bills/Bonds
Municipal bonds
Mortgages
Credit card debt
Student loans
Interest payments
Principal payments
Overview of Financial Markets
Fixed Income Cash Flows: An Example

Loan with FV $ 20M, Semi-Annual Coupons & 5%
Interest rate

Initial Capital Injection
Principal
Payment
    
Semi-Annual Coupon Payments
16
Overview of Financial Markets
Features of a Debt Contract




Maturity – length of loan term
Interest Rate – e.g. fixed or floating
Face value – The value of the principal owed at
maturity
Payment Schedule



Optionality – e.g. prepayment options


If interest rates fall, borrowers may have the option of
paying off their existing loans and issuing new debt at
the lower interest rate
Covenants

17
Frequency of coupon payments
(Potentially no coupon payments)
Provisions which give the lender control rights in
particular scenarios
Overview of Financial Markets
Revisiting the lemonade stand

18
What were the features of the loan your parents
made to you?

Interest rate?

Optionality?

Maturity?

Payment schedule? (e.g. coupons)
Overview of Financial Markets
Market Value of Debt vs. Face Value



Firm has debt of face value 10M
Tomorrow the firm will either be worth
20 w / prob  1 3

15 w / prob  1 3

0 w / prob  1 3
What is the market value of the firm’s debt?
Firm Value
20M
15M
Value
of Debt
Value of equity


Market value of debt:
Market value of equity:
19
Overview of Financial Markets
0M
Equity Financing

An equity claim contains

Cash-flow rights: the right to the firms cash flows
once debt-holders are paid off



Voting rights
Cash flows rights


20
An infinite stream of dividends
Dividends
Should capital gains count?
Overview of Financial Markets
Debt vs. Equity

SeatGeek.com is financed through debt and equity:



Current value of equity: 6M
Current value of debt: 9M, assume the face value of debt is also 9M
Presented with an investment opportunity which costs $11M and has
payoffs given by:

30 w / prob  1 3
Payoff = 
12 w / prob  1 3

0 w / prob  1 3

What is the expected value of this project?

What is the firms value if it decides to undertake the project?
21

Overview of Financial Markets
Debt vs. Equity

Goal: find the new value of debt and the new value
of equity
Case 1: 
Project Payoff 30M
Case 2: 
Case 3: 
12M
0M
Firm Value
Debt Payoff
Equity Payoff



Value of debt:
Value of equity:
Should management invest in the project?
22
Overview of Financial Markets
Any questions on Debt and/or Equity?
23
Overview of Financial Markets
Or what about a hybrid? – Preferred Equity


Attributes of both debt and equity
Bond-like




No voting power
Priority over common stock
Rated by credit-rating agencies
Stock-like


24
Subordinate to debt
Cash-flows are in the form of dividend payments
Overview of Financial Markets
One clever type of preferred stock: Poison pills

(This is an example of a potential “current event”
topic)
- Financial Times
25
Overview of Financial Markets
Some background: What is a Poison Pill?
“In connection with the adoption of the
Shareholder Rights Plan, the Board of Directors
declared a dividend distribution of one
Marty Lipton
preferred stock purchase right for each
outstanding share of Tegal’s common stock to
shareholders of record as of the close of
business… Under the Plan, the rights generally
will become exercisable if a person becomes
an `acquiring person’ by acquiring 15% or more
of the common stock of Tegal… If a person
becomes an ‘acquiring person,’ each holder of
a right (other than the acquiring person) would
be entitled to purchase, at the then-current
exercise price, such number of shares of
preferred stock which are equivalent to shares
of Tegal’s common stock having a value of
twice the exercise price of the right.”
-Tegal press release – April 13,
2011
26
Overview of Financial Markets
How does it work




27
Hostile take-over triggers the right to exercise
the option
2-for-1 exchange means any shares not
exercised have been diluted to half their value
Acquirer cannot exercise
Is this “rights plan” actually good for
shareholders ?
Overview of Financial Markets
Back go Airgas versus Air Products
28
Overview of Financial Markets
How should a firm finance it’s investments?

