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Essentials of Investments
© 2001 The McGraw-Hill Companies, Inc. All rights reserved.
F ourth Edition
Irwin / McGraw-Hill
Bodie � Kane � Marcus1
Chapter 13
Equity Valuation
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Essentials of Investments
© 2001 The McGraw-Hill Companies, Inc. All rights reserved.
F ourth Edition
Irwin / McGraw-Hill
Bodie � Kane � Marcus2
Fundamental Stock Analysis: Modelsof Equity Valuation
� Basic Types of Models
± Balance Sheet Models
± Dividend Discount Models ± Price/Earning Ratios
� Estimating Growth Rates and
Opportunities
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Essentials of Investments
© 2001 The McGraw-Hill Companies, Inc. All rights reserved.
F ourth Edition
Irwin / McGraw-Hill
Bodie � Kane � Marcus3
Intrinsic Value and Market Price
� Intrinsic Value
± Self assigned Value
± Variety of models are used for estimation
� Market Price
± Consensus value of all potential traders
� Trading Signal
± IV > MP Buy ± IV < MP Sell or Short Sell
± IV = MP Hold or Fairly Priced
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Essentials of Investments
© 2001 The McGraw-Hill Companies, Inc. All rights reserved.
F ourth Edition
Irwin / McGraw-Hill
Bodie � Kane � Marcus4
Dividend Discount Models:General Model
V
D
k o
t
t
t ! !
g
§ ( )11
� V0 = Value of Stock
� Dt = Dividend
� k = required return
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Essentials of Investments
© 2001 The McGraw-Hill Companies, Inc. All rights reserved.
F ourth Edition
Irwin / McGraw-Hill
Bodie � Kane � Marcus5
No Growth Model
V D
k o
!
� Stocks that have earnings and dividends that
are expected to remain constant� Preferred Stock
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Essentials of Investments
© 2001 The McGraw-Hill Companies, Inc. All rights reserved.
F ourth Edition
Irwin / McGraw-Hill
Bodie � Kane � Marcus6
No Growth Model: Example
E1 = D1 = $5.00
k = .15
V0 = $5.00 / .15 = $33.33
V D
k o
!
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Essentials of Investments
© 2001 The McGraw-Hill Companies, Inc. All rights reserved.
F ourth Edition
Irwin / McGraw-Hill
Bodie � Kane � Marcus7
Constant Growth Model
Vo
D g
k g
o!
( )1
� g = constant perpetual growth rate
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Essentials of Investments
© 2001 The McGraw-Hill Companies, Inc. All rights reserved.
F ourth Edition
Irwin / McGraw-Hill
Bodie � Kane � Marcus8
Constant Growth Model: Example
Vo
D g
k g
o!
( )1
E1
= $5.00 b = 40% k = 15%
(1-b) = 60% D1 = $3.00 g = 8%
V0 = 3.00 / (.15 - .08) = $42.86
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Essentials of Investments
© 2001 The McGraw-Hill Companies, Inc. All rights reserved.
F ourth Edition
Irwin / McGraw-Hill
Bodie � Kane � Marcus9
Estimating Dividend Growth Rates
g ROE b! v
� g = growth rate in dividends
� ROE = Return on Equity for the firm
� b = plowback or retention percentage rate
± (1- dividend payout percentage rate)
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Essentials of Investments
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Bodie � Kane � Marcus10
Shifting Growth Rate Model
V Dg
k
D g
k g k
o o
t
t t
T T
T !
!
§( )
( )
( )
( )( )
1
1
1
1
1
1
2
2
� g1 = first growth rate
� g2 = second growth rate� T = number of periods of growth at g1
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Shifting Growth Rate Model: Example
D0 = $2.00 g1 = 20% g2 = 5%
k = 15% T = 3 D1 = 2.40
D2 = 2.88 D3 = 3.46 D4 = 3.63
V0 = D1/(1.15) + D2/(1.15)2 + D3/(1.15)3 +
D4 / (.15 - .05) ( (1.15)3
V0 = 2.09 + 2.18 + 2.27 + 23.86 = $30.40
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F ourth Edition
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Bodie � Kane � Marcus12
Specified Holding Period Model
0
1
1
2
2
1 1 1V
D
k
D
k
D P
k
N N
N !
