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Transcript of Review Prof. Ian Giddy New York University Stern School of Business.
Review
Prof. Ian GiddyNew York University
New York UniversityStern School of Business
Copyright ©2001 Ian H. Giddy Investing and Trading 2
Topics
The Financial Markets Time Value of Money and Yields Money and Bond Markets Risk and Return Risk and Diversification Valuation and Asset Pricing (CAPM) Arbitrage and Market Efficiency
Copyright ©2001 Ian H. Giddy Investing and Trading 3
Topics (continued)
International Financial Markets Equity Valuation Cash, Futures, FRAs and Swaps Options Portfolio Management and Performance
Evaluation
Copyright ©2001 Ian H. Giddy Investing and Trading 4
R isk-F ree A sset
B onds R eal E s tate
C onE d V iacom C hase S iemens
Security Selection
S tocks C om m odities FX
A sset A llocation
R isky A ssets
C apital A llocation
Managing a Portfolio
Copyright ©2001 Ian H. Giddy Investing and Trading 5
Performance Benchmarking:Buy Kellogg?
Conclusion: Benchmarks are needed because performance is
relative
Copyright ©2001 Ian H. Giddy Investing and Trading 6
The Players, such as Institutional Investors and Money Managers
Institutional Investors Money Managers
Mutual Funds
Insurance Companies
Pension Funds
Hedge funds, Central banks, etc.
Stocksand
bonds
Money managers
Copyright ©2001 Ian H. Giddy Investing and Trading 7
The Instruments
What Investments?
Treasury Bills?(risk-free)
Stocks and Bonds?(risky)
Copyright ©2001 Ian H. Giddy Investing and Trading 8
M unicipa l Bonds M ortgage-Backed Securities
Foreign Bonds Private P lacem ents
Euroyen Bonds, etc.
Euro$bonds
C orporate Bonds
U S T reasury Bonds
Fixed-Income Securities
Copyright ©2001 Ian H. Giddy Investing and Trading 9
Maturity(years)
Yield toMaturity
12345678910
5.426.026.426.696.826.927.077.167.247.23
Fixed-Income Securities
Copyright ©2001 Ian H. Giddy Investing and Trading 10
Future Value
20%
15%
5%0%
Future Valueof One Dollar ($)
Periods
1.00
Copyright ©2001 Ian H. Giddy Investing and Trading 11
Future Values: Summary
Single amount:the amount times the future value of interest factor, or
FVIFk,n :
Annuity:the periodic payment times the future value of annuity
factor, or FVIFAr,n :
FVA PMTxFVIFA PMTx rrr n r n
n
, ,( )
1 1
FV PVxFVIF PVx rr n r nn
, , ( ) 1
Copyright ©2001 Ian H. Giddy Investing and Trading 12
If J&J’s new pharmaceuticals facility in Mexico can produce the following dollar profits for the next four years, at a discount rate of 6%, what is the present value of the cash flow stream?Year 1 2 3 4Cash Flow $100 $400 $1000 $300
$100 $400 $1,000 $300
1 2 3 4
$ 94.30 (PVIF6%,1) = .943 356.00 (PVIF6%,2) = .890 840.00 (PVIF6%,3) = .840 237.60 (PVIF6%,4) = .792
$1,527.90 = Present Value of cash flow stream (HP:1,519.24)
Present Value(Example: J&J Mexico)
Copyright ©2001 Ian H. Giddy Investing and Trading 13
Present Values: Summary
Single amount:
the amount times the present value of interest factor, or
PVIFr,n :
Annuity:
the periodic payment times the present value of annuity
factor, or PVIFAr,n :
PVA PMTxPVIFA PMTx rrr n r n
n
, ,/( )
1 1 1
PV FVxPVIF FVxrr n r n n, , ( )
1
1
Copyright ©2001 Ian H. Giddy Investing and Trading 14
J&J leases $12,000 of computer equipment from Hewlett-Packard. How much would its annual end-of-year payments have to be at a 15% interest rate if the cost must be fully repaid in 3 years?
