Giddy/ING Barings
Equity Instruments /1
New York University/ING Barings
Equity Instruments
And
Portfolio Construction
Prof. Ian Giddy
New York University
Equity Instruments
Equity in financing
l Rights
l Warrants
l Convertibles
l
Copyright ©1998 Ian H. Giddy
Equity instruments 2
Giddy/ING Barings
Equity Instruments /2
Equity
What it is
l How it’s issued
l
Copyright ©1998 Ian H. Giddy
Equity instruments 3
Debt vs. Equity
Copyright ©1998 Ian H. Giddy
Assets
Liabilities
Value
Value
of
offuture
future
cash
cashflows
flows
Claims
Claimson
on
the
cash
flows
the cash flows
Equity instruments 4
Giddy/ING Barings
Equity Instruments /3
Debt vs Equity
Assets
Liabilities
Debt
Value
Value
of
offuture
future
cash
cashflows
flows
Contractual
Contractualint.
int.&&principal
principal
No
upside
No upside
Senior
Seniorclaims
claims
Control
Controlvia
viarestrictions
restrictions
Equity
Residual
Residualpayments
payments
Upside
Upsideand
anddownside
downside
Residual
claims
Residual claims
Voting
Votingcontrol
controlrights
rights
Copyright ©1998 Ian H. Giddy
Equity instruments 5
Methods of Issuing New Securities
Method
Public Offerings
Negotiated Cash Offer
Type
Definition
Firm Commitment
Cash Offer
Company negotiates agreement
with investment banker to
underwrite and distribute the new
stocks.
Investment bankers sell as much
as possible at the agreed-upon
price. No guarantee as to how
much cash will be raised.
Company offers new stock directly
to existing stockholders.
Similar to direct rights offer, but
net proceeds are guaranteed by
the underwriters.
Best Efforts Cash Offer
Privileged Subscription
Direct Rights Offer
Standby Rights Offer
Copyright ©1998 Ian H. Giddy
Equity instruments 6
Giddy/ING Barings
Equity Instruments /4
Methods of Issuing New Securities
(concluded)
Method
Public Offerings
Nontraditional Cash Offer
Type
Definition
Shelf Cash Offer
Qualifying companies can
authorize all shares they expect to
sell over a two year period and sell
them when needed.
Company can elect to award
underwriting contract through a
public auction instead of
negotiation.
Competitive Firm
Cash offer
Private Offerings
Private
Direct Placement
Securities are sold directly to
purchaser, who, at least until very
recently, generally could not resell
securities for at least two years.
Copyright ©1998 Ian H. Giddy
Equity instruments 7
Equity Issuance: A Red Herring
Subject to Completion, Dated December 19, 1989
25,000,000 Shares
The Reader’s Digest Association, Inc.
Class A Nonvoting Common Stock
(par value $0.01 per share)
Of the 25,000,000 shares of Class A Nonvoting Common Stock offered,
21,000,000 are being offered hereby in the United Sates and 4,000,000 are being
offered in a concurrent international offering outside the United States. The initial
public offering price and the aggregate underwriting discount per share will be
identical for both Offerings. The closing of the U.S. Offering is a condition to the
closing of the International Offering, but the closing of the International Offering is
not a condition to the closing of the U.S. Offering. See “Underwriting”.
All of the shares of Class A Nonvoting Common Stock offered are being sold by
the Selling Stockholders. See “Selling Stockholders”. The Company will not receive
any of the proceeds from the sale of shares by the Selling Stockholders. (continued)
Copyright ©1998 Ian H. Giddy
Equity instruments 8
Giddy/ING Barings
Equity Instruments /5
A Red Herring (continued)
Prior to the Offerings, there has been no public market for shares of Class A
Nonvoting Common Stock. It is currently anticipated that the initial public offering
price will be in the range of $18 to $22 per share. For the factors to be considered in
determining the public offering price, see “Underwriting”.
Application will be made to list the shares of Class A Nonvoting Common Stock
on the New York Stock Exchange.