( ) ( ) ( )
...
� PN
= the expected sales price for the stock at
time N
� N = the specified number of years the stock isexpected to be held
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Partitioning Value: Growth and NoGrowth Components
V E
k PVGO
PVGOD g
k g
E
k
o
o
!
!
1
11( )
( )
� PVGO = Present Value of GrowthOpportunities
� E1 = Earnings Per Share for period 1
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Bodie � Kane � Marcus14
Partitioning Value: Example
� ROE = 20% d = 60% b = 40%
� E1 = $5.00 D1 = $3.00 k = 15%
� g = .20 x .40 = .08 or 8%
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Bodie � Kane � Marcus15
V
NGV
PVGO
o
o
!
!
! !
! !
3
15 0886
515
33
86 33 52
(. . )$42.
.$33.
$42. $33. $9.
Partitioning Value: Example
VVoo = value with growth= value with growthNGVNGVoo = no growth component value= no growth component value
PVGO = Present Value of Growth OpportunitiesPVGO = Present Value of Growth Opportunities
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Price Earnings Ratios
� P/E Ratios are a function of two factors
± Required Rates of Return (k)
± Expected growth in Dividends� Uses
± Relative valuation
± Extensive Use in industry
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Essentials of Investments
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Bodie � Kane � Marcus17
P/E Ratio: No expected growth
P E
k
P
E k
0
1
0
1
1
!
!
� E1 - expected earnings for next year ± E1 is equal to D1 under no growth
� k - required rate of return
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Essentials of Investments
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Bodie � Kane � Marcus18
P/E Ratio with Constant Growth
P D
k g
E b
k b ROE
P
E
b
k b ROE
0
1 1
0
1
1
1
!
!
v
!
v
( )
( )
( )
� b = retention ration� ROE = Return on Equity
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Essentials of Investments
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Bodie � Kane � Marcus19
Numerical Example: No Growth
E0 = $2.50 g = 0 k = 12.5%
P0 = D/k = $2.50/.125 = $20.00
PE = 1/k = 1/.125 = 8
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Numerical Example with Growth
b = 60% ROE = 15% (1-b) = 40%
E1 = $2.50 (1 + (.6)(.15)) = $2.73
D1 = $2.73 (1-.6) = $1.09
k = 12.5% g = 9%
P0 = 1.09/(.125-.09) = $31.14
PE = 31.14/2.73 = 11.4
PE = (1 - .60) / (.125 - .09) = 11.4
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Bodie � Kane � Marcus21
Chapter 10
Bond Prices and Yields
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Essentials of Investments
© 2001 The McGraw-Hill Companies, Inc. All rights reserved.
F ourth Edition
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Bodie � Kane � Marcus22
Bond Characteristics
� Face or par value
� Coupon rate
± Zero coupon bond
� Compounding and payments
± Accrued Interest
� Indenture
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Provisions of Bonds
� Secured or unsecured
� Call provision
� Convertible provision� Put provision (putable bonds)
� Floating rate bonds
� Sinking funds
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Essentials of Investments
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Bodie � Kane � Marcus24
Default Risk and Ratings
� Rating companies
± Moody¶s Investor Service
± Standard & Poor¶s ± Duff and Phelps
± Fitch
� Rating Categories ± Investment grade
± Speculative grade
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Factors Used by Rating Companies
� Coverage ratios
� Leverage ratios
� Liquidity ratios� Profitability ratios
� Cash flow to debt
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Bodie � Kane � Marcus26
Bond Pricing
P C
r
ParValue
r B
t
T
t
T
T
T ! !§ ( ) ( )1 11
PB = Price of the bond
Ct = interest or coupon paymentsT = number of periods to maturity
r = semi-annual discount rate or the semi-annualyield to maturity
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CCtt = 40 (SA)= 40 (SA)PP = 1000= 1000
TT = 20 periods= 20 periodsr r = 3% (SA)= 3% (SA)
PB = $1,148.77
Solving for Price: 10-yr, 8% Coupon
Bond, Face = $1,000
tt=1=1
++772020
==PPBB 4040 11
(1+.03)) t1000 1
(1+.03) 20
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Essentials of Investments
