FoF - Unit 2 Flashcards
Future Value
measures the nominal future sum of money that a given sum of money today is “worth” at a specified time in the future assuming a certain rate of return.
FV=PV x (1+r)^T
Discount factor (Present Value Factor)
1/(1+r)^t
Arbitrage pricing theory (APT)
is a multi-factor asset pricing model based on the idea that an asset’s returns can be predicted using the linear relationship between the asset’s expected return and a number of macroeconomic variables that capture systematic risk.
Present Value
PV=FV / (1+r)^t
Yeild (not coupon) Formula
r = (FV/PV)^1/t -1
For a bond, the yield is also called ________________
yield to maturity (YTM)
For single payment bond, the interest rate and the ________ are the same thing. Mor complicated for multiple-payment bonds
yield
Equations for Time
t= log(FV/PV) / log(1+r)
zero coupon bond
a bond that pays no interest/coupon, only the face value at maturity. Lower interest rates the higher PV/price of bond will be
multiple payment security (bond)
collection of zero coupon bonds.
PV= C0 + C1/(1+r) + Ct/(t+r)
FV= C0(1+r)^t + C1(1+r)t-1 + … + Ct
perpetuity (consol)
a bond that pays a fixed payment C forever. No principal payment. By convention, the payment in the current period has already happened
PV=C/r (diff. if starting in 10 years)
annuities
pays a fixed cash flow C for T periods
PV= C(1/r -1/r(1+r)^t)
Calculating Returns: Compounding
Annual Percentage rate (APR)
Effective annual rate (EAR)
Calculating Returns: Single-period realized return
(annualized) holding period return (HPR)
Calculating Returns: Multi-period returns
arithemetic average
geometric average
internal reate of return (IRR)
Annual Percentage Rate (APR)
lenders are required by law to report APR
APR = (rate per period)(# of periods per year)
Effective annual rate (EAR)
if interest is compounded m times a year:
EAR = (1 + APR/m)^m -1
Holding Period Return (HPR)
is the rate (return) that your initial investment earned in order to generate the final value of the investment. Reflects both change in the resale value, and any cashflows
HPR = (ending price + ending cash dividens / beginning price ) -1
Ann HPR
is the corresponding rate per year (annual return)
annHPR = (1+ HPR)^1/T -1
(other equations on Onenotes)
geometic avg.
= [(1+r)…(1+rt)] ^ 1/t -1
Internal Rate of Return (IRR)
that solves the equation. Equates the initial price to the PV of all future cash flows.
“Dollar-weighted” average return
In the context of a bond, IRR is call the yield
