CFA II Flashcards
What are the three approaches to estimating VaR?
- Parametric method
- Historical simulation
- Monte Carlo simulation
What are the three steps when estimating VaR of a portfolio?
- Decompose risk factors
- Collect historical data
- Third step depends on approach used
How many trading days are there in one year?
250
What is the z-score for a one-tailed test with a 5% significance level?
1.645
What is the z-score for a two-tailed test with a 5% significance level?
1.96
What is surplus at risk cause by?
A mismatch between the duration of the assets and the duration of the liabilities
Leverage for banks (formula)
RWAs
———
Equity
Information Ratio (formula)
Information Coefficient x (Breadth)^0.5 (x Transfer Coefficient)
Or
Active Return
——————— (x Transfer Coefficient)
Active Risk
Optimum Level of Active Risk
IR
——— x sd(b)
SR(b)
Sharpe Ratio of Actively Managed Portfolio (formula)
SR(p)^2 = SR(b)^2 + IR^2
Risk Neutral Probability (Formula)
1 + r - d
————
u - d
What view does a positive delta signify?
Bullish
What view does a negative delta signify?
Bearish
When is gamma at its highest?
When it is ATM and near to expiry
What accounting method(s) is used for <20% ownership in a company?
Cost or FV
What accounting method is used for 20-50% ownership in a company?
Equity method
What accounting method(s) is used for >50% ownership in a company?
Consolidation method
R^2
RSS
——
SST
Standard deviation of the residuals (SEE)
(MSE)^0.5
Adjusted R^2 (formula)
n - 1
1 - [(————) x (1 - R^2)]
n - k - 1
How do you correct for serial correlation? (2 methods)
- Adjust the coefficient standard errors using the Hansen method
- Improve the specification of the model
How to detect serial correlation? (Two methods)
- Scatter plot with residuals
- Durbin-Watson test
How do you detect heteroskedasticity? (Two methods)
- Scatter plot
- Breusch-Pagan Chi-Squared test
Breusch-Pagan test statistic (formula)
n x R^2(resid)
How do you correct for heteroskedasticity?
Use White-corrected standard errors
How do you correct for multicollinearity?
Drop one of the correlated variables
How do you detect multicollinearity? (Two methods)
- Conflicting t and F statistics
- Correlations among independent variables (if k = 2)
Mean-reverting level
b(0)
————
1 - b(1)
Standard error of estimated autocorrelation (Formula)
1
———
T^0.5
How do you detect serial correlation for AR models?
Test the autocorrelations of the residuals using the t-test (NOT the Durbin-Watson test, which is only for trend models)
What are two advantages of simulations?
- Promote better input quality
- Provide a distribution of expected values rather than a single point estimate
Fisher relation (Formula)
R(nom) = R(real) + E(inflation)
Covered interest rate parity (Forward)
1 + R(price)
F = S x ——————
1 + R(base)
Uncovered interest rate parity (Formula)
E(%ΔS) = R(price) - R(base)
Absolute purchasing power parity (Formula)
CPI(price)
S = —————
CPI(base)
Relative purchasing power parity (Formula)
%ΔS = Inflation(price) - Inflation(base)
International Fisher effect (Formula)
R(price) - R(base) = E(infl,price) - E(infl,base)
Slope coefficient (Formula)
cov(x,y)
b(1) = ————
var(x)
Accuracy (Formula)
TP + TN
—————————
TP + TN + FP + FN
F1 score (Formula)
2 x P x R
————
P + R
True positive rate (Formula)
TP
————
TP + FN
False positive rate (Formula)
FP
————
FP + TN
Normalised X(i)
X(i) - X(min)
————————
X(max) - X(min)
Standardised X(i)
X(i) - X̄
————
sd
F-statistic (Formula)
MSR
———
MSE
Value of forward contract prior to expiration (Formula)
[FP(t) - FP] x (contract size)
—————————————
[1 + r(days/360)]
Sustainable growth rate of output per capita (Formula)
θ
g* = ———
1 - α
Sustainable growth rate of output (Formula)
θ
G* = ——— + ΔL
1 - α
Output per worker
Y/L = T(K/L)^(α)
Growth rate in potential GDP (Formula 1)
Long-term growth rate in technology + α(long-term growth rate of capital) + (1 - α)(long-term growth rate in labour)
Growth rate in potential GDP (Formula 2)
Long-term growth rate of labour force + long-term growth rate of labour productivity
How is in-process R&D recognised?
