Checkpoint 1 (Quant, Econ, FSA, Corp)

R² Coefficent of determination

(SST-SSE)/SST

RSS/SST

Adjusted R²

AIC

Forecast/Predictions

n * (ln(SSE/n)) + 2(k+1)

BIC

Better Fit

n x ln(SSE/n) + ln(n) x (k+1)

F-Test 1Tail

Test to see if adding additional variables contributed to explaining more of the model and if the coefficients are sig diff than 0

BP X² Test

n * R_residual²

Heteroskedasticity test

Variance Inflation Factor and crit values

Multicolinearity

VIF = 1/(1-R_j²)

Rj is one variable on others

VIF	Interpretation
VIF > 5	Warrants further investigation (possible multicollinearity)
VIF > 10	Serious multicollinearity, correction required
VIF = 1	No correlation with the other independent variables

Leverage

3(k+1)/n

Logit Regression

ln(p/1-p) = b0 + b1×1 + b2×2 + e

odds / probability

odds = e^y

prob = odds / ( 1- odds) = 1/(1-e^y)

Likelihood Ratio

LR = -2(log likelihood restricted - log likelihood unrestricted)

method to assess the fit of logistic regression models and is based on the log-likelihood metric that describes the fit to the data.

0 is good

AutoCorrelation Test

Mean Reversion Form

xt = b0/1-b1

Random Walk

xt = xt-1 + e

Random Walk with Drift

xt = b0 + b1xt-1 + e

ARCH

Normalized

(xi - xmin)/(xmax - xmin)

Precision

CORRECTLY PREDICTED POSITIVES OF ALL PREDICTED POSITIVES

TP / (TP + FP)

TP + FP = predicted positives

TYPE I ERROR

Recall

CORRECTLY PREDICTED POSITIVES FOR ALL ACTUAL POSITIVES

TP / (TP + FN)

TP+FN = all actual positives

TYPE II ERROR

Accuracy

CORRECTLY PREDICTED FOR ALL

(TP + TN) / (TP + TN + FP + FN)

F1 Score

(2 x P x R) / (P + R)

R = Recall

P = Precision

0-100 range high is better

True Positive Rate

TP/(TP + FN)

TP + FN = All positives

False Positive Rate

FP / (FP + TN)

FP + TN = All negatives

RMSE

Forward Premium/Discount

F - S0

Mark to Market Value

Covered Interest Rate Parity

Uncovered Interest Rate Parity

E(%ΔS)_(A/B) = R_A − R_B

Forward Rate Parity

F = E(S1)

If the forward rate is equal to the expected future spot rate, we say that the forward rate is an unbiased predictor of the future spot rate. In such an instance, F = E(S₁); this is called forward rate parity. In this special case, if covered interest parity holds (and it will; by arbitrage) uncovered interest parity would also hold (and vice versa). Stated differently, if uncovered interest rate parity holds, forward rate parity also holds (i.e., the forward rate is an unbiased predictor of the future spot rate).

Domestic Fisher Relation

R_nominal = R_real + E(inflation)

Fisher Relation

R_{nominal A} − R_{nominal B} = E(inflation_A) − E(inflation_B)

Purchasing Power Parity

S(A/B) = CPI(A) / CPI(B)

Internation Parity Relationship Chart

Cobb Douglas

Y = TKαL(1 − α)

Labor Productivity

output per worker = Y/L = T(K/L)^α

Marginal Product of Capital

MPK = αY/K

Grinold-Kroner (2002)

E(R) = DY + ΔEPSR + π – ΔS + ΔP/E

ERP = [DY + Δ(P/E) + i + g – ΔS] – E(r_f).

E(R) = dividend yield (DY) + expected capital gains yield (CGY)

expected capital gains yield = EPS growth (Δ EPS) + expected repricing (ΔP/E)

EPS growth = real EPS growth (ΔEPSR) + inflation (π) – change in shares outstanding (ΔS)

Cobb Douglas Growth Relation

growth rate in potential GDP

long-term growth rate of technology + α (long-term growth rate of capital) + (1 − α) (long-term growth rate of labor)

Sustainable growth of output per capita NEOCLASSICAL

g*=θ/(1−α)

Sustainable growth of output per capita (or output per worker)(g*) is equal to the growth rate in technology (θ) divided by labor's share of GDP (1 – α).