PVA3 = $12,000; r = 15%; n = 3PVA3 = PMT x PVIFA15%,3
PMT = PVA3/PVIFA15%,3 = $12,000/2.283= $5,256.24
Loan Amortization Schedule - A schedule of equal payments to repay a loan. It shows the allocation of each loan payment to interest and principal.
Loan Amortization Example
Copyright ©2001 Ian H. Giddy Investing and Trading 15
Basic Bond Valuation
WHERE: Bo = value of the bond at time zero
I = annual bond interest in dollars (interest payment) M = par value of the bond rt = required rate of return n = number of years to maturity
B Ix PVIFA Mx PVIF
B Ir
Mr
r n n
t nt
n
0
01 1 1
( ) ( )
( ) ( )
,
Copyright ©2001 Ian H. Giddy Investing and Trading 16
The Zero Approach
Use zero-coupon rates to value each cash flow - then add them!
Where can we get the z’s? One place is from the Treasury strip market.
B Cz
Cz
Mzn
n01
12
21 1 1
( ) ( )...
( )
Copyright ©2001 Ian H. Giddy Investing and Trading 17
Bond Lego
To value this bond, break it up into its component cash flows - e.g. 1st coupon of (5 3/4)/2 in Feb 1996, and so on...
Then use zero’s to see what each is worth, and add the total.
In general, breaking up a security into its component parts is an excellent path to valuation.
Rate6
M aturity, M o/Y rD ec 97
B id Asked99:29 99:31
Ask Y ld.6.01
A Treasury Noteas quoted in the W all Street Journal Monday, July 24, 1995
Copyright ©2001 Ian H. Giddy Investing and Trading 18
Forward Interest Rates
4
55.5 5.7
6 6.25
0
1
2
3
4
5
6
7
3 mo 6 mo 9 mo 1 yr 15 mo 18 mo
EURODOLLAR INTEREST RATES
The rate that can be locked in is the implied forward rate that equateslong term rates with short term rates
Copyright ©2001 Ian H. Giddy Investing and Trading 19
I can buy a 2-year note or buy a 1-year note and reinvest it at some "forward" rate f:
(1+y2)2=(1+y1)(1+f)
Find f!
Calculating Implied Forward Rates
Copyright ©2001 Ian H. Giddy Investing and Trading 20
Theories of Term Structure
Expectations Liquidity Preference
Upward bias over expectations Market Segmentation
Preferred Habitat
Copyright ©2001 Ian H. Giddy Investing and Trading 21
Identifying Undervalued Securities
BondsSpotRates
“Correct”pricing
Comparewith actual
Copyright ©2001 Ian H. Giddy Investing and Trading 22
A $1 Investment in Different Types of Portfolios: 1926-1996
0.1
1
10
100
1000
10000
1925 1935 1945 1955 1965 1975 1985 1995
Index ($)
$4,495.99
$33.73$13.54$8.85
$1,370.95
Small Company Stocks
Large Company StocksLong-Term
Government Bonds
Treasury BillsInflation Year-End
Copyright ©2001 Ian H. Giddy Investing and Trading 23
The Price-Yield Relationship
Selling at a discount is when a bond sells for less than its par value (i.e., the quote is <100)
Selling at premium is when a bond sells for more than its par value (i.e., the quote is >100)
100
9%
Price of a 9% bond
Copyright ©2001 Ian H. Giddy Investing and Trading 24
Bond Price Changes:Actual vs. Duration-Based
There’s an error in duration-based estimation, because duration is linear.