As an intangible asset under both IFRS and US GAAP
Plan assets at end of period (Formula)
Plan assets at beginning of period + employer contributions + actual return - benefits paid
PBO at end of period
PBO at beginning of period + service cost + interest cost + past service cost +/- actuarial losses/gains - benefits paid
Funded status (Formula)
Plan assets - PBO
Total periodic pension cost (Formula 1)
Employer contributions - (ending funded status - beginning funded status)
Total periodic pension cost (Formula 2)
Current service cost + interest cost - actual return of plan assets +/- actuarial losses/gains + prior service cost
IFRS periodic pension cost on income statement(Formula)
Current service cost + prior service cost +/- net interest cost/income
US GAAP periodic pension cost on income statement (Formula)
Current service cost + interest cost - expected return on plan assets +/- amortisation of actuarial losses/gains* +/- amortisation of prior service cost/benefit
Which method do you use if the functional and presentation currency are different?
The current rate method
Which method do you use if the functional and presentation currency are the same?
The temporal method
Underwriting loss ratio (Formula)
Claims paid + Δ loss reserves
——————————————
Net premium earned
Expense ratio (P&C company) (Formula)
Underwriting expenses
———————————
Net premium written
Combined ratio (Formula 1)
Total insurance expenses
————————————
Net premium earned
Combined ratio (Formula 2)
Underwriting loss ratio + expense ratio
Loss and loss adjustment ratio (Formula)
Loss expense and loss adjustment expense
————————————————
Net premium earned
Dividends to policyholders ratio (P&C companies) (Formula)
Dividends to policy holders
—————————————
Net premium earned
Combined ratio after dividends (CRAD) (Formula)
Combined ratio + dividends to policyholders ratio
Receivables turnover
Net annual sales
—————————
Average receivables
Days of sales outstanding (Formula)
365
——————————
Receivables turnover
What do you do with subsidiaries in hyper inflationary economies under IFRS?
Restate financial statements for inflation and convert at current rate
What do you do with subsidiaries in hyper inflationary economies under US GAAP?
Use temporal method
Dividend/interest income and interest expense classification under IFRS?
Operating or financing cash flows
Dividend/interest income and interest expense classification under US GAAP?
Operating cash flows only
Modigliani and Miller proposition I (No taxes)
Capital structure is irrelevant and the value of the firm is not affected
Modigliani and Miller proposition II (No taxes)
The cost of equity increases linearly as a company increases its proportion of debt financing, exactly offsetting the benefits of debt financing and resulting in no change to the WACC
Modigliani and Miller proposition I (with taxes)
Value is maximised at 100%, as the tax shield provided by debt causes the WACC to decline as leverage increases
Modigliani and Miller proposition II (with taxes)
WACC is minimised at 100% debt as the tax shield provided by debt causes the WACC to decline as leverage increases
Accruals (balance sheet approach)
Net operating assets (end) - net operating assets (beg)
Accruals ratio (Formula)
NOA(end) - NOA(beg)
————————————
(NOA(end) + NOA(beg))/2
Accruals (cash flow approach)
Net income - CFO - CFI
Estimated cash flow (Formula)
EBIT + depreciation/amortisation
What does a ratio of proportional CapEx to proportional assets greater than 1 signify?
The firm is growing that business segment
Cash generated from operations (Formula)
CFO + cash interest paid + cash taxes paid
How do you adjust operating income for pension items?
Add back reported pension expense (difference formulas depending on IFRS or US GAAP)
What is pecking order theory?
Managers prefer financing choices that send the least visible sign to investors (internal capital, then debt financing, then equity financing)
What is static trade-off theory?