Some possible considerations







29
Accessibility of debt versus equity
Management incentives
Asymmetric information
Bankruptcy costs
Tax advantages
Reporting costs
You can learn more about capital structure in
corporate finance
Overview of Financial Markets
Financing the Firm – The Role of Limited
Liability

Limited Liability – The concept whereby a person’s
financial liability is limited to a fixed sum (typically
the value of the person’s financial investment)

Can you think of how
this would be important
in a firm’s ability to gain
financing?
What are some costs?

30
Overview of Financial Markets
Back to the (fictional) story of SeatGeek.com
Two college
grads have a
great business
idea.
Personal loan
from friends
& family
Must hire
employees to
increase
website
functionality
Expand
operations by
entering ticket
brokering
business
Issue
corporate debt
VC funding
(equity)
2000
31
2002
Enter
agreement
with AMEX
to purchase
concierge
services
business
Issue public
equity (IPO)
2003
Overview of Financial Markets
2006
How will SeatGeek.com do an IPO?

The role of investment banks




Determine size & features of offering
“Place shares”
Number of IPOS
Legal issues
200
Pricing issues 180
160
140
120
100
80
60
40
20
0
32
Overview of Financial Markets
1st Day Return
16
14
12
10
8
6
4
2
0
A Closer Look
SUPPLIERS OF
CAPITAL

CAPITAL
MARKETS
How are these financial
Assets traded?
33
Overview of Financial Markets
CONSUMERS OF
CAPTIAL
Market Mechanics
The primary and secondary markets for financial assets
Primary Market


SeatGeek works with an investment bank to
structure an IPO
The company is now owned by multiple classes of
investors
Debt Holders
DEBT
Equity Holders
EQUITY
35
Overview of Financial Markets
Primary and Secondary Market



36
After new issues occur through the primary
market
Later some investors may want to change their
holdings
Secondary market allows investors to trade
securities
Overview of Financial Markets
An Interesting Aside: Relative Sizes of Secondary
Markets



Total value of US bond market – $31 trillion
Total value of US stock market - $22 trillion
Value of average daily dollar trade volume in some
secondary markets?

US Stock Market ?

US Bond Market ?

Foreign Exchange ?
37
Overview of Financial Markets
How are trades completed? Not this way

In a “direct search market” buyers and sellers
transact without an intermediary
Seller
Buyer
38
Overview of Financial Markets
Brokered Market

Sellers and buyers transact through brokers
Seller
Broker
Broker
Broker
Buyer
Broker
39
Overview of Financial Markets
Dealer Market


Dealers specialize in particular securities
They absorb supply and demand shocks through
their own books
Seller
Broker
Broker
Dealer
Buyer
Dealer
40
Broker
Overview of Financial Markets
Broker
Auction Market

Transactions occur centralized through an auction
Broker
Seller
Broker
Broker
Broker
Broker
Exchange
Buyer
Broker
41
Broker
Overview of Financial Markets
Broker
Secondary Markets

Auction Market (NYSE, AMEX)


Call Auction
Continuous Auction:



Dealer (Market Maker) Market (NASDAQ)
Electronic Communication Network

What determines the price?

42
Floor Trading (open outcry system)
Limit Order Book
Overview of Financial Markets
Call Auction



43
All orders are aggregated into demand
and supply schedules
Transactions are conducted at a
specified time
A single price is determined such that
supply equals demand
Overview of Financial Markets
Call Auction – Building the Supply & Demand
Curves
Buy 1,000 shares at $101
Buy 500 shares at $103
Buy 2,000 shares at $100
Buy 1,500 shares at $102
Sell 2,000 shares at $104
Sell 500 shares at $102
Sell 1,500 shares at $101
$104
$103
$102
$101
$100
1,000
44
2,000
3,000
Overview of Financial Markets
4,000
5,000
Continuous Auction