PRICE
YIELD9%
100Actual
Duration
Error
Copyright ©2001 Ian H. Giddy Investing and Trading 25
Calculating Duration:MacCauley and Modified
D
tCFr
P
D P dPP
Dr
MAC
tt
t
n
MOD
( )
%( )
1
1
1
Copyright ©2001 Ian H. Giddy Investing and Trading 26
Assets (each $10m):1-year E$ deposit5-year, 6% T-note
Duration=4.39-year Strip
Fixed liabilities:$10m 3 years$15m 5 years$5m 7 years
Asset Duration = .33(1)+.33(4.3)+.33(9) Liab Duration = .33(3)+.50(5)+.17(7)
Net duration is 4.77-4.67 = 0.10
Portfolio Duration
Copyright ©2001 Ian H. Giddy Investing and Trading 27
Lostyur Trust
Item Cash LoansTreas note IBM bond 6-mo CD 5-yr bond EquityFace value 2 13 20 6 3 33Settle date 1/1/97 1/1/97 1/1/97 1/1/97 1/1/97 1/1/97Mat date 1/1/97 4/1/97 1/1/01 1/1/04 7/1/97 1/1/02Rate - 10.25% 6.00% 7.90% 4.00% 9.00%Yield - 10.25% 6.35% 8.23% 4.00% 9.00%Frequency - 2 2 2 2 2
Price 100 100.00 98.78 98.27 100.00 100.00 46.52Value 2 13.00 19.76 5.90 3.00 33.00 4.65Modified duration 0 0.2 3.5 5.3 0.5 4.0
Assets Liab.+Eq. NetValue 40.65 40.65Modified duration 2.54 3.25 -0.71
Copyright ©2001 Ian H. Giddy Investing and Trading 28
International
Exchange Rate Risk is the risk arising from fluctuating exchange rates between two currencies
Copyright ©2001 Ian H. Giddy Investing and Trading 29
Foreign Exchange Quotations
Spot Forward points
Copyright ©2001 Ian H. Giddy Investing and Trading 30
Exchange Rates
CurrencyHowquoted
Spot(2 businessdays)
Forward(90 days)
Britishpounds(GBP)
US$perGBP
1.632 1.617
Japaneseyen (JPY)
Yen perUS$
117.5 116.3
Copyright ©2001 Ian H. Giddy Investing and Trading 31
A Typical Forward Contract
We agree today to pay a certain price for a currency in the future
Sony B of A
JPY
Copyright ©2001 Ian H. Giddy Investing and Trading 32
Interest-Rate Parity
$1 (1 + / E$) = ($1/ S t )(1 + /EBP) Fnt
where St is the spot exchange rate (dollars per British
Pound) and Fnt is the forward rate.
to a close approximation,(/E$ - /EBP) = [(Ft n - St)/St] (365/n) 100
Interest-rate differential = forward premium or discount
Copyright ©2001 Ian H. Giddy Investing and Trading 33
Returns with FX
(1 + rUS) = (1 + rFM) (1 + rFX)
rUS = return on the foreign investment in US Dollars
rFM = return on the foreign market in local currency
rFX = return on the foreign exchange
Copyright ©2001 Ian H. Giddy Investing and Trading 34
Hedging International Equity Investments
Buy foreign equity and hedge the anticipated future value, P+E(r)?
Use short-term, value-adjusted, roll-over hedges?
Do nothing, because equities bear no currency sign?
AnticipatedActualInitial
Copyright ©2001 Ian H. Giddy Investing and Trading 35
Categories of Financial Ratios
Short-Term Solvency or Liquidity Ability to pay bills in the short-run
Long-Term Solvency/Leverage Ability to meet long-term obligations
Asset Management Intensity and efficiency of asset use
Profitability Market Value
Going beyond financial statements
Copyright ©2001 Ian H. Giddy Investing and Trading 36
Returns, Standard Deviations, and Frequency Distributions: 1926-1996
Source: © Stocks, Bonds, Bills, and Inflation 1997 Yearbook™, Ibbotson Associates, Inc., Chicago (annually updates work by Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved.
– 90% + 90%0%
Average Standard Series Annual Return Deviation Distribution
Large Company Stocks 12.7% 20.3%
Small Company Stocks 17.7 34.1
Long-Term Corporate Bonds 6.0 8.7
Long-Term Government Bonds 5.4 9.2
U.S. Treasury Bills 3.8 3.3
Inflation 3.2 4.5
Copyright ©2001 Ian H. Giddy Investing and Trading 37
The Normal Distribution
Probability
Return onlarge companystocks
68%
95%
> 99%
– 3 – 48.2%
– 2 – 27.9%
– 1 – 7.6%
012.7%
+ 1 33.0%
+ 2 53.3%
+ 3 73.6%
Copyright ©2001 Ian H. Giddy Investing and Trading 38
Credit Risk versus Market Risk
Copyright ©2001 Ian H. Giddy Investing and Trading 39
Portfolio Optimization
“Efficient frontier”
Individual assets
Global minimum-variance portfolio
E(r)
Copyright ©2001 Ian H. Giddy Investing and Trading 40
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) = wj kj where wj = weight of asset j, kj = return on asset j
Copyright ©2001 Ian H. Giddy Investing and Trading 41
Measuring Portfolio Risk
The variance of a 2-asset portfolio is:
where wA and wB are the weights of A and B in the portfolio.