Managers will try to balance the benefits of debt with the costs of financial distress, and thus there is an optimal level of debt
Initial outlay for an expansion project (Formula)
FCInv + NWCInv
After-tax operating cash flows for an expansion project (Formula)
(S - C)(1 - T) + TD
Terminal-year non-operating cash flows for an expansion project (Formula)
Sal(t) + NWCInv - T[Sal(t) - B(t)]
Impairment of goodwill under IFRS
Single step approach; impairment exists when the carrying amount is greater than the recoverable value; impairment loss is carrying amount - recoverable value
Impairment of goodwill under US GAAP
Two step approach; impairment exists if carrying value exceeds the fair value; impairment loss is the difference between the carrying value of goodwill and the implied fair value of goodwill
Economic profit (Formula)
NOPAT - $WACC
Market Value Added (Formula)
Economic profit(t)
Sum of ————————
(1 + WACC)^t
Economic income (Formula 1)
Cash flow + (ending market value - beginning market value)
Economic income (Formula 2)
Cash flow - economic depreciation
Residual income
Net income - equity charge (using beginning of period book value of equity)
NOPAT (Formula)
EBIT(1 - tax rate)
FCFE (NI Formula)
NI + non-cash charges - FCInv - WCInv + net borrowing
FCFE (CFO Formula)
CFO - FCInv + net borrowing
FCFE coverage ratio (Formula)
FCFE
————————————
(Div. + share repurchases)
Dividend coverage ratio (Formula)
Net income
——————
Dividends
Dividend payout ratio (Formula)
Dividends
——————
Net income
Equity method on balance sheet (Formula)
Share of net assets + share of net income - share of dividends - share of extra depreciation - share of derecognised profits
Equity method on income statement (Formula)
Share of net income - share of extra depreciation - share of derecognised profits
Porter’s Five Forces
- Threat of new entrants
- Threat of substitutes
- Bargaining power of buyers
- Bargaining power of suppliers
- Rivalry among existing competition
What discount rate should be used for an FCFF model?
The WACC of the firm
What discount rate should be used for an FCFE model?
The cost of equity of the firm
Justified leading P/E (Formula)
P(0) 1 - b
—— = ———
E(1) r - g
Justified trailing P/E (Formula)
P(0) (1 - b)(1 +g)
—— = ——————
E(0) r - g
What does the remeasurement component of periodic pension cost include?
Actuarial gains and losses on pension obligation and the net return on plan assets
Single-stage residual income model (Formula)
(ROE - r) x B(0)
V(0) = B(0) + ———————
r - g
WCInv (Formula)
Accounts receivable + inventory - accounts payable
FCFF (EBIT Formula)
EBIT(1 - tax rate) + Dep - FCInv - WCInv
FCFF (EBITDA Formula)
EBITDA(1 - tax rate) + Dep x (tax rate) - FCInv - WCInv
FCFF (CFO Formula)
CFO + [Int x (1 - tax rate)] - FCInv
FCFE (DR Formula)
NI - [(1 - DR) x (FCInv - Dep)] - [(1 - DR) x WCInv]
Justified P/B ratio (Formula)
ROE - g
————
r - g
Discount for lack of control (Formula)
1
1 - (——————————)
1 + control premium
Total discount with DLOC and DLOM (Formula)
1 - [(1 - DLOC)(1 - DLOM)]
Present value of growth opportunities (Formula)
E(1)
V(0) = —— + PVGO
r
Value of perpetual preferred shares (Formula)
D(p)
V(p) = ——
r(p)
H-model (Formula)
D(0) x [1 + g(l)]
———————— +
r - g(l)
D(0) x H x [g(s) - g(l)]
———————————
r - g(l)
PEG ratio (Formula)
P/E ratio
————
g
Justified dividend yield (Formula)
D(0) r - g
—— = ———
P(0) 1 + g
Justified P/S multiple (Formula)
Net profit margin x trailing P/E ratio
Residual income valuation (Formula)
[ROE - r] x B(0)
B(0) + (———————)
r - g
PV of continuing residual income in year T-1 (using persistence factor formula)
RI(t)
————
1 + r - w
PV of continuing residual income in year T-1 (using decline to long-run rate formula)
[P(t) - B(t)] + RI(t)
—————————
1 + r
Clean surplus relation (Formula)
B(t) = B(t - 1) + E(t) - D(t)
Unlevered beta (Formula)
Beta(L)
—————
1 + D/E
Where are actuarial assumptions included in the financial statements?
Notes to financial statements
What is the day basis for an FRA contract?
360
What is the day basis for foreign currency contracts?