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Bodie � Kane � Marcus28
Bond Prices and Yields
Prices and Yields (required rates of return) have an inverse relationship
� When yields get very high the value of the bond will be very low
� When yields approach zero, the value of
the bond approaches the sum of thecash flows
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Bodie � Kane � Marcus29
Prices and Coupon Rates
Price
Yield
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Approximate Yield to Maturity
YTM = (Avg. Income) / (Avg. Price)
Avg. Income = Int. +(Par-Price) / Yrs to maturity
Avg. Price = (Price + Par) / 2
Using the earlier example
Avg. Income = 80 + (1000-1149)/10 = 65.10
Avg. Price = (1000 + 1149)/2 = 1074.50 Approx. YTM = 65.10/1074.50 = .0606 or
6.06%
Actual YTM =6.00%
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Bodie � Kane � Marcus31
Term Structure of Interest Rates
� Relationship between yields to maturityand maturity
� Yield curve - a graph of the yields onbonds relative to the number of years tomaturity
± Usually Treasury Bonds
± Have to be similar risk or other factorswould be influencing yields
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Bodie � Kane � Marcus32
Yield Curves
Yields
Maturity
UpwardUpward
SlopingSloping
DownwardDownward
SlopingSloping
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Bodie � Kane � Marcus33
Theories of Term Structure
� Expectations
� Liquidity Preference
± Upward bias over expectations� Market Segmentation
± Preferred Habitat
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Bodie � Kane � Marcus34
Chapter 11
Managing Fixed-
Income Investments
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Managing Fixed Income Securities:
Basic Strategies
� Active strategy
± Trade on interest rate predictions ± Trade on market inefficiencies
� Passive strategy
± Control risk
± Balance risk and return
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Bond Pricing Relationships
� Inverse relationship between price andyield
� An increase in a bond¶s yield to maturityresults in a smaller price decline thanthe gain associated with a decrease inyield
� Long-term bonds tend to be more pricesensitive than short-term bonds
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Bond Pricing Relationships (cont.)
� As maturity increases, price sensitivityincreases at a decreasing rate
� Price sensitivity is inversely related to abond¶s coupon rate
� Price sensitivity is inversely related to
the yield to maturity at which the bond isselling
F h
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Duration
� A measure of the effective maturityof a bond
� The weighted average of the timesuntil each payment is received, withthe weights proportional to thepresent value of the payment
� Duration is shorter than maturity for all bonds except zero coupon bonds
� Duration is equal to maturity for zerocoupon bonds
F h
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Bodie � Kane � Marcus39
Duration: Calculation
t t
t w CF y ice! ( )1 Pr
D t w
t
T
t ! v!
§1
CF Cash Flow for period t t !
F th
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Essentials of Investments
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Bodie � Kane � Marcus40
Duration Calculation
8%Bond
Timeyears
Paymen PV o CF10%
Weigh C1 XC4
1 80 72.727 .0765 .0765
2 80 66.116 .0690 .1392
Sum
3 1080 811.420
950.263
.8539
1.0000
2.5617
2.7774
F th41
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Duration/Price Relationship
Price change is proportional to durationand not to maturity
(P/P = -D x [((1+y) / (1+y)D* = modified duration
D* = D / (1+y)
(P/P = - D* x (y
Fourth42
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Uses of Duration
� Summary measure of length or effectivematurity for a portfolio
� Immunization of interest rate risk(passive management)
± Net worth immunization
± Target date immunization
� Measure of price sensitivity for changesin interest rate
i l fFourth
B di K M43
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Bodie � Kane � Marcus43
Chapter 16
O pti
ons Markets
E i l f IFourth
B di K M44