These securities have not been approved or disapproved by the securities and
exchange commission nor has the commission passed upon the accuracy or
adequacy of this prospectus. Any representation to the contrary is a criminal
offense.
(continued)
Copyright ©1998 Ian H. Giddy
Equity instruments 9
A Red Herring (continued)
Initial Public
Underwriting
Proceeds to Selling
Discount (1)
Stockholders (2)
Offering Price
Per Share............ $
$
$
Total (3)............... $
$
$
(1) The Company and the Selling Stockholders have agreed to indemnify the
Underwriters against certain liabilities, including liabilities under the
Securities Act of 1933.
(2) Before deducting expenses, estimated to be $
, of which
$
will be payable by the Company and $
will be payable by
the Selling Stockholders.
(3) The Selling Stockholders have granted the U.S. Underwriters an option for 30
days to purchase up to an additional 3,150,000 shares at the initial
public offering price per share, less the underwriting discount, solely to
cover over-allotments. Additionally, the Selling Stockholders have granted an
over-allotment option with respect to an additional 600,000 shares as part of the
International Offering. If such options are exercised in full, the total initial public
offering price, underwriting discount and proceeds to
Selling Stockholders will be $
and $
, respectively.
See “Underwriting”. (continued)
Copyright ©1998 Ian H. Giddy
Equity instruments 10
Giddy/ING Barings
Equity Instruments /6
A Red Herring (concluded)
The shares offered hereby are offered severally by the U.S. Underwriters, as
specified herein, subject to receipt and acceptance by them and subject to their
right to reject any order in whole or in part. It is expected that the certificates for the
Shares will be ready for delivery at the offices of Goldman, Sachs & Co., New York,
New York on or about
, 1990.
`
Goldman, Sachs & Co.
Lazard Freres & Co.
The date of this Prospectus is
,1990.
Information contained herein is subject to completion or amendment. A registration
statement relating to these securities has been filed with the Securities and Exchange
Commission. These securities may not be sold nor may offers to buy be accepted prior to
the time the registration statement becomes effective. This prospectus shall not constitute
an offer to sell or the solicitation of an offer to buy nor shall there be any sale of these
securities in any State in which such offer, solicitation or sale would be unlawful prior to
registration or qualification under the securities laws of any such State.
Copyright ©1998 Ian H. Giddy
Equity instruments 11
Tombstone Ad of an Equity Offering
58,750 Shares
Consolidated Rail Corporation
Common Stock
(par value $1.00 per share)
__________
Price $28 Per Share
__________
The shares are being sold by the United States Government pursuant to the Conrail Privatization
Act. The Company will not receive any proceeds from the sale of the shares.
Upon request a copy of the Prospectus describing these securities and the business of the Company may be
obtained within any State from any Underwriter who may legally distribute it within such State. The securities are
offered only by means of the Prospectus, and this announcement is neither an offer to sell nor a solicitation of any
offer to buy.
52,000,000 Shares
The portion of the offering is being offered in the United States and Canada by the undersigned.
(continued)
Copyright ©1998 Ian H. Giddy
Equity instruments 12
Giddy/ING Barings
Equity Instruments /7
Tombstone Ad (continued)
Goldman, Sachs & Co.
The First Boston Corporation
Merrill Lynch Capital Markets
Morgan Stanley & Co.
Salomon Brothers, Inc.
Shearson Lehman Brothers, Inc.
Alex Brown & Sons Dillon, Read &Co. Inc. Donaldson, Lufkin & Jenrette Drexel Burnham Lambert Hambrecht & Quist E.F. Hutton & Co. Inc.
Incorporated
Securities Corporation
Kidder, Peabody & Co.
Lazard Freres & Co.
Incorporated
Montgomery Securities
Incorporated
Prudential-Bache Capital Funding
Rbertson, Colman & Stephens
Incorporated
L.F. Rothschild, Unterberg, Towbin, Inc.
Smith Barney, Harris Upham & Co.
Wertheim Schroeder & Co.
Incorporated
Dean Witter Reynolds Inc.