Sustainable growth rate of output (G*) NEOCLASSICAL

G*=θ/(1−α)+ΔL

ENDOGENOUS GROWTH

Growth = s·c − δ − n

• saving rate

• consumption

• depn

• labor force growth rate

Interest Income

Coupon +- Amortization

Equity Method Income

Profit x %confirmed x %shares owned - DepN/AmortN%

Equity Method Balance Sheet

Beg Balance + NI% - dividends received

CTA

• Ending retained earnings
  Ending RE=Beginning RE+Net income−Dividends

• Ending CTA as plug in equity
  CTA end=Assets translated−Liabilities translated−Common stock historical−Ending RE

• Period translation gain/loss under current rate method
  ΔCTA=CTAend−CTAbeg​

• Where it goes
  Under the current rate method, translation gain/loss goes to OCI and accumulates in CTA in equity.

Temporal method: remeasurement gain/loss

• No CTA under temporal method

• Remeasurement gain/loss goes to the income statement

• Income statement link through retained earnings
  Ending RE=Beginning RE+Net income after remeasurement gain/loss−Dividends

• If you solve for net income from RE:
  Net income after remeasurement=Ending RE−Beginning RE+Dividends

• Remeasurement gain/loss
  Remeasurement gain/loss=Net income after remeasurement−Net income before remeasurement

Full Goodwill and NCI

• Purchase Price/ % shares owned - FV

• NCI = fair value of the NCI (e.g., market price per share × number of shares held by minority shareholders)

  • Full goodwill is higher than partial goodwill because it also includes the NCI's share of goodwill.

• NCI at period end = NCI at acquisition + (NCI % × subsidiary net income) − (NCI % × dividends paid by the subsidiary)

Partial Goodwill

• Purchase Price - (% Owned * FV net identifiable assets) = % owned * full goodwill

• NCI = NCI % × fair value of the subsidiary's identifiable net assets

• NCI at period end = NCI at acquisition + (NCI % × subsidiary net income) − (NCI % × dividends paid by the subsidiary)

IFRS Goodwill Impairment

CV(asset + gw) - Recoverable amount(FV)

• higher of selling costs or value in use

GAAP Goodwill Impairment

• IF CV > FV

  • FV - FV net identifiable assets = implied FV Goodwill

    • GW - Implied FV GW = Impairment Loss

Tax Deduction for Stock Grants

share price on settlement date * # of shares vested

Tax Deduction for Stock Options

(Stock price - strike) * # of shares

Number of Treasury Shares

Number of Treasury Shares = assumed proceeds / avg share price in report period

assumed proceeds = cash proceeds + average unrecognized SBC

cash proceeds = number of options x strike

avg unrecognized SBC = avg last 2 period end value of unamortn expense

• The treasury stock method nets gross new shares from options/RSUs against a hypothetical buyback funded by their proceeds, so only the shares left over count as dilution.

• Shares repurchased = assumed proceeds ÷ average market price

• Net dilution = gross shares − shares repurchased

Funded Status

FV of planned assets - PBO

Net interest Cost (IFRS)

Beginning funded status × discount rate

Interest Cost

Beginning PBO × discount rate

Expected Return on Plan Assets

expected rate × beginning plan assets

Ending PBO

Ending PBO = Beginning PBO + Current service cost + Interest cost + Past service cost ± Actuarial G/L − Benefits paid

Ending Planned Assets

Beg Planned Assets + Employee Contr + Actual Returns - Benefits paid

Pension Expense (IFRS / GAAP) income statement

• IFRS

  • Current Service Cost + Net Interest cost + PSC

• GAAP

  • Current SC + Int Cost - E(R) + AmortN G/L + Amort PSC

Liquidity Coverage Ratio

Highly liquid assets / expected cash outflows

Highly liquid assets are those that are easily convertible into cash, while expected cash flows are the estimated one-month liquidity needs in a stress scenario. The standards recommend a minimum LCR of 100%.

