TEST Flashcards
What is the formula for the Coefficient of Determination, R2?
R2 = total variation − unexplained variation
Total variation can also be expressed as SST − SSE, which equals explained variation (RSS)
What does Adjusted R2 account for in regression analysis?
Adjusted R2 accounts for the number of predictors in the model
It adjusts the R2 value to penalize for adding non-significant predictors.
What is Akaike’s Information Criterion (AIC) used for?
AIC is used if the goal is to have a better forecast
A lower AIC value indicates a better model fit.
What is the purpose of the F-statistic in regression analysis?
To evaluate nested models
It helps to determine if the inclusion of additional predictors improves the model significantly.
What is heteroskedasticity?
Non-constant error variance
It can be detected with scatter plots or Breusch–Pagan test.
How can autocorrelation among error terms be detected?
Using the Durbin–Watson test or Breusch–Godfrey test
Correcting it often involves using robust standard errors.
What does the Variance Inflation Factor (VIF) measure?
Multicollinearity among independent variables
A high VIF indicates a high correlation among predictors.
What is the formula for the odds in logistic regression?
odds = ey
Where P = odds / (1 + odds) = 1 / (1 + e−ŷ).
What does the term ‘covariance stationary’ mean?
Mean and variance stable over time
To conclude a time series is covariance stationary, one can plot data or conduct a Dickey-Fuller test.
What is a unit root in time series analysis?
Coefficient on lagged dependent variable = 1
A series with a unit root is not covariance stationary.
What is the purpose of normalization in big data projects?
Scales values between 0 and 1
Normalization is important for ensuring comparability across different scales.
What is the F1 score in machine learning?
F1 score = (2 × P × R) / (P + R)
Where P is precision and R is recall.
What is the bid-ask spread?
Bid-ask spread = ask quote − bid quote
It represents the difference between the buying price and selling price of a currency.
What is covered interest rate parity?
F = (1 + RA) / (1 + RB) × S
It ensures that the returns on investments in different currencies are equal when hedged.
What does the Cobb-Douglas production function represent?
Y = TKαL(1–α)
It describes the relationship between output (Y), technology (T), capital (K), and labor (L).
What is the primary focus of the Neoclassical Growth Theory?
Sustainable growth rate is a function of population growth, labor’s share of income, and the rate of technological advancement
It emphasizes the role of technology in economic growth.
What is the balance sheet funded status?
Funded status = fair value of plan assets − PBO
It indicates the financial health of a pension plan.
What is the purpose of the Beneish model?
Detects earnings manipulation using eight variables
An M-score greater than -1.78 suggests potential earnings manipulation.
What does the term ‘sustainable earnings’ refer to?
Earnings expected to recur in future periods
High-quality earnings are considered sustainable.
What is the current ratio formula?
current ratio = current assets / current liabilities
It measures a company’s ability to pay short-term obligations.
What does Basel III establish?
Minimum levels of capital and liquidity
It aims to strengthen regulation, supervision, and risk management within the banking sector.
What does the term ‘defensive interval’ refer to?
Daily cash expenditures
It is important for financial institutions due to their systemic importance.
What is the formula for calculating cash and marketable securities?
cash + marketable securities
This calculation is essential for assessing liquidity.
What are current liabilities?
Obligations that a company needs to settle within one year.
What is the formula for total current assets?
cash + marketable securities + receivables
Total current assets are vital for understanding short-term financial health.
What defines financial institutions as different from other companies?
Systemic importance and regulated status.
What does the term ‘defensive interval’ refer to?
Daily cash expenditures.
What are the minimum levels of capital and liquidity established by Basel III?
Regulations for financial institutions to maintain financial stability.
What does CAMELS stand for?
- Capital adequacy
- Asset quality
- Management
- Earnings
- Liquidity
- Sensitivity
What is the liquidity coverage ratio?
Expected cash outflows to be covered by highly liquid assets.
What is the net stable funding ratio?
Available stable funding to required stable funding.
What is the underwriting loss ratio formula?
(claims paid + Δ loss reserves) / net premium earned
What does the expense ratio measure?
Underwriting expenses including commissions relative to net premiums.
What is the receivables turnover formula?
annual sales / average receivables
What is the formula for inventory turnover?
cost of goods sold / average inventory
What is the formula for days of sales outstanding?
365 / receivables turnover
What does the payables turnover ratio measure?
total purchases / average payables
What is the total asset turnover formula?
revenue / average total assets
What is the fixed asset turnover formula?
revenue / average fixed assets
What is the gross profit margin formula?
gross profit / revenue
What is the operating profit margin formula?
operating profit / revenue
What is the net profit margin formula?
net income / revenue
What is the sustainable growth rate in the PRAT model?
g = net income - dividends / net income
What is the interest coverage ratio formula?
EBIT / interest expense
What does the return on assets measure?
net income / average total assets
What is the financial leverage ratio formula?
total assets / total equity
What is the payout ratio?
dividends paid / net income
What is the retention ratio formula?