Incorporated
William Blair & Company J.C. Bradford & Co. Dain Bosworth A.G. Edwards & Sons, Inc. McDonald & Company Oppenheimer & Co., Inc.
Incorporated
Piper, Jaffray & Hopwood
Incorporated
Incorporated
Prescott, Ball & Turben, Inc.
Thomson McKinnon Securities Inc.
Wheat, First Securities, Inc.
Incorporated
Advest, Inc.
American Securities Corporation
Arnhold and S.Bleichroeder, Inc.
Robert W. Baird & Co.
Bateman, Eichler, Hill Richard's
Incorporated
Incorporated
Sangfroid C. Bernstein & Co Inc Blunt Ellis & Loewl Boettcher & Co Inc Burns Fry and Timmins Inc Butcher & Singer Inc Cowen & Company
Incorporated
Dominion Securities Corporation
Eberstadt Fleming Inc
Furman Selz Mager Dietz & Birney
Gruntal & Co Inc
Eppler, Guerin & Turner Inc
First of Michigan Corp.
Howard, Well, Laboulsse, Friedrichs
Incorporated
First Southwest Company
Interstate Securities Corporation
Incorporated
Janney Montgomery Scott Inc Johnson, Lane Smith & Co Inc. Johnston, Lemon & Co. Josephthal & Co. Ladenburg, Thalmann & Co Inc.
Incorporated
Incorporated
Cyrus J. Lawrence Legg Mason Wood Walker Morgan Keegan & company Inc Moseley Securities Corporation Needham & Company Inc.
Incorporated
Neuberger & Berman
Incorporated
The Ohio Company Rauscher Pierce Refanes Inc
Stifel, Nicolaus & Company
Sutro & Co.
Incorporated
The Robinson-Humphrey Co Inc
Tucker, Anthony & R. L. Day, Inc.
Rothschild Inc
Underwood, Neuhaus & Co.
Incorporated
Stephens Inc
Wood Grudy Corp.
Incorporated
(continued)
Copyright ©1998 Ian H. Giddy
Equity instruments 13
A Tombstone Ad (concluded)
This special bracket of minority-owned and controlled firms assisted the Co-Lead
Managers in the United States Offering pursuant to the Conrail Privatization Act:
AIBC Investment Services Corporation
WR Lazard Securities
Daniels & Bell, Inc.
Pryor, Govan Counts & Co. Inc.
Dolsey Securities, Inc.
Muriel Siebbert & Co., Inc.
6,750,000 Shares
This portion of the offering is being offered outside the United States and Canada by the undersigned
Goldman Sachs International Corp.
First Boston International Limited
Merrill Lynch Capital Markets
Morgan Stanley International
Salomon Brothers International Limited
Shearson Lehman Brothers International
Algemene Bank Nederland N.V.
Banque Bruxelles Lambert S.A.
Banque Nationale de Paris
Cazenove & Co.
The Nikko Securities Co.
(Europe) Ltd.
Nomura International
N.M.. Rothschild & Sons
J. Henry Schroder Wagg & Co.
Societe Generale
S. G. Warburg Securities
Limited
Limited
Limited
ABC International Ltd.
Banque Paribas Capital Markets Limited
Calsse Nationale de Credit Agricole
Compagnie de Banque et d’investissements,
CBI
Credit Lyonnais
Daiwa Europe
IMI Capital Markets (UK) Ltd.
Joh. Berenberg, Gossier & Co.
Leu Securities Limited
Limited
Morgan Greenfell & Co.