P2
A2
A2
B2
B2
A B A B A B = w + w + 2 w w
Copyright ©2001 Ian H. Giddy Investing and Trading 42
Case Study: A Portfolio
Weight E(R) Std DevGPU 0 0.1267 0.1715Teledyne 0.25 0.1396 0.2893Kodak 0.25 0.1402 0.3082Thai Fund 0 0.2075 0.3278Merck 0 0.1781 0.341ATT 0.5 0.1126 0.1606TOTAL 1
Copyright ©2001 Ian H. Giddy Investing and Trading 43
Portfolio Risk Computation
CORRELATION MATRIXPRODUCT STD DEV GPU TeledyneKodakThai FundMerck ATT
GPU 0.1715 1Teledyne 0.2893 0.44 1Kodak 0.3082 0.17 0.65 1Thai Fund 0.3278 0.22 0.44 0.24 1Merck 0.341 0.35 0.15 0.13 0.03 1ATT 0.1606 0.68 0.4 0.43 0.23 0.6327 1
Portfolio Variance 3.48%Portfolio Std Deviation 18.66%
Copyright ©2001 Ian H. Giddy Investing and Trading 44
Plotting the Efficient Frontier
0
0.05
0.1
0.15
0.2
0.25
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
ORIGINAL
ATT
THAI FUND
Copyright ©2001 Ian H. Giddy Investing and Trading 45
Finding the Optimal Portfolio:Computations
Given the Risk-Free rate is: 5.00%
OPTIMAL PORTFOLIOSRisk Ratio
Return Std. Dev. Premium RP/SDGPU 11.26% 0.1606 6.26% 0.390
11.50% 0.1548 6.50% 0.42012.00% 0.1494 7.00% 0.46912.50% 0.1475 7.50% 0.508
MIN RISK 12.83% 0.1471 7.83% 0.53213.00% 0.1472 8.00% 0.54314.00% 0.1509 9.00% 0.59615.00% 0.1572 10.00% 0.63616.00% 0.168 11.00% 0.65517.00% 0.184 12.00% 0.65218.00% 0.2045 13.00% 0.63619.00% 0.2282 14.00% 0.613
THAI 20.75% 0.3278 15.75% 0.4800
0.05
0.1
0.15
0.2
0.25
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
That's the one!
Copyright ©2001 Ian H. Giddy Investing and Trading 46
Equity Risk and Return
Investors diversify, because you get a better return for a given risk.
There is a fully-diversified “market portfolio” that we should all choose
The risk of an individual asset can be measured by how much risk it adds to the “market portfolio.”
Copyright ©2001 Ian H. Giddy Investing and Trading 47
Types of Risk
PortfolioRisk
kp
Number of Securities (Assets) in Portfolio1 5 10 15 20 25
}}{
TOTAL RISK
NONDIVERSIFIABLE RISK
DIVERSIFIABLE RISK
Copyright ©2001 Ian H. Giddy Investing and Trading 48
Optimal Overall Portfolio
Indifference curve
Opportunity set
CALE(r)
P
Optimal complete portfolio (one example)
OPTIMAL RISKY PORTFOLIO
Copyright ©2001 Ian H. Giddy Investing and Trading 49
Security Market Line
Nondiversifiable Risk, 0 .50 1.0 1.5 2.0 . . .
