Dealing a round

Formula sheet with key words (all 76)

Time value of money

#1$PV=\frac{FV}{(1+i)^n}$present value, worth today, lump sum, single future amount, discount back

#2$PV=FV\,e^{-i t}$PV with continuous compounding, continuously compounded rate, e

#3$FV=PV(1+i)^n$future value, grow to, compounded annually, lump sum invested today

#4$FV=PV\,e^{i t}$FV with continuous compounding, continuously compounded rate, e

#5$PV=\frac{CF_1}{(1+i)^1}+\frac{CF_2}{(1+i)^2}+\cdots+\frac{CF_n}{(1+i)^n}$uneven / different cash flows each year, cash flow stream, project cash flows, NPV

#6$PV=\frac{CF}{i}-\frac{CF/i}{(1+i)^n}$annuity as perpetuity minus delayed perpetuity, perpetuity (CF/i), forever

#7$PV=CF\left[\frac{1-(1+i)^{-n}}{i}\right]$PV of annuity, equal payments each period, loan repayment, mortgage, pension

#8$FV=\frac{CF}{i}(1+i)^n-\frac{CF}{i}$FV of annuity (perpetuity form), regular savings, accumulate

#9$FV=CF\left[\frac{(1+i)^n-1}{i}\right]$FV of annuity, saving each year, regular deposits, how much will you have

#10$APR=\text{Monthly rate}\times 12$APR, annual percentage rate, quoted / nominal rate, monthly rate

#11$EAR=\left(1+\frac{APR}{m}\right)^{m}-1$effective annual rate, EAR, compounded monthly / quarterly, true annual rate

Return statistics

#12$E(r)=\sum_{s=1}^{n}p(s)\,r(s)=\frac{1}{n}\sum_{s=1}^{n}r(s)$expected return, scenarios, states of economy, probability, mean / average return

#13$g=TV^{1/n}-1$geometric average, CAGR, compound annual growth, time-weighted return

#14$TV_n=(1+r_1)(1+r_2)\cdots(1+r_n)$terminal value, value of $1 invested, holding period return over several years

#15$\sigma_x^2=\sum_{i=1}^{n}p_i(x_i-\bar{x})^2$variance with probabilities, scenarios, standard deviation, volatility, total risk

#16$\sigma_x^2=\frac{1}{n}\sum_{i=1}^{n}(x_i-\bar{x})^2$variance from historical data, equally weighted, standard deviation

#17$\hat{\sigma}^2=\frac{1}{n}\sum_{s=1}^{n}\left[r(s)-\bar{r}\right]^2$variance of returns, historical sample, standard deviation estimate

#18$\bar{x}=\sum_{i=1}^{n}p_i x_i$mean with probabilities, expected value

#19$\bar{x}=\frac{1}{n}\sum_{i=1}^{n}x_i$mean of historical data, arithmetic average

#20$\hat{S}=\frac{1}{N}\sum_{t=1}^{N}\frac{(x_t-\bar{x})^3}{\hat{\sigma}^3}$skewness, asymmetry, left / right tail, crash risk

#21$\hat{K}=\frac{1}{N}\sum_{t=1}^{N}\frac{(x_t-\bar{x})^4}{\hat{\sigma}^4}$kurtosis, fat tails, excess kurtosis (minus 3), extreme outcomes, normality

Portfolio risk

#22$U=E(r)-\tfrac{1}{2}A\sigma^2$utility, risk aversion A, which portfolio does the investor prefer, certainty equivalent

#23$E(r_p)=w_xE(r_x)+w_yE(r_y)$portfolio expected return, weights, x% in A and rest in B

#24$\sigma_p^2=w_x^2\sigma_x^2+w_y^2\sigma_y^2+2w_xw_y\sigma_{x,y}$two-asset portfolio risk / standard deviation, diversification, covariance