Peterbroeck, van Campenhout & Cie SCS
Swiss Volksbank
Vereins-und Westbank
Aldengrundschaft
J. Vontobel & Co. Ltd.
M. M. Warburg-Brinckmann, Wirtz & Co.
Westdeutsche Landesbank
Yamaichi International (Europe)
Limited
March 27, 1967
Copyright ©1998 Ian H. Giddy
Equity instruments 14
Giddy/ING Barings
Equity Instruments /8
Rights Offerings
l Rights
offering
l Share rights
l Offering terms
l Subscription price
l Number of rights to purchase
a share
l Value of a right
Copyright ©1998 Ian H. Giddy
Equity instruments 15
Ex Rights Stock Prices
Rights On
Announcement
date
September 30
Rights-on
price
$20.00
Ex Rights
Ex-rights
date
October 13
Record
date
October 15
$3.33 =Value of a right
Ex-rights
price
$16.67
Copyright ©1998 Ian H. Giddy
Equity instruments 16
Giddy/ING Barings
Equity Instruments /9
The Value of a Right
The value of a right equals the difference in the
price of the issuer’s outstanding shares
before and after the rights offering, and is
determined by three factors:
- the total amount of money to be raised,
- the subscription price of the new shares,
and
- the number of existing shares.
The number of new shares to be issued equals
(Funds to be raised)/Subscription price
Copyright ©1998 Ian H. Giddy
Equity instruments 17
The Value of a Right (concluded)
The number of rights needed to buy one share
equals
(Number of old shares)/(Number of new
shares)
After the offering, the new value of the firm is
Pre-offering firm value + funds raised,
and the new share price must be
(New firm value)/(Total number of shares
outstanding).
The value of the right must equal
Old share price - new share price.
Copyright ©1998 Ian H. Giddy
Equity instruments 18
Giddy/ING Barings
Equity Instruments /10
Rights Offering: Example
Rio Algom Mining Co. is proposing a rights offering.
Presently there are 250,000 shares outstanding at
$50 each. There will be 50,000 new shares offered at
$40 each.
a. What is the new market value of the company?
b. How many rights are associated with one new
share?
c. What is the ex-rights price?
d. What is the value of a right?
e. Why might a company have a rights offering rather
than a general cash offer?
Copyright ©1998 Ian H. Giddy
Equity instruments 19
Rights Offering: Example (cont.)
a. New value = (250,000 × $50) + (50,000
× $40) = $14.5 million
b. There will be (250,000/ _______ ) = ____
rights associated with each new share.
c. The ex-rights price is $14.5 million/300,000 =
$48.33.
d. The value of one right equals $____ − 48.33
= $1.67.
Copyright ©1998 Ian H. Giddy
Equity instruments 20
Giddy/ING Barings
Equity Instruments /11
What is the Effect of an Equity Offering
on Shareholder Value?
l Dilution
- loss in existing
shareholders’ value
l Dilution of proportionate
ownership
l Dilution of market value
l Dilution of book value and
earnings per share (EPS)
l Under what circumstances does
market value dilution occur?
Copyright ©1998 Ian H. Giddy
Equity instruments 21
Debt vs Equity
Assets
Liabilities
Debt
Value
Value
of
offuture
future
cash
cashflows
flows
Contractual
Contractualint.
int.&&principal
principal
No
upside
No upside
Senior
Seniorclaims
claims
Control
Controlvia
viarestrictions
restrictions
Equity
What if...
Claims
are inadequate?
Returns
are inadequate?
Residual
Residualpayments
payments
Upside
and
Upside anddownside
downside
Residual
Residualclaims
claims
Voting
Votingcontrol
controlrights
rights
Copyright ©1998 Ian H. Giddy
Equity instruments 22
Giddy/ING Barings
Equity Instruments /12
When Debt and Equity are Not Enough
Assets
Liabilities
Alternatives
n
Debt
Value
Value
of
offuture
future
cash
cashflows
flows
Contractual
Contractualint.
