1. business and industrial

CFA Level 2 notes – created by Thomas Ip
Std of Professional Conduct I) professionalism A) knowledge of the law B) independence and objectivity (> approval from compliance) C)
misrepresentation D) misconduct II) integrity of capital markets A) material nonpublic information (mosaic theory) B) market manipulation III)
duty to clients A) loyalty, prudence and care B) fair dealing C) suitability D) performance presentation E) preservation of confidentiality IV)
duties to employers A) loyalty B) additional compensation arrangements C) responsibilities of supervisors V) investment analysis,
recommendations, and actions A) diligence and reasonable basis B) communication with clients and prospective clients C) record
retention(7yr) VI) conflicts of interest A) disclosure of conflicts B) priority of transaction C) referral fees VII) responsibilities as a CFA Institute
member or CFA candidate A) conduct in CFA program B) reference to CFA Institute, CFA Designation (cannot be a noun), and CFA Program
This Std do not require compliance with GIPS Soft Dollar Std I) brokerage is the property of the client II) investment managers have a
fiduciary duty to obtain best execution, minimize transaction costs, and use client brokerage to benefit clients. Dollars from internal trades are
clients’. This Std is voluntary Prudent Investor Rulenew – Prudent Man Ruleold = 5 use of total return (income + capital growth), risk
management, evaluation in a portfolio context, less security restrictions, delegation of duty general fiduciary std care, skill, caution, loyalty,
impartiality; last 2 are the same
Classical (population is related)
Neoclassical (exogenous, Solow–Swan)
New growth (endogenous, perpetual motion)
exogenous LT levelGDP, but not LT growthGDP, depends on country’s saving rate endogenous LT levelGDP depends on country’s saving rate
rule of 70 approximate #yr to double = 70/g 1/3 rule 1%↑ capital/labor hour = 1/3%↑ GDP/labor hour, remaining is tech factors of production
land, labor, capita goods, entrepreneurial ability sources of economic growth markets, property rights, monetary exchange keys to ↑economic
growth (productivity speedup) savings, R&D, international trade, education persistent economic growth savings, investment in new capital and
human capital, technology types of gov regulation cost-of-service, rate-of-return, social regulation trade restriction tariff, quota, VER reasons
for restrictions national security, protect infant industries, prevent dumping (no 搶爛市 from exporters) are weak reasons
auction/order driven HK, Fr, Jp(trading halt), Ger; central auto electronic limit order book; use elec comm networks; lower cost to traders;
high speed, efficient for small trades; bad for large trades due to lack of market depth; transparency risk price/quote/dealer driven NASDAQ,
London; mkt makers (dealers) present and post bid-ask prices; automated system; anonymity↓ execution cost commissions, market impact,
opportunity cost; net return = E(R) – turnover ratio x execution cost (buy+sell) cost reduction program trading large baskets of securities
internal crossing usually applied for passive investment strategies external crossing utilizes electronic crossing network, anonymous trades
but OC↑ as trade can be stale principal trades guaranteed by the trader, OC↓, exposure risk↑ agency trades aim for best execution to ↓(price
impact, OC) but ↑(commission cost, exposure risk) futures contract OC↓ but have basis risk, well-suited for diversified portfolio indication of
interests ↓anonymity, best for passive managers ECN ↓cost and no market impact as trade at mid-price; anonymous; no immediacy; traded in
sessions ADR I) OTC, xSEC II) bourses + SEC III) bourses + IPO + SEC close-ended fund = NAV ± prem/disct, illiquid, hard to redeem,
correlated with US, e.g. country fund open-ended fund notify redemption and get $ shortly, has time lag thus CF problem, e.g. MFs, ETFs
sensitivity analysis adjust one variable situational adjustment control premiums, discount for lack of marketability, illiquidity discount
country analysis SR – forecast business cycle and short term economic growth; LR – business cycle & sustainable growth rateGDP;
business cycle: recovery, early upswing, late upswing, economy slows, recession; growth (independent of life cycle), defensive, cyclical
industry analysis demand & supply analysis, value net & creation, ILC, profitability analysis, competitive adv & strategies, sector rotation
▪ industry life cycle (ILC) pioneer, rapid growth, mature growth, stabilization/mature, deceleration of growth/decline
▪ external factors affect long term fortune: technology, government, social changes, demography, foreign influences
▪ industry pricing factors product segmentation, industry concentration, ease of industry entry, supply input price
5 forces fleeting/transient factors industry growth rate(not always +ve), innov & tech, government policies, complementary products
GDP + net property income from abroad = GNI; GNI – dep (aka capital consumption) = NNI; real wage x labor hour = real GDP
NNI is most comprehensive, but hard to estimate dep, thus little practical value; net property income from abroad minor effect on GDP in SR
nd
GDP x include transfer payment (social security, pension), gift, unpaid domestic activities, barter txn, 2 hand txn, intermediate txn, leisure,
depletion of resources, environmental costs, allowance for non-profit-making and inefficient activities, allowance for changes in quality
C + I = total domestic exp
+ Ex (foreigners’ spending) = total final exp
- Im (spending abroad) = GDP
GPDmarket + factor cost adj = GPDat factor cost factor cost adj = subsidies – indirect tax
BOP current ac + capital ac + official reserve ac = 0
reserve ac = exchange rate adjustment, negative if reserve increase
current ac = export – imports + net int income + net transfers capital ac = foreign invest here – here invest abroad + stat discrepancy
expansionary monetarySR dep, real r↓, ↑(inflation very slowly “sticky price”)
expansionary monetaryLR dep, real r↓, financial ac↓, current ac↓ as ↑(inflation, economic growth, imports) (real r will back to equilibrium)
expansionary fiscal
app, real r↑, financial ac↑ > current ac↓ as ↑(inflation, economic growth, imports)
deregulation effect SR ↓(high cost producers, quality), ↑prices, unions and employees less powerful LR ↑competition, ↓price
a:b = b/a = 1.25 = 1.25b/a, is a direct quote if you are b a:b = 1.2–1.3, dealer buy a @1.2
and sell a @1.3 b:a = 1/1.3–1/1.2 = 0.77–0.83
a:b = 1012–1013 b:c = 1.24969–1.25 a:c = 1264.69–1266.25 i.e.擺好 a:b, b:c 個陣,細 x 細,
大 x 大 aim to achieve the smallest and biggest
spread = (ask – bid)/ask when quotes range not overlap there is arbitrage opportunity;
undervalue = buy = borrow; overvalue = sell = lend
long forward a:b = receive b paying a at expiration at the rate
CFA Level 2 notes – created by Thomas Ip
t
 1  RDC (n/360) 
 1  inf lationDC 
 relative PPP E(St)= S0 

covered IRP F = S0 
 1  inf lation  all hold in LR

FC 
 1  RFC (n/360) 

uncovered IRP = PPP + international Fisher effect, just econ theory, use E(S)
IRP forward prem/disct (F – S)/S = (RDC – RFC)/(1 + RFC), annualize needed, ~RDC – RFC
if forward a:b > spot a:b, a is trading at premium relative to b, a is strong
if RF a > RF b then a is trading at forward discount against b
邊個 RF 高, 邊個 dep thus trade at forward discount
International Fisher Effect
relative PPP %∆Sreal ≈ %∆S – (E(I)DC – E(I)FC)
hold in LR “international” means Rreal are constant, ↑Rnominal  ↑E(I)  dep
1  Rnominal A
1  E(inf lation)A

1

R
1  E(inf lation)B
nominal B
precise
1+R
= (1 + R )(1 + E(I))
Sreal = S(PFC/PDC) or Sreal = E(S)(PFC/PDC)
F, X and S in direct quotation i.e. DC/FC
nominal
real
S = nominal
FCapp/dep = s = (S1 – S0)/S0
Rnominal A – Rnominal B ≈ E(I)A – E(I)B
approximation Rnominal ≈ Rreal + E(I)
∆nominal NWC = ∆real NWC x inflation
E(I) = (1 + YTM20yr T-bond)/(1 + YTM20yr TIPS) – 1
E(S) = S(1 – (E(I)FC – E(I)DC))
邊個 inflate, 邊個 dep, by roughly the same %
hedged RDC = RFC + (F – S0)/S0 = E(RFC) + rF DC – rF FC
unhedged RDC = RFC + E(s) = E(RFC) + [E(S1) – S0]/S0
Ex-post returns = (1 + RF FC)(1 ± FCapp/dep) – 1 = E(R) + real appreciation
Ex-post returns ≈ RF FC + FCapp/dep = RF DC + FCRP = RF DC + FCapp/dep – (RF DC – RF FC)
E(S1) - S0
E(S1) - F
FCRP = FCapp/dep – interest differential =
– (RF DC – RF FC) (=
if IRP holds), F = 0 if forward rate is unbiased
S0
S0
If IRP holds and unbiased F, FCRPLT = 0; If FCRP = 0, Runhedged = Rhedged; if FCRP > 0, Runhedged > Rhedged, implying a forward premium
ICAPM = RF DC + βworld (RPworld) + ΣΓNFCRPN
domestic currency exposure on a foreign asset Γ = (RFC + s)/s = Γ(FC) + 1, where Γ(LC) = 1, Γ(FC) = sensitivity of foreign stock to FC
Domestic CCY vs equity price traditional model J-curve (long term negative) money demand model positive
Domestic CCY vs bond price free markets theory negative gov intervention theory positive
Quantitative Finance
n
n

sample covariance covX,Y =
(Xi - X)(Yi - Y )
i 1
i
2
sample variance σ X =
n -1
 (X - X)
2
i 1
n -1
sample correlation coefficient r =
cov x, y
σ xσ y
Limitationscorrelation analysis outliers, spurious correlation, nonlinear relationship
if sample, denom = n – 1, except sample mean; co = 2
Limitationsregression analysis parameter instability, limited usefulness if other market participants also aware of and act on it, if assumptions are
violated, hypotheses are not valid, and coefficients are biased and inconsistent
Assumptionslinear regression linear relationship b/w Y and X exists via b0 and b1; X is not random; Y uncorrelated w/ ε; E(ε) = 0; homoskedasticity: E(εi2 )  σ2ε ; ε independently and normally distributed multiple Xs are not random and no linear relation b/w (no multicollinearity)
Test
2-tailed t
(2-tailed 1% =
1-tailed 0.5% x 2)
test statistic
bˆ 1 - b1
r n-2
sbˆ
1- r2
1-tailed F
(always)
dfnumerator = k
MSR
RSS / k
2
(=t if simple)

