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