1 - payout ratio
What is the formula for earnings per share?
(net income - preferred dividends) / average common shares outstanding
What defines corporate restructuring?
Actions including investment, divestment, or restructuring to improve performance.
What are investment actions in corporate restructuring?
- Equity investments
- Joint ventures
- Acquisitions
What are divestment actions?
- Sales
- Spin-offs
What are restructuring actions aimed at?
Improving ROIC through cost cutting and balance sheet restructurings.
How is materiality defined?
By both size and fit.
What are the valuation methods for corporate restructurings?
- Comparable company analysis
- Comparable transaction analysis
- Premium paid analysis
What is the formula for Free Cash Flow to Firm (FCFF)?
FCFF = NI + Dep + [Int × (1 - tax rate)] - FCInv - WCInv.
What is the formula for Free Cash Flow to Equity (FCFE)?
FCFE = FCFF - [Int × (1 - tax rate)] + Net borrowing.
What are Porter’s Five Forces of Industry Structure?
- Rivalry (intra-industry)
- Threat of new entrants
- Threat of substitutes
- Bargaining power of suppliers
- Bargaining power of buyers
What conditions should be met to use discounted cash flow (DCF) methods?
When the firm has a dividend history and stable dividend policy.
When should free cash flow (FCF) models be used?
When the firm lacks a stable dividend policy.
What is the Gordon Growth Model (GGM)?
V = D0(1 + g) / (r - g)
What does the H-Model formula represent?
V0 = [D0 × (1 + gL)] / (r - g) + [D0 × H × (gS - gL)] / (r - gL)
What is the required return formula from the Gordon Growth Model?
r = (D1 / P0) + g
What is the effective tax rate formula?
corporate tax rate + (1 - corporate tax rate) × (individual tax rate)
What is the target payout adjustment model?
expected increase in dividends = (expected target - previous) / adjustment ratio
What is the dividend coverage ratio?
dividend coverage = net income / dividends
What does an unexpected share repurchase indicate?
Good news for the company.
What are the advantages of share repurchases?
- Tax advantages
- Share price support
- Increased flexibility
- Offsetting dilution
- Increased leverage
What are ESG-related risk exposures?
Downside risk in fixed-income and both upside and downside in equity analysis.
What does the Grinold-Kroner model calculate?
ERP = [DY + ∆P/E + i + G - ∆S] - rf
What is the weighted average cost of capital (WACC) formula?
WACC = (we × r) + [wd × rd × (1 - tax rate)]
What is the Price-to-Earnings (P/E) ratio?
market price per share / EPS over previous 12 months
What is the Price-to-Book (P/B) ratio?
book value of equity / market value of equity
What is the Price-to-Sales (P/S) ratio?
total sales / market value of equity
What is the Price-to-Cash Flow ratio?
cash flow / market value of equity
What is the formula for expected exposure in credit analysis?
Amount a risky bond investor stands to lose before any recovery is factored in.
What is the loss given default?
loss severity × exposure
What is the formula for the single-stage RI model?
(ROE − r) × B
ROE = Return on Equity, r = required rate of return, B = book value
What components make up the value of callable and putable convertible bonds?
- Straight value of bond
- Value of call option on stock
- Value of call option on bond
- Value of put option on bond
What is expected exposure in credit analysis models?
Amount a risky bond investor stands to lose before any recovery is factored in.
What is the formula for loss given default?
Loss given default = loss severity × exposure
What does the economic value added (EVA) measure?
EVA = NOPAT − $WACC
What is the market value added (MVA) formula?
MVA = market value − total capital
What does NOPAT stand for and how is it calculated?
NOPAT = EBIT × (1 − t)
EBIT = Earnings Before Interest and Taxes, t = tax rate
What is the probability of default?
Likelihood in a given year.
What is the recovery rate?
% of $ received upon issuer default
What is the formula for expected loss?
Expected loss = prob. default × loss given default
What is a credit valuation adjustment (CVA)?
Sum of the present values of expected losses for each period.
What are the four phases of the Real Estate Cycle?
- Recovery
- Expansion
- Oversupply
- Recession
What is the value of an interest rate swap to a fixed payer?
Value = ΣZ × (SFR − SFR) × days × notional
What are the binomial stock tree probabilities for an up move?
πU = (1 + Rf − D) / (U − D)
What is put-call parity?
S0 + P0 = C0 + PV(X)
What is dynamic delta hedging?
- # of short call options = delta of call option
- # of long put options = − delta of put option
What is the Black–Scholes–Merton option valuation model for a call option?
C0 = S0e^(-δT) N(d1) − e^(-rT) XN(d2)
What does the hazard rate represent?
Conditional probability of default.
What is the formula for the price of an equity forward with discrete dividends?
FP(on an equity security) = (S − PVD) × (1 + R)^T
What is the NAV approach to REIT share valuation?