dfdenom = n – k – 1
MSE SSE / (n - k - 1)
smallest level of significance we can reject the null
2
k
n R 2 , 2nd regression of ε from the
p-value
2
1-tailed BP X
(heteroskedasticity)
coef f icient
standard error
Df
n–k–1
n – 2 commonly
1
ε
1st regression on the independent
≈ 2(1 – r)
reject H0 condition (Ha is wt u believe)
tcalculated > +tcritical or tcalculated < -tcritical
abs (tcalculated) > +tcritical
confidence interval not include ρ
H0
ρ=0
or
ρ = b1
Fcalculated > Fcritical
b1 = 0
p-value < significance level (α)
testcalculated > testcritical
ρ = b1
H0 = no
problem
Durbin-Watson
k
2 = no corr., < 2 greatly = +ve
(serial-correlation)
DW calculated < DW critical (= +ve)
reject =
0.5
AR (= lagged)
autocorrelation / std err where std err = 1/n
n–k
tcalculated > +tcritical or tcalculated < -tcritical
problem
special t
k = #lagged terms
reject H0, +ve
inconclusive
accept H0
inconclusive
reject H0, –ve
where H0 = no serial correlation
0
dl
du
4-du
4-dl
4  DW critical
regression sum of square
sum of squared error
total sum of square
k = #independent; n = #observation
RSS = explained
SSE = unexplained
TSS = total variation
t test result = p-value result
n
n
n
+
=
F test is for testing groups
ˆ - Y )2
ˆ )2
(Y
( Yi - Y
( Yi - Y )2
RSS =
SSE =
SST =
1 – confidence = significance
i
for independent variables, rejection = significant
i 1
i 1
i 1
^ 2
^ 2
sum of squared errors (SSE) is minimized by the regression line SSE = Σ(Y - Y) = Σ( ε)
standard error of estimate (SEE) = unexplained standard deviation of estimate (aka error, residual, regression)
cov ariance cov x, y
2
regression/slope coefficient bˆ 1 =
=
= βx bˆ 1 confidence interval = bˆ 1 ± tcritical x sbˆ sbˆ =seregression[1+1/n+(b1-bmean) /(n-1)(var)]
1
1
v ariance
σ 2X



(regression coefficient ± tcritical x coefficient standard error), interpreted as given a forecasted value of X, we are confident (at a level) that the
predicted value of Y will fall b/w the range
CFA Level 2 notes – created by Thomas Ip
source of variation
regression (explained)
error (unexplained)
total
SS
df
mean sum of square = SS / df
standard error of estimate
reject null = estimate is
statistically significantly diff
RSS
k
MSR = RSS / k
SSE
SEE = MSE 
from 0 = significance is
SSE
n–k–1
MSE = SSE / (n – k – 1)
n-2
supported
SST
n–1
sample variance = SST/(n – 1)
coefficient
standard error
t-stat
 ^Y = 0.0079 + 2.2308b1
 total = regression + residual
b0
0.0079
0.0091
0.8635
←(=coefficient/std err)
 n = total + 1
b1
2.2308
0.2299
9.7034
←(=coefficient/std err)
 t-stat = (coefficient – 0)/ std error
ANOVA
df
SS
MSS
F-stat
significance F
0.5
 std error = (unexplained variation)
regression
2 (=k)
0.8649 (RSS)
0.4324
86.448
5.48 (p-value)
0.5
= (firm-specific risk)
residual
57(=n-k-1)
0.2851 (SSE)
0.005
↖

SS = explained variation = systematic
total
59 (=n-1)
1.15 (SST)
↑=0.2851/57
=0.4324/0.005
risk
0.5
std err (=SEE)
0.0707
←=(0.2851/58)
 SS/df = MSS
2
R
0.7521
←=0.8649/1.15
2
 t > 2, p ~ 0, larger F, R , smaller
2 x 0.5
multiple R (=R
)
0.8672
significance F are preferred
observations
60(=n)
SST - SSE RSS
2
2
R coefficient of determination 
(= r for linear regression w/ 1 independent) = systematic risk / total risk beauty

SST
SST
2
R may not be a reliable measure of the explanatory power in a multiple regression model, due to overestimation as increase in variables
2
2
2
Ra2 = 1   n  1 x (1  R2 ) < R for >1 independent variable, ↑ or ↓ when the non-negative R increase, and can be –ve if R is low enough
n  k 1