45
Continuous Auction or Dealer Market: Bid and
Ask Prices
Bid Price = Price at which a seller can sell an
asset
Ask Price = Price at which a buyer can buy an
asset
Which Price should be higher? Why?
Overview of Financial Markets
Continuous Action – Limit Order Book - 11:05
11:00
Sue: ASK 500 @ 20
Bill: BID 500 @ 17
Jane: BID 2000 @ 21
Jim: ASK 2000 @ 19
11:05
Rob: BID 1500 @ 18
Anne: ASK 2000 @ 18
Time
Trade ?
Buyer
Seller
Quantity
Price
11:01
11:03
11:04
11:07
11:08
46
Overview of Financial Markets
Post Bid
Post Ask
The Role of the Dealer (a.k.a. Market Maker)
47

Dealer Holds inventory and quotes bid
and ask prices

Provides a service of liquidity in exchange
for the bid-ask spread

Bears risk of holding inventory

Bid-ask spread compensates dealer for
risk and liquidity services
Overview of Financial Markets
The Dealers Inventory: Some Thought Questions




48
What happens to the value of inventory if the
stock price goes up? Down?
What happens to the size of the dealer’s
inventory if bid-ask spread moves up? Down?
How does volume of trade affect inventory
risk?
How does competition affect the spread?
Overview of Financial Markets
US Equity Markets Today: Future of the NYSE
49
Overview of Financial Markets
Types of Trading Orders

Market Order


Limit Order (Our dealer book example)


Order to sell (buy) shares at or above (below) a
specified price
Stop Orders

50
Buy or sell orders to be executed
immediately at the market price
Order to sell (buy) if prices falls below (rises above)
a specified level
Overview of Financial Markets
Short Sales
Speculator: Buy Low, Sell High
 How can we profit if we believe the
price is going to go down?

51
Overview of Financial Markets
Short Sales in Practice

Legal Issues



Securities lending




52
Naked short selling
Occasional restrictions on shorting certain securities
An industry allows for shorting in the presence of
naked short restrictions
Which securities can be lent?
Transparency issues in the securities lending market
(This is my research area – email me if you
want to know more about shorting or sec
lending.)
Overview of Financial Markets
A Closer Look
SUPPLIERS OF
CAPITAL
CAPITAL
MARKETS
•How do investors
decide what assets to
invest in?
53
Overview of Financial Markets
CONSUMERS OF
CAPITAL
The Investment Management Industry

Difficult for individual investors to access
certain financial opportunities


Economies of scale



54
Can you think of what features make some assets
more inaccessible than others?
Trading costs
Ability to net trades
Governance Issues
Overview of Financial Markets
Investment Management Vehicles



Money Market Funds
Pension Funds
Mutual Funds



Hedge Funds
Other funds


55
Passive vs. Active
VC/PE Funds
Fund of Funds
Overview of Financial Markets
How can Investors choose the best Investment
opportunity

Important considerations for an Investor





Tools to evaluate these concepts:


56
Investment Horizon
Risk tolerance
Level of Sophistication
Fees
The time value of money
Time-adjusted return measures
Overview of Financial Markets
Returns and Return Measures
A framework for evaluating investment opportunities
Time Value of Money
58
Overview of Financial Markets
Time Value of Money

Main axiom of finance:


Money in the future is worth less than the same amount
of money is worth today
Why is this true?