int.&&principal
principal
No
upside
No upside
Senior
Seniorclaims
claims
Control
Controlvia
viarestrictions
restrictions
Equity
Residual
Residualpayments
payments
Upside
Upsideand
anddownside
downside
Residual
claims
Residual claims
Voting
Votingcontrol
controlrights
rights
Copyright ©1998 Ian H. Giddy
n
n
n
n
n
Collateralized
Asset-securitized
Project financing
Preferred
Warrants
Convertible
Equity instruments 23
Equity-Linked Bonds
Bonds with warrants
l Convertible Bonds
l Index-linked Bonds
l
These are all example of hybrid bonds
and should be priced by decomposition
Copyright ©1998 Ian H. Giddy
Equity instruments 24
Giddy/ING Barings
Equity Instruments /13
Stock-Purchase Warrants
l
l
l
l
l
Warrants are usually detachable and trade on the
securities exchanges
Warrants are often added to a large debt issue as
“sweeteners” to enhance the marketability of the
issue
Exercise price
Warrants usually have a limited life of about 10
years or less
Warrants differ from rights and convertibles
Copyright ©1998 Ian H. Giddy
Equity instruments 25
The Implied Price of an Attached
Warrant
l
l
l
To determine the implied price of an attached
warrant, the implied price of all warrants attached
to a bond must be determined
Implied price of all warrants = price of bond with
warrants attached - the straight bond value (of
similar-risk bonds)
The implied price of a single warrant is the implied
price of all warrants divided by the number of
warrants attached to each bond
Copyright ©1998 Ian H. Giddy
Equity instruments 26
Giddy/ING Barings
Equity Instruments /14
The Value of Warrants
l
l
A warrant has a “theoretical value” at any point in
time prior to its expiration date
The theoretical value can be calculated as:
TVW = (Po - E) x N
WHERE:
TVW =
Po
=
E
N
=
=
Theoretical value of a warrant
Current market price of one share of
common stock
Exercise price of the warrant
Number of shares of common stock
obtainable with one warrant
Copyright ©1998 Ian H. Giddy
Equity instruments 27
Sony Warrants
l
l
Sony Electronics has outstanding warrants
exercisable at Yen400/share that entitle holders
to purchase three shares of common stock per
warrant. If Sony’s common stock is currently
selling for Y45/share, the TVW =
TVW = (Y45 - Y40) x 3 = Y15
The market value of a warrant is generally greater
than its theoretical value; the difference, known
as the warrant premium is due to investor
expectations and opportunities for further gain
before expiration.
Copyright ©1998 Ian H. Giddy
Equity instruments 28
Giddy/ING Barings
Equity Instruments /15
Copyright 1994, HarperCollins Publishers
Values and Warrant Premium
V
a
l
u
e
o
f
W
a
r
r
a
n
t
Market
Value
Market Premium
“Theoretical
Value”
($)
0
Price Per Share of Common Stock ($)
Copyright ©1998 Ian H. Giddy
Equity instruments 29
Convertible Bonds
Bond may be converted into stock
l The Conversion Ratio is the number of
shares of common stock that can be
received in exchange for each
convertible security
l The Conversion Price is the per share
common stock price at which the
exchange effectively takes place
l
Copyright ©1998 Ian H. Giddy
Equity instruments 30
Giddy/ING Barings
Equity Instruments /16
Convertibles
u
u
u
The Conversion Period is a limited time
within which a security may be exchanged
for common stock
The Conversion Value is the market value of
the security based upon the conversion
ratio times the current market price of the
firm's common stock
Earnings effects:
w Firms must report Primary EPS, treating all contingent securities
that derive their value from their conversion privileges or
common stock characteristics as common stock
w Firms must report Fully Diluted EPS treating all contingent
securities as common stock
Copyright ©1998 Ian H. Giddy
Equity instruments 31
Example: Hyundai Euroconvertible
l
If Hyundai issues a Eurobond with a $1,000 par
value that is convertible at $40 per share of
common stock, the conversion ratio =
$1,000 = 25
$40
l If Hyundai had stated the conversion ratio at 20,
the conversion price =