#25$\sigma_p^2=w_x^2\sigma_x^2+w_y^2\sigma_y^2+w_z^2\sigma_z^2+2w_xw_y\sigma_{x,y}+2w_xw_z\sigma_{x,z}+2w_yw_z\sigma_{y,z}$three-asset portfolio variance

#26$\sigma_p^2=W\,\Sigma\,W^{T}$covariance matrix, variance-covariance matrix, many assets, Excel MMULT

#27$\sigma_{x,y}=\sum_{i=1}^{n}p_i(x_i-\bar{x})(y_i-\bar{y})$covariance with probabilities, joint scenarios, co-movement

#28$\sigma_{x,y}=\frac{1}{n}\sum_{i=1}^{n}(x_i-\bar{x})(y_i-\bar{y})$covariance from historical data, move together

#29$\text{Cov}(r_x,r_y)=\sigma_{x,y}=\rho_{x,y}\,\sigma_x\sigma_y$convert correlation to covariance

#30$\rho_{x,y}=\frac{\sigma_{x,y}}{\sigma_x\sigma_y}$correlation coefficient, perfectly negative / positive correlation, uncorrelated

#31$y^{*}=\frac{E(r_P)-r_f}{A\sigma_P^2}$optimal allocation / proportion in risky portfolio, y*, risky vs risk-free split, complete portfolio

Index model & CAPM

#32$R_i=\alpha_i+\beta_iR_m+\varepsilon_i$single-index model, index model, alpha, beta, residual, characteristic line

#33$R^{*}_{i,t}=\alpha_i+\beta_iR^{*}_{m,t}+e_{i,t}$index model regression of excess returns, security characteristic line, intercept / slope

#34$E(R_i)=\alpha_i+\beta_iE(R_m)$expected return under index model, forecast with alpha and beta

#35$\sigma_i^2=\beta_i^2\sigma_m^2+\sigma^2_{\varepsilon_i}$firm-specific / residual / unsystematic / idiosyncratic / diversifiable risk, systematic risk, R-squared

#36$\sigma_{i,j}=\beta_i\beta_j\sigma_m^2$covariance between two stocks via index model, correlation through the market

#37$\alpha_p=\sum_{i=1}^{n}w_i\alpha_i$portfolio alpha, weighted average alpha

#38$\beta_p=\sum_{i=1}^{n}w_i\beta_i$portfolio beta, weighted average beta

#39$\beta_i=\frac{\sigma_{i,m}}{\sigma_m^2}$calculate beta, covariance with market over market variance, regression slope

#40$\beta_{adj}=\tfrac{2}{3}\beta_{reg}+\tfrac{1}{3}(1)$adjusted beta, Blume / Merrill Lynch, beta mean-reverts towards 1, forecast beta

#41$\text{SML: }E(r_i)=r_f+\left[E(r_m)-r_f\right]\beta_i$CAPM, required return, fair return, cost of equity, under / overpriced, alpha vs SML

#42$\text{CAL: }E(r_C)=r_f+\frac{\sigma_C}{\sigma_P}\left[E(r_P)-r_f\right]$capital allocation line, risky portfolio + T-bills, Sharpe ratio, reward-to-volatility

#43$\text{CML: }E(r_C)=r_f+\frac{\sigma_C}{\sigma_m}\left[E(r_m)-r_f\right]$capital market line, market portfolio, passive strategy, efficient portfolios

#44$E(r_P)=\sum_k w_kE(r_k)$portfolio expected return, weighted average

#45$\beta_P=\sum_k w_k\beta_k$portfolio beta under CAPM, target beta, adding a stock

#46$R_i^{*}=\alpha_i+\beta_iR_m^{*}+e_i$index model in excess returns, alpha, beta, residual

#47$R_i=E(R_i)+\beta_{i,F_1}F_1+\beta_{i,F_2}F_2+\beta_{i,F_3}F_3+e_i$APT, multifactor model, factor betas, factor surprises, macroeconomic factors