violation
definition
conditional heteroskedasticity
serial (auto) correlation
multicollinearity
non-constant residual variance related
residuals are correlated, common in
2 or more highly, not perfectly
to level of independents
trend models
correlated independents
effect
type 1 errors, F-test fails (↓OLS s, ↓std err, ↑t, ↓MSE, ↑F for +ve correlation)
type 2 errors (↑OLS s, ↑std err ↓t)
2
2
2
detection
Durbin-Watson
(for
trend
model
only;
low t but high F or R ; high correlation
Breusch-Pagan X test n R ε
for AR use special t ≈ 2(1 – r))
among independents (> 0.7 for n = 2)
correction 1) White-corrected  robust std err, a
1) Hansen method  robust std err
drop one of the correlated variables
better std err only 2) generalized least
only thus no heteroskedasticity 2)
using stepwise regression to minimize
squares
modify equation
problem
Type 1 reject null when it is true Type 2 hypothesis not rejected when it is false
model misspecification (biased and inconsistent coefficient) 1) misspecified functional form a) variables are omitted b) variables should be
transformed (nonsensical result) c) improperly pooled data 2) independents and dependents are correlated w/ ε in time series a) a lagged
dependent as independent b) forecasting the past – a function of dependent is used as in independent c) independent are measured w/ error
non-OLS models that use qualitative or dummy dependents probit normally distributed logit lognormally distributed; both use maximum
likelihood to estimate coefficients discriminant analysis result a score in linear function similar to an ordinary regression
time series log-linear trend (ln y = b0 + b1t + ε) caters for exponential constant growth rate in a linear trend time series. AR caters for
nd
autocorrelation that log-linear cannot eliminate, by introducing lagged terms. AR(2) = 2 lags = 2 df = 2 order, #observationsAR =
#observationsoriginal – 2. AR(1) + seasonal lag ≠ AR(2). DW test will not work to test autocorrelation in AR since there exists lagged terms,
0.5
2
0.5
instead, use special t-stat (1/n ). Lower root mean squared error RMSE = (ΣΔ )/n) for out-of-sample data provides better predictive power
for AR models. Stationary time series may need periods to return to mean reverting level = b0/(1 – b1); only if we have reason to believe the
time series is stationary, a longer series of data is desirable covariance stationary (for time series model) requirement constant and finite
mean-reverting level, expected value, variance and covlead or lagged. To use linear regression to model more than 1 time series, must stationary,
either 1) no unit root, or 2) both unit root and cointegrated
AR (w/ or w/o seasonal lags) models are correctly specified if no autocorrelation. b1 in AR(1) = 1 =
random walk = unit root = covariance non-stationary = mean and variance do change = AR model will
not work w/o transforming data detection 1) plot graph 2) run AR and examine autocorrelation, or 3)
st
Dickey Fuller test reject null is good, rooted when H0: g = b1 – 1 = 0 correction 1 differencing data,
which model the ∆ in value of dependable variables. For two time series data, cointegration makes
them = stationary = reliable, residuals tested by DF with tcalculated from Engle and Granger (DF-EG test,
2
2
H0 = unit root, just like DF). ARCH ε = b0 + b1ε t-1 exists if variance of ε in one period is dependent on
ε in a previous period, though it can predict variance of future εs, detected if lag 1 coefficient is
significant (probably by p-value), thus to be ARCH(1), and solved by generalized least squares.
Random walk: xt = b0 + b1xt-1 + ε (b0 = 0 = random walk, b0 = 1 = random walk w/ a drift, b1 = 1)
Accounting additional PIC = (Pxissued – Pxpar)#sharesissued PPE measurement IFRS FV or cost – depacc US cost – depacc tangible
revaluation IFRS optional, writeup goes to reserve equity not IS, if reserve becomes –ve, record L in IS US x reversible intangiblelimited life
amortized intangibleunlimited life test for impairment annually inventory US tax-saving LIFO optional, if use for tax purpose must also use for
reporting; ↓(taxincome exp, NI, WC, A, RE, equity, current ratio, profitability) ↑(CFO, V, D/E) no change(L, D); LIFO liquidation occurs if inv end <
invbeg and ↓LIFOreserve; Co under USGAAP change to LIFO x need retrospective; lower or cost InvFIFO – LIFOreserve = InvLIFO COGSFIFO +
ΔLIFOreserve = COGSLIFO – charges NIFIFO = NILIFO + ΔLIFOreserve(1 – t) + charges REFIFO = RELIFO + LIFOreserve(1 – t) inv = gross ≠ net
inventory writedown US x reversible IFRS L goes to IS maybe on COGS depreciation exclu land st.line deducts salvage(except for cap-bug)
declining balance x consider salvage @yr dep constant double dep Σyrs digit @yr dep #yr/sum ,yr in descending order units of production
MACRS in US for tax purpose only, half year convention, double-declining; dep simply = asset x %, not consider salvage capitalize exp better
at beginning ↑(A, dep, CFO) ↓(CFIinitial) smoothen(NI, RE, equity) R&D normally expensed capitalize int ↑(dep, int exp, CFO) ↓(CFI) capital
lease worse at beginning ↑(A, dep, CFO) ↓(CFFinitial), Σdep(CFO) + Σint(CFF) =Σrentop lease(CFO) both discourage nonrecurring income US
has extraordinary items SPE both consol if indicate of control, absorb loss or share profit, QSPE (no need to be consol) x allowed
CFA Level 2 notes – created by Thomas Ip
goodwill Pxpurchase – %BVnet asset = excess Pxpurchase (will be amortized) attributables = %(FV – BV) excess Pxpurchase – Σattributables = GW =
Pxpurchase – %FVnet asset BVnet asset ~ equity for prop consol US only full ↑(A, E), FVsub – FVnet identifiable A, minority interest = %FVsub IFRS partial
or full Pxpurchase – %FVnet identifiable A or simply equity, minority interest = %FVnet identifiable A; full GW x % = partial GW both same debt, IS items
test IFRS by loss event; may use allowance account; impaired if carrying or BV > recoverable US by comparing carrying value; impaired if
carrying > FVsub impairment IFRS impairment loss = carrying – recoverable US GWimplied = FVsub – FVsub’s identifiable asset; impairment loss =
GW carrying – GW implied both GW new = GW current – impairment loss, loss goes to IS as continuing operations
finance leverage ratio = A/E or 1) LT D-to-capitalization ratio
LT debt
=
LT debt  minority interest  equitycommon and preferred
2) total D-to-capitalization ratio
LT debt  current liabilities
=
LT debt  minority interest  equitycommon and preferred  current liabilities
current assets - inv entories
current assets
quick, aka acid-test ratio =
current liabilities
current liabilities
sales, or COGS
EBITDA
EBITDA coverage =
inventory turnover =
inv
inv entory ,or av g
annual interest expense
cash ratio = cash & equivalents / current liabilities current ratio =
EBIT/interest coverage =
debt service coverage =
EBIT
annual interest expense
interest  f reeoperating cash f low
interest  annual principal pay ment
categories
investment in financial assets
investment in associates
business combinations
joint ventures
total debt
discretionary cash f low
accounting treatments
all have same impact on NI, equity
(if has no non-controlling interest
HTM, AFS, HFT/designated at FV
NCI) and RE (thus same ROE)
equity method
A/L/sales are highest under
consolidation
acquisition but lowest under equity
IFRS prop consolidation preferred
A need – NCI, equity no need
US generally, equity method required
HTM
AFS
HFT/DFV
IFRS defines, US similar; NI is not
considered; Investment in financial assets:
type debt only
debt or equity (LT)
debt or equity (ST)
1
all are recorded at cost (=FV at acquisition +
BS
amortized cost
FV (exclu txn cost at remeasurement)
FV (exclu txn cost)
transaction cost)
unrealized G/L (in equity reserve OCI)
impairment test IFRS no active market or
IS
int/div, realized G/L
credit downgrade alone can’t signal
(include amortization) unrealized G/L for FX under IFRS only
unrealized G/L
impairment US impaired if permanent both
from \ to
HTM
AFS
HFT
IFRS unrealized G/L  OCI; FV – BV  OCI,
G/L goes to IS normally reversibility IFRS
amortized
over
life
US
free
in
reclassification,
HTM
----IFRSV IFRSX
all but AFSsecurities x reversible US all x
unrealized G/Lsecurities  IS
AFS
IFRSdebt only ----IFRSX
reversible both equity investment x reversible
unrealized G/Ldebt  OCI
HFT
IFRSX
IFRSX ----bond at HTM carrying2 = carrying1 – amortization amortization = coupon – interest coupon = par x stated rate interest2 = carrying1 x rate
bond at sale: N = remaining period; PMT = face x rate, periodic; I = new rate (per period); FV = face; CPT  PV
Equity most favorable results: ↓leverage(D/E) ↑(net PM, ROA)
▪ BSone-line %balancebegin at cost (as noncurrent asset, no need concern FV) + %equity income – %div = balanceend
▪ ISone-line %equity income = %NI – %dep△PPE FV – %unconfirmed profit; no div; dep = attributable / #yrs; goes to parent NI level no need tax
Acquisition (exclude intercompany transactions; minority interest = %not owned x equity or NI) (consolidation = 100%acquisition)
▪ BS
A/Lall are combined, equity (may change if fund is raised) and RE are ignored. Minority interest is created when <100%
▪ IS
R/Eall are combined. NI recalculated
Proportionate consolidation least favorable results: ↑leverage(D/E) ↓(net PM, ROA)
▪ BS
%A/L are combined, equity is ignored, thus no minority interest
▪ IS
%R/E are combined, NI ignored
IFRS All-current
own%
< 20
20-50
> 50
50/50
debt payback period =
US Temporal
degree of influence
insignificant
significant
control
shared control
Hyperinflation
parent’s presentation currency
IFRS all-current
sub’s functional currency
remeasurement
US temporal
local currency
3
self-contained and highly-integrated US define 1.26 – 1 = 100
independent
into parent
G/L rec at IS
IFRS all-current
monetary A/L
current
non-monetary A/L
current
BS
common stock and div paid
equity (taken as a whole)
current
revenues and SG&A
average
COGS
average
IS
dep & amortization
average
NI
average
exposure
net asset (equity)
plug**
translation G/L
equity (as CTA*)
volatility
higher in… BS items
translation
functional currency is determined by management; unaffected pure BS
and pure IS ratios are only for all-current method
inflation IFRS non-monetary A/L, IS items and equity are restated using a
price index, thus will not expose to purchasing power G/L; monetary A/L
are ignored thus will be affected US restatement is not allowed
inflation must use temporal and judge GL by net monetary A/L
standalone MVfirm = MVfirm - %MVassociates; implied PE = standalone MVfirm /
(E – equity income)
US temporal
current
historical
historical
mixed
average
historical
historical
mixed
net monetary asset
income statement*
NI and EPS
*CTA is accumulative, thus recalculated RE +
common stock + CTA = total equity
**start from BS, calculate REend  NI  remeasurement G/L
REbeg + NI + OCI – DIV = REend
Securitized things ↑A,L
EPSt = Bt x ROE
cash collection = revenue – ↑receivables only +
↑unearned revenue
core operating margin = (sales – COGS –
SG&A) / sales
CFA Level 2 notes – created by Thomas Ip
earnings quality = persistence and sustainability (reduced by conservatism practice) revenue cash collection, large ∆(receivables and
unearned revenue), ↑DSO, “bill and hold” (acceleration), channel stuffing, barter transaction, inconsistent growth in sale, seasonal effect on
non-seasonal firm expense large ∆(fixed A and inv), ↑DOH, LIFO liquidation, ↓core operating margin then negative spikes, capitalizing exp(↑A,
↓exp) (better not capitalize), reserve/ restructuring/ reversal BS large ∆(deferred tax A/L), sales of rec w/ recourse, inter-cooperation
investment, lessee use op.lease (better use financial lease), impaired GW, write off, SPV, CF E ≠ CFO, CFO before interest and tax ≠
operating income, compare growth in operating lease with firm’s asset growth, ↓discretionary spending near year end
Accrual adopts matching principal, reflects econ value, more transitory but less persistent (due to manipulation and estimation error) than cash
NOAEnd - NOABeg
B/S approach accrualsBS = NOAend – NOAbeg accruals ratioBS =
(NOAEnd  NOABeg )/2
CF approach accrualsCF = NI – CFO – CFI
3-part DuPont ROE
= net profit margin x asset turnover x leverage
NI
sales assets
=
x
x
sales assets eqtuiy
accruals ratioCF =
NI - CFO - CFI
(NOAEnd  NOABeg )/2
5-part DuPont ROE
= tax burden x interest burden x operating margin x asset turnover x leverage
av gassets
NI
NI
EBT EBIT
sales
=
, where
=1–t
x
x
x
x
EBT
EBT EBIT sales av gassets
equity
Pension
discount rate ≠ RF
rate of compensation growth
expected rate of return
definition (IFRS only
base on rates of high quality
average annual rate that compensation is
LT rate of return on the
has PBO only)
fixed income w/ similar maturity
expected to increase
investments of the plan
relationship of...
with BOs
PBO
+ve ultimately
-ve due to PV
nil
ABO (x in DCP) /VBO
nil (only current salary level is considered)
relationship of...
with pension expense
current service cost
-ve due to PV
+ve 1st
nil
interest cost
-ve except mature plan*
expected return
nil
+ve
pension expense
-ve except mature plan*
+ve 2nd
-ve
1
+ funded status
+ BObeg ± any impactBO – expected return (S ) ± any impactBO
+ FV of plan Abeg
+ current service cost
+ current service cost
+ actual return
= FV of plan A – PBO (US stops here)
+ interest cost
+ interest cost
+ contributions
± unrecognized deferred L(G) (S)
2
+ past service cost
+ past service cost (S )
– benefits paid
± unrecognized past service cost (S)
3
= FV of plan Aend
± actuarial L(G)*
± actuarial L(G) (S )
± unrecognized transition L(A) (S)
= pension exp (US oneline)
– benefits paid
= net pension A on BS (IFRS, limited)
= BOend
past service cost = plan amendments
thus smoothened and less leverage
1
3 2
3
S recorded in OCI to be amortized S α goes to S S IFRS vested portion must be expensed immediately S can use corridor method:
amortized when the accumulated > 10%(max (FV, PBO)), thus pension expUS no necc = expIFRS
*from α and changed assumptions
reconciliation US PBO and plan A IFRS fund status and net pension A; discount rate and rate of compensation growth should be consistent
w/ inflation; SFAS158 = USGAAP, applied to other post-employment benefits plans and affects net pension A only, reflects economic reality
funded statusbeg + contribution – econ pension exp = funded statusend funded statusUS = economic one
econ pension exp is true cost of pension, if contribution > it, the ∆, classified CFI, is like repayment or borrowing (net of tax) and affects BO
econ pension exp is more volatile than reported by eliminating smoothing accounts and including actual return
net periodic benefit cost = reported pension exp = NCC exp = service + interest – expected return + recognized (pass service, net actuarial L)
(econ pension exp – reported pension exp)(1 – t) = amount to adjust NI
CF adj 1) + net periodic benefit cost 2) – contribution IS adj 1) remove all pension-related components from net operating expenses except
service cost, settlement and curtailments 2) interest cost goes to interest exp 3) actual return goes to investment G/L; other post-employment
benefits like the healthcare = defined benefits except 1) unfunded and 2) dr replaced by inflation rate
E.g. benefit payment for 20 years and is given credit for 10 years of prior service with immediate vesting. current salary 50000; years until
retirement T 5yr; annual compensation growth 4.75%; dr 6%; benefit formula 1.5%
T-1
final year salary = 50000(1.06) = 60198.56
yrservice = yrvesting + yractual = 15
Vretirement = final year salary x benefit x yrservice
if lump sum 60198.56(1.5%)(yrservice) = 13544.68 if not lump sum PV 20yr = 155356.41 closing obligation1 = opening obligation2
benefit \ year
1
2
5
prior years
103,570.94 113,928.03 annual unit credit x yrprior inclu vesting
10357.09 x 10
annual unit credit
+
10,357.09
10,357.09 value at retirement/yrservice
155356.41/15 (constant)
total benefits earned
= 113,928.03 124,285.12 annual unit credit x yrprior inclu vesting +1 10357.09 x 11
T-t
opening obligation
77,394.23
90,241.67 prior years/(1+ dr)
103570.94/1.06^5
interest
+
4,643.65
5,414.50 opening obligation x dr
77394.23 x 0.06
T-t
current service cost
+
8,203.79
8,696.01 annual unit credit/(1+ dr)
10357.09/1.06^4
T-t
closing obligation
=
90,241.67 104,352.18 prior years/(1+ dr)
103570.94/1.06^4
Vretirement
share-based compensation exp (solely depends on the FV on the grant date) are recognized over the service period
Intrinsic value method: recognize only if options are in-the-money on the grant date
option exercise 會減公司 E by Pxex x #options
Fair value method: FV of options on grant date by pricing models / service (vesting) period. Not affected by exercise or sold thereafter
stock grants restricted or performance stock stock appreciation rights differ in forms of payment, reduce dilution phantom stock another
CFA Level 2 notes – created by Thomas Ip
Capital Budgeting decisions based on incremental ATCF, discounted at OC of fund which already captured the financing cost (thus CFs no
need to adjust such cost); Claims valuation approach evaluates asset by claims against the asset; Payment period needs decimal place with
12 as base. If NPV < 0, do not have any discounted payment period; avg accounting rate of return (AAR) = avg net income / avg BV, but not
concern time value and base on accounting numbers; profitability index PI = 1 + NPV/initial investment; project β and r preferred
t
t
NPV = – outlay + ΣCFOt/(1+r) + Terminal CFO/(1+r)
where
CF0
outlay = FCInv + WCInv – Salold + t (Salold – BVold)
dep = total cost/#yr, not consider salvage
CF1 to t after-tax CFO = (S – C – D)(1 – t) + D = (S – C)(1 – t) + Dt
(S – C – D)(1 – t) = NI; (S – C – D) = EBIT = operating income
after-tax CFOreplacement = (∆S – ∆C)(1 – t) + ∆Dt
tax effect = CF = (S – C – D)–t = (S – C)–t + Dt
CFt
terminal after-tax non-op CFO = SalT – t (SalT – BVT) + NWCInv
terminal after-tax non-op CFOreplacement = ∆SalT – t(∆SalT – ∆BVT) + NWCInv
Equivalent Annual Annuity preferred than NPV. PV  NPV; N  same n as individual project; I  WACC; CPT  PMT, pick highest!
Least Common Multiple input every single CF, or consider several NPVs. Note: match CF nominal/real with discount ratenominal/real
Real options: timing, abandonment, expansion, flexibility, fundamentals; overall NPV = NPV – option cost + option value
Common capital budgeting pitfalls not incorporating econ responses, template errors, pet projects, basing other items like EPS, NI, ROE or
IRR, bad accounting for CF, overhead cost, dr error, misuse capital budget, mislook investment alternatives, mishandle sunk and OC
MM1 (x tax) MVfirm is determined by CFs not by capital structure MM2 (x tax) cost of equity ↑linearly as debt financing increase, w/ constant
WACC MM1 (w/ tax) MVfirm is maximized at 100% debt due to tax shield MM2 (w/ tax) WACC is minimized at 100% debt
MM
I
II
re > WACC = (D/V)(1 – t)rd + (E/V)re use target weight in capital structure
Vfirm = D + E
higher than unexpected inflation ↓real dep tax savings,
w/o tax VL = VU
re new = re o + (re o – rd)(D/E)
w/ tax
VL = VU + tD
re new = re o + (re o – rd)(D/E)(1 – t) ↓real AT int exp, ↑real taxes
country specific sectors
efficient legal system
has common law (not private)
less information asymmetry
favorable tax rates on equity
bank-based financial system
more liquid markets
more institutional investor
higher inflation
higher GPD growth
D/E
lower
lower
lower
lower
higher
NA
lower
lower
lower
maturity
longer
longer
longer
NA
NA
longer
longer
shorter
longer
business risk sales risk and operating risk financial risk on common holders when
debt↑, b/w EBIT and EPS financial distress cost result from debt, can be direct or
indirect agency cost of equity conflict of interest b/w owners and managers,
include monitoring cost, bonding cost and residual loss, reducible by using debt,
good corp gov and acct transparency asymmetric information increases when
equity↑ static trade-off theory MVfirm is maximized and WACC is minimized, at a
point where benefit of tax-shield = additional borrowing cost peking order theory
internal fund > debt > new equity financial disclosure risk incomplete; Fr, Jp and
Italy more leveraged; N America and emerged more long-term
Residual Incomet = NIt – reBVt-1 = (ROEt – re)BVt–1 = NIt – chargeequity = NOPATt – chargecapital = NOPATt – TICt-1(WACC) = EVA = ΣEP
BV = BVequity = BVcommon + BVReE ~ A – L
NOPAT = EBIT(1 – t) = NI + int(1 – t) = net operating profit after tax
chargecapital = chargeequity + chargedebt
chargeequity = BVequity x re
chargedebt = BVdebt x rd(1 – t)
re ≠ cost of equity
TIC = NWC + net fixed asset = BVequity + BVlong term debt
MVA = MVfirm – BVTIC = MVequity + MVlong term debt – BVTIC
BV0 + E1 – D1 = BV1 = clean surplus relation, affects NI only but not BV, affected by those bypass income statement to equity directly
MVdebt  MVequity
ROE - re
ROE - re
t
t
V0 = B0 + ΣRIt/(1 + r) + (PT – BT)/(1 + r)
V0 = B0 + B0
or g = re – B0
Tobin’s Q =
V0  B0
re  g
replacement cost of total assets
E.g. A = 2M, L = 1M, E = 1M, re = 12%, rd = 7%, EBIT = 200000, t = 30%;
int exp = 70000, so pretax = 130000, tax = 39000, NI =
91000; equity charge = 120000, debt charge = 49000, capital charge = 169000; RI = 91000 – 120000 = 140000 – 169000 = -29000
Value of ω
1
0
0 < ω <1
independent to ω
if ROE >(<) r,
justified P/B >(<)1,
Represents
RI persists at
RI drops
RI declines
RI declines to long-run
PVRI is +ve(-ve);
current level
sharply to 0
over time to 0
level in mature industry
if ROE = r,
PV of continuing RI at
(P
B
)

