Rates And Returns Flashcards
We must interpret interest rates as either
Required Rates of Return, Discount rates, or Opportunity Costs
Equilibrium Interest Rates are the:
Required Rate of Return for a particular investment, in which investors require as a rate of return in exchange for willingly lending out their funds
Interest rates (discount rate)
If an individual can borrow at the interest rates of 10%, then that individual should discount payments to be made in the future at that rate to get their equivalent value
Interest rates (Opportunity Cost)
“Cost of current current consumption” rather than postponing consumption. Buying a 5% 1 year t-note, earning an additional 5% is the opportunity forgone
Real Risk-Free rate (of interest) is the
The theoretical rate on a single-period loan that contains no exception of inflation and zero probability of default
When we speak of a real rate of return, we are referring to
An investor’s increase in purchasing power (after adjusting for inflation).
T-Bills are a nominal risk-free rate because they contain
an Inflation Premium
Nominal risk-free rate =
(At a bare minimum)
Real risk-free rate + expected inflation rate
Default Risk is the risk that
A borrower will not make the promised payments in a timely manner
Liquidity risk is
the risk of receiving less than fair value for an investment if it must be sold quickly for cash
Maturity risk as it comes in fixed income
The prices of longer-term bonds are more volatile than those for shorter-term bonds.
The longer-maturity bonds have more maturity risk than shorter-term
Bonds and require a maturity risk premium.
Nominal risk-free rate =
(Loaded up with all types of risks)
Real risk-free rate + inflation premium + default risk premium + liquidity premium + maturity premium
Holding Period Return (HPR)
Is the percentage increase in the value of an investment over a given period
Today’s value + dividends rec - beg. value
__________________________________________
Beginning value
Returns over multiple periods re. HPR
(1+HPRyear 1) (1+HPRyear 2) (etc) -1
AKA: Annualized return
Arithmetic Mean Return is the
Simple average of a series of periodic returns
(Return year 1 + Return year 2 + etc.)
______________________________________
N (number of years)
The geometric mean return is
a compound rate.
It is always less than than or equal to the arithmetic mean, and the difference increases as the ranges of observations increases.
The only time the arithmetic and the geometric means are equal is if there is no variability in observations. (All observations are equal)
Harmonic mean
Is used for certain computations, such as the average cost of shares purchased over time
The relationship among Arithmetic, Geometric, and Harmonic means can be stated as follows:
Arithmetic mean x Harmonic mean = (Geometric mean)^2
For values not all equal:
Harmonic mean < Geometric mean < Arithmetic mean
Appropriate uses for the various return measures
Arithmetic mean - include all values and outliers
Geometric - compound rate of returns over multiple years
Harmonic - Calculate the avg. share cost from periodic purchases in a fixed money amount (spending $1,000 a month on MF)
Trimmed or winsorized mean - decrease the effect of outliers
Real Interest Rates are
Those that have been adjusted for Inflation of an interest rate for which the inflation premium has been subtracted
Solving for quoted continuously compounded rates given actual holding period returns is
[LN] (1+HPR) = Rcc
If an investment grows from $50 to $55, what is the quoted continuously compounded rate of return for the period?
[LN] (1+HPR)
HPR = END/ BEG -1 = .1
55/50 =1.1
[LN] (1+ HPR) = [LN] (1.1) = 9.53%
Continuously compounded rates are _____ over multiple periods
additive
To Compound or Discount at continuously compounded rates,
Multiply or Divide by e^Rcc