SML
}Market RiskPremium: 4%} Asset Z’s Risk
Premium: 6%
1716151413121110987654321
kz =
km =
RF =
RequiredReturn, k(%)
RF m z
Copyright ©2001 Ian H. Giddy Investing and Trading 50
The Equation for the CAPM
kj = RF + j (km - RF)where:kj = Required return on asset j;RF = Risk-free rate of return
j = Beta Coefficient for asset j;km = Market return
The term [j(km - RF)] is called the risk premium and (km-RF) is called the market risk premium
Copyright ©2001 Ian H. Giddy Investing and Trading 52
Diversification and Asset Pricing: Summary
Investors diversify, because you get a better return for a given risk.
There is a fully-diversified “market portfolio” that we should all choose
The risk of an individual asset can be measured by how much risk it adds to the “market portfolio”
The CAPM tells us how the required return relates to the relevant risk.
Copyright ©2001 Ian H. Giddy Investing and Trading 53
Value is Not Price
What is Intrinsic Value?Self assigned ValueVariety of models are used for estimation
Market PriceWhat stock can be sold for or bought at
Trading Signal IV > MP Buy IV < MP Sell or Short Sell IV = MP Hold or Fairly Priced
More, less, or same as market portfolio?
Copyright ©2001 Ian H. Giddy Investing and Trading 54
Equity Valuation: From the Balance Sheet
Value of Assets Book Liquidation Replacement
Value of Liabilities
Book Market
Value of Equity
Book ValueLiquidation
ValueReplacement
ValueTobin’s Q:
Market/Replacement tends to 1?
Copyright ©2001 Ian H. Giddy Investing and Trading 55
The Balance SheetTotal Value of Liabilities
and Shareholders’ EquityTotal Value of Assets
NetWorkingCapitalCurrent
Assets
Fixed Assets
1. Tangible fixed assets
2. Intangible fixed assets
Current Liabilities
Long-Term Debt
Shareholders’Equity
Copyright ©2001 Ian H. Giddy Investing and Trading 56
Valuing a Firm with DCF: An IllustrationHistorical financial results
Adjust for nonrecurring aspects
Gauge future growth
Adjust for noncash items
Projected sales and operating profits
Projected free cash flows to the firm (FCFF)
Year 1 FCFF
Year 2 FCFF
Year 3 FCFF
Year 4 FCFF
Terminal year FCFF
Stable growth model or P/E comparable
Present value of free cash flows
+ cash, securities & excess assets
- Market value of debt
Value of shareholders equity
…
Discount to present using weighted average cost of capital (WACC)
Copyright ©2001 Ian H. Giddy Investing and Trading 57
Specified Holding Period Model
01
12
21 1 1V Dk
Dk
D Pk
N NN
( ) ( ) ( )...
PN = the expected sales price for the stock at time N
N = the specified number of years the stock is expected to be held
Copyright ©2001 Ian H. Giddy Investing and Trading 58
No Growth Model: Example
E1 = D1 = $5.00
k = .15V0 = $5.00 / .15 = $33.33
V Dk
o
Copyright ©2001 Ian H. Giddy Investing and Trading 59
Constant Growth Model: Example
Vo D gk go
( )1
E1 = $5.00b = 40% k = 15%
(1-b) = 60% D1 = $3.00 g = 8%
V0 = 3.00 / (.15 - .08) = $42.86
Copyright ©2001 Ian H. Giddy Investing and Trading 60
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 = $30.40
Copyright ©2001 Ian H. Giddy Investing and Trading 61
The Gains From an Acquisition
Gains from merger
Synergies Control
Top line Financialrestructuring
BusinessRestructuring
(M&A)
Bottom line
Copyright ©2001 Ian H. Giddy Investing and Trading 62
Using The Restructuring Framework($ Millions of Value)
RestructuringFramework
1
2
CurrentMarketPrice
3
Optimalrestructuredvalue
Potentialvalue withinternaland externalimprovements
Potentialvalue withinternalimprovements
Companyvalue as is