365
Fixed swap rate (Formula)
1 - final discount factor
———————————
Sum of discount factors
Value of an interest rate swap (Formula)
ΣZ x [SFR(new) - SFR(old)]
days x ——— x notional principal 360
N(-d1) (Formula)
1 - N(d1)
N(-d2) (Formula)
1 - N(d2)
BSM Model call option (Formula)
S(0)N(d1) - e^(-rT)XN(d2)
BSM Model put option (Formula)
e^(-rT)XN(-d2) - S(0)N(-d1)
Capitalisation rate (Formula)
NOI
———————
Property value
Property value (cap rate Formula)
NOI
————
Cap rate
FFO (Formula)
Accounting net earnings + depreciation and amortisation expense - gains from sales of property + losses from sales of property
AFFO (Formula)
FFO - non-cash rent adjustment - recurring maintenance-type capital expenditures and leasing commission
How can you value REITs and REOCs? (Three methods)
- NAVPS
- Relative value (price-to-FFO and price-to-AFFO)
- Discounted cash flow
NAV before distributions (Formula)
NAV after distributions in prior year + capital called down - management fees + operating results
NAV after distributions (Formula)
NAV before distributions - carried interest - distributions
What does a ratchet do within private equity?
Enables the management team to increase its equity allocation depending on the company’s actual performance and the return achieved by the PE firm
Per-share effective spread transaction cost
Side x (transaction cost - misquote price)
Effective spread
2 x per-share effective spread transaction cost
Linear regression assumptions (x6)
- There is a linear relationship between the dependent and independent variable
- Independent variable is uncorrelated with the residuals
- Expected value of the residual term is zero
- The variance of the residual term is constant for all observations
- Residual term is independently distributed
- The residual term is normally distributed
How many tails does an F-Test have?
One
Three conditions of being covariance stationary?
- Constant and finite expected value
- Constant and finite variance
- Constant and finite covariance between values at any given leg
What criterion is used to compte the accuracy of AR models in forecasting out-of-sample values?
Root mean squared error (RMSE)
How do data scientists reduce overfitting? (Two methods)
- Complexity reduction
- Cross validation
What is complexity reduction?
Method that adds a penalty to exclude features that do not meaningfully contribute to model
What is cross validation?
Estimates out-of-sample error rates directly from the validation sample
What is k-fold cross validation?
- Sample divides into k parts
- Training sample = k-1; validation sample = 1
- Repeat k times
- Compile average in-sample and out-of-sample error rates
Least absolute shrinkage and selection operator (LASSO)
Minimises SSE and the sum of the absolute values of the slope coefficients
Support vector machine
Linear classification algorithm that separates data into one of two possible classifieds by determining a boundary farthest away from all observations
K-nearest neighbour (KNN)
Technique used to classify an observation based on nearness to observations in the training data (k is hyperparameter, and algorithm looks for the ‘k’ nearest neighbours)
What does principal component analysis (PCA) produce?
Eigenvectors, each with an eigenvalue
What does an eigenvalue tell us?
The proportion of data explained by the eigenvector
What types of hierarchical clustering are there?
- Agglomerative (each data point starts as a cluster)
- Divisive (start with one giant cluster)
How many hidden layers does a deep neural network (DNN) have?
Often more than 20
Data analysis steps (5)
- Conceptualisation
- Data collection
- Data preparation and wrangling
- Data exploration
- Model training
What is Winsorisation?
Replacing extreme values by the maximum value allowable for that variable
Bag-of-words procedure
Collects all words and a document term matrix puts them into structured data
N-grams
Used to represent word sequences (e.g. bigrams, trigrams)
What is an FX carry trade a bet against?
Uncovered interest rate parity
Preconditions for economic growth (6 preconditions)
- Savings and investment
- Financial markets and intermediaries
- Political stability, rule of law, and property rights
- Investment in human capital
- Tax and regulatory systems
- Free trade and unrestricted capital flows
Equity price correlation to GDP (short-term)
ΔP = ΔGDP + Δ(E/GDP) + Δ(P/E)
Equity price correlation to GDP (long-term)
ΔP = ΔGDP
Cobb-Douglas production function (formula)
Y = TK^(α)L^(α-1)
Growth accounting relation (growth rate in potential GDP)
ΔY/Y = ΔA/A + α x (ΔK/K) + (1-α) x (ΔL/L)
What is “Dutch disease”?
When natural resource-rich countries see their currency appreciate heavily due to demand for those natural resources, making all exports more expensive and other domestic industries less competitive
Absolute convergence hypothesis
Less developed countries will achieve equal living standards over time
Conditional convergence hypothesis
States that convergence in living standards will only occur for countries with the same savings rates, population growth rates, and production functions
Club convergence hypothesis
Countries may be part of a club (with similar institutional features) and able to rapidly catch up to richer peers within that club
Classical growth theory
Growth in real GDP per capita is temporary - when the GDP per capita rises above the subsistence level, a population explosion occurs, driving GDP per capita back to the subsistence level
Neoclassical growth theory
Sustainable growth rate of GDP is a function of population growth, labour’s share of income, and the rate of technological advancement. Growth gains from other means are only temporary
Endogenous growth theory
Investment in capital can have constant returns (unlike neoclassical theory), which allows for a permanent increase in growth rate attributable to an increase in savings rate
What are self-regulatory bodies (SRBs)?