RI
t
t
t
RI
RI
RI
RIt
RIt
t
t
t
(same tend)
justified P/B =1,


year t-1 (simply add to
1 r
1

r
ω
1

r
0
1

r
r
1

r
w
justified MV = B
CFt)
RI (focuses on economic profitability rather than just on accounting profitability) accounting adjustments:
▪ clean surplus violations – FX translation, pension accounting, and changes in FVfinancial instruments
▪ variations for FV – capitalize operating leases; consolidate SPEs; adjust reserves and allowances; adjust to FIFO by adding LIFO reverse;
pension A/L should be adjusted to reflect funded status; deferred tax liabilities should be eliminated to equity if not expected to reverse
▪ others – goodwill should be included in BV; amortization of goodwill should be excluded from ROE; remove nonrecurring and aggressive
accounting practices; adjust for international accounting differences
t
Economic income EI = CF1 + MV1 – MV0 = CF ± MVapp/dep(MV0>MV1); MV = PV of Σremaining ATCF/(1 + WACC) , ignore outlay or terminal
t
t
Economic profit EP includes EVA, MVA and RI
NPVMVA = MVA = ΣEPt /(1 + WACC)
NPVRI = ΣRIt / (1 + re)
TICcap-bug will be reduced by dep; ↑dep, ↑ATCFs; EVA spread = ROC – WACC = EVA / invested capital, where ROC = NOPAT / invest capital
%EBIT
S - TVC
Q (P - V)
Q (P - V)
S - TVC
=
=
, this denom = EBIT
DTL = DOL x DFL =
=
%Sales Q (P - V) - F S - TVC - F
Q (P - V) - F - int S - TVC - F - int
%EPS
FC
EBIT
DFL =
=
QBE =
%EBIT EBIT - int
P - VC
Pcum date – Pex date = Div (1 – TD)/(1 – TCG)
US double taxation Aus, NZ, Fr dividend imputation UK modified imputation
effective tax rate = 1 – (1 – corp rate)(1 – individual rate) for double-taxation and split-rate system. Tax-imputation is individual rate
DOL =
CFA Level 2 notes – created by Thomas Ip
Investors in non-domestic common stock normally avoid double taxation on div by receiving a tax credit for taxes paid to the country where the
investment is made; Div ↓agency conflicts b/w managers and shareholders, but ↑conflicts b/w shareholders and debtholders
Stable div (target ratio) approach expected div = previous div + (expected ∆EPS x target payout ratio x 1/n), where n = #yrs
Residual div approach 900 planned spending or FCInv, target 60%, debt 40% equity, 500 E1, Div = E1 – FCInv x equity% = 140
Residual div approach 1000 equity, debt-equity ratio = 0.5; so need debt 500 = total 1500, spend 900 left 600, 600 x 2/3 = payout
Stock-split same (div yield, P/E, MV), change (#shares outstanding, stock px, EPS, DPS) by multiplying 3/2, for a 3-for2 split
Share repurchase = cash div if tax treatment is the same, has potential tax adv, signaling a good investment, added managerial flexibility,
offsetting dilution from employee stock options, ↑financial leverage due to ↓equity Regular div may increase PE as r and g in DDM
If earnings yield >(<) after-tax cost of borrowing, post-repurchase EPS will increase (decrease)
If repurchase price >(<) original BVPS, post-repurchase BVPS will decrease (increase)
M & A good corp-gov obj in the best interest of stakeholders primarily investors 1) eliminate conflicts among stakeholders, particularly b/w
managers and shareholders 2) ensure asset are used efficiently and productively practices independent (≥75%, experienced, expert, ethical,
committed and dedicated BOD; independent chairman; election of all BOD members annually; annual BOD members self-assessment; BOD
meets annually, preferably quarterly, in separate sessions, i.e. w/o management; independent audit committee includes only independent,
experienced directors, oversee directly internal audit staff, have full access, authority to cooperation of management, meet with auditors in
separate sessions; independent nominating committee to identify management and BOD member candidates; reward manager based mainly
on bonus instead of fixed salary; independent legal counsel; statement of gov policies; respond to shareholder proxy votes corp-gov risks if
failure, operating risk to investors accounting risk incomplete, misleading or misstated financial statement asset risk abuse assets liability risk
↑debt at the cost of equity holders strategic policy risk benefit management or directors but not shareholders financial disclosure risk ESG
risks legislative and regulatory risk, reputational risk, operating risk, financial risk good reporting practices no nonrecurring gains and
noncash earnings; use LIFO (allowed only in US) during inflation; min. capitalization of interest, overhead, computer software costs; expensing
startup costs; use of completed contract method; expense employee stock option compensation, w/ the option valued by option pricing model
ILC
pioneer
growth
mature growth
stabilized
decline
types of merger
conglomerate
hori
hori, vert
hori
all 3
Bootstrap effect occurs when high growth (↑PE) issue shares to acquires low growth (↓PE) and
post-merger PEacquirer does not decline, thus EPS↑ but no economic gain. E = ΣE; MV = ΣMV;
#sharestotal = #sharesacquirer + #sharesissued; #shareissued = MVtarget/Pxacquirer; used in internet bubble
and 3rg merger wave MVcombined = MVA + MVT + Syn – Cash Syn = GainT + GainA GainT = TP =
PT – MVT GainA = Syn – TP = Syn – (PT – MVT) Pcombined = MVcombined/#shares stock offer(cash
= 0): Pxpost-merger = MVcombined/↑#shares PT = Pxpost-merger x #sharesnewly issued + A’s original
business combinations IFRS no differentiation US M&A, consol, SPE both no pooling (aka uniting, use BV not FV, smaller A – L, no GW, no
effect on revenue, operating result restated as if has been combined) but acquisition acquisition A + 0.xB = A merger A + B = A statutory
merger totally immersed subsidiary merger become subsidiary consolidation A + B = C stock purchase pay shareholders, need majority vote,
for hostile use, CG tax at shareholder level, involve entire company, target’s tax loss is allowable asset purchase pay company, assets > 50%
need majority vote, tax at corporate level, focus on parts of company divestitures sale of a portion to outside, paid in cash equity crave-outs
separate entity, small portion for outside, remaining are parent’s spin-offs separate entity, for existing shareholders(they own 2 Co.s now), nocash split-offs parent’s shares exchange for new shares (shareholders own 1), no-cash; liquidation friendly merger definitive merger
agreement hostile merger to board: bear hug to shareholders: tender offer(take over) to buy shares or proxy fight to replace board pre-offer
defense poison pill very effective by giving shareholders the right to purchase additional shares of stock at extremely attractive prices (flip-in
pill target buy target flip-over pill target buy acquirer dead-hand provision cancel the bill only by continuing directors) poison put bondholders
can demand immediate redemption and cause cash burden restrictive takeover laws in certain states staggered board; restricted voting rights
reduce tender offer effectiveness supermajority voting rights > 51% fair price amendment; golden parachutes pays managers if they leave the
target after a merger post-offer defense “just say no”; litigation; greenmail rarely used now, target payoff to acquirers share repurchase
rd
increase debt leveraged recapitalization use huge debt for share repurchase crown jewel defense maybe illegal, sells major asset to 3 party
Pac-man defense eat back, rarely used white-knight defense; white squire defense junior knight buy enough target to block takeover, often
involve litigation
N firm concentration ratio = ΣMSlargest N firms; Herfindahl index (HHI) = Σ MS i2 H < 0.1 or 1000 ↓con and
↓oligopolistic, ↑competitive, no antitrust; 0.1 ≤ H ≤ 0.18 moderate con (∆>0.01 or 100 = likely antitrust); H >
0.18 highly con (∆>0.005 = antitrust) all base on post-merger; 1/HHI = #firms of same size, more is
competitive, less threat of new entry
unlevered income = NI + after-tax net interest exp = NI + (interest exp – interest income)(1 – t)
NOPLAT = unlevered income + ∆deferred tax
FCF = NOPLAT + NCC – ∆NWC – FCInv
comparable company analysis 1) obtain benchmark’s PE, P/CF, P/BV, P/S, apply
mean/median/mode/high/low of them 2) multiply them to target’s EPS, CF, BV, S, average (equally or
weighted) the results 3) times 1 + takeover premium comparable transaction analysis same as above but
the P is recent transaction price rather than stock price
+
+
+
-
NI
after-tax net interest exp
unlevered NI
∆deferred tax
NOPLAT
NCC
∆NWC
FCInv
FCF
P0
g
pay outratio 1 - b
1 1
1