$1,000 = $50
20
Copyright ©1998 Ian H. Giddy
Equity instruments 32
Giddy/ING Barings
Equity Instruments /17
Financing With Convertibles
l
l
Motives for using convertibles include:
u It is a deferred sale of common stock that decreases
the dilution of both ownership and earnings
u They can be used as a “sweetener” for financing
u They can be sold at a lower interest rate than
nonconvertibles
u They have far fewer restrictive covenants than
nonconvertibles
u It provides a temporarily cheap source of funds
(assuming bonds) for financing projects
Most convertibles have a call feature that enables the
issuer to force conversion when the price of the common
stock rises above the conversion price
Copyright ©1998 Ian H. Giddy
Equity instruments 33
Determining the Value of a Convertible
Bond
There are three values associated with a
convertible bond:
u Straight
Bond Value is the price at which the bond
would sell in the market without the conversion feature
u The Conversion Value is the product of the current
market price of stock times the conversion ratio of the
bond
u The Market Value is the straight or conversion value
plus a market premium based upon future (expected)
stock price movements that will enhance the value of
the conversion feature
Copyright ©1998 Ian H. Giddy
Equity instruments 34
Giddy/ING Barings
Equity Instruments /18
Siam Cement
l
Siam Cement sold a $1,000 par value, 20-year convertible bond with
a 12% coupon. A straight bond would have been sold with a 14%
coupon. The conversion ratio is 20
l Straight Bond Value
$120 x (PVIFA14%,20) + $1,000 x (PVIF14%,20) =
$120 x (6.623) + $1,000 x (.073) = $867.76
u Conversion
Value at various market prices of stock
Stock Price
Conversion Value
$30
40
50 (Conversion Price)
60
70
80
$
600
800
1,000 (Par Value)
1,200
1,400
1,600
The straight bond value is the minimum price at which the convertible
bond would be traded
l
Copyright ©1998 Ian H. Giddy
Equity instruments 35
Values and Market Premium
V
a
l
u
e
Conversion Value
Market Premium
o
f
C
o
n
v
e
r
t
i
b
l
e
Straight
Bond Value
B
o
n
d
($) 0
Price Per Share of Common Stock
Copyright ©1998 Ian H. Giddy
Equity instruments 36
Giddy/ING Barings
Equity Instruments /19
Equity Markets and Instruments
l
What is Equity?
u Common
u Rights
offerings
u Hybrids: warrants & convertibles
l
What Influences Equity Values?
u Macroeconomic
factors
u Industry
factors
u Firm factors
Copyright ©1998 Ian H. Giddy
Equity instruments 37
Framework of Analysis
l
l
l
Fundamental Analysis
Approach to Fundamental Analysis
u Domestic and global economic analysis
u Industry analysis
u Company analysis
Why use the top-down approach?
Copyright ©1998 Ian H. Giddy
Equity instruments 38
Giddy/ING Barings
Equity Instruments /20
New York University/ING Barings
Portfolio Diversification
and the
Capital Asset Pricing Model
Prof. Ian Giddy
New York University
Equity Risk and Return: Summary
Investors diversify, because you get a
better return for a given risk.
l There is a fully-diversified “market
portfolio” that we should all choose
l The risk of an individual asset can be
measured by how much risk it adds to
the “market portfolio.”
l
Copyright ©1998 Ian H. Giddy
Equity instruments 40
Giddy/ING Barings
Equity Instruments /21
Capital Allocation Possibilities:
Treasuries or an Equity Fund?
Expected Return
THE EQUITY FUND
E(rP)
=17%
P
10%
rf=7%
7%
σ P=27%
Risk
Copyright ©1998 Ian H. Giddy
Equity instruments 41
We Can Buy Some T-bills and Some of
the Risky Fund...
E(R)
17%
ONE PORTFOLIO:
30% Bills, 70% Fund
E(R)=.3X7+.7X17=14%
SD=.7X27=18.9%
C.A.L.
SLOPE=0.37
14%
rf=7%
18.9%
Copyright ©1998 Ian H. Giddy
27%
SD
Equity instruments 42
Giddy/ING Barings
Equity Instruments /22
...Or Buy Two Risky Assets
E(r)
A
B
σ
Copyright ©1998 Ian H. Giddy
Equity instruments 43
Diversification
Asset F
R
e
t
u
r
n
R
e
t
u
r
n
k
Time
Copyright ©1998 Ian H. Giddy
Portfolio of
Assets F and G
Asset G
R
e
t
u
r
n
k
Time
k
Time
Equity instruments 44
Giddy/ING Barings
Equity Instruments /23
Portfolio Return...
