CFA QuickSheet

Practice flashcards covering key quantitative methods, economics, financial statement analysis, corporate issuers, equity, fixed income, derivatives, alternative investments, portfolio management, and ethics for Level II CFA exam preparation.

What are the formulas for Akaike's information criterion (AIC) and Schwarz's Bayesian information criterion (BIC), and when is each preferred?

$\text{AIC} = n \times \ln\left(\frac{\text{SSE}}{n}\right) + 2(k + 1)$ and $\text{BIC} = n \times \ln\left(\frac{\text{SSE}}{n}\right) + \ln(n) \times (k + 1)$. AIC is used if the goal is to have a better forecast, while BIC is used if the goal is a better goodness of fit. Lower values of each are better.

How is the adjusted $R^2$ ($R_a^2$) calculated in a multiple regression model?

$$R_a^2 = 1 - \left[\left(\frac{n - 1}{n - k - 1}\right) \times (1 - R^2)\right]$$

What are the degrees of freedom for the F-statistic used to evaluate nested models?

The F-statistic has $q$ and $(n - k - 1)$ degrees of freedom, where $F = \frac{(\text{SSE}_R - \text{SSE}_U) / q}{\text{SSE}_U / (n - k - 1)}$.

What are four common causes of regression model misspecification?

(1) Omitting a variable that should be included, (2) variable should be transformed for linearity, (3) inappropriate scaling of the variable, and (4) incorrectly pooling data (e.g., across different regimes).

How is heteroskedasticity detected and corrected in multiple regression analysis?

It is detected using scatter plots or the Breusch-Pagan test, and corrected using White-corrected standard errors.

How is serial correlation (autocorrelation) detected and corrected in regression analysis?

It is detected using the Durbin-Watson (DW) test or the Breusch-Godfrey (BG) test, and corrected using robust (Newey-West corrected) standard errors.

How is multicollinearity detected and what is the formula for the variance inflation factor (VIF)?

It is indicated when the F-test is significant but t-tests are insignificant, and detected using the variance inflation factor: $\text{VIF}_j = \frac{1}{1 - R_j^2}$. It is corrected by dropping correlated X variables.

What does covariance stationary mean for a time series, and what three methods can be used to conclude stationarity?

It means the mean and variance are stable over time. To conclude a time series is covariance stationary: (1) plot the data, (2) regress an AR model and test correlations, or (3) perform a Dickey-Fuller test.

What is the formula for the mean-reverting level of an AR(1) model?

$$\text{Mean-reverting level} = \frac{b_0}{1 - b_1}$$

How is an autoregressive conditional heteroskedasticity (ARCH) model detected, and what is the formula for the variance of an ARCH series?

Detected by estimating an ARCH(1) model: $\hat{\varepsilon}_t^2 = a_0 + a_1 \hat{\varepsilon}_{t-1}^2 + \mu_t$. The variance is: $\hat{\sigma}_{t+1}^2 = \hat{a}_0 + \hat{a}_1 \hat{\varepsilon}_t^2$.

What are the formulas for precision, recall, and the F1 score in evaluating a machine learning algorithm?

$\text{precision} = \frac{\text{true positives}}{\text{true positives} + \text{false positives}}$, $\text{recall} = \frac{\text{true positives}}{\text{true positives} + \text{false negatives}}$, and $\text{F1 score} = \frac{2 \times P \times R}{P + R}$.

What is the formula for the value of a forward currency contract prior to expiration ($V_t$)?

$$V_t = \frac{(\text{FP}_t - \text{FP})(\text{contract size})}{1 + R_A\left(\frac{\text{days}}{360}\right)}$$

What is the formula for covered interest rate parity?

$$F = S_0 \times \frac{1 + R_A\left(\frac{\text{days}}{360}\right)}{1 + R_B\left(\frac{\text{days}}{360}\right)}$$

How is profit on an FX carry trade calculated?

$$\text{Profit on FX carry trade} = \text{interest differential} - \text{change in the spot rate of investment currency}$$

What is the key implication of the Dornbusch overshooting model?