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Option Terminology
� Buy - Long
� Sell - Short
� Call� Put
� Key Elements
± Exercise or Strike Price ± Premium or Price
± Maturity or Expiration
E ti l f I t tFourth
B di K M45
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Market and Exercise Price
RelationshipsIn the Money - exercise of the option would be
profitable
Call: market price>exercise price
Put: exercise price>market priceOut of the Money - exercise of the option would
not be profitable
Call: market price>exercise price
Put: exercise price>market price
At the Money - exercise price and asset priceare equal
E ti l f I t tFourth
B di K M46
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American vs European Options
American - the option can be exercised atany time before expiration or maturity
European - the option can only beexercised on the expiration or maturitydate
E ti l f I t tFourth
B die Kane Marc s47
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Different Types of Options
� Stock Options
� Index Options
� Futures Options� Foreign Currency Options
� Interest Rate Options
E ti l f I t tFourth
Bodie � Kane � Marcus48
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Payoffs and Profits on Options at
Expiration - CallsNotation
Stock Price = ST Exercise Price = X
Payoff to Call Holder
(ST - X) if ST >X
0 if ST < XProfit to Call Holder
Payoff - Purchase Price
Essentials f In estments F ourth
Bodie � Kane � Marcus49
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Payoffs and Profits on Options at
Expiration - CallsPayoff to Call Writer
- (ST - X) if ST >X
0 if ST < XProfit to Call Writer
Payoff + Premium
Essentials of Investments F ourth
Bodie � Kane � Marcus50
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ProfitProfit
Stock PriceStock Price
0
Call riter Call riter
Call Holder Call Holder
Profit Profiles for CallsProfit Profiles for Calls
Essentials of Investments F ourth
Bodie � Kane � Marcus51
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Payoffs and Profits at Expiration -
PutsPayoffs to Put Holder
0 if ST > X
(X - ST) if ST < X
Profit to Put Holder
Payoff - Premium
Essentials of Investments F ourthdBodie � Kane � Marcus52
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Payoffs and Profits at Expiration -
PutsPayoffs to Put Writer
0 if ST > X
-(X - ST) if ST < X
Profits to Put Writer
Payoff + Premium
Essentials of Investments F ourthEdi iBodie � Kane � Marcus53
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Profit Profiles for PutsProfit Profiles for Puts
0
Profits
Stock Price
Put riter
Put Holder
Essentials of Investments F ourthEdi iBodie � Kane � Marcus54
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Equity, Options & Leveraged Equity -
Text ExampleInvestment Strategy Investment
Equity only Buy stock @ 80 100 shares $8,000
Options only Buy calls @ 10 800 options $8,000
Leveraged Buy calls @ 10 100 options $1,000
equity Buy T-bills @ 2% $7,000Yield
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Equity, Options & Leveraged Equity -
PayoffsMicrosoft Stock PriceMicrosoft Stock Price
$75$75 $80$80 $100$100
All Stock All Stock $7,500$7,500 $8,000$8,000 $10,000$10,000
All OptionsAll Options $0$0 $0$0 $16,000$16,000
Lev EquityLev Equity $7,140$7,140 $7,140$7,140 $9,140$9,140
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Equity, Options & Leveraged Equity -
Rates of ReturnMicrosoft Stock PriceMicrosoft Stock Price
$75$75 $80$80 $100$100
All Stock All Stock --6.25%6.25% 0%0% 25%25%
All OptionsAll Options --100%100% --100%100% 100%100%
Lev EquityLev Equity --10.75%10.75% --10.75%10.75% 14.25%14.25%
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Put-Call Parity Relationship
ST < X ST > X
Payoff forCall Owned 0 ST - X
Payoff for
Put Written-( X -ST) 0
Total Payoff ST - X ST - X
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Payoff of Long Call & Short Put
Long Call
Short Put
Payoff
Stock Price
Combined =
Leveraged
Equity
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Arbitrage & Put Call Parity
Since the payoff on a combination of along call and a short put are equivalent
to leveraged equity, the prices must beequal.
