This document discusses various topics related to pricing shares and stock markets. It begins by defining stocks/shares and describing their nominal, book, and market values. It then distinguishes between ordinary shares and preferred shares, noting their different risk profiles and dividend payment priorities. Various models for valuing shares are presented, including dividend discount models assuming no growth, constant growth, and the capital asset pricing model (CAPM) for calculating the required rate of return. The primary and secondary stock markets are defined, with the primary market involving a company's initial public offering of shares and the secondary market comprising subsequent trading on exchanges. Finally, extraordinary corporate events like capital increases and takeovers are briefly covered.

1. 1
Pricing Shares
A. Caggia, M. Armanini
Financial Investments & Pricing
2015/2016

2. 2
Stocks(Shares)
 Stocks or shares represent the participation of an
individual in the activities of a company in the role of
share-holder, involving some «risk capital».
 Nominal value
 Book value
 Market value
 The cash flow generated by the assets of a company
pay debt obligations and tax first and the remaining goes
to equity.
 Residual Claim characteristic.

3. Ordinary Shares
 Ordinary shares are the most commonly traded shares,
and they give you a vote in company matters.
 They earn a dividend as long as the company is earning
money, and this dividend directly corresponds to the
profit made by the company. High profits mean high
dividends for you.
 Ordinary shares have no special rights or restrictions.
Whilst they have the highest risk, they also have the
potential to bring the biggest financial gains.
3

4. Preferred Shares
 In direct contrast to common shares, these shares are
given preference when it comes to dividend payments.
 More importantly, if a company goes bankrupt, these
shares are paid back before common shares.
 The shareholders of preference shares, however, do not
enjoy normal voting rights.
 Dividends of preference shares have a fixed rate, and
therefore provide more security, but this means that if
the profits of the business increase, the value of
preference shares remains the same. Low risk but only
moderate returns.
4

5. Share valuation (I)
 In order to determine the value today of a share, just like
in any other financial instrument, we must estimate the
PV of its future cashflows
 Shares involve two possible cashflows...
1. Dividends: received by share-holders at regular intervals
2. Market price: received at the time the share-holder decides to
sell its share in the company
5

6. Share valuation (II)
 A share is a financial instrument without a predefined
maturity (perpetual)
 Its price therefore must be calculated from the infinite
series of future dividends or cash flows to equity
 However, the exact value of these future dividends is
unknown. Some simplifications are thus used:
 (a) constant dividends
 (b) constant interest rates
6

7. Dividend Discount Models:
General Model
7
V0 = Value of Stock
Dt = Dividend
k = required return
V
D
k
o
t
t
t
=
+=
∞
∑( )11

8. Dividend Discount Models:
No Growth Model
8
Stocks that have earnings and dividends that are
expected to remain constant
Preferred Stock
V
D
k
o =

9. Dividend Discount Models:
No Growth Model (Example)
9
E1 = D1 = $5.00
k = .15
V0 = $5.00 / .15 = $33.33
V
D
k
o =

10. Dividend Discount Models:
Constant Growth Model
10
g = constant perpetual growth rate
Vo
D g
k g
o
=
+
−
( )1

11. CAPM: a way to calculate K
(Re)
 Assumption: the return of a single stock is related to the
return of the market index
 The relationship according to CAPM is
K=Rf+Beta*(Rm-Rf)=Re
 Where
 K or Re expected return of the single stock (equity)
 Rf risk free rate
 Beta correlation coefficient
 Rm expected return of the market index
11

12. Security Market LineSecurity Market Line

13. Look for AlfaLook for Alfa

14. Beta as a function of Risk PremiaBeta as a function of Risk Premia
 Beta=(Re-Rf)/(Rm-Rf)

15. Share Valuation (III)
 The value of the equity of a company could be calculated as
the difference between the total value of the company and
its debt.
 This methodology implies an estimate of the future cash
flows generated by the business of the company
 This cash flows are then discounted at weighted average
cost of capital
 The value of the debt is then subctracted and the resulting
number represent the value of equity
 This methodology is considered the most accurate and
needs a deep understanding of the company in order to
model its business
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16. Stockmarkets
16

17. Stockmarkets
 The primary market is the market where
securities are created
 The secondary market is one in which they are
traded among investors.
 Knowing how the primary and secondary
markets work is key to understanding how
stocks trade.
17