)(
) = 1/r + PVGO/E1 =
= tangible(static) PE + franchise(growth) PE =  ( 
r-g
r-g
r r ROE r  g
E1
tangible(static) PE = 1/r; franchise(growth) PE = PVGO/E1 = franchise factor x growth factor = FF x G
g
NI
NI - div sales assets
1
1
x
x
x
FF = 
;G=
, g = ROE × b = PRAT =
PA = ROA, T = equity multiplier, PAT = ROE
r ROE
r g
sales
NI
assets equity
If ROE > r, franchise factor > 0, the more company retains, growth factor ↑, franchise P/E↑, intrinsic P/E↑, P/B > 1
If ROE = 0, franchise P/E = 0, P/B = 1
PEG = PE / g, the lower the better, does not consider risk, duration growth and assume linear
If ROE > cost of capital, then intrinsic P/E > tangible P/E
P
1
Justified leading 0 =
, if ↑flow thru rate, ↑P/E, approach 1/Rnominal if 100%
all 用 industry value
E1 real r  (1 f low thru rate) x inf lation
Intrinsic PE = leading PE =
CFA Level 2 notes – created by Thomas Ip
P0 (1 - b) (1  g)
P
=
= intrinsic PE (1 + g) = Justified leading 0 (1 + g) = P/avgEprevious 4 quarters
r-g
E0
E1
Justified P0B0 ratio = (ROE – g) / (r – g) = 1 + (PVfuture RI/B0)
Justified P0S0 ratio = (E0/S0) (1 – b) (1 + g) / (r – g) = profit margin x justified trailing PE, less preferable than P/S
Justified D0P0 ratio = (r – g) / (1 + g)
D0 = recent divquarter x 4 or sum of divsemiannual if interim and final div differs largely
Yardeni model CEY = E/P = CBY – β x LTEG + ε, where CEY = the current earnings yieldmarket index, CBY = current Moody’s A-rated coporate
bond yield, LTEG = earnings growth rate5yr, β = weight the market gives to 5yr earnings projection P/E = 1/(CBY – β x LTEG + ε)
V0 = D1/(r-g) = E0/re + PVGO, E0/re = Vno-growth as PVGO = 0 for a no-growth company i.e. no +NPV projects. PVGO = –ve if ROE < re
Justified trailing
GGM P0 =
E (1 - b)
D
D1
~ 1
; re = 1  g
re - g
re - g
P0
n
DDM Vt-1 = 
Dt
t  1 (1 r )
e
t

Pn
(1  re )
n
\__ H-model V0 =
D0 (1  gL ) D0 x t/2 (gS - gL )

