Formulas Flashcards
Dividend Discount Model
V = value
D1 = dividend in period 1
r = required return
g = growth of dividend
determine the value of a stock based on a stream of dividend payments that is increasing at a constant rate of growth
r will either be given or can be calculated using CAPM
if given past dividends, solve for growth rate using TVM
D1 = D0 x (1+g)
Standard Deviation of a Two-Asset Portfolio
sum of the weights must equal 100% (W variables)
covariance b/t assets i & j = SDi x SDj x p (p = correlation b/t assets i & j)
if correlation is zero, then covariance will be zero
if correlation is one, then SD of the portfolio will equal the weighted average of the standard deviations
if correlation is -1, then portfolios move in opposite direction; portfolio achieves maximum diversification
Covariance
p = correlation b/t two assets
measure of how much two assets move together; combines volatility of one stock’s returns w/ the tendency of those returns to move up or down at the same time that another stock’s returns move up or down
relative measure
the more positive the covariance, the more they move together
when two assets that move together are combined in a portfolio there is little risk reduction
the less their movements are together the greater the diversification (risk reduction)
Expected Rate of Return
r = (D1/P) + g
r = expected ROR
D1 = dividend in period 1
g = growth rate of dividend
P = current stock price
manipulation of dividend discount model
dividend divided by price gives us dividend yield
expected ROR on a stock is equal to the expected dividend yield plus a growth factor
the return to an equity investor will come from the dividend yield &/or the growth in the value of the asset (capital appreciation)
Beta
COV = covariance b/t asset & the market
p = correlation b/t asset & the market
Bi = COVim / SDm^2 = Pim x SDi / SDm
measure of an asset’s systematic risk (good measure for a well diversified portfolio)
beta measures an asset’s nondiversifiable risk
beta measures an asset’s market risk
Conversion Value of a Convertible Bond
*no longer on CFP board formula sheet!
CV = (Par / CP) x Ps
CV = conversion value
CP = conversion price
Ps = current stock price
CP = the price at which the shares can be converted
Par / CP = total # of shares (conversion ratio) that will be received upon conversion
Standard Deviation
on formula sheet, use sample, done on calculator
Risk-Adjusted Measures of Portfolio Performance - Sharpe Ratio
Rp = portfolio return
Rf = risk free rate
SDp = portfolio standard deviation
risk-adjusted measure of portfolio performance
numerator = excess return that portfolio earned in excess of risk free ROR
dividing by SD gives us excess portfolio return per unit of total risk
relative measure of performance (must be compared to another Sharpe ratio; difficult to interpret on its own)
**use if low r^2
Risk-Adjusted Measures of Portfolio Performance - Treynor Ratio
Rp = portfolio return
Rf = risk free rate
Bp = portfolio beta
risk-adjusted measure of portfolio performance
excess portfolio return per unit of systematic risk
relative measure of performance
Risk-Adjusted Measures of Portfolio Performance - Jensen’s Alpha
Rm = return on the market portfolio
Bp = portfolio beta
Rp = portfolio return
Rf = risk free rate
absolute measure of performance
indicates the value added to or subtracted from the portfolio through portfolio management
simply the actual portfolio return minus CAPM or actual portfolio return minus the return that the investor expected to earn when they invested in the asset
Risk-Adjusted Measures of Portfolio Performance - Information Ratio
Rp = return of portfolio
Rb = return of index or benchmark
SDa = SD of difference b/t returns of portfolio & returns of benchmark portfolio (also known as tracking error)
ratio of a portfolio’s return in excess of the returns of a benchmark (such as an index) to the SD of those excess returns
ratio indicates portfolio manager’s ability to consistently beat the index
the higher the IR, the more consistent the manager is in generating excess returns
Bond Duration: Macaulay
time weighted payback w/ each future cash flow weighted by the year in which it occurs
c = coupon rate
y = YTM
t = time to maturity
D = Macaulay duration
coupon rate, yield entered as decimals, time entered in as whole #
*if calculating in semi-annual enter semi-annual inputs, duration will be in semi-annual periods, then divide # of semi-annual period by 2 to obtain duration in years
Modified Duration = macaulay duration / (1 + y)
change in bond price = -1 x modified duration x change in yield
Capital Asset Pricing Model (a.k.a. the Security Market Line)
Ri = required ROR on asset i
Rf = risk free rate
Rm = return on the market
Bi = beta of asset i
used to determine the required ROR on an asset given its level of systematic risk
risk premium = B(Rm - Rf)
market risk premium = Rm - Rf
SML line intersects w/ risk free rate at y axis
Arithmetic Mean
simple average
Effective Annual Rate (EAR)
i = stated annual interest rate
n = # of compounding periods
investment’s annual rate of return when compounding occurs more than once per year