59
What if you KNOW you don’t need money until
tomorrow?
What if there is absolutely no default risk?
Overview of Financial Markets
Time Value of Money

Which cash flow would you prefer?
$20
$10
$20
$10
Today

1 Year Later
Today
1 Year Later
What about:
$20
$10
Today
60
$20
$10
1 Year Later
Today
Overview of Financial Markets
1 Year Later
Time Value of Money

Which of these cash flows would you prefer?
$20
$10
Today

$20
$10
1 Year Later
Today
1 Year Later
Need a concept that allows us to evaluate these
options systematically
61
Overview of Financial Markets
Time Value of Money & Financial Assets


Financial assets we have discussed thus
characterized by exchanging some capital today for
claims on future cash flows
Equity


Purchase a part of an investment opportunity today with
the prospect of making money on the investment in the
future
Bonds

62
Lend money today in exchange for receiving your
investment back with interest
Overview of Financial Markets
Time Value of Money

We will ask:



Future value: How much is $1 invested today worth in 1
year
Present Value: How much is $1 received in 1 year worth
today
Note: Knowing the answer to one of the above
questions implies the answer to the other

63
Why is this?
Overview of Financial Markets
Understanding interest rates

Poll: I need $100 today – how much would you
want me to promise to pay you in 1 year to make
the loan to me?






The answer to this question determines the
interest rate
For this class, we will take the interest rate as
given

64
102?
105?
108?
112?
If you want to learn more about the determinates of
interest rates, consider taking macroeconomics or
forecasting debt instruments
Overview of Financial Markets
Future Value


Suppose Interest Rate is 10%
Then investors are indifferent between these two cash
flows:
$110
$100
Today

65
1 Year Later
So they are indifferent between making this investment
and keeping their $100
Overview of Financial Markets
Future Value


Interest rate is still 10%
How much money would an investor need in two
years to lend $110 in 1 year
?
$110
$100
Today

1 Year Later
2 Years Later
Answer: $110*(1.1) = $121
66
Overview of Financial Markets
Future Value


Interest rate is still 10%
What if you were lending $100 today and receiving
$X in 2 years? What should X be?
?
$100
Today

1 Year Later
2 Years Later
Answer: $100*(1.1)2 = $121
67
Overview of Financial Markets
Future Value

In general: FV = PV*(1+r)T

In the previous 3 slides we could have
used this formula to calculate the future
value using:




68
1: PV = 100, r = 10%, T = 1
2: PV = 110, r = 10%, T = 1
3: PV = 100, r = 10%, T = 2
You get a $250 present from your family as
a graduation present. If you invest it today,
what will it be worth in 5 years?
Overview of Financial Markets
Future Value of $1
69
T/ R
5%
10%
15%
20%
1
1.0500
1.1000
1.1500
1.2000
2
1.1025
1.2100
1.3225
1.4400
3
1.1576
1.3310
1.5209
1.7280
4
1.2155
1.4641
1.7490
2.0736
5
1.2763
1.6105
2.0114
2.4883
Overview of Financial Markets
Present Value – just the converse:

You need $1000 in 1 year to pay for a vacation. How
much should you invest today at an interest rate of
5%?
1000
?
Today

We can use the same formula: PV =
70
5 Years Later
FV/(1+r)T
Overview of Financial Markets
Present Value of $1
71
T/ R
5%
10%
15%
20%
1
0.9524
0.9091
0.8696
0.8333
2
0.9070
0.8264
0.7561
0.6944
3
0.8638
0.7513
0.6575
0.5787
4
0.8227
0.6830
0.5718
0.4823
5
0.7835
0.6209
0.4972
0.4019
Overview of Financial Markets
Single Cash Flow

The formula relates:




Present Value
Future Value
Interest rate
Time (number of periods)
FV=PV*(1+r)T
72
Overview of Financial Markets
PV, FV, r, t are tied together
If you know any 3, you can find the 4th
 Interest rate: r


Investment Period: t

73
You know PV and FV at a given future time t,
how do you figure out the interest rate?
You know PV, you know the interest rate, and
the FV. For how many periods do you need to
invest?
Overview of Financial Markets
Example I – Single Cash Flow



74
Your grandmother promised you $5,000 upon
your graduation (two years from now).
However, you want to use the money now.
How much can you borrow today against this
future $5,000, if the interest rate is 8% ?
Assume that grandmother is fully reliable
Overview of Financial Markets
Example II – Single Cash Flow