Private organisations that represent as well as regulate their members
What are self-regulating organisations (SROs)?
SRBs that are recognised by the government. They are independently funded
Regulatory capture
A regulatory body will, at some point in time, be influenced or even possibly controlled by the industry that is being regulated
Regulatory competition
Where regulators compete to provide the most business-friendly regulatory environment
Regulatory arbitrage
Where businesses shop for a country that allows a specific behaviour rather than changing the behaviour
Regulatory tools (three)
- Price mechanisms (taxes / subsidies)
- Restricting or requiring certain activities
- Provision of public goods or financing of private projects
Regulatory burden
Refers to the cost of compliance for the regulated entity
Net regulatory burden
Regulatory burden minus the private benefits of regulation
What accounting treatment do joint ventures require?
Equity method (almost always) under both IFRS and US GAAP
Two criteria for amortised cost (debt securities only) for investments in financial assets?
- Business model test - debt securities being held to collect contractual cash flows
- Cash flow characteristic test - cash flows are either principal, or interest in principal, only
Can you reclassify equity securities once classified as FVPL or FVOCI?
No
Goodwill created in purchase (equity method)
Excess of purchase price less excess allocated to equipment
What values are the two coefficients in the Taylor equation?
0.5
How do you account for a variable interest entity (VIE)?
It must be consolidated by the primary beneficiary
What are the characteristics of a VIE?
- At-risk equity that is insufficient to fianance the entity’s activities without additional financial support
- Equity investors that lack any of the following:
- Decision making rights
- Obligation to absorb expected losses
- Right to receive expected residual returns
Where is remeasurement (temporal method) gain or loss recognised?
Income statement
Where is translation (current rate method) gain or loss recognised?
Shareholder’s equity
Three pillars of the Basel III framework?
The maintenance of minimum levels of:
- Capital
- Liquidity
- Stable funding
What does the CAMELS approach entail?
C - Capital adequacy A - Asset quality M - Management E - Earnings L - Liquidity S - Sensitivity
Liquidity coverage ratio (LCR)
Highly liquid assets
———————————
Exp. cash outflows (1-month stress)
Net stable funding ratio (NSFR)
Available stable funding
———————————
Required stable funding
What is a soft pricing period?
When P&C insurers cut prices during periods of heightened competition
What is a hard pricing period?
After insurers leave the industry following soft pricing periods, the industry enters a healthier pricing environment and fatter margins
What does Basel III recommend for LCR and NSFR ratios?
100%
What is the Beneish Model?
A pro it regression model estimating the probability of earnings manipulation using 8 dependent variables. A higher M-score indicates higher probability of manipulation
What is the Altman model?
A Z-score model developed to assess the probability that a firm will file for bankruptcy
What are three characteristics of high-quality financial balance sheet reporting?
- Completeness
- Unbiased measurement
- Clarity of presentation
6-step process for financial statement analysis?
- Establish the objectives
- Collect data
- Process data
- Analyse data
- Develop and communicate conclusions
- Follow up
Cash generated from operations (CGO) (formula 1)
EBIT + non-cash charges - increase in working capital
Cash generated from operations (CGO) (formula 2)
CFO + cash taxes paid + cash interest paid
Which of sunk costs, externalities, and opportunity costs should be included in capital budgeting analysis?
Sunk costs - no
Externalities - yes
Opportunity costs - yes
NWCInv (formula)
Δnon-cash current assets - Δnon-debt current liabilities
Replacement project initial outlay (formula)
FCInv + NWCInv - Sal(0) + T[Sal(0) - B(0)]
Replacement project incremental operating cash flows (formula)
(ΔS - ΔC)(1-T) + ΔDT
Replacement project terminal year non-operating cash flow (formula)
[Sal(TNew) - Sal(TOld)] + NWCInv - T[(Sal(TNew) - B(TNew) - (Sal(TOld) - B(TOld)]
What option is an abandonment option the equivalent of?
Put option
What option is an expansion option the equivalent of?