Net Stable Funding Ratio

available stable funding / required stable funding

• Available stable funding is a function of the composition and maturity distribution of a bank's funding sources (i.e., capital, deposits, and other liabilities). Required stable funding is a function of the composition and maturity distribution of the bank's asset base.

• Enough for 1 year horizon

Underwriting Loss Ratio

price adequacy

• increase in loss reserve bad

• decrease is good

Underwriting Expense Ratio

underwriting expenses including commissions / net premium written

• operational efficiency

Loss and loss adjustment expense ratio

success in est. risk/losses

Dividends to policyholders ratio

CF to premium income

Combined Ratio & Combined Ratio After Dividends

• L&L adj exp ratio + underwriting exp ratio

• combined ratio + divs to policyholders

low is generally good for both

dupont 6 stage

ROE = NI/EBT x EBT/EBIT x EBIT/REV x REV/ASSET x ASSET/EQ

Accrual & Accrual Ratio (BS)

• Accrual

  • NOAend - NOAbeg

• Accural Ratio

  • NOAend-NOAbeg / avg(NOAend - NOAbeg)

Accrual & Accrual Ratio (CF)

• Accrual

  • NI - CFO - CFI

• Accural Ratio

  • NI - CFO - CFI / avg(NOAend - NOAbeg)

Cash generated from operations

CGO = EBIT + NCC - change in NWC

• common ratios

  • CGO/EBIT

  • CGO/CAPEX

  • CGO/total debt

  • CGO/int coverage

Market Value of Decomposition (PE ratio)

(Mkt Cap of Parent - Associate Mkt Cap) / (NI - parent % of associate earnings)

Benish M Score

• M-score = −4.84 + 0.920 (DSR) + 0.528 (GMI) + 0.404 (AQI) + 0.892 (SGI) + 0.115 (DEPI) − 0.172 (SGAI) + 4.679 (Accruals) − 0.327 (LEVI)

• M-score = Score indicating probability of earnings manipulation

• DSR (days sales receivable index) = (Receivables_t/Sales_t)/(Receivables_t−1/Sales_t−1).

  • Changes in the relationship between receivables and sales could indicate inappropriate revenue recognition.

• GMI (gross margin index) = Gross margin_t−1/Gross margin_t.

  • Deterioration in margins could predispose companies to manipulate earnings.

• AQI (asset quality index) = [1 − (PPE_t + CA_t)/TA_t]/[1 − (PPE_t−1 + CA_t−1)/TA_t−1], where PPE is property, plant, and equipment; CA is current assets; and TA is total assets.

  • Change in the percentage of assets other than in PPE and CA could indicate excessive expenditure capitalization.

• SGI (sales growth index) = Sales_t/Sales_t−1.

  • Managing the perception of continuing growth and capital needs from actual growth could predispose companies to manipulate sales and earnings.

• DEPI (depreciation index) = Depreciation rate_t−1/Depreciation rate_t, where Depreciation rate = Depreciation/(Depreciation + PPE).

  • Declining depreciation rates could indicate understated depreciation as a means of manipulating earnings.

• SGAI (sales, general, and administrative expenses index) = (SGA_t /Sales_t)/(SGA_t−1/Sales_t−1).

  • An increase in fixed SGA expenses suggests decreasing administrative and marketing efficiency, which could predispose companies to manipulate earnings.

• Accruals = (Income before extraordinary items⁹ − Cash from operations)/Total assets.

  • Higher accruals can indicate earnings manipulation.

• LEVI (leverage index) = Leverage_t/Leverage_t−1, where Leverage is calculated as the ratio of debt to assets.

  • Increasing leverage could predispose companies to manipulate earnings.

CRP from Sovereign Yield Spread and std