Suppose you open a savings account today with
$100
Suppose that the interest rate is 5% per year.
How long will it take for you to become a
millionaire?
75
Overview of Financial Markets
Developing Valuation Tool
Multiple Periods
One Period
Future
Value
Present
Value
Pricing
Real
Securities
76
r
r
$
?
?
r
$
r
r
$
r
?
r
r
?
$
?
r
r
$
r
r
$
Zero
Coupon
Bond
Multiple Multiple
Periods Payments
$
r
r
$
?
$
Coupon Bond
Annuities
Overview of Financial MarketsPerpetuities
$
Valuing Zero-Coupon Bonds



Makes one cash flow at maturity
Consider a T-Bill issued by the government that pays
$1000 in one year; the interest rate is 10%
What is the price of the bond?
1000
?
Today
77
1 Year Later
Overview of Financial Markets
Valuing Coupon Bonds



A coupon bond makes pays back only the principal at
the maturity but makes intermittent interest payments
Consider a T-Bill issued by the government that pays
$1000 in 5 years and $10 in every prior year
What is the price of the bond?
1000
50
Today
78
5 Years Later
Overview of Financial Markets
Developing Valuation Tool
Multiple Periods
One Period
Future
Value
Present
Value
Pricing
Real
Securities
79
r
r
$
?
?
r
$
r
r
$
r
?
r
r
?
$
?
r
r
$
r
r
$
Zero
Coupon
Bond
Multiple Multiple
Periods Payments
$
r
r
$
?
$
Coupon Bond
Annuities
Overview of Financial MarketsPerpetuities
$
FV of Multiple Cash Flows

Consider the following investment plan:




Time Line:
t0
$7,000
80
You deposit $7,000 today
You deposit $4,000 at the end of each of the next
3 years
Assuming the interest rate is 8%, how much will
you have in 4 years?
t1
$4,000
t2
t3
t4
$4,000
$4,000
?
Overview of Financial Markets
FV of Multiple Cash Flows

Method 1: Rolling over cash-flows
t0
$7,000
81
t1
x1.08
$4,000
$7,560
$11,560
t2
t3
$4,000.0
$4,000.00
x1.08
x1.08
$12,484.8
$17,803.58
$16,484.8
$21,803.58
Overview of Financial Markets
t4
x1.08
23,547.87
FV of Multiple Cash Flows

Method 2: Calculate the future value of each cash
flow
t0
t1
t2
t3
$7,000
$4,000
$4,000.0
t4
$4,000.00
x1.08
x(1.08)2
x(1.08)3
x(1.08)4
$4,320.00
$4,665.60
$5,038.85
$9,523.42
$23,547.87
82
Overview of Financial Markets
PV of multiple cash flows

Pricing a stream of cash flows
t0
t1
Get $CF(1)
$CF(1)/(1+r)
$CF(2)/(1+r)2
$CF(3)/(1+r)3
t2
t3
Get $CF(2)
G
Get $CF(3)
P
83
t 1
CF (t )
(1  r ) t
Get $CF(4)
/(1+r)
/(1+r)2
/(1+r)3
/(1+r)4
$CF(4)/(1+r)4
4
t4
Overview of Financial Markets
Pricing Coupon Bonds

Bond w/ $100 FV, maturity of 4 years, $5 annual coupon,
discounted at 10% interest rate
t0
t1
Get $5
$5/(1+.10)
$5/(1+.10)2
$5/(1+.10)3
$105/(1+.10)4
4
P
t 1
84
t2
Get $5
/(1+.10)
/(1+.10)2
/(1+.10)3
/(1+.10)4
CF (t )
 84.15
t
(1  r )
Overview of Financial Markets
t3
Get $5
t4
Get $105
Developing Valuation Tool
Multiple Periods
One Period
Future
Value
Present
Value
Pricing
Real
Securities
85
r
r
$
?
?
r
$
r
r
$
r
?
r
r
?
$
?
r
r
$
r
r
$
Zero
Coupon
Bond
Multiple Multiple
Periods Payments
$
r
r
$
?
$
Coupon Bond
Annuities
Overview of Financial MarketsPerpetuities
$
Perpetuity

