Unformatted text preview: Computing Index Prices
Critical relationship between &, and g
full price = PV at last coupon date x (1 + YTM) UT
Forward Contract Value
At time :
Each security in the put-call parity relationship can
accrued interest = coupon payment x (t/T)
Modified duration is the approximate change in a
be expressed as:
bond's price given a 1% change in its YTM:
C = S+ p - T
LEVEL I SCHWESER'S QuickSheet
= days from most recent coupon payment to
( 1 + Rf ) T -
(1+ RF)T P
. Small changes in difference between k, and g
( 1 + Rf )
2Vo ( Ay )
At expiration (time t = 1):
CRITICAL CONCEPTS FOR THE 2017 CFA EXAM
L(current prices)(# shares)
Matrix pricing: For illiquid bonds, use yields of bonds
payoff to long = S, - F.(T)
[(base year prices)(# base year shares)"
nt growth rate
Effective duration is required if a bond has
Futures vs. Forwards
(1 + RF) T
T = S+ p - c
(1 + RF) T
estimate yield; adjust for
ETHICAL AND PROFESSIONAL
Approximation formula for nominal required rate:
E(R) = RFR + IP + RP
Expected return, variance of 2-stock portfolio:
E(RP) = WAE(RA ) + WBE(RB)
Types of Orders
maturity differences with linear interpolation.
Execution instructions: how to trade; e.g., market
Earnings Multiplier Model
The present value of the forward price of the
underlying asset, F,(T) / (1 + Rf), can be
Guaranteed by clearinghouse
substituted for S, in any of the put-call parity
Knowledge of the Law.
sample/population, divided by # of observations.
var (RP) = WAG?(RA) + who?(RB)
Validity instructions: when to execute; e.g., stop
PQ = /En _ payout ratio
Price change estimates based on duration only are
Little or no regulation
relationships at time 0.
Independence and Objectivity.
Geometric mean: used when calculating investment
. Domestic bonds. Domestic issuer and currency.
Clearing instructions: how to clear and settle; for sell
improved by adjusting for convexity:
Forward Rate Agreements (FRA)
ns over multiple periods or to measure
Integrity of Capital Markets
Normal distribution is completely described by its
lend money at a certain rate at some future date.
I(A) Material Nonpublic In
leading P/E =
II(B) Market Manipulation.
mean and variance.
Interest Rate Swaps
Duties to Clients
RC= (1+R, )x...x(1+RN)|"-1
68% of observations fall within + lo.
Order-driven markets: buyers and sellers matched
forecast EPS next 12 mo.
price per share
Residential MBS: home mortgages are collateral.
May be replicated by a series of off-market FRAS
Event-driven strategies: merger arbitrage; distressed/
Loyalty, Prudence, and Care.
harmonic mean =
trailing P/E =
EPS previous 12 mo.
Forms of EMH
Underwritten offering: Investment banks buy entire
loans and need credit enhancement.
book value per share
. Buyer of a call option-long asset exposure.
III(E) Preservation of Confidentiality.
Prepayment risk: contraction risk from faster
asset-backed fixed income; general fixed income;
Variance and Standard Deviation
Z-score: "standardizes" observation from normal
. Writer (seller) of a call option-short asset
Variance: average of squared deviations from mean.
distribution; represents # of standard deviations a
Shelf registration: Register entire issue with
Equity strategies: market neutral; fundamental
ional Compensation Arrangements.
given observation is from population mean.
P/S = price per share
regulators but sell over a period of time.
CMOs: pass-through MBS are collateral. May have
observation - population mean _x-
Investment Analysis, Recommendations,
price per share
Macro strategies: based on global economic trends.
population variance = 02 = i-
V(A) Diligence and Reasonable Basis.
cash flow per share
intrinsic value of a put option = Max[0, X - S]
Communication with Clients and
Convertible: Bondholder may exchange bond for
Credit card ABS: credit card receivables are
a stock, movements (up/down). A binomial model
Conflicts of Interest
can describe changes in the value of an asset or
Assumes perfect markets in which all information
Hard hurdle rate: incentive fee only on return
is cost free and available to everyone at the same
CDOs: Bonds, bank loans, MBS, ABS, or other
above hurdle rate.
time. Even with inside info, investor cannot
Basic Features of Bonds
CDOs are collateral.
Standard deviation: square root of variance.
Issuer. Sovereign, non-sovereign, quasi-government,
but only paid if return is greater than hurdle rate.
VI(C) Referral Fees.