#48$R_{it}=\alpha_i+\beta_{i,M}R_{Mt}+\beta_{i,SMB}SMB_t+\beta_{i,HML}HML_t+e_{it}$Fama-French three-factor, SMB size, HML value, book-to-market

Performance evaluation

#49$R=r-r_f$excess return over T-bill

#50$S=\frac{R_p-r_f}{\sigma_p}$Sharpe ratio, reward to total risk, excess return per unit of standard deviation

#51$T=\frac{R_p-r_f}{\beta_p}$Treynor measure, reward to systematic risk, excess return per unit of beta

#52$J=R_p-\left[r_f+(r_m-r_f)\beta\right]$Jensen's alpha, abnormal return, did the manager add value, vs CAPM

#53$M^2=r_{P^{*}}-r_M$M-squared, M2, risk-adjusted return, match market volatility with T-bills

#54$d=r_{p,t}-r_{b,t}$active return, return over benchmark

#55$IR=\frac{\bar{d}}{\sigma_d}$information ratio, appraisal ratio, active return per unit of tracking error

#56$TE=\sigma_d$tracking error, volatility of active return

Equity valuation

#57$g=ROE\times b$sustainable growth, retention / plowback ratio, payout ratio, ROE

#59$P=\frac{D_0(1+g)}{k-g}$dividend discount model, Gordon growth, constant growth, D0 just paid, intrinsic value

#60$P=\frac{D}{k}$no growth, constant dividend forever, preferred stock, perpetuity

#61$P=PE\times E$P/E ratio, price-earnings multiple, relative valuation, comparables, EPS

#62$\text{Working capital}=\text{current assets}-\text{current liabilities}$working capital, NWC, change in working capital

#63$FCFF=EBIT(1-t)+\text{Dep. \& Amort.}-\text{Cap. Exp.}-\Delta NWC$FCFF, free cash flow to firm, EBIT, capex, depreciation

#64$FCFE=FCFF-\text{Interest}\times(1-t)+\Delta\text{Debt}$FCFE, free cash flow to equity, net borrowing, after-tax interest

#65$V=\frac{FCFF_0(1+g)}{WACC-g}$firm value, enterprise value, WACC, DCF with constant growth

#66$P=\frac{FCFE_0(1+g)}{r-g}$equity value, FCFE valuation, cost of equity

Bonds & term structure

#58$P=C\left[\frac{1-(1+i)^{-n}}{i}\right]+\frac{Par}{(1+i)^n}$bond price, coupon, par / face value, yield to maturity, premium / discount bond

#67$(1+f_n)=\frac{(1+y_n)^n}{(1+y_{n-1})^{n-1}}$forward rate, implied forward, spot rates, term structure, yield curve

#68$(1+y_n)^n=(1+y_{n-1})^{n-1}(1+f_n)$long-term yield from forward rates, rolling over

#69$1+y_n=\left[(1+f_1)(1+f_2)\cdots(1+f_n)\right]^{1/n}$yield as average of forward rates, expectations hypothesis

#70$\frac{\Delta P}{P}=-D\times\frac{\Delta(1+y)}{1+y}$bond price change using Macaulay duration

#71$D=\sum_{t=1}^{T}t\times w_t$Macaulay duration, weighted average time to cash flows, effective maturity

#72$w_t=\frac{CF_t/(1+y)^t}{\text{Bond price}}$duration weights, PV of each cash flow / price

#73$D^{*}=\frac{D}{1+y}$modified duration, convert Macaulay

#74$\frac{\Delta P}{P}=-D^{*}\,\Delta y$interest rate risk, price sensitivity, yield changes by x bp, % price change

#75$\text{Convexity}=\frac{1}{P(1+y)^2}\sum_{t=1}^{T}\left[\frac{CF_t}{(1+y)^t}(t^2+t)\right]$convexity, curvature of price-yield curve

#76$\frac{\Delta P}{P}=-D^{*}\Delta y+\tfrac{1}{2}\left[\text{Convexity}\times(\Delta y)^2\right]$duration plus convexity, large yield change, more accurate price estimate