Security that pays a fixed cash flow, C, every
period, forever. The interest rate is r.
t=0
Pay $P
t=1
t=2
Get $C
Get $C
t=3
Get $C
…
C
C
C
P

2 
3 ..
1 r (1 r) (1 r)

C

t
t 1 (1 r)
86
Overview of Financial Markets
Deriving the perpetuity formula

Eq1:

Eq2 = Eq1*(1+r):

Subtract Eq1 from Eq2:
C
C
C
P

2 
3 ...
1 r (1 r) (1 r)
C
C
 P(1 r) C 

2  ...
1 r (1 r)
 P(1 r)  P  C
C
P
r


C
C

t
prove
r
t 1 (1 r)
Extra credit:
expansion. Due next class.
87

using a Taylor
Overview of Financial Markets
Example III- Perpetuity

Paying Forever:



88
Suppose that maintenance of a grave costs $100 every
year, forever.
The interest rate is 5% per year.
How much should you leave the trustee of a grave?
Overview of Financial Markets
Annuity


t=0
Security that pays a fixed cash flow, C, for T
periods. The interest rate is r.
How can we relate this to our perpetuity
formula?
T
C
C 
1 
P 
 1 
t 
T 
(1
r)
r
(1
r)


t 1
t=1
t=2
t=3
Get $C
Get $C
Get $C
…
t=T

Pay $P
89
Overview of Financial Markets
Get $C
Example IV - Annuity

What value car can you afford?
 You have no cash now
 You can afford to pay $632 per month
 The interest rate is 1% per month
 You want to have paid the loan in full in 48 months
C
C 
1 
P 
 1 
t 
T 
r  (1 r) 
t 1 (1 r)
T

90
Overview of Financial Markets
Developing Valuation Tool
RWJ 4, 5.1-5.2
Multiple Periods
One Period
Future
Value
Present
Value
Pricing
Real
Securities
91
r
r
$
?
?
r
$
r
?
H1_4
H1_1
r
r
$
r
?
r
Multiple Multiple
Periods Payments
$
$
r
r
$
Zero
Coupon
Bond
Overview of Financial Markets
?
r
r
$
r
r
$
?
$
$
Coupon Bond
Annuities
Perpetuities
H1_2
Putting it all together – Single vs.
Multiple Cash Flow


You win the New York State Lottery, Jackpot is
$3.0 million
You have a choice:




92
$1.5 million today
$150,000 annual payments for 20 years
The interest rate available to you is 5% a year
Which option do you prefer?
Overview of Financial Markets
Putting it all together – Single vs.
Multiple Cash Flow
Time 0
1 Year
2 Years
3 Years
4 Years
1 Year
2 Years
3 Years
4 Years … 20 Years
5 Years
$1.5m
Time 0
$150,000 $150,000 $150,000 $150,000
93
Overview of Financial Markets
$150,000
Adding Risk




94
What changes if the cash flows are risk?
How much a 50% chance of getting $100 in 1
month worth?
Is it worth more or less than a 60% chance of
$100 in a month
Is it worth more or less than a 100% chance of
getting $50 in one month?
Overview of Financial Markets
Return Measures
Return Measures
96

Price: amount paid for an asset

Return: measure of profits earned
on the investment

Return = Realized Payoff/Price
Overview of Financial Markets
Outline: Return Measures

Fixed Income Returns (Interest Rates)




Quoted rate (= Annual Percentage Rate)
Effective Annual Rate
Continuous Compounding
Stock Returns

Single-period return:


Multiple-period returns:



97
Holding Period Return
Arithmetic average
Geometric average
Internal Rate of Return
Overview of Financial Markets
Compounding






98
Up to now: annual compounding
Suppose you can invest $100 in an account that
compounds every six months (pays 5% every six
months)
How much do you have in six months? In one
year?
Is this the same as 10% compounded annually?
Is this the same as 10.25% compounded annually?
This rate is quoted as “10% per year with semiannual compounding” (this is the convention)
Overview of Financial Markets
Quoted Interest Rates and EAR

FORMULA: Quoted interest rates are in the
following format:
“[quoted rate] compounded [period]”
• For example: “10% compounded semi annually”
means that the investment is compounded twice a
year at a periodic rate of 5%.