Restrictive monetary policy leads to short-term appreciation of the currency, followed by slow depreciation back toward its purchasing power parity (PPP) value.

What are the steady state growth rate of output per worker ($g^*$) and steady state growth rate of output ($G^*$) in Neoclassical Growth Theory?

$g^* = \frac{\theta}{1 - \alpha}$ and $G^* = \frac{\theta}{1 - \alpha} + \Delta L$

In employee compensation accounting, how is the number of treasury shares calculated for a stock grant?

$\text{number of treasury shares} = \frac{\text{assumed proceeds}}{\text{average share price during reporting period}}$, where assumed proceeds equal cash proceeds plus average unrecognized share-based compensation expense.

What is the formula for ending projected benefit obligation (PBO) in pension accounting?

$$\text{Ending PBO} = \text{beginning PBO} + \text{interest cost} + \text{current service cost} + \text{past service cost} \pm \text{actuarial losses/gains} - \text{benefits paid}$$

How do IFRS and U.S. GAAP differ regarding the discount rate and expected return on plan assets in periodic pension cost?

Under U.S. GAAP, expected return on plan assets reduces periodic pension cost in P&L, and interest cost equals discount rate times beginning PBO. Under IFRS, the discount rate is used as the expected rate of return on plan assets, reporting net interest income or expense equal to discount rate times beginning funded status.

Under the temporal method for multinational operations, which balance sheet items are translated at the current exchange rate and which at historical rates?

Monetary assets and liabilities are translated at the current rate, while nonmonetary assets and liabilities are translated at historical rates.

How is hyperinflation defined, and how do U.S. GAAP and IFRS differ in accounting for operations in hyperinflationary economies?

Hyperinflation is cumulative inflation exceeding $100\%$ over 3 years. U.S. GAAP requires using the temporal method. IFRS requires first restating foreign currency financial statements for inflation and second translating them using current exchange rates, with net purchasing power gain/loss reported in income.

What threshold in the Beneish model indicates potential earnings manipulation?

An M-score greater than $-1.78$ (i.e., less negative or positive) indicates potential earnings manipulation.

What are the five components of the extended DuPont equation for Return on Equity (ROE)?

$\text{ROE} = \left(\frac{\text{NI}}{\text{EBT}}\right) \times \left(\frac{\text{EBT}}{\text{EBIT}}\right) \times \left(\frac{\text{EBIT}}{\text{revenue}}\right) \times \left(\frac{\text{revenue}}{\text{average assets}}\right) \times \left(\frac{\text{average assets}}{\text{average equity}}\right)$ (Tax Burden $\times$ Interest Burden $\times$ EBIT Margin $\times$ Total Asset Turnover $\times$ Financial Leverage).

What is the formula for the accruals ratio using the balance sheet approach?

$$\text{accruals ratio}_{\text{BS}} = \frac{\text{NOA}_{\text{END}} - \text{NOA}_{\text{BEG}}}{(\text{NOA}_{\text{END}} + \text{NOA}_{\text{BEG}}) / 2}$$

How is partial goodwill calculated under IFRS?

$$\text{partial goodwill} = \text{purchase price} - (\% \text{ owned} \times \text{FV of net identifiable assets of the subsidiary})$$

How is Free Cash Flow to the Firm (FCFF) calculated starting from Net Income (NI), assuming depreciation is the only noncash charge?

$$\text{FCFF} = \text{NI} + \text{Dep} + [\text{Int} \times (1 - \text{tax rate})] - \text{FCInv} - \text{WCInv}$$

How is Free Cash Flow to Equity (FCFE) calculated when forecasting using the debt ratio (DR)?

$$\text{FCFE} = \text{NI} - [(1 - \text{DR}) \times (\text{FCInv} - \text{Dep})] - [(1 - \text{DR}) \times \text{WCInv}]$$

What are the formulas for justified leading P/E and justified trailing P/E?