C - P = S0 - X / (1 + r f )T
If the prices are not equal arbitrage will bepossible
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Put Call Parity - Disequilibrium
ExampleStock Price = 110 Call Price = 17
Put Price = 5 Risk Free = 10.25%
Maturity =.5
yr X = 105
C - P > S0 - X / (1 + r f )T
17- 5 > 110 - (105/1.05)
12 > 10
Since the leveraged equity is less expensive,acquire the low cost alternative and sell thehigh cost alternative
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Put-Call Parity Arbitrage
ImmediateImmediate Cashflow in Six
MonthsCashflow in Six
Months
PositionPosition CashflowCashflow SSTT<105<105 SSTT>> 105105
Buy Stock Buy Stock --110110 SSTT SSTT
BorrowBorrow
X/(1+r)X/(1+r)TT = 100= 100 +100+100 --105105 --105105
Sell CallSell Call +17+17 00 --(S(STT--105)105)
Buy PutBuy Put --55 105105--SSTT 00
TotalTotal 22 00 00
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Option Strategies
Protective Put
Long Stock
Long Put
Covered Call
Long Stock
Short Call
Straddle (Same Exercise Price)Long Call
Long Put
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Option Strategies
Spreads - A combination of two or more calloptions or put options on the same asset withdiffering exercise prices or times to expiration
Vertical or money spread
Same maturity
Different exercise price
Horizontal or time spreadDifferent maturity dates
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Chapter 17
O pti
on Valuati
on
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Option Values
� Intrinsic value - profit that could bemade if the option was immediately
exercised ± Call: stock price - exercise price
± Put: exercise price - stock price
� Time value - the difference between theoption price and the intrinsic value
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Time Value of Options: Call
O ption
value
XStock Price
Value of Call
Intrinsic Value
Time value
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Factors Influencing Option Values:
CallsFactor Effect on value
Stock price increases
Exercise price decreasesVolatility of stock price increases
Time to expiration increases
Interest rate increasesDividend Rate decreases
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Black-Scholes Option Valuation
Co = Soe-HTN(d1) - Xe-r TN(d2)
d1 = [ln(So/X) + (r ± H + W2/2)T] / (WT1/2)
d2 = d1 - (WT1/2)where
Co = Current call option value.
So = Current stock priceN(d) = probability that a random draw from a
normal dist. will be less than d.
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Black-Scholes Option Valuation
X = Exercise price.
H = Annual dividend yield of underlying stock
e = 2.71828, the base of the nat. log.
r = Risk-free interest rate (annualizescontinuously compounded with the samematurity as the option.
T = time to maturity of the option in years.
ln = Natural log function
W Standard deviation of annualized cont. compounded rate of return on the stock
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Call Option Example
So = 100 X = 95
r = .10 T = .25 (quarter)
W= .50 H = 0d1 = [ln(100/95)+(.10-0+(5 2/2))]/(5 .251/2)
= .43
d2 = .43 - ((5.251/2)= .18
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Probabilities from Normal Dist.
N (.43) = .6664
Table 17.2
d N(d).42 .6628
.43 .6664 Interpolation
.44 .6700
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Probabilities from Normal Dist.
N (.18) = .5714
Table 17.2
d N(d).16 .5636
.18 .5714
.20 .5793
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Call Option Value
Co = Soe-HTN(d1) - Xe-r TN(d2)
Co = 100 X .6664 - 95 e- .10 X .25 X .5714
Co = 13.70Implied Volatility
Using Black-Scholes and the actual price
of the option, solve for volatility.
Is the implied volatility consistent with thestock?
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Put Option Value: Black-Scholes
P=Xe-r T [1-N(d2)] - S0e-HT [1-N(d1)]
Using the sample data
P = $95e(-.10X.25)(1-.5714) - $100 (1-.6664)P = $6.35
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Put Option Valuation: Using Put-Call
ParityP = C + PV (X) - So
= C + Xe-rT - So
Using the example dataC = 13.70 X = 95 S = 100
r = .10 T = .25
P = 13.70 + 95 e -.10 X .25 - 100P = 6.35
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Using the Black-Scholes Formula
Hedging: Hedge ratio or delta
The number of stocks required to hedge againstthe price risk of holding one option
Call = N (d1)Put = N (d1) - 1
Option Elasticity
Percentage change in the option¶s valuegiven a 1% change in the value of theunderlying stock
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Portfolio Insurance - Protecting
Against Declines in Stock Value� Buying Puts - results in downside
protection with unlimited upsidepotential
� Limitations
± Tracking errors if indexes are used for theputs
± Maturity of puts may be too short
± Hedge ratios or deltas change as stockvalues change
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Chapter 18
Futures Markets
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Futures and Forwards
� Forward - an agreement calling for a futuredelivery of an asset at an agreed-upon price
� Futures - similar to forward but feature
formalized and standardized characteristics
� Key difference in futures
± Secondary trading - liquidity
± Marked to market ± Standardized contract units
± Clearinghouse warrants performance
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Key Terms for Futures Contracts
� Futures price - agreed-upon price atmaturity
� Long position - agree to purchase� Short position - agree to sell
� Profits on positions at maturity
Long = spot minus original futures priceShort = original futures price minus spot
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Types of Contracts
� Agricultural commodities
� Metals and minerals (including energy
contracts)� Foreign currencies
� Financial futures
Interest rate futuresStock index futures
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Trading Mechanics
� Clearinghouse - acts as a party to allbuyers and sellers.