99
RESULT OF FORMULA: Effective Annual Rate
(EAR) in this case is 10.25% year
Overview of Financial Markets
Quoted Interest Rates

Quoted rate: 10% , compounded semi-annually
2
 10% 
EAR  1 
 -1
2% 

$100
x(1+.05)
$105
x(1+.05)
$110.25
x(1+.1025)
1\1\2008
100
7\1\2008
Overview of Financial Markets
1\1\2009
Quoted Interest Rates

The relationship between quoted rates and EAR
(M is number of compounding periods):
M
 quoted rate 
EAR  1 
 -1
M


$100
x(1+q/M)
$105
x(1+q/M)
$110.25
x(1+EAR)
1\1\2008
101
7\1\2008
Overview of Financial Markets
1\1\2009
Quoted Interest Rates

Which loan would you prefer?



102
Bank A :15% compounded monthly
Bank B: 15.1% compounded quarterly
Bank C: 15.2% compounded annually
Overview of Financial Markets
Continuous Compounding





Consider increasingly frequent compounding:
annually, quarterly, daily, every second,…
What happens to the EAR?
When Compounding happens “all the time”, it is
called continuous compounding
Quoted Rate = 10%
EAR = exp(quoted rate) – 1
In our example: EAR = 10.52


q

 r
EAR  lim 1   - 1   e  1
M 


 M 

Period
M
EAR
Year
1
10.000000%
QRT
4
10.381290%
Month
12
10.471310%
Day
365
10.515580%
M
Minute 525,600 10.517090%
103
Overview of Financial Markets
APR




104
Lenders are required by law to report the Annual
Percentage Rate, APR.
APR is the Quoted Rate we discussed: APR =
periodic rate * #periods per year
The APR represents simple interest and therefore
is the incorrect way to measure annual returns
Nonetheless, credit cards and others making loans
to consumers are often required to report it
Overview of Financial Markets
Example - APR

Your credit card has the following terms:




Quoted Rate = 18%, compounded monthly
Periodic Rate = 1.5% per month
APR = 12*1.5% = 18% per year
You missed a payment of $1 today, how
much will the credit card company charge
you in a year?
12
 0.18 
EAR  1 
 - 1  19.56%
12 

105
Overview of Financial Markets
Outline: Return Measures

Fixed Income (Interest Rates)




Quoted rate (= Annual Percentage Rate)
Effective Annual Rate
Continuous Compounding
Stock Returns

Single-period return:


Multiple-period returns:



106
Holding Period Return
Arithmetic average
Geometric average
Internal Rate of Return
Overview of Financial Markets
Holding Period Return (HPR) Example

Holding Period Return – general definition:
Ending Value Of Asset
HPR 
1
Beginning Value Of Asset

Holding Period Return for stock:
ending price  cash dividend
HPR 
beginning price

Annualized HPR for holding period of T years:
Annualized HPR  (1  HPR)1/ T  1
107
Overview of Financial Markets
1
Holding Period Return (HPR) – Stock
Example
Firm
$86
Investor A buys a
stock for $86
Dividend
of $1.60
Investor A
Investor B
$99
99  1.60
HPR 
 1  17%
86
1
AHPR  1.17 4  1  4%
1y
108
After 4 years, she
gets a dividend of
$1.60 and sells
the stock for $99
2y
3y
4y
Overview of Financial Markets
5y
Stock Examples – Holding Period Return (HPR)