Call option
Required rate of return on equity from MM proposition II no taxes (Formula)
D
r(0) + — [r(0) - r(d)]
E
Amount of capital gains required if differential in tax rates between capital gains and dividends (formula)
[1 - T(d)]
D x —————
[1 - T(cg)]
What six factors affect a company’s dividend payout policy?
- Investment opportunities
- Expected volatility of future earnings
- Financial flexibility
- Tax considerations
- Flotation costs
- Contractual and legal restrictions
Effective tax rate under a double-taxation system (formula)
Corporate tax rate + (1 - corporate tax rate)(individual tax rate)
What is a split-rate corporate tax system?
A system where corporate earnings paid out as dividends are taxed as a lower rate than corporate earnings otherwise
Imputation tax system
Taxes are paid at the corporate level but are attributed to the shareholder so that all taxes are paid at the shareholder’s rate (shareholder pays [shareholder tax rate - corporate tax rate] in tax)
Expected increase in dividends under target payout adjustment model
[(expected earnings x target payout ratio) - previous dividend] x adjustment factor
What is the residual dividend model?
Dividends are paid from residual earnings after the optimal capital structure has been financed
What are the four common methods for share buybacks?
- Open market transactions
- Fixed price tender offer
- Dutch auction
- Repurchase by direct negotiation
Five common rationales for share repurchases (versus dividends)
- Potential tax advantages
- Share price support / signalling
- Added flexibility
- Offsetting dilution from employee stock options
- Increasing financial leverage
When will EPS increase if share repurchases are financed by borrowing?
When the after-tax cost of borrowing is less than the initial earnings yield of the shares
Five major ownership structure factors impacting corporate governance
- Director independence
- Board structure
- Special voting arrangements
- Corporate governance codes, laws , and listing requirements
- Stewardship codes
What is a statutory merger?
Where the acquiring company acquired all of the targets assets / liabilities and the target company ceases to exist
What is a subsidiary merger?
Where the target company becomes a subsidiary of the acquirer
What is a consolidation (merger)?
Where both companies cease to exist and they form a new company
What is a horizontal merger?
Both companies operate in the same or similar industries
What is a vertical merger?
Acquiring company seeks to move up or down the supply chains
What is a conglomerate merger?
Both companies operate in completely separate industries
What are the two forms of acquisition?
Stock purchase and asset purchase
What is a poison pill (pre-offer defence)?
Gives current shareholders the right to purchase additional shares at attractive prices, increasing the cost to the acquirer
What is a poison out (pre-offer defence)?
Gives bondholders the right to demand immediate repayment in the case of a merger
What are golden parachutes (pre-offer defence)?
Compensation agreements between the target and its senior management for lucrative payouts if they leave following a merger
What is greenmail (post-offer defence)?
Payoff to the potential acquirer to terminate a hostile takeover attempt
What is a crown jewel defense (post-offer defence)?
Selling a key asset
What is a pac-man defense (post-offer defence)?
Target acquired the acquirer
What is a white knight defense (post-offer defence)?
Friendly third party acquires the target
What is a white squire defense (post-offer defence)?
Friendly third party acquires a minority interest in target
FCFF (corporate finance topic formula)
Net income + net interest after tax + change in deferred taxes + net no cash charges - change in net working capital - capital expenditures
Post-merger value (formula)
Pre-merger value of acquirer + pre-merger value of target + synergies - cash paid to target shareholders
Gain accrued to target (formula)
Price paid to target - pre-merger value of target (this overall equals takeover premium)
Gains accrued to acquirer (formula)
Synergies - takeover premium
PRAT model (formula)
Profit margin x retention rate x asset turnover x financial leverage
FCInv (formula assuming no long-term assets have been sold)
Ending net PP&E - beginning net PP&E + depreciation
FCInv (formula assuming long-term assets were sold)
Ending net PP&E - beginning net PP&E + depreciation - gain on sale of long-term assets
What is the difference between Total Invested Capital (TIC) and EV?