Maximumrestructuringopportunity
Financialengineeringopportunities
4
Disposal/Acquisitionopportunities
Strategicand operatingopportunities
CurrentperceptionsGap: “Premium”
5
$ 25
$ 975
$ 300
$ 1,275$ 350
$ 1,625
$ 10
$ 1,635
$ 635
$1,000
Eg Increase D/E
Copyright ©2001 Ian H. Giddy Investing and Trading 63
Optika OptikaGrowth 5%Tax rate 35%Initial Revenues 3125COGS 89%WC 10%Equity Market Value 1300Debt Market Value 250Beta 1Treasury bond rate 7%Debt spread 1.5%Market risk premium 5.50%
T+1Revenues 3281-COGS 2920-Depreciation 74=EBIT 287EBIT(1-Tax) 187-Change in WC 16=Free Cash Flow to Firm 171Cost of Equity (from CAPM) 12.50%Cost of Debt (after tax) 5.53%WACC 11.38%
Firm Value 2278
CAPM:7%+1(5.50%)
Debt cost(7%+1.5%)(1-.35)
WACC:ReE/(D+E)+RdD/(D+E)
Value:FCFF/(WACC-growth rate)
Equity Value:Firm Value - Debt Value = 2680-250 = 2430
2680
Copyright ©2001 Ian H. Giddy Investing and Trading 64
Optika-Schirnding with SynergySchirnding-Optika
Optika Schirnding Combined SynergyGrowth 5% 5% 5% 5%Tax rate 35% 35% 35% 35%Initial Revenues 3125 4400 7525 7525COGS 89% 87.50% 86.00%WC 10% 10% 10% 10%Equity Market Value 1300 2000 3300 3300Debt Market Value 250 160 410 410Beta 1 1 1 1Treasury bond rate 7% 7% 7% 7%Debt spread 1.5% 1.5% 1.5% 1.5%Market risk premium 5.50% 5.50% 5.50% 5.50%
T+1 T+1 T+1Revenues 3281 4620 7901 7901-COGS 2920 4043 6963 6795-Depreciation 74 200 274 274=EBIT 287 378 664 832EBIT(1-Tax) 187 245 432 541-Change in WC 16 22 38 38=Free Cash Flow to Firm 171 223 394 503Cost of Equity (from CAPM) 12.50% 12.50% 12.50% 12.50%Cost of Debt (after tax) 5.53% 5.53% 5.53% 5.53%WACC 11.38% 11.98% 11.73% 11.73%
Firm Value 2278 3199 5859 7479Increase 1620
2680
Copyright ©2001 Ian H. Giddy Investing and Trading 65
What’s a Company Worth?Alternative Models
The options approachOption to expandOption to abandon
Creation of key resources that another company would pay forPatents or trademarksTeams of employeesCustomers
Examples?
Lycos
Messageclick.com
Copyright ©2001 Ian H. Giddy Investing and Trading 66
Commodities: Spot and Forward
$1584.5
$1607.0
ALUMINUM PRICEper tonne
3 MONTHS 6 MONTHSSPOT
How can Coke’s canners cap their can costs?
Copyright ©2001 Ian H. Giddy Investing and Trading 67
I can buy a 2-year note or buy a 1-year note and reinvest it at some "forward" rate f:
(1+y2)2=(1+y1)(1+f)
Find f!
Calculating Implied Forward Rates
Copyright ©2001 Ian H. Giddy Investing and Trading 68
Swaps
GE Chase
8% Fixed
3-mo Libor,floating
Ongoingshort-term
funding
Copyright ©2001 Ian H. Giddy Investing and Trading 69
Cost-of-Carry Theory Applied to Stock Futures
Stock that pays no cash dividendno storage costsno seasonal patterns in prices
Strategy 1: Buy the stock now and hold it until time T
Strategy 2: Put funds aside today to perform on a futures contract for delivery at time T that is acquired today
Copyright ©2001 Ian H. Giddy Investing and Trading 70
PayoffPayoff
Stock PriceStock Price
0
Call OptionCall Option
Options
Copyright ©2001 Ian H. Giddy Investing and Trading 71
PayoffPayoff
Stock PriceStock Price
0
Call WriterCall Writer
Call HolderCall Holder
Payoff Profiles for Calls
Copyright ©2001 Ian H. Giddy Investing and Trading 72
Put-Call Parity Relationship
ST < X ST > X
Payoff for
Call Owned 0 ST - X
Payoff for
Put Written -( X -ST) 0
Total Payoff ST - X ST - X
Copyright ©2001 Ian H. Giddy Investing and Trading 73
Arbitrage & Put Call Parity
Since the payoff on a combination of a long call and a short put are equivalent to leveraged equity, the prices must be equal.