109
You bought Coca-Cola shares for $47.99 on 1/1/09
and sold them six months later on 6/1/09 for
$49.02. Suppose there was no dividend payment
in these six months. What is the HPR and the
annualized HPR?
You bought Nike shares on 6/1/07 at $56.70 and
sold the shares 2 years later at $57.05. Suppose
the only dividend is $1.50 paid at the end of year
2. What is the HPR? What is the annualized HPR?
Overview of Financial Markets
Outline: Return Measures

Fixed Income (Interest Rates)




Quoted rate (= Annual Percentage Rate)
Effective Annual Rate
Continuous Compounding
Stock Returns

Single-period return:


Multiple-period returns:



110
Holding Period Return
Arithmetic average
Geometric average
Internal Rate of Return
Overview of Financial Markets
Multiple-Period Return – Arithmetic Average

Simple Average Return (Arithmetic Return)
definition:
1
rA  (r1  r2  r3  ...  rT )
T


111
Not equivalent per-period return because it
neglects compounding
Useful for forecasting the return next period
Overview of Financial Markets
Multiple-Period Return – Geometric Average

Geometric Return definition:
rg  [(1  r1 )(1  r2 )...(1  rT )]
1/ T

Gives the equivalent per-period return
112
Overview of Financial Markets
1
Hedge Fund Example – MultiplePeriod Return

Suppose an Emerging Markets hedge fund has
the following returns:




What is the forecasted return for year 3?
What is the return if:


113
Year 1: r1 = -50%
Year 2: r2 = 100%
1st year profits are reinvested?
1st year profits are held as cash?
Overview of Financial Markets
Hedge Fund Example – MultiplePeriod Return

Suppose an Emerging Markets hedge fund has
the following returns:




What is the forecasted return for year 3?
What is the return if:


114
Year 1: r1 = 100%
Year 2: r2 = -50%
1st year profits are reinvested?
1st year profits are held as cash?
Overview of Financial Markets
Net Present Value




115
NPV: The difference between an investment’s
present value and its cost
NPV = PV(cash flows) – initial costs
If NPV > 0, value is created, undertake
investment
Is it really that simple? What information do we
need to calculate NPV?
Overview of Financial Markets
Discount Rates and Rates of Return
T
FV=PV*(1+r)
HPR = FV/PV - 1 =
116
T
(1+r) -
Overview of Financial Markets
1
Internal Rate of Return (IRR)

IRR is the return that sets the present value of
future cash flows equal to the initial cost
T
C (t )
P(0)  PV  
t
(
1

IRR
)
t 1

P(0)
Used to evaluate projects
117
Overview of Financial Markets
C(1)
C(2)
C(3)
Project Valuation Example:
Internal Rate of Return (IRR)


Pfizer wants to compute the opportunities in
a potential project
The Business plan projects the following cash
flows:





118
Initial investment: $100k
Sales in year 1: $50k
Sales in year 2: $50k
Sales in year 3: $30k
What is the IRR?
Overview of Financial Markets
Outline: Return Measures

H1_6

RWJ 5.3


Quoted rate (= APR)
Effective Annual Rate
Continuous Compounding
Single-period return:


H1_5
Holding Period Return
Multiple-period returns:



119
H1_3
Arithmetic average
Geometric average
Internal Rate of Return
Overview of Financial Markets
BKM 5.1
Next

Reading:


Today: Review concept questions after chapter 4
and chapter 5 of RWJ
Required reading for next class:



120
BKM: 5.1, 5.2, 5.3, 5.5
Investment Game 1 – due class Tuesday, May 31
Problem Set 1 – Due Tuesday, May 31
Overview of Financial Markets
Outline – Week 1


Course Overview
Financial Markets


Why they exist
How they work




Returns

Time value of money




Single cash flow
Multiple cash flows
Perpetuities/annuities
Measures


121
How do borrowers access markets
How do capital markets work
How do investors access markets?
Compounding
Equity cash flows
Overview of Financial Markets