Risk and return (Lecture 1) Flashcards
(16 cards)
NPV formula
-NPV = sum of : Ct/ (1+r)^t - intital investment
-Ct = cash, r = discount rate
Net Present Value (NPV) is the total of all future cash flows discounted to the present, minus the initial investment.
Formula Equivalent Annual Rate (EAR) with continuous compounding
EAR (continous compounding) = e^r - 1
-r is the quoted rate
formula for present value PV + PV with multiple years of cash flow + defintiion
pv = FV/Cashflow / (1+r)t, ct is cash flow at time t.
-with multiple years sum the discounted cash flows which have been discounted to the correct year.
- future cash flows discounted to the present by an appropriate discount rate.
(PV) is the current value of future cash flows, discounted to the present by an appropriate discount rate, which reflects the time value of money and the risk associated with future cash flows.
define Equivalent Annual Rate (EAR)
(EAR) is the annual interest rate reflects the effect of compounding over a given period, showing the true rate of return/ cost of borrowing taking into acccount compoiunding.
reflects the true interest rate when compounding occurs more than once per yea
formula for Equivalent Annual Rate (EAR) with discrete compounding
EAR (normal compounding) = (1 + quoted rate r/n)^n - 1.
r = Nominal annual interest rate (as a decimal)
n = compounding periods per year (e.g., 12 for monthly, 4 for quarterly)
The rate of return is also called…
discount rate, hurdle rate, and opportunity cost of capital
expected holding-period return HPR normal + with different states/probabilities
-Multiple states:
-e(HPR) = sum(pi * HPRi)
-HPRi = expected holding-period return state i, pi = prob state i occuring
-Normal:
HPR = (P1+ D1))/ P0 - 1
-future price + div all over initial price all monus 1
or HPR = p1 - p0 + d1 / p0
-p1:Expected price of the asset at the end of the holding period, p0: initial asset price, d1: expected dividend income during the period
When comparing investments with different horizons, the ____________ provides the more accurate comparison.
The effective annual rate provides the more accurate comparison of investments with different horizons because it expresses the returns in a common period.
What is the inverse of compounding
discounting
-discount invesre of compounding
arithmetic and geometric mean + difference
-The arithmetic mean (often just called the “average”) is calculated by adding up all the values and dividing by the number of values. Tells return in ‘average year’ over a time period.
-R = [(1+r1)(1+r2)…*(1+rn)]^1/2 - 1
geometric average returns way to measure the average rate of return over multiple periods, accounting for the compounding effect/volatility.
-Arithmetic assumes no compounding, while the geometric mean accounts for compounding and provides a more accurate measure of the average rate of return over time, especially when returns fluctuate/volatile.
fisher effect
describes relationshipn between nominal returns/interst rate and real returns/rates and inflation
1+R = (1+r)*(1+h)
-R - nominal rate, r- real rate, h inglation rate
Describe APR
Annual Percentage Rate (APR) refers to the yearly cost of borrowing or the return on investment (which is expressed as a percentage) including interest and certain fees (management/payment fees) but excluding compounding effects.
-within uk all loans must state apr and lender must state total amount paid at end of loan.
Calculating expected standard deviation/variane using HPR
-First find the Expected Holding Period Return E(HPR):
∑ pi*HPRi
-Variance σ^2 = ∑ pi*(HPRi - E(HPRi))^2
-SD is sqrt of variance
Formula for estimated rates of return
- can be used to see if asset is over or undervalued.
estimated return =( pt+1 - pt ) / pt + dt+1/pt
aka =( p1 - p0) / p0 + d1 / p0
-If estimated return > required rate of return –> asset is undervalued thus BUY.
-If estimated return < required rate of return –> asset overvalued thus sell.
Risk premium define + risk free rate
RiskPremium=PortfolioReturn−Risk-FreeReturn
-RFR refers to the basic interest rate assuming no uncertainty/inflation and reflects the pure time value of money.
Formula for future value FV
FV=PV×(1+r)^t