18. Primary market
 The primary market is the one in which a security
is first issued
 Companies use the primary market to raise capital
 If a company decides to issue securities in order to
raise short- or long-term capital, it enters the
money or capital market as an issuer
 Companies can issue different kinds of securities:
shares, bonds, debt securities, warrants etc
 The proceeds from issuing shares constitute or
increase the company's equity capital. Issuing a
bond constitutes or increases its debt capital 18

19. Primary market
 In a first step, securities such as shares and bonds
are placed directly with investors or indirectly via
banks
 If trading on a stock exchange is desired
(secondary market), among other things, this
involves the duty to publish a prospectus, the
subscription period and the lodging of a listing
application with the stock exchange
 When a joint-stock company goes public, the first
share issue is called the Initial Public Offering
(IPO) 19

20. Secondary market
 The secondary market is the market in which
securities are traded on the stock market
 In the secondary market, companies are not in
search of capital
 You as an investor deal with other buyers and
sellers of securities
 This is where actual stock-exchange trading
takes place. All traded securities are public and
available to everyone.
20

21. Secondary market
 In order for a security to be traded on the
Exchange, the company has to successfully
complete the issuing process and meet various
requirements set out in the Listing Rules
 In order to remain listed, issuers have to carry
out certain duties such as publication of price-
sensitive data. This is why news about listed
companies is published in the media on an
almost daily basis
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22. Secondary market
 The national exchanges are secondary markets
and includes the New York Stock Exchange
(NYSE), Nasdaq and all major exchanges
around the world
 A market where investors purchase securities or
assets from other investors, rather than from
issuing companies themselves
 If you go to buy IBM stock, you are dealing only
with another investor who owns shares in IBM.
IBM (the company) is in no way involved with the
transaction 22

23. Auction vs Dealer Markets
 The secondary market can be further broken down
into two specialized categories:
Auction Market and Dealer Market
 The difference between these two market systems
lies in what is displayed in the market in terms of
orders and bid and ask prices
 The Auction Market is an “Order Driven” market
and displays all of the bids and asks
 The Dealer Market is a “Quote Driven” market
and focuses only on the bids and asks of market
makers and other designated parties 23

24. Quote Driven Market
 Participants are joined through electronic networks
 The dealers hold an inventory of the security in which they
“make a market”
 The dealers then stand ready to buy or sell with market
participants
 These dealers earn profits through the spread between the
prices at which they buy and sell securities
 Nasdaq is a dealer market: here the dealers (market makers)
provide firm bid and ask prices at which they are willing to
buy and sell a security
 The theory is that competition between dealers will provide
the best possible price for investors 24

25. Order Driven Market
 In the auction market, all individuals and institutions that
want to trade securities announce the prices at which they
are willing to buy and sell
 These are referred to as bid and ask prices
 An efficient market should prevail by bringing together all
parties and having them publicly declare their prices
 The best price of a good need not be sought out because
the convergence of buyers and sellers will cause mutually-
agreeable prices to emerge
 The biggest advantage is its transparency: it clearly shows
all of the market orders and what price people are willing to
buy at or sell for
 NYSE is an auction market 25

26. Market Order Book
 An order book is the list of orders (manual or
electronic) that a trading venue (in particular stock
exchanges) uses to record the interest of buyers and
sellers in a particular financial instrument
 A matching engine uses the book to determine which
orders can be fulfilled i.e. what trades can be made
 Market orders:
At market
Limit order (create the order book)
Stop loss / Take profit order
Vwap order … 26

27. Market Order Book
27
Last Time +/- % VWAP Open High Low
44,500€ 10:08:14 0,750€ 1,71% 44,100€ 43,800€ 45,000€ 43,500€
No Quantity Quantity No
4 8119 6418 8
3 4718 1427 2
5 2854 7193 3
2 2323 5670 9
3 3980 2520 2
10 4299 2002 3
1 1047 9939 6
6 7737 3711 4
9 5572 2011 2
7 3109 5278 5
43,9100
44,1600
44,1800
44,4600
44,5000
44,7600
44,8400
45,0700
45,1800
45,2400
45,3700
43,8100
43,7300
43,7100
43,6800
43,5400
SELL
44,5500
44,6100
44,6900
44,7000
BUY

28. 28

29. 29

30. Extraordinary Events
 A company could increase its capital by:
1. Free capital increase
2. Paid capital increase (with or without
prehemption rights)
3. A mixture of the two
 Listed stocks could be subject to takeover offers
1. There are strict stockmarkets rules in case of
takeover offers aimed at protecting minority
shareholders
2. The price of shares might be strongly influenced
by takeover activities
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31. Teoretical Ex Right Price
31