C - P = S0 - X / (1 + rf)T
If the prices are not equal arbitrage will be possible
Copyright ©2001 Ian H. Giddy Investing and Trading 74
Option Pricing
94.5
Option Price= Intrinsic value + Time value
Option Price
UnderlyingPrice
94.75
Time value depends on Time Volatility Distance from the strike price
Copyright ©2001 Ian H. Giddy Investing and Trading 75
Market priceof instrument
Profit(gain or loss)
+
0
_
K F
K F
Time Value
F-K
Time Value
E(FJ *FJ >K)
How a Change in the Futures Price Changes the Option’s Price
Copyright ©2001 Ian H. Giddy Investing and Trading 76
Trading Options: Delta Hedging
Delta
We’ve written a put option
Hedged with 40% short
futures
Copyright ©2001 Ian H. Giddy Investing and Trading 77
Goal: Understand Options’ Sensitivity
An option trader has a portfolio of options with different deltas, gammas, etc. The goal is to discover the sensitivities of the portfolio to changes in rates, time, volatility, etc, and to neutralize them.
Greek Measures Delta Sensitivity of portfolio value to change in
price of the underlying asset Gamma Sensitivity of delta to change in price of
underlying asset Theta Sensitivity of portfolio value to change in
time Lambda
(Vega)Sensitivity of portfolio value to change involatility
Rho Sensitivity of portfolio to change in interestrate
Copyright ©2001 Ian H. Giddy Investing and Trading 78
Capital Allocation
R isk -F ree A sse t
B on d s R ea l E s ta te
C on E d V iacom C h ase S iem en s
S ecu rity S e lec tion
S tocks C om m od ities F X
A sse t A lloca tion
R isky A ssets
C ap ita l A lloca tion
Copyright ©2001 Ian H. Giddy Investing and Trading 79
Portfolio Performance Evaluation
How well did the portfolio do? How do we adjust for risk, to compare
different managers? Why?
RiskTimingAsset allocationSecurity selection
Copyright ©2001 Ian H. Giddy Investing and Trading 80
Performance Evaluation Measures
Sharpe’s measureThe portfolio’s average excess return per unit of total risk Treynor’s measureThe portfolio’s average excess return per unit of systematic risk Jensen’s measureThe excess of the portfolio’s return over that predicted by the
CAPM Appraisal ratioPortfolio’s abnormal return per unit of risk that could be
diversified by holding a market index portfolio
Copyright ©2001 Ian H. Giddy Investing and Trading 81
Performance Attribution
Asset allocation choicesBroad market allocations: equity, bonds, etc.Industry choicesSecurity selection
Evaluation: compare the portfolio returns at each level with returns on the appropriate index (benchmark portfolio or passive strategy)
Copyright ©2001 Ian H. Giddy Investing and Trading 82
Active Portfolio Management
Stock-picking and active portfolio management must pay, else the market would not be efficient!
The optimal risky portfolio maximizes the reward-to-variability ratio; the slope of the CAL:
PASSIVECAPITAL ALLOCATON LINE
ACTIVECAPITAL ALLOCATON LINEE(rp)
Copyright ©2001 Ian H. Giddy Investing and Trading 83
Conclusion: Hold Three Things
Risk-free asset Passive portfolio Active portfolio
Copyright ©2001 Ian H. Giddy Investing and Trading 84
Topics
The Financial Markets Time Value of Money and
Yields Money and Bond
Markets Risk and Return Risk and Diversification Valuation and Asset
Pricing (CAPM)
International Financial Markets
Equity Valuation Cash, Futures, FRAs
and Swaps Options Portfolio Management
and Performance Evaluation
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Ian Giddy
Ian H. GiddyNYU Stern School of BusinessTel 212-998-0332; Fax [email protected]://giddy.org