re - gL
re - gL
g = 1yr forecasted div yield on market index + LT earnings growth – LT gov bond yield
r = required return not cost of equity
Vperpetuity/preferred = D/re = (par x %)/re
div yield = D/P = D/V
earnings yield = E/P = rankable absolutely
Diluted PE (due to option) = P/ [#option/(#shares current + #option)]
n
arithmeticmean ≥ geometricmean ≥ harmonicmean; weightedmean ≥ weighted harmonicmean = 1 /
X
i 1
w1
, X = price multiples like PE
1
BV = BVequity = common shareholders’ equity = E – claims that are senior than common = A – L – preferred
EV = PVEI + other EI + debt investment – txn cost, used along with pre-interst measures like Sales, EBITDA
EV is total company value = MVcommon + MVpreferred + MVdebt + minority interest – cash, cash equivalents and ST investments
MVtotal invested capital = TIC = MVcommon + MVpreferred + MVdebt + minority interest
MVtotal invested capital = TIC = MVequity + MVdebt = WCInv + PPE
PPEbeg – dep + FCInv = PPEend
EBIT = operating earnings = operating income = operating profit
CF = NI + NCC; adjusted CFO = CFO + int(1 – t)
EBITDA = recurring NI from continuing operations + interest + tax + depreciation + amortization = EBIT + depreciation + amortization
NOPLAT = EBITDA – dep – tax = operating profit (EBITA) – tax = NI + int(1 – t) FCF = NOPLAT + dep – FCInv – WCInv
earnings can be –ve and volatile; EBITDA poor proxy for CF, will overstate CFO if WC is growing, good for comparing firms with different
financial leverage, valuing capital-intensive business with high dep, adequate if capital expenses = dep, and usually positive even though
when EPS is not, works best with MVTIC. EV/EBITDA better than PE for companies with diff financial leverage, EBITDA is also good for capitalintensive companies. P/CFO, P/FCFE are least affected by international accounting diff
abnormal earnings are earnings in excess of WACC, e.g. RI underlying (aka persistent, continuing, core or normalized) earnings are nonreportable under IFRS = earnings excludes nonrecurring items, such as G/L from asset sales, assets write-downs, provisions for future losses,
and changes in accounting estimates normalized (aka normal) earnings are the estimate of EPS in the middle of the business cycle to
eliminate the Molodovsky effect. To calculate, the method of average ROE (arithmetic average ROE x current BVPS) is preferred than the
method of historical average EPS (simply arithmetic mean) standardized unexpected earnings SUE = EPS – E(EPS) / σEPS – E(EPS), the
higher the more surprise, +ve means good surprise. Momentum indicators include earnings surprise, SUE and relative strength
Estimating emerging market stuff – DCF / WACC (net of country risk premium)
▪ RF = 10-yr US government bond yield + inflationemerging – inflationUS
▪ β = regress industry β (x individual) relative to a broad-based global market index that is well-diversified
▪ market risk premium = extra return on a globally diversified portfolio over RF (4-6% avg, 4.5-5.5% avgLT)
▪ pre-tax cost of debt = RF emerging + US credit spread on comparable debt
▪ marginal tax = local tax applied to interest expense on debt
▪ capital structure weight = estimated global industrial
Estimating required rate and value of PE firms for transaction, compliance or litigation purpose (normalized E preferred)
▪ expanded CAPM = CAPM + size premium + specific premium
▪ build-up method = RF 20yr+ equity premium + size premium + industry premium + company specific premium
▪ income approach – FCF for large mature PE capitalized CF method is FCFF/(WACCtarget – g) or FCFE/(rtarget – g), deno = capitalization rate,
use if g is constant excess earning (aka residual income) method measure intangible value
= (normalized E – rWCWC – rFAAFixed)/(rintangible – g) + WC + AFixed = Aintangible /(rintangible – g) + WC + AFixed
▪ market approach – guideline public company, guideline transaction, prior transaction. Multiples have to be adjusted for risk and growth of
subject company. For GPC, add control premium if buyer of the PE may exist. MultiplesGT is better than MultiplesGPC
▪ asset-based approach – not going-concern basis or for very small PE with limited history or heavily asset-based, provide the least value
DLOC = 1 – 1/(1 + control premium) needed for PT, no need for GPC, may for CF; total discount = 1 – (1 – DLOC)(1 – DLOM)
Estimating market capitalization rate (MV = ROI/(r – g))
▪ market extraction (direct income capitalization) – cap R0 = NOI1 / MV0, where MV = sales (arith mean for industrial values)
▪ band-of-investment (BOI) – mortgage weight x mortgage cost + equity weight x equity cost; mortgage cost = cost of capital + sinking fund
factor (= annuity of $1 at the interest rate r, N = yr x 12; I/Y = r/12; PV = 0; FV = -1; PMT=? x 12)
e.g.
weight
rate
weighted
 Assume cap rate = 0.1. mortgage cost = mortgage constant; return on funds = cost of
capital = mortgage rate; return of capital to lender = sinking fund factor; cash on cash return
loan
0.7
0.101
0.07…
= equity dividend rate ~ equity cost
equity
0.3
0.096
0.03…
▪ built-up method = pure interest rate + liquidity premium + recapture premium (=return net of appreciation) + risk premium
▪ MVA / GIA = GI multiplier M = salesA / GIA, can be distorted by gross rent, unlike others, does not consider cost
CFA Level 2 notes – created by Thomas Ip
Firm value
= MVequity + MVdebt + MVpreferred = Aoperating + Anon-operating FCFF / FCFE
t
Firm value
= Σ1 to nFCFFt / (1 + WACC) = FCFF1/(WACC – g)
t
Equity value
= Σ1 to nFCFEt / (1 + re) = FCFE1/(re – g) (re from models like CAPM)
Use FCFF if -ve FCFE, on cyclical companies, high or changing debt levels or capital
structure (as net borrowing affects FCFE); Div, share repurchases and ∆#outstanding
shares do not affect both. ↑leverage ↑FCFE at first by net borrowing, ↓FCFE later by int(1–t).
In short, FCFF will not change. FCFF and FCFE are more linked to valuation theory. FCFE
is preferred, easier, straight forward, usually <FCFF, but more
IFRS
US
volatile than CFO
int rec
O or I O
FCFF = NI + NCC – WCInv – FCInv + Int(1– t)
int paid O or F O
FCFE = NI + NCC – WCInv – FCInv + Net borrowing
div rec
O or I O
FCFE = NI – net investment in operating asset + Net borrowing
div
paid
O or F F
FCFE = NI – (1 – DR) (net investment in operating asset)
FCFE = NI – (1 – DR) (WCInv + FCInv – DEP)
NCC items
FCFE = FCFF – Int(1 – t) + Net borrowing
NI = pref div + NIavailable to common for FCFF
depreciation
amortization and
impairment of intangibles
CFO = NI + NCC – WCInv
FCFF = CFO – FCInv + Int(1 – t)
FCFE = CFO – FCInv + Net borrowing
restructuring charges
(expense)
NI = (EBIT – Int) (1 – t) = EBIT(1 – t) – Int(1 – t)
FCFF = EBIT (1 – t) + Dep – WCInv – FCInv
FCFF = EBITDA (1 – t) + Dep(t) – WCInv – FCInv
restructuring charges
(income from reversal)
losses
gains
amortization of LT bond
discounts
+
+
+
+
-
+
FCFE coverage = FCFE / (div paid + repurchase$)
WCInv = ∆WC accounts = ∆Acurrent – ∆Lcurrent (e.g. AC rec’,
amortization of LT bond
inv, AC payable, accrued L, ignore cash, sec and debtST)
premiums
FCInv = ∆gross PPE = ∆net PPE + ∆dep = capex (–
deferred taxes
+
proceed from salesA LT); net capex = capex – dep
VPS = FCFE/#shares
NI ~ EPS
Net borrowing = DR(FCInv + WCInv – Dep) = new LT debt/note issues – debt repayments
(exclu ↑in liabilities); DR = debt/(debt+equity)
net sales px
GI
sales px
net sales px
- vacancy & collection fees
- sales cost
- purchase px
- purchase px
effective GI
net sales px
G recognized on sale
+ depaccumulated 拆#1
G realized on sale 拆二計稅
- operating exp
NOI
NOI
net sales px
G realized on sale 拆二計稅
- deptax purpose
- annual debt service
- mortgage baloutstanding
- int = loaninitial x int?
BTCF
BTER
- deprecaptured 拆#1
G recognized on sale 拆#2
taxableincome
- Taxpayable
- TaxDep recaptured
xt
ATCF
- TaxCG
Taxpayable
ATER
annual debt service: PV = loan amt, FV = 0, I/Y = mortgage r; N = #periods, CPT > PMT, annualize it, its level throughout the loan period
TaxDep recaptured = Depaccumulated x t
TaxCG = G recognized on sale x t Tdue on sale = TaxDep recaptured + TaxCG
If net selling price > purchase price, gain on sale = appreciation + recaptured Dep (= accumulated dep), tax must include capital gain
If net selling price > book value only (= purchase price – accumulated dep), gain on sale = recaptured dep, tax may include capital gain
t
t
NPV = PVCF – equity investments = ΣATCFt/(1 + r) + ATER/(1 + r) – equity investments
Exit value = investment cost + earnings growth + increase in price multiple + reduction in debt
PIC – cumulative amount called down or utilized by GP (=個倉直到而家有幾多) committed capital (=理想個倉係幾多)
DPI – LP’s cumulative realized, or cash on cash return = cumulative distributions / cumulative invested capital = cumulative distributions / PIC
RVPI – LP’s unrealized return (fees netted) = value of LP’s holdings in the fund / cumulative invested capital = NAV AD / PIC
TVPI – LP’s realized and unrealized return (fees netted) = DPI + RVPI
NAV BD1 = NAV AD0 + capital called down – management fees (based on PIC) + operating results
NAV AD1 = NAV BD1 – carried interest (based on NAV BD – committed capital and ∆NAV BD thereafter) – distributions
Gross IRR: capital called down, operating result > net IRR: capital called down, operating result – carried interest – management fees
prei + Ii = posti
pre1 / PVfactor = post0
βequity = βasset (D + E)/E, where βasset = enterprise beta
posti = Vexit / PVfactor
fi = Ii / posti
shareVC = (sharefounder/existing + any shares) x fi/ (1 – fi) pricei = Ii / sharesVCi
CF for debt payment in LBO = NI + dep + amortization – reinvested dep – capital expenditures – NWC
VC creates value thru 1) reengineer by expertise 2) access credit market 3) better interest alignment b/w PE firm owners and management VC
econ terms management fee annually to GP, % of committed capital, NAV or TIC, ~1.5-2.5% transaction fee to GP, or 50/50 b/w GP and LP
carried interest 20% of profit to GP if over hurdle ratchet determine equity allocation b/w management and shareholders hurdle rate ~7-10%,
IRR that GP require to receive carried interest target fund size; vintage year; term of the funds corp gov terms key man clause limit GP’s
investments if named key staff leave disclosure and confidentiality; clawback provision; distribution waterfall deal-by-deal; total return 1)
carried interest calculated only after the entire committed capital is retired 2) exit value exceed invested capital by a threshold ~20% tag-alone
drag alone rights ensure acquisition need to pass thru all shareholders and management of the co no-fault divorce ~>75% vote can kick a GP
CFA Level 2 notes – created by Thomas Ip
out removal for “cause” allow removal of GP or retirement of the fund for causes investment restrictions impose min. level of diversification coinvestment LPs have the right to co-invest limitedly to reduce conflict of interest like crossover investment
Hedge fund types long/short the largest in terms of asset size, long/short on common stock, very volatile, worldwide, market-neutral but tend
to be long market-neutral earn RF, type of long/shirt, may use derivatives, net zero exposure, may not be 0 beta global macro fund bet on
market, currency, interest rate, large leverage and rely upon derivatives event-driven funds specific events fixed income large leverage Merrill
Lynch High Yield index f.income hedge funds Russel3000 equity hedge funds fund risks investment risk due to limited information, ∆credit
spread, equity market risk, style drift and leverage. F.income and equity hedge funds risk are large than commonly thought fraud risk;
operational risk high yield issuers often use bank debt (floating rate, short term, most senior) and reset notes, its corp structure as well as CFs
maybe complex hedge fund data shortcomings 1) listing is up to managers 2) include small funds but miss large funds 3) data not verified
by publishers 4) funds are subject to turnover 5) survivor and backfill bias overestimate returns 6) large fund closed to new investors may
over/underestimate returns 7) autocorrelation may underestimate volatility 8) short track records leverage f.income arbitrage > convertible
arbitrage > risk arbitrage > equity market neutral > long/short equity = distressed securities risk measurement maximum drawdown, VAR, std
deviation, sortino ratio
▪ sport rate curve on-the-run Treasury – newest and most accurate, bootstrapping needed; large maturity gap particularly after 5 yrs, rates