$\text{justified leading P/E} = \frac{P_0}{E_1} = \frac{1 - b}{r - g}$ and $\text{justified trailing P/E} = \frac{P_0}{E_0} = \frac{(1 - b)(1 + g)}{r - g}$

What is the formula for the Target Payout Adjustment Model?

$\text{expected increase in dividends} = [(\text{expected earnings} \times \text{target payout ratio}) - \text{previous dividend}] \times \text{adjustment factor}$, where adjustment factor $= \frac{1}{\text{years of adjustment}}$.

What is the formula for the equity risk premium (ERP) under the Grinold-Kroner model?

$$\text{ERP} = [\text{DY} + \Delta(\text{P/E}) + i + G - \Delta S] - r_f$$

What is the H-Model formula for dividend valuation?

$V_0 = \frac{D_0 \times (1 + g_L)}{r - g_L} + \frac{D_0 \times H \times (g_S - g_L)}{r - g_L}$, where $H$ is the half-life (in years) of the high-growth period.

What are the components of the PRAT model for sustainable growth rate ($g$)?

$g = \left(\frac{\text{net income} - \text{dividends}}{\text{net income}}\right) \times \left(\frac{\text{net income}}{\text{sales}}\right) \times \left(\frac{\text{sales}}{\text{total assets}}\right) \times \left(\frac{\text{total assets}}{\text{stockholders' equity}}\right)$ (Profit margin, Retention rate, Asset turnover, and financial leverage).

What is the formula for Economic Value Added (EVA)?

$$\text{EVA} = \text{NOPAT} - \$ \text{WACC} = [\text{EBIT} \times (1 - t)] - (\text{WACC} \times \text{total capital})$$

How is the total valuation discount calculated from the discount for lack of control (DLOC) and discount for lack of marketability (DLOM)?

$$\text{Total discount} = 1 - [(1 - \text{DLOC})(1 - \text{DLOM})]$$

What is the forward rate model formula relating spot rates and forward rates?

$$[1 + f(j,k)]^k = \frac{[1 + S(j+k)]^{j+k}}{[1 + S_j]^j}$$

What is 'rolling down the yield curve' and under what yield curve condition does it outperform?

It is the strategy of buying bonds with maturity greater than the investment horizon. It outperforms when the yield curve is upward-sloping.

How do the Cox-Ingersoll-Ross (CIR) and Vasicek term structure models differ in their interest rate drift equations?

CIR includes a term proportional to the square root of the short rate in volatility: $dr = a(b - r)dt + \sigma\sqrt{r}dz$, whereas Vasicek assumes constant volatility: $dr = a(b - r)dt + \sigma dz$.

How do an increase in interest rate volatility affect callable and putable bond prices?

Value of the embedded call rises ($V_{\text{call}} \uparrow$) so callable bond value drops ($V_{\text{callable bond}} \downarrow$); value of the embedded put rises ($V_{\text{put}} \uparrow$) so putable bond value rises ($V_{\text{putable bond}} \uparrow$).

What are the formulas for effective duration and effective convexity?

$\text{effective duration} = \frac{\text{BV}_{-\Delta y} - \text{BV}_{+\Delta y}}{2 \times \text{BV}_0 \times \Delta y}$ and $\text{effective convexity} = \frac{\text{BV}_{-\Delta y} + \text{BV}_{+\Delta y} - (2 \times \text{BV}_0)}{\text{BV}_0 \times (\Delta y)^2}$

How are capped floaters and floored floaters valued?

$\text{Value of capped floater} = \text{straight floater value} - \text{embedded cap value}$; $\text{Value of floored floater} = \text{straight floater value} + \text{embedded floor value}$.