Holding Period Return (HPR)
supranational, corporate, SPE.
Effective yield depends on periodicity. YTM =
Secured bonds are backed by specific collateral and
Responsibilities as a CFA Institute
Member or CFA Candidate
RAPID, P, +D._
Sampling distribution: probability distribution of
Maturity. Money market (one year or less); capital
effective yield for annual-pay bonds.
Par value. Bond's principal value (face value).
Semiannual bond basis: YTM = 2 x semiannual
Unsecured bonds are general claims to issuer's cash
Factors that Affect Option Values
VII(A) Conduct as P
product as Participants in CFA Institute
Coefficient of Variation
Internal credit enhancement: Excess spread,
Coefficient of variation (CV): expresses how much
managers), management buy-ins (new managers)
Designation, and the CFA Program.
Global Investment Performance Standards
dispersion exists relative to mean of a distribution
External credit enhancement: Surety bonds, letters of
Formative stage: angel investing, seed stage, early
Central Limit Theorem
Growth: rapid growth, falling prices, limited
. Compliance statement: "[Insert name of firm] has
Central limit theorem: when selecting simple
prepared and presented this report in compliance
standard deviation of a distribution by the mean or
er growth, intense competition,
Price, Yield, Coupon Relationships
expected value of the distribution:
declining profitability, cost cutting, weaker firms
Bond prices and yields are inversely related.
Investment grade: Baa3/BBB- or above
Global Investment Performance
are: slow growth, consolidation, stable prices,
comparables; discounted cash flow; asset-based.
high barriers to entry.
Decline: negative growth, declining prices,
construction, disclosures, presentation and
Sharpe ratio: measures excess return per unit of risk.
Standard error of the sample mean is the standard
future date. "ly3y" = 3-year forward rate 1 year
loss severity = percent of value lost if borrower
reporting, real estate, private equity, and wrap
Five Competitive Forces
Includes residential property; commercial property;
feel separately managed account portfolios.
Example of spot-forward relationship:
expected loss = default risk x loss severity
real estate investment trusts (REITs); farmland/
recovery rate = 1 - expected loss percentag
"Except some deep-in-the-money European puts.
Bullet: All principal repaid at maturity.
5. Power of suppliers.
Fully amortizing: Equal periodic payments include
G-spread: Basis points above government yield.
The put-call parity relationship for European
I-spread: Basis points above swap rate.
options at time .
Time Value of Money Basics
For both ratios, larger is better.
One-Period Valuation Model
Expected Return/Standard Deviation
Partially amortizing: Periodic payments include
Z-spread: Accounts for shape of yie
Option-adjusted spread: Adjusts Z-spread for effects
Arbitrage and Replication
( 1 + RF )
Contango: futures price > spot price.
Confidence interval: gives range of values the mean
Expected return: E(X) = _P(x; ) X,
value will be between, with a given probability (say
Interest Rate Risk
ts with identical cash
flows in the future, regardless of future events,
V/(1 + I/Y)N.
E(X) = P(x1 ) x, + P(x2 ) * 2 + ... + P(x) x,
90% or 95%). With known variance, formula for a
Sinking fund: Schedule for early redemption.
confidence interval is:
Be sure to use expected dividend D, in calculation.
as two components: reinvestment risk
. Collateral yield: return on T-bills posted as margin.
Floating-rate: Coupon payments based on reference
Price return: due to change in spot price.
Probabilistic variance :
rate plus margin.
and market price risk from YTM changes. These risks
Supernormal growth model (multi-stage) DDM.
Ordinary annuity: cash flow at end-of-time period.
futures price & spot
= P( x, ) [ x, - E(X ) ] + P( x2 ) [ x2 - E(X) ]
Zo2 = 1.645 for 90% confidence intervals
- convenience yield
(YTM) to find PV. This is a bond's flat price (does
Long-lived assets for public use, including
Standard deviation: take square root of variance.
transportation, utility, communications, social
Correlation and Covariance
Correlation: covariance divided by product of the
(significance level 1%, 0.5% in each tail)
Constant growth model:
Full price includes accrued interest. Government
duration. This is the weighted average of times
until a bond's cash flows are scheduled to be paid.
Greenfield: Infrastructure to be built
2. Expected inflation rate premium (IP).
two standard deviations .
initiation. Value may change during the contract's
life with opposite gains/losses to the long and short.
E(R) = (1 + RFReal)(1+IP)(1 + RP)-1
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- Summer '18