r^2 (coefficient of determination) - Answer: (SST-SSE)/SST = RSS/SST = explained variation/total variation MSE - Answer: SSE/(n-k-1) MSR - Answer: RSS/k adjusted R^2 - Answer: 1 - ((n-1)/(n-k-1))(1-R^2) Akaike's information criterion (AIC) - Answer: n*ln(SSE/n)+ln(n)*(k+1) F-statistic for nested models - Answer: ((SSEr-SSEu)/q)/(SSEu/(n-k-1)) with q and n-k-1 degrees of freedom F-stat for overall model fit - Answer: ((SSEr-SSEu)/q)/(SSEu/(n-k-1)) = ((SSTu-SSEu)/k)/(SSEu/(n-k-1)) = (RSSu/k)/(SSEu/(n-k-1)) Logistic regression (logit) models - Answer: ln(p/1-p) = b0+b1X1+b2X2+...+e odds = e^y hat P = odds/(1+odds) = 1/(1+e^-yhat) Likelihood Ratio (LR) - Answer: -2(log likelihood restricted model - log likelihood unrestricted model) CFA Level II Formulas Mean reverting level for AR(1) - Answer: b0 / (1 - b1) normalized Xi - Answer: (Xi-Xmin)/(Xmax-Xmin) Standardized Xi - Answer: (Xi-u)/SD Accuracy - Answer: (TP+TN)/(TP+TN+FP+FN) F1 Score - Answer: (2*P*R)/(P+R) Recall (True positive rate (TPR)) - Answer: TP / (TP + FN) Precision - Answer: TP / (TP + FP) False positive rate (FPR) - Answer: FP / (FP + TN) RMSE - Answer: sqrt((sum(predicted-actual)^2)/n) value of a forward currency contract prior to expiration - Answer: Vt=((FPt−FP)(contract size))/[1+R(days/360)] Covered interest rate parity - Answer: F=([1+Ra(days/360)]/[1+Rb(days/360)])S0 uncovered interest rate parity - Answer: E(%ΔS)(a/b) = Ra − Rb CFA Level II Formulas Relative Purchasing Power Parity - Answer: %ΔS(A/B) = inflation(A) − inflation(B) where: %ΔS(A/B) = change in spot price (A/B) Interpolate - Answer: R1 + ((R2-R1)/(t2-t1))*(tn-t1) output per worker - Answer: Y/L = T(K/L)^α Growth accounting relation - Answer: growth rate in potential GDP = long-term growth rate of technology + α (long-term growth rate of capital) + (1 − α) (longterm growth rate of labor) or growth rate in potential GDP = long-term growth rate of labor force + long-term growth rate in labor productivity neoclassical growth theory - Answer: sustainable growth of output per capita (g*) equals growth rate in technology (θ) divided by labor's share of GDP (1 − α) g*=θ/(1−α) sustainable growth rate of output (G*) equals sustainable growth rate of output per capita plus growth of labor (ΔL) G*=(θ/(1−α))+ΔL Funded status of plan - Answer: Fair value of plan assets - PBO CFA Level II Formulas Plan assets - Answer: Fair Value at beginning of year + Contributions + Actual Return -Benefits Paid = Fair value of plan assets at yr end PBO - Answer: PBO at beginning of year + Service Cost + Interest Cost + Past Service Cost +/- Actuarial losses/gains - Benefits paid