Formulas Flashcards
Utility function
E(R)-0.5A sigma^2
CML
R= risk free + ((market-risk free)/sigma m) * sigma p
Sharpe ratio portfolio
(market- risk free) / sigma m
Treynor ratio
(portfolio - risk-free) / beta
Sharpe CAPM
(portfolio - risk-free)/sigma p
SML
R = risk free + (market- risk free)*beta
Estimated return
= (P1+Div1-P0)/P0
How to tell if under-priced
estimated - expected > 0
IR ratio
(portfolio-benchmark)/sigma er
Sortino
(Rp - T)/DR
Downside risk
1/n sum (R- mean R)^2 for all R less than mean
APT
risk-free + sum of beta*lambda
Price of bond
C*(1/r - 1/r(1+r)^t) + FV/(1+r)^t
present value for perpetuity
Cash flow/return
Current yield
Coupon / Price
Fisher relation
(1+R)=(1+r)*(1+h)
Zero growth price
Div/r
Constant (Pt)
Divt*(1+g)/(r-g)
Non-constant P0
D1/1+r + D2/(1+r)^2 + D3/(1+r)^3 + P3/(1+r)^3
WACC
cost of equityweight of equity + cost of debtweight of debt*(1-tax rate)
Value of a firm
V= c/WACC
Expected return on asset with capital structure
Ra= (D/D+E)Rd +(E/E+D)Re
return of equity equation
Re=Ra+ D/E(Ra-Rd)
Present value of interest rate shield
Value of debt* tax rate
Value of levered firm
VL = Vu + tax*debt value
Beta of capital structure with no taxes
Ba= (E/E+D)Be + (D/D+E)Bd
Beta of capital structure with taxes
Ba= (E/E+D(1-T)Be + (D(1-T)/E+D(1-T))Bd
Risk on equity of levered firm
𝛽𝐸 = 𝛽𝐴 + 𝐷(1−𝑇𝑐)/𝐸 (𝛽𝐴 − 𝛽𝐷)