To compute the return of a portfolio: use the
weighted average of the returns of all
assets in the portfolio, with the weight given
each asset calculated as
(value of asset)/(value of portfolio).
The portfolio return E(Rp) is:
E(Rp) = (w1k1)+(w2k2)+ ... (wnkn) =
Σ
wj kj
where wj = weight of asset j, kj = return on asset j
Copyright ©1998 Ian H. Giddy
Equity instruments 45
...and Risk (Standard Deviation)
Portfolio return is the weighted average
of all assets’ returns,
l But portfolio standard deviation is
normally less than the weighted average
of all assets’ standard deviations!
l The reason: asset returns are
imperfectly correlated.
l
Copyright ©1998 Ian H. Giddy
Equity instruments 46
Giddy/ING Barings
Equity Instruments /24
Risk and Return of Stocks, Bonds and
a Diversified Portfolio
Rate of Return
State
Prob. Equity Bond Portfolio
Recession 1/3
-7%
+17%
+5%
Normal
1/3
+12%
+7%
+9.5%
Boom
1/3
+28%
-3%
+12.5%
Expected Return
11%
7.0%
Variance
204.7% 66.7%
Standard Deviation 14.3% 8.2%
9.0%
9.5%
3.1%
Copyright ©1998 Ian H. Giddy
Equity instruments 48
The Correlation Between Stock and
Bond Returns
l Covariance
= ∑ ps [Rs,e − E(Re )] × [Rs ,b − E(Rb )]
n
s=1
= 0.3333(-7-11)(17-7) + 0.3333(12-11)(7-7)
+0.3333(28-11)(-3-7)
= -116.67
l
Correlation
cove,b
σeσ b / 14.3(8.2)
= -116.66
=
= -0.99
Copyright ©1998 Ian H. Giddy
Equity instruments 49
Giddy/ING Barings
Equity Instruments /25
Portfolio Return and Standard
Deviation
Given:
W S = 0.5
W B = 0.5
RS = 12%
RB = 9%
σS = 25%
σB = 12%
and ρS,B = 0.2
Rp = 0.5(12)+0.5(9) = 10.5%
σP = [(0.5)2(25) 2+(0.5) 2(12) 2+2(0.5)(0.5)(25)(12)(0.2)]1/2
= (156.25+36+30)1/2
= (222.25) 1/2
= 14.91%
Copyright ©1998 Ian H. Giddy
Equity instruments 50
The Minimum-Variance Frontier of
Risky Assets
E(r)
Efficient frontier
Individual
assets
Global minimumvariance portfolio
Copyright ©1998 Ian H. Giddy
σ
Equity instruments 51
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The Efficient Frontier of Risky Assets
with the Optimal CAL
E(r)
CAL(P)
Efficient frontier
rf
σ
Copyright ©1998 Ian H. Giddy
Equity instruments 52
The Capital Asset Pricing Model
(CAPM)
CAPM Says:
u The
total risk of a financial
asset is made up of two
components.
A. Diversifiable
(unsystematic) risk
B. Nondiversifiable
(systematic) risk
rf
u The only relevant risk is
nondiversifiable risk.
E(r)
CAL(P)
σ
Copyright ©1998 Ian H. Giddy
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Giddy/ING Barings
Equity Instruments /27
The Equation for the CAPM
Rj = RF + βj (Rm - RF)
where:
Rj
=
RF =
βj
Rm
=
=
Required return on asset j;
Risk-free rate of return
Beta Coefficient for asset j;
Market return
The term [β j(Rm - RF)] is called the risk premium and
(Rm-RF) is called the market risk premium
Copyright ©1998 Ian H. Giddy
Equity instruments 54
www.giddy.org
Ian Giddy
NYU Stern School of Business
Tel 212-998-0332; Fax 212-995-4233
ian.giddy@nyu.edu
http://www.giddy.org
Copyright ©1998 Ian H. Giddy
Equity instruments 58