distorted by repo market
▪ on and off-the-run Treasury – 20, 25yr off-the-run added, bootstrapping needed; ignores other information, rates distorted by repo market
▪ all T-coupon security and bills – utilizes all Treasury, econ modeling or stat curve fitting techniques used; information is not all current
▪ Treasury coupon strip – observable zero-coupon securities to simply directly create spot rate curve; biased due to liquidity premium and tax
disadvantages, and some non-US tax laws are such ma fan that only coupon strip rates are useful, no bootstrapping needed
swap or LIBOR rates are preferred than gov bond yield as1) no gov regulation 2) swap market standbys 3) credit risk are comparable than
sovereign risk 4) many maturities available slope of yield curve yield30yr – yield3mon or 2yr affected by 1) level of interest rates 2) slope 3)
curvature term structure of int rate pure expectations (aka unbiased expectations) forward rates = E(spot rates), no recognition of interest
rate and reinvestment risk biased expectations – forward rates ≠ E(spot rates) a) liquidity preference b) preferred habitat; A portfolio has many
key rate durations, one effective duration = Σkey rate durationi yield risk is measured by σ, the mean adopts compound return = Σ100 x
1/2
ln(yt/yt–1) /n; σannual =σdaily x #days in year Yield volatility follows pattern overtime, which can be modeled and forecasted using AR models
swap spread = swap fixed rate – gov, gauge credit risk of banks
vendors report different ED due to different assumptions for: ∆rate, prepayment model, OAS from Monte Carlo and refinancing spread
interest rate risk is measured with %∆ in bond price
BV Δy  BV Δy  (2 x BV0 )
BV Δy  BV Δy
2
EC 
= duration effect + convexity effect ≈ -ED x ∆y x 100 + EC x ∆y x 100
ED 
2
2 x BV0 x Δ y
2 x BV0 x Δx
6
To compare yieldMBS with T securities, use bond equivalent yield = 2[(1 + monthly cash flow yield) – 1] = 2 x effective semiannual rate
Nominal spread cannot reflect prepayment risk. The Z-spread (OAS in Monte Carlo) is the spread when added to T spot, makes the PV CFs of
MBS equals market price plus accrued interest. Monte Carlo alone cannot generate arbitrage-free trees, need to add OAS.
ED, EC are for bonds with embedded options like MBS. D CF is a form of ED, commonly used. Both allow CFs/prepayment to change when
rates change, Dmodified does not. ED (use Monte Carlo) > DCF (naive) > Dmodified; Other EDs: DCC use market price; DED use historical data
“modified” assume CF x change if int rate change, “effective” is opposite (binominal model). Binominal model has inputs that are variable to
users 1) volatility assumption 2) benchmark used 3) call rule, thus have diff result
Convertible Bond conversion ratio = #shares
market conversion price = MVconvertible bond / conversion ratio = investor indifference
conversion price = parconvertible bond / conversion ratio
market conversion prem = market conversion price – MVstock
conversion value = MVstock x conversion ratio
market conversion prem ratio = (market conversion prem / MV stock) – 1
max downside (movable unless RF ST=RF LT) = straight value = CFs discounted at r = no options, CB trades upside potential for max downside
min value = max (straight value, conversion value), straight value >/=/< conversion value, busted convertible/ hybrid /stock equivalent
prem over straight value = downside risk = (MVconvertible bond / straight value) – 1, the greater the less attractive
prem payback period = market conversion prem / favorable income difference = #yrs needed to recover prem/share
favorable income difference = (coupon interest – conversion ratio x div) / conversion ratio, coupon > div
callable CB value = straight value + call on stock – call on bond
putable CB value = straight value + put on bond
soft put can be redeemed for cash, stock or subordinated notes or a combination of all three at co's discretion hard put redeemed only in cash
Credit risk = default + credit spread + downgrade rating ST PD LT PD + loss
upgrade/downgrade watch ±2 +ve/stable/-ve outlook ±1
Credit risk model for corp bond structural model use BSM and base on firm asset value reduced form model independent
Credit analysis of corp bond business and operating risk 4C capacity to pay (ratios & CF), collateral, covenants and character (corp gov)
Credit analysis of non-corp bond MBS prepayment risk ABS and non-agency MBS credit quality of collateral and seller/servicer, CF stress,
payment and legal structure; in true securitization servicer only collect and distribute CF, otherwise it’s a hybrid or quasi-corporate municipal
bond tax-backed debt structure, budgetary policy, gov revenue availability, socio environment, almost same with corp bond except with
revenue bond type of municipal, additional concern of limit of basic security, flow of funds structure, rate or user charge covenants, priority-ofrevenue claim and additional bond test sovereign bond economic and political risk local
CCY domestic gov policy foreign CCY BOP and structure of of external balance sheet.
Altman’s credit Z-score model Z = (s1)WC/A + (s2)RE/A + (s3)EBIT/A + (s4)MVequity/L +
(s5)S/A
MBS has embedded option, measured by WAC and WAM (+ve related to interest rate risk,
use to calculate spread), basic form is MPS CMO contains bond classes, transfer
prepayment risk, structured as: sequential tranche – every tranche receive interest, but
principal goes sequentially, avg life = Σ(#month x principal payment)/(12 x tranche par)
serving fee = (WAC – pass-through rate)/12; accrual tranche – zero-coupon bond, simply
ranked last and has no effect on prepayments; floating-rate tranche; structured IO – no
principal is paid to IO, IO’s coupon rate is the highest; PAC tranche – PAC1 > PAC2 > … >
CFA Level 2 notes – created by Thomas Ip
support (busted if support used up), pay principal to PAC holder by minimum principal within PAC collar/band so as to reduce extension and
contraction risk of PAC investors at the cost of support tranche, if actual PSA within PAC collar, avg life of PAC tranche will not change, collar
will alter depends on actual prepayment, better use effective collar, the narrower the collar, the more specific prepayment date; non-agency
CMO = whole loan CMO ABS divided into prepayment or timing tranche like sequential and credit tranche like senior/subordinate HEL targets
borrowers with impaired credit history or the payment-loan ratio is too large, the loan is used to settle personal debt rather than buying new
house. It has variable fund cap with NAS or PAC structure, use PPC instead of PSA, which is unique to each issuer manufactured housingBS agency-backed, prepayment is stable as not sensitive to refinancing due to small loan, low quality of borrowers and high Dep of asset
auto-loan ABS low prepayment (not sensitive to interest change) as already low rates due to promotion and small loan SMM = ABS / (1 –
ABS(m – 1)), m = #month, ABS = absolute prepayment speed of original amount student loan-BS guaranteed by gov, floating-rate loan, reset
quarterly or monthly and based on the prime rate, prepayment may occur due to defaults or loan consolidation credit card-BS revolving and
non-amortizing, may have lock-out period for reinvestment CMBS unlike residential, is nonrecourse (limited liability for borrower) and has
loan-level call protections that include prepayment lockout (~2-5yrs), defeasance, penalty fees and yield maintenance fee, structured
protection and balloon (balloon risk = extension risk) maturity protection (renegotiate the loan). LTV and DSC ratios are key indicators.
CDO pools bonds (CBO) and loans (CLO); contains floating A-grade senior 70-80% (protected against credit deterioration measured by
coverage test), ≥B fixed mezzanine, no-rating fixed subordinate/equity; requires an int rate swap for mismatch A/L CFs cash CDO purchase
cash market debt instruments synthetic CDO purchase credit derivative instruments; bondholders take on the economic risks not legal
ownership of assets; senior 90% junior 10%; asset managers buys CDS from junior bondholders who receive income from high quality debt
and CDS premium why synthetic CDO? senior section requires no funding, shorter ramp up, cheaper to acquire exposure via CDS rather than
actually buying arbitrage CDO is dominating and aims to actively earn return spread balance sheet CDO aims to remove assets from BS, less
regulatory requirement CF CDO proceeds are from interest and principal from underlying, include ramp up, reinvestment and pay down phase,
pay from administration and management fee to equity tranche MV CDO proceeds are from total return of the portfolio
Minsky’s financial instability hypothesis when one buys an asset
using loan the income generated can repay: hedge unit interest and
principal, stable type speculative unit interest only, like a balloon payment
Ponzi unit none, -ve amortization w/ balloon payment = original principal
+ unpaid interest. Minsky states that the longer the stable period the more
unstable it will be
PSA 100 (cap 左 at 6%先乘) CPR = 6% x m/30 x PSA
SMM = 1
1/12
12
– (1 – CPR)
CPR = 1 – (1 – SMM)
CPR > SMM
prepaymentM = SMM x (monthM beg outstanding balance – scheduled
principal paymentsM),
SMM interpreted as projected prepayment in month M; CPR interpreted
as % of outstanding balBEG prepaid by the end of yea
Non-agency = nonconforming (foreign residential MBS is in this form),
suffer from credit risk thus need credit enhancements:
▪ external suffers from “weak link” philosophy: corporate guarantees, letter of credit and bond insurance, it is the first buffer
▪ internal reserve funds (cash reserve and excess servicing spread), overcollateralization and senior-subordinate structure (↓credit risk)
The shifting interest mechanism reduces credit risk at the expense of increased contraction risk for the senior tranches
net operating income
current mortgage amount
debt-to-service coverage ratio =
loan-to-value ratio =
debt serv ice
current apprased v alue
CF yield
Exercise
Interest rate path
CF yield – T spot
e.g.
2 approaches to value fixed
income or ABS: Z or OAS
option-free
Zdiscounted CF
credit card
Z – OAS = option cost
option embedded
X intend
Z
autoloan, HEL
↓option cost = cheaper
option embedded
V intend
independent
OASbinominal
callable/puttable corp
option embedded
V intend
dependent
OASMonte Carlo
MBS or real estate-BS
nominal / zero-volatility / option-adjusted are spreads relative to T yield curve and T spot curve. Interest rate benchmark candidates:
OAS treasury benchmark
sector benchmark (higher grade)
Issuer-specific benchmark
comparison using issuer-specific
benchmark reflects no credit risk;
>0
undervalued (cheap) if actual OAS > required OAS
undervalued
OAS spread reflects no option
overvalued (rich) if actual OAS < required OAS
risk, other all reflect credit, liquidity
=0
fairly priced
overvalued (rich)
and modeling risk
(as our bonds have credit risk so do expect +ve OAS)
<0
overvalued
3
(current rate)(1yr forward rate 1yr from now)(1yr forward rate 2yr from now) = (yr3 spot rate)
Forward / Futures
forward price FP
T
no arbitrage, T-Bill fut
S0 (1 + RF) + FV(NC) –
FV(NB)
equity; discrete; stock
futures
(S0 – PVDiv)(1 + RF)
T
S0 (1 + RF) – FVDiv
equity; continuous; equity
index futures
S0 e(R f D
fixed-income; T-Bond fut
(semiannual coupon,
multiple deliverable)
c
c
T
value of long position VT
FP
St –
(1  R F ) T - t
St – PVDiv t –
St
Dc x (T - t)
)xT
[(S0 – PVC)(1 + RF) ] / CF
T
[S0 (1 + RF) – FVC] / CF
St – PVCt –
T in yrs, half = 0.5; T-t = time remaining
FP
(1  R F ) T - t
FP
–
e
T
No-arbitrage assumptions: no txn cost, no
credit risk, unlimited financing at RF
e
Rcf x (T - t)
FP
(1  R F ) T - t
RFc
RFc = ln(1 + RF) RF = e
rate
–1 見 e 用 continuous
FRA price = FRA contract rate = implied
annualized forward rate from FRA expiration
to maturity of the loan
CFA Level 2 notes – created by Thomas Ip
currency – St and FT in DC
/ FC (covered IRP)
S0
currency – continuous time
price and value
S0 e (RDC RFC ) x T
(1  R DC ) T
(1  R FC )
c
T
St
T-t
(1  RFC )
c
e
St
c
R FC
x (T - t)
–
FT
(1  R DC ) T - t
–
e
FT
c
R DC
x (T - t)
Fut > forward, if ρ(Vasset, r) > 0 due to MTM
Fut = forward, if interest rates are known OR
constant; Fut price ≠ fut value
FP > S = contango; FP > E(S) = normal
contango, due to hedgers and speculators
 1  y dayLIBOR (y /360)  360
precise 1/(1+ratea(a/360)) – (1+ rateFRA(y-x)/360))/(1+ rateb(b/360))
n=b–a=y–x