± Obligated to deliver or supply delivery� Closing out positions
± Reversing the trade
± Take or make delivery
± Most trades are reversed and do notinvolve actual delivery
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Margin and Trading Arrangements
Initial Margin - funds deposited to providecapital to absorb losses
Marking to Market - each day the profitsor losses from the new futures price andreflected in the account.
Maintenance or variance margin - anestablished value below which atrader¶s margin may not fall.
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Margin and Trading Arrangements
Margin call - when the maintenancemargin is reached, broker will ask for additional margin funds
Convergence of Price - as maturityapproaches the spot and futures priceconverge
Delivery - Actual commodity of a certaingrade with a delivery location or for some contracts cash settlement
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Trading Strategies
� Speculation -
± short - believe price will fall
± long - believe price will rise� Hedging -
± long hedge - protecting against a rise inprice
± short hedge - protecting against a fall inprice
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Basis and Basis Risk
� Basis - the difference between thefutures price and the spot price
± over time the basis will likely change andwill eventually converge
� Basis Risk - the variability in the basisthat will affect profits and/or hedging
performance
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Futures Pricing
� Spot-futures parity theorem - two waysto acquire an asset for some date in thefuture
± Purchase it now and store it
± Take a long position in futures
± These two strategies must have the same
market determined costs
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Parity Example
Stock that pays no cash dividend
± no storage costs
± no seasonal patterns in pricesStrategy 1: Buy the stock now and hold it
until time T
Strategy 2: Put funds aside today toperform on a futures contract for delivery at time T that is acquired today
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Parity Example OutcomesParity Example Outcomes
Strategy A:Strategy A: ActionAction Initial flowsInitial flows Flows at TFlows at T
Buy stock Buy stock --SSoo SSTT
Strategy B:Strategy B: ActionAction Initial flowsInitial flows Flows at TFlows at T
Long futuresLong futures 00 SSTT -- FFOO
Invest in BillInvest in BillFFOO(1+r(1+rf f ))
TT -- FFOO(1+r(1+rf f ))TT FFOO
Total for BTotal for B -- FFOO(1+r(1+rf f ))TT SSTT
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Price of Futures with Parity
Since the strategies have the same flowsat time T
FO / (1 + r f )T
= SO
FO = SO (1 + r f )T
The futures price has to equal the
carrying cost of the stock
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Chapter 9
The Eff
icient MarketHypothesis
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Efficient Market Hypothesis (EMH)
� Do security prices reflect information ?
� Why look at market efficiency
± Implications for business and corporatefinance
± Implications for investment
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� Random Walk - stock prices are random
± Actually submartingale
� Expected price is positive over time
� Positive trend and random about the trend
Random Walk and the EMH
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SecuritSecuritPricesPrices
TimeTime
Random alk with Positive TrendRandom alk with Positive Trend
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� Why are price changes random?
± Prices react to information
± Flow of information is random
± Therefore, price changes are random
Random Price Changes
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EMH and Competition
� Stock prices fully and accurately reflectpublicly available information
� Once information becomes available,market participants analyze it
� Competition assures prices reflectinformation
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Forms of the EMH
� Weak
� Semi-strong
� Strong
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Types of Stock Analysis
� T ec hnical Analysis - using prices and volumeinformation to predict future prices
± Weak form efficiency & technical analysis
� Fundamental Analysis - using economic andaccounting information to predict stock prices
± Semi strong form efficiency & fundamentalanalysis
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� Active Management
± Security analysis
± Timing
� Passive Management
± Buy and Hold
± Index Funds
Implications of Efficiency for Active or
Passive Management
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Even if the market is efficient a roleexists for portfolio management
� Appropriate risk level� Tax considerations
� Other considerations
Market Efficiency and Portfolio
Management