How is the market conversion price of a convertible bond calculated?

$$\text{Market conversion price} = \frac{\text{market price of convertible bond}}{\text{conversion ratio}}$$

How is the value of credit-risky debt modeled from an option perspective in structural models?

$$\text{value of risky debt} = \text{value of risk-free debt} - \text{value of put option on the company's assets}$$

What is the formula for the upfront payment paid by the protection buyer in a Credit Default Swap (CDS)?

$$\text{Upfront CDS payment} = \text{PV}(\text{protection leg}) - \text{PV}(\text{premium leg}) \approx (\text{CDS spread} - \text{CDS coupon}) \times \text{duration} \times \text{notional principal}$$

What are the put-call parity formulas for synthetic call and synthetic put options?

$\text{synthetic call} = \text{put} + \text{stock} - \text{riskless bond}$ and $\text{synthetic put} = \text{call} - \text{stock} + \text{riskless bond}$

What is the formula for dynamic delta hedging using short call options?

$$\text{\# of short call options} = \frac{\text{\# shares hedged}}{\text{delta of call option}}$$

What are the three term structure theories of commodity futures?

(1) Insurance theory (implied normal backwardation), (2) Hedging pressure hypothesis (includes long hedgers causing contango and short hedgers causing backwardation), and (3) Theory of storage ($\text{futures price} = \text{spot price} + \text{storage cost} - \text{convenience yield}$).

What is the formula for roll return on commodity futures and when is it positive?

$\text{roll return} = \frac{\text{price of expiring futures contract} - \text{price of new futures contract}}{\text{price of expiring futures contract}}$. It is positive in backwardation.

What are the four phases of the Real Estate Cycle?

Recovery (trough, little construction, tight credit), Expansion (economic growth, easing credit, higher prices, new construction), Oversupply (growth slows, property glut, lower prices/rents), and Recession (slowdown, tight credit, construction and price lows).

How is adjusted funds from operations (AFFO) calculated in REIT valuation?

$$\text{AFFO} = \text{FFO} - \text{non-cash rents} - \text{recurring maintenance-type capital expenditures}$$

What is the Taylor rule formula for the nominal target short-term interest rate?

$r = R_n + \pi + 0.5(\pi - \pi^*) + 0.5(y - y^*)$, where $R_n$ is real neutral rate, $\pi$ is expected inflation, $\pi^*$ is target inflation, and $y - y^*$ is output gap.

What additional risk premia are added to the nominal rate to determine the discount rate for commercial real estate?

The commercial real estate discount rate adds credit risk spread ($\gamma$), equity risk premium versus risky debt ($\kappa$), terminal value risk ($\kappa$), and illiquidity premium ($\phi$): $\text{Discount rate} = R + \pi + \theta + \gamma + \kappa + \phi$.

What is the 'Full' fundamental law of active management formula for expected active return?

$E(R_A) = (\text{TC})(\text{IC})\sqrt{\text{BR}}\,\sigma_A$, where $\text{TC}$ is transfer coefficient, $\text{IC}$ is information coefficient, $\text{BR}$ is breadth, and $\sigma_A$ is active risk.

What is the formula for the 5% annual dollar Value at Risk ($5\% \text{ annual } \$ \text{VaR}$)?

$$5\% \text{ annual } \$ \text{VaR} = [\text{mean annual return} - (1.65 \times \text{annual standard deviation})] \times \text{portfolio value}$$

What are the definitions of survivorship bias, look-ahead bias, and data snooping in backtesting?

Survivorship bias is using data that only includes entities persisting until today; look-ahead bias is using information unavailable at the decision date; data snooping occurs when a model is selected purely based on superior backtest performance.

What are the seven main Standards in the CFA Institute Standards of Professional Conduct?

Standard I: Professionalism; Standard II: Integrity of Capital Markets; Standard III: Duties to Clients; Standard IV: Duties to Employers; Standard V: Investment Analysis, Recommendations, and Actions; Standard VI: Conflicts of Interest; Standard VII: Responsibilities as a CFA Institute Member or CFA Candidate.