NAV = estimated cash NOI ÷ assumed cap rate
What is contango in futures markets?
Futures prices > spot prices
What does the term ‘backwardation’ mean?
Futures prices < spot prices
What is the debt service coverage ratio (DSCR)?
DSCR = NOI1 ÷ debt service
What is the formula for the price-to-FFO approach to REIT share valuation?
NAV/share = FFO ÷ shares outstanding × sector average P/FFO multiple
What is the definition of a credit default swap (CDS)?
Upon credit event, protection buyer compensated by protection seller.
What is the main goal of the merger arbitrage strategy?
Bets on a corporate takeover succeeding.
What is the definition of active return?
Active return = portfolio return − benchmark return
What is the formula for the information ratio?
Information ratio = Active return / Active risk
What does the term ‘survivorship bias’ refer to?
Using data that only includes entities that have persisted until today.
What is the purpose of stress testing in portfolio management?
Examines performance under the worst combinations of events and scenarios.
What is the definition of an ETF premium (discount)?
ETF premium (discount) % = (ETF price − NAV per share) / NAV per share
What is the marginal utility of current consumption?
Marginal utility of consuming 1 unit in the future / marginal utility of current consumption of 1 unit
What does the term ‘real risk-free rate of return’ signify?
The return on an investment with no risk of financial loss.
What is the formula for calculating nominal short-term interest rate (r)?
r = real risk-free rate + inflation premium
What is the formula for the marginal utility of consuming 1 unit in the future?
marginal utility of current consumption of 1 unit
This reflects the concept of utility in economics, comparing future and current consumption.
What is the formula for the real risk-free rate of return (R)?
R = _ = _ − 1
This formula relates to the calculation of the real risk-free rate.
What is the price of a default-free, inflation-indexed, zero coupon bond?
P = _E(P1) + cov(P , m) / (1 + R)
This equation is used to determine the price of bonds considering expected future cash flows.
What is the nominal short-term interest rate (r) formula?
r = real risk-free rate (R) + expected inflation (π)
This reflects the relationship between nominal rates and inflation expectations.
What is the formula for the nominal long-term interest rate?
R + π + θ
θ represents the risk premium for inflation uncertainty.
What does the Taylor rule formula represent?
r = Rn + π + 0.5(π − π) + 0.5(y – y)
This rule guides central banks on setting interest rates based on inflation and output gaps.
What is the Break-even inflation rate (BEI)?
yield non-inflation indexed bond − yield inflation indexed bond
BEI indicates the inflation rate at which investors are indifferent between the two types of bonds.
What is the formula for BEI for longer maturity bonds?
expected inflation (π) + inflation risk premium (θ)
This accounts for both expected inflation and the risks associated with inflation variability.
What is the required return formula for credit risky bonds?
R + π + θ + γ
γ represents the risk premium for credit risk.
What does the discount rate for equity include?
R + π + θ + γ + κ
κ is the risk premium for equity versus risky debt.
What is the formula for the discount rate for commercial real estate?
R + π + θ + γ + κ + φ
φ is the illiquidity premium.
What does the Arbitrage Pricing Theory formula express?
E(R) = R + Σ(β(λ))
This indicates expected return as a function of risk factors and their premiums.
What is the expected return formula in a multifactor model?
risk-free rate + Σ(factor sensitivity) × (factor risk premium)
This model helps attribute returns to various risk factors.
What is the formula for active return?
factor return + security selection return
Active return measures the performance of an investment strategy relative to a benchmark.
What is the formula for active specific risk?
∑(w − w )² 𝜎²
This calculates the risk associated with specific investments in a portfolio.
Define Value at Risk (VaR).
Minimum ($ or %) loss with a given probability over a specified period.
VaR is a common risk management tool used to assess potential losses.
What is Conditional VaR (CVaR)?
The expected loss given that the loss exceeds the VaR.
CVaR provides insight into the tail risk of an investment.
What does Incremental VaR (IVaR) measure?
The change in VaR from a specific change in the size of a portfolio position.
IVaR helps in understanding the impact of position adjustments on overall risk.
What is Marginal VaR (MVaR)?
∆ in portfolio VaR for small ∆ in position.
MVaR estimates the contribution of individual positions to the total portfolio risk.
What is the formula for the variance of a portfolio comprising two funds A and B?
σ² = W²σ²_A + W²σ²B + 2W_AW_BCov{AB}
This formula calculates the overall risk of a portfolio based on the weights and covariances of its components.
What is the formula to annualize standard deviation?
√250 × (daily standard deviation)
This conversion is used to compare daily volatility to annual volatility.
What is the formula for % change in value vs. change in YTM?
−duration (∆Y) + ½ convexity (∆Y)²
This formula helps assess the impact of interest rate changes on bond prices.
For Macaulay duration, how is ∆Y modified?
Replace ∆Y by ∆Y / (1+Y)
This adjustment accounts for the bond’s yield in the duration calculation.