TIC includes cash and short-term investments
Conversion value of convertible bond
Market price of stock x conversion ratio
Market conversion price of convertible bond
Market price of convertible
—————————————
Conversion ratio
Market conversion premium per share for convertible bond
Market conversion price - stock’s market price
Value of noncallable, nonputable convertible bond
Straight value + value of call option on stock
Value of callable convertible bond
Straight value + value of call option on stock - value of call option on bond
CDS upfront payment (by protection buyer)
PV(protection leg) - PV(premium leg)
Upfront CDS premium %
(CDS spread - CDS coupon) x duration
Profit for CDS protection buyer
Change in spread x duration x notional principal
Forward price (if no storage costs)
S(0) x (1 + R(f))^T
Forward price of an equity security with dividends
(S(0) - PVD) x (1 + R(f))^T
Forward price on an equity index (continuous dividends)
S(0) x e^[(R(cf) - D(c)) x T]
Forward price of a coupon-paying fixed income security
(S(0) - PVC) x (1 + R(f))^T
Quoted futures price of a bond
[(full price)(1 + R(f))^T - AI(T) - FVC)
1
x ——
CF
Value to payer in interest rate swap
Sum of discounts x (SFR(new) - SFR(old)) x settlement period days/360 x notional principal
Hedge ratio (formula)
C(+) - C(-)
—————
S(+) - S(-)
BSM call value
S(0) x N(d1) - e^(-rT) x X x N(d2)
BSM put value
e^(-rT) x X x N(-d2) - S(0) x N(-d1)
BSM call value (dividend-paying stock)
S(0) x e^(-dT)x N(d1) - e^(-rT) x X x N(d2)
BSM put value (dividend-paying stock)
e^(-rT) x X x N(-d2) - S(0) x e^(-dT)x N(-d1)
Black Model call value
e^(-RcfT) x [(Ft x N(d1)) - (X x N(d2)]
How do you replicate a long FRA using options?
Long interest rate call and short interest rate put
How do you replicate a short FRA?
Short interest rate call and long interest rate put
How do you replicate an interest rate cap?
Series of interest rate call options with different maturities and the same exercise price
How do you replicate an interest rate floor?
A series of interest rate put options
How to replicate a payer swap?
Long interest rate cap and short interest rate floor with the same exercise rate
How do you replicate a receiver swap?
Short interest rate cap and long interest rate floor with same exercise rate
Number of short call options to delta hedge
Number of shares hedged
————————————
Delta of call option
Number of long put options to delta hedge
Number of shares hedged
- ————————————
Delta of put option
Three sources of value creation in PE
- Re-engineering portfolio company so that it operates more efficiently
- Obtain debt financing on more advantageous terms
- Superior alignment of interests between management and owners
r* (adjusted for failure of VC firm)
1 + r
—— - 1
1 - q
What factor does the Carhart model extend the Fama and French model by?
Momentum
Information coefficient for market timer (formula)
2 x (% correct) - 1
Breadth for correlated decisions (formula)
N
——————
1 + (N - 1)r
Modigliani and Miller value of leverage company (formula)
EBIT(1 - t)
—————
WACC
What type of banks generally use swaps?
Wholesale banks
Common adjustments when calculating EVA
- R&D expenses should be capitalised and amortised
- Eliminate deferred taxes (only recognise cash taxes)
- Convert LIFO to FIFO (add LIFO reserve)
- Treat operating leases as capital leases
- Adjust for non-recurring items
What is the intercept and slope of the security market line?
Intercept = risk free rate (Rf) Slope = equity risk premium (Rf - Rm)
Intercept for fundamental factor model
Not necessarily the risk-free rate due to standardised betas
Ibbotsen-Chen formula
[(1 + expected inflation) x (1 + expected growth in real earnings per share) x (1 + expected growth in P/E)] + expected income component - risk-free rate (+ other risk premiums)
CDS upfront premium
(Credit spread - Fixed coupon) x CDS duration
CDS price (per 100 notional)
100 - upfront premium
What are one’s positions on credit risk if you buy or sell a CDS?
Buy: short credit risk (pay premiums)
Sell: long credit risk (receive premiums)
Is one allowed to impact market price if trading solely for tax purposes?
Yes
How to check whether an autoregressive model is correctly specified?
Check there is no autocorrelation between the residuals
Covariance formula
E[x(i) - x(avg)][y(i) - y(avg)]
———————————————
n - 1
Sample Variance formula
E[x(i) - x(avg)]^2
—————————
n - 1
Currency spread formula
Ask - Bid
—————
Ask
What companies is the capitalised cash flow method suitable for?
Small private companies (not large private or public companies)
Information coefficient (correlation formula)
E(Ra) Ra
Corr[——— , ———]
sd sd
Transfer coefficient (correlation formula)
E(Ra)
Corr[——— , Δw x sd]
sd