- 1
rough
1)
cal
new
rate
(see
left)
2)
(new
rate
–
old
rate
)(n/360)/(1+
rateb(b/360))
FRA
FRA
FRA
1

xday
LIBOR
(x/360)
(y
x)


Eurodollar futures are good for LIBOR-based only, can’t perfectly hedge others as implied rate fut ≠ implied forward rateFRA
Off-market forward requires non-0 value at start, +ve = long pays
Commodity return = price return (spot)+ roll or convenience yield (on avg is contango, ie –ve) + collateral yield (=T-bill, can be enhanced by
active management), lowly correlated with other assets thus add diversification why commodity LT return; reduce portfolio risk; return-timing
diversification (Pxcommodity respond much more faster); inflation-liability matching strategies index fund, index plus, active long-only
T
T
-0.0488T 0.0583T
Single period: 0.5(1.06) /(1.05)
continuous compounding: (0.5e
)e
, as ln1.05 = 0.0488 and ln1.06 = 0.0583
X - FT
X
options on fut/forwards P  C 
D% = 1/U%
U% = 1/D%
C
 P  S - PVCF form synthetics
(1  RF )T
(1 R F ) T
FRA
xxy
1  RF  D
; πD = 1 – πU (=0.5 for bonds)
UD
The last fixed-income security price calculation: I/Y: that node; PMT: coupon per period; N: 1; FV = 100; CPT  PV
risk-neutral probability of an up-move πU =
Deltacall =
C1  C1
S1  S1
=
ΔC
≈ N(d1)
ΔS
Deltaput =
C1  C1
S1  S1
≈ abs(N(d1) – 1); 0 ≤ N(x) ≤ 1; N(-x) = 1 – N(x)
BSM assumptions underlying asset price
follows a lognormal distribution; underlying
asset returns and continuous RF is
constant and known (thus inappropriate in
valuing options on bonds and interest
rate); frictionless mkt; no-arbitrage;
underlying asset generates no CFs;
European options. BM is for calculating
the value of European options on forwards
and futures
Due to MTM, USoptions on fut > EUoptions on fut,
USoptions on forward = EUoptions on forward.
PUS > PEU; CUS > CEU if significant div
presents, if not CUS = CEU
#options = #share / delta
hedge ratio = 1/ call delta
 start discount at end, simply par +
coupon
Fig19 – 0.9048 = 1/1.1051; 0.8846 = 1/1.1304 etc. the % is one-period interest rate; 0.6479 is price of 4-period zero bond
++
–
Fig20 – 0.7417 = 0.5(0.8424 + 0.8751)/1.1578; 2-period call optionzero bond c = max(0, 0.7417-0.8); c = 0.5(0 + 0.0583)/1.1025
Fig21 – 0.9877 = 0.11(0.9048+0.8106+0.7254) + 1.11(0.6479); 0.9840 = 0.11(0.8945) + 1.11(0.7417) 2-period call optioncoupon bond same
++
–
Fig22 – 2-period cap = 2 caplets; 2-period call optioninterest rate c = max(0, 0.1578 – 0.105)/1.1578 = 0.0456; c = 0.5(0.0116 + 0)/1.1025
–rT
–rT
c
2
0.5
0.5
BSM
c = S0N(d1) – Xe N(d2) p = Xe [1 – N(d2)] – S0[1 – N(d1)] d1 = [ln[(S0 – PVCF)/X)] + (r + σ /2)T] / σT^ d2 = d1 – σT^
-rT
-rT
2
0.5
0.5
BM
c = e [f0(T)N(d1) –XN(d2)]
p = e (X[1 – N(d2)] – f0(T)(1 – N(d1)]
d1 = [ln(f0(T)/X) + (σ /2)T] / σT^
d2=d1–σT^
c
σ = annualized std dev of the continuously compounded return on stock; r = continuously compounded RF; N = normal dist; f0(T) = fut px
–forward rate(days/365)
BM in interest rate options: we need discount the payoff by e
p, then times days/365, then times notional
capletannual payoff = EUcall option on annual rate =
max {0, notional principal (1y r rate - cap rate) x actual day s/360}
1  1y r rate
cap = Σcaplets = ΣEUcall
floorletannual payoff = EUput option on annual rate =
max {0, notional principal (f loor rate - 1y r rate) x actual day s/360}
1  1y r rate
floor = Σfloorlets = ΣEUput
1
1  ZN
, where ZN =
Z1  ...  ZN
(1  spot rate(n/360))N
PVremaining fixed = fixed swap rateXannual(Σall new dr) + new last dr
Vswaption at expiration = (exXannual – new fixed swap rateXannual)(Σall dr)
fixed swap rate =
swap rateannualized = fixed swap rate(
st
360
) valuefixed = PVfixed – PVfloat
n
st
PVremaining float = [1 + (original 1 dr) n/360] new 1 dr
st
(original 1 dr) n/360 = floating payment
CFA Level 2 notes – created by Thomas Ip
swap OTC, at least one floating, 0 value and low credit risk for both at start, netted payment if same CCY, after MTM use new rates to recal
new fixed rate interest rate swap series of off-market FRA, payer swap = pay-fixed swap = bond (issue fixed + long floating) = options
(long(short) call + short(long) put) long cap(floor) = long packages of puts(calls) on fixed income = long packages of calls(puts) on interest
rates; payoffcap = max(0,(cap rate – ex)/(12/x-month freq)) interest rate collar = long interest rate cap + short interest rate floor CDS has no
interest rate risk while corp bond has credit and interest rate risk, protection buyer = short the credit = pays premium
2
Equity assumptions domestic CAPM E(R), σ , and Cov are only needed; all investors are homogeneous about them; all assets are
marketable competitively; investors are price-takers whose B/S decision has no effect on asset prices; investors can borrow and lend at RF;
unlimited short selling; frictionless market extended CAPM addition: investors throughout the world have identical consumption baskets; PPP
holds exactly at any point in time; assumes exchange rate changes are predictable thus no real exchange rate risk standard CAPM investors
are risk-averse; homogeneous expectations; concern with nominal returns in home currency; investors can borrow and lend at RF; frictionless
market ICAPM need to assess FCRP associated with each currency, normatively lead to separation theorem, descriptively lead to risk-pricing
relation market model E(ε) = 0; εs uncorrelated with the market return; firm specific surprises are uncorrelated across assets APT a factor
model describes asset returns; many assets so can eliminate asset-specific risk; no arbitrage opportunities among well-diversified portfolios
Treynor–Black nearly efficient mkt w/ limited undervalued securities, expected return and risk, and α of the A, expected risk and return of M
can be estimated; If CAPMrequired return >(<) investorrequired return, stock is overpriced(underpriced), treat r like price
E(excess) = E(Ri) – RF
HPR = r + alpha
required returni = RF + βi(equity risk premium) = RF + equity risk premium ± prem/disct
E(alpha) = E(Ri) – [RF + βi(RM – RF)] = E(Ri) – required return historical 1) meanarith preferred than meangeo 2) LT bond preferred than bill 3)
survivorship bias, div and +ve events inflates r, we should adjust downward forward 1) survey estimates
2) equity risk premiumsupplyside (macroecon) or Ibbotson-Chen = (1+E(ILT))(1+E(real growthEPS or GDP))(1+E(growthPE)) – 1 – E(RF LT) + E(yield or income)
3) equity risk premiumGGM = 1yr ahead div yield on market index + SGR – LT gov bond yield
E(real growthEPS or GDP) = labor productivity growth rate + labor supply growth rate adjusted dr for probability of failure q, r* = (r + q)/(1 – q)
Beta estimates for thinly traded stocks and nonpublic companies
1) identify a benchmark publicly company (PC) which is similar to ABC
2) estimate βPC
debt ABC
debtPC
3) unlev eredBPC  BPC / (1 
4) lever up (relever) the unlevered BPC estimated BABC = unlev eredBPC x (1 
)
)
equityABC
equityPC
Ri = RF + βi (RM – RF), where (RM – RF) = equity risk premium
E(Ri) = RF + β1λ1 + … + βnλn where λ = factor risk premium or factor price; result is intercept of multifactor model
r = RF + risk premium1 + … + risk premiumn, where risk premium = factor sensitivity x factor risk premium
r = RF + βM,j(RM – RF) + βSMB,j(R3small – R3big) + βHML,j(R2HBM – R2LBM) (market, small/mkt cap, value risks/growth)
FFM + liquidity factor
r = RF + risk as surprise in confidence (R20yr corp bond – R20yr gov bond), time horizon (R20yr gov bond – R30day T-Bill), inflation
(-ve correlated), business cycle (real business growth/activity), market timing (residual)
Macroecon Factor/S. RAM 9 factors: econ growth, credit quality(-ve is better), long rates, short rates, inflation shock(surprise only), tradest
weighted dollar, residual market, small-cap premium, residual factor; 1 6 macro econ, last 3 are uncorrelated
risk factors
value vs growth; size vs big; momentum, success or relative strength effect, perfST past = perfST Future
Build-up
r = RF + equity risk premium + size + specific-risk premium
for closely-held companies where βs X available
bond-yield plus RP
YTMLT Bond + risk premium (~3-4%) for companies with publicly-traded debt
country spread
r = risk premiumdeveloped mkt + country premium (= LT US gov bond yield – same maturity USDdenominated local bond’s
stripped yield, do not simply use sovereign risk premium, and the spread should < 5%)
E(surprise) = 0. If talking abt surprise, replace RF by return from normal calculation; If Rself-expected > Rmodel, undervalued, so believe in oneself
CAPM
APT
Multifactor
Fama-French (FMM)
Pastor-Stambaugh (PS)
Macroecon Factor/BIRR
Portfolio
2-asset portfolio variance σ p2  w 12 σ12  w 22 σ 22  2w 1w 2 Cov1,2 (arith-avg if ρ = 1) ρ1,2 
equally weighted portfolio σp2 
CAL E(Rp) = RF +
Cov1,2
β
σ1σ 2
1 2 n 1
 1 ρ

2
σi 
Cov furthermore if with same σ σp = σi2 
 ρ
n
n
n


Covi,M
2
σM

ρi,MσiσM
2
σM
 σ 
 ρi,M  i 
 σM 
σC = wTσT (c = overall portfolio)
E(RT )  RF
σC Beta = Sharpe = return investor demand for extra risk E(Rp) = (1-wT)RF + wTE(RT) use to determine w
σT
E(RM )  RF
σC Beta is the market price of risk
GML = relation(beta, RP)
σM
SML / CAPM E(Ri) = RF + βi[E(RM) – RF], [E(RM) – RF] = expected excess return on the market = market/equity risk premium = slope
+ investment to existing portfolio if Sharpenew > Sharpeold x ρ(RNew, ROld); standardized β (in fund. Model) = (attributei – attributeavg) / σattribute
2
2
2
W of an assets in the minimum-variance portfolio W A = [σB – Cov(A, B)] / [σA + σB – 2Cov(A, B)] W of an assets in the optimal portfolio
2
2
2
WA = [(E(RA) – RF)σB – (E(RB) – RF))Cov(A, B)] / [(E(RA) – RF)σB + (E(RB) – RF))σA – [E(RA) – RF + E(RB) – RF)]Cov(A, B)
2
2
Market model n #means, n #σ , n(n – 1)/2 #Cov, (n + 3n)/2 #total parameters if using traditional historical estimates
CML E(Rp) = RF +
2
2
Covij  βiβ jσM
ρij = Covij/(σi
σj
)
σi2  βi2σM
 σ2ε (systematic + unsystematic)
Blume’s adjusted beta β = 1/3 + 2/3(5yr regression β), mean reverting = 1
↑wrisky by ↓wRF ↑systematic and unsystematic
active return (tracking error) = returnportfolio – returnbenchmark = RP – RB = Σ(sensitivityportfolio – sensitivitybenchmark)factor return + asset selection
2x0.5
Ri = αi + βiRM + εi
active risk (tracking risk) = σactive return = σ(RP-RB) =
(R
Pt
- RBt )2
n -1
2
active factor riskfactor = active factor sensitivity x variancefactor
active factor risk↑ = greater deviation from benchmark beta
2
2x0.5
2
(active risk) = active factor risk + active specific risk (=Σwiσεi )
2
marginal contribution to (active risk) = active factor riskfactor/(active risk)
2
CFA Level 2 notes – created by Thomas Ip
mean activ ereturn

rP - rB

αA
beauty r deno = σεa Arbitrage portfolio have 0 net exposure to a factor
activ erisk
σ(rP - rB)
0
2
0
0
2
2 2
2
Treynor–Black model
wi = αi/σε
wi = wi / Σwi
αA = Σwiαi
βA = Σwiβi
σA = Σwi σε
adjusted α = R α
0
2
2
0
0
wA = (αA/σA ) / (αM/σM ) wA = wA / [1 + (1 – βA)wA ]
wA + wM = 1
optimal risky portfolio
σ are nonsystematic σε
2
2
2
2
E(RP) = wAαA + (wM + wAβA)E(RM) βP = wM(1) + wAβA
σP = (wM + wAβA) σM + (wAσA)
2
2
2
2
2
2
2
2
SP = SM + SA = IRM + IRA = (αM/σεM ) + (αA/σεA)
M = RF + SPσεM – RM
optimal portfolio = risk-free portfolio + optimal risky portfolio (P = optimal active portfolio A + passive market-indexed portfolio M)
short-sell restriction = select only positive alpha stocks
cost of restriction = △S (restricted and unrestricted)
Portfolio αA = forecast return – CAPM required return = w1αi + … + wnαn
Portfolio return = w1E(R1) + … + wnE(Rn) =αA + CAPM required return
Portfolio variance and covariance are just the same with market model
α
αn
2
Weighting of asset i in actively managed portfolio wi = i /
, α could be adjusted (shrunk) by multiplying R
σ 2εi
σ 2εn
derivatives FV hedging ineffective go to IS CF hedging effective go to OCI FC hedging all translation G/L go to equity speculative all IS
information ratio IR =
σA

@2011