CFA 1_Quant Methods Flashcards
Nominal risk-free rate
real risk-free rate + expected inflation rate
Effective Annual Rate (EAR)
EAR = (1 + periodic rate)^n
periodic rate = stated annual rate / n = number of compounding periods per year
FV and PV equation
FV = PV*(1 + I/Y)^n
I/Y = annual rate of return / n
n = number of compounding periods per year
PV = FV / (1 + I/Y)^n
Annuity due (TI BA II Plus)
2nd > BGN > 2nd > Set
OR take FV/PV of ordinary annuity and multiply by (1 + I/Y)
FVAd = FVAo * (1 + I/Y)
PVAd = PVAo * (1 + I/Y)
Don’t forget to change back to END!
PV of a perpetuity
PMT / I/Y
PV of uneven CF series
Cpt PV of each cashflow, OR, use the CF function in your calculator and cpt the NPV.
Determining principal component of a PMT
- Interest component = beginning balance (PV in period) * periodic coupon interest rate
- Principal component = PMT - interest component
- Beginning balance of next period = prior beginning balance - principal component (principal component amortizes the principal balance)
NB: PMT is the same each year… but the PV changes. It is the PV on which you base the interest component calculation.
Principal component is PMT - interest component. Try making an amortisation table.
Computing PV if series of PMTs doesn’t start until a future period
- Cpt PV of future series of payments
- Discount that PV by the number of years until that PMT series started. BUT, be careful you are using the right “N”. If it starts 5 years from today, N should be 4, because that PV comes at the “end” of year 4/beginning of year 5.
Holding period return (HPR)
The % change in the value of an investment over the period it is held.
HPR = (ending value - beginning value + CF received) / beginning value
HPR = ((ending value + CF received) / beginning value) -1
Money-weighted return
The IRR talking into account all cash inflows/outflows.Use CF function then Cpt IRR. If funds are contributed to portfolio just before a period of poor performance, the money-weighted RoR will be lower than the time-weighted.If funds are contributed to portfolio just before a period of good performance, the money-weighted RoR will be higher than the time-weighted.
Time-weighted rate of return
Measures compound growth unaffected by timing of cash inflows/outflows.
- Disaggregate period into subperiods based on major cash flow events
- Cpt HPRs of these subperiods
HPR = ((ending value + CF received) / beginning value) -1
- Multiply HPRs of each subperiod. If more than a year, must use geometric mean.
(1 + time-weighted RoR)^2 = (1 + HPRa)*(1 + HPRb)
time-weighted RoR = [(1 + HPRa)*(1 + HPRb)]^.5
Bank discount yield (BDY)
How T-Bills are quoted. Discount based on FACE VALUE of bond, rather than market price.
rBD: bank discount return
rBD = (D / F) * (360 / t)D = dollar discount, the difference b/w face value and purchase price
F = face value (par) of bond
t = number of days remaining until maturity
360 = bank convention of # days in year (market convention is 365)
BDY is not representative of return earned by an investor.
Holding period yield (HPY)
Same as HPR. Just using specific terms. The actual return an investor will receive if money market instrument is held until maturity.
HPY = (P1 - P0 + D1) / P0HPY = ((P1 + D1) / P0) - 1
Effective annual yield (EAY)
Annualized HPY on basis of 365-day year, incorporating effects of compounding.
EAY = (1 + HPY)^365/t - 1
HPY = (P1 - P0 + D1) / P0
HPY = ((P1 + D1) / P0) - 1
Money market yield (CD equivalent yield)
Annualized HPY based on price using 360 days (bank days). Does not account for effects of compounding—assumes simple interest.
rMM: money mkt return
rMM = HPY * (360 / # days)
Given the bank discount yield (rBD):
rMM = (360 * rBD) / (360 - (t * rBD))
Bond-equivalent yield (BEY)
2 * semiannual discount rate
HPY * (365/days to maturity)
Measurement scales (four)
Nominal: no particular order
Ordinal: relative ranking, ordered by assigned categories
Interval: relative ranking and equal distances (eg celcius)
Ratio: ranking and equal distance and true zero point (money)
NOIR
Mean (Arithmetic)
Sum of observation values / Number of observations
Arithmetic mean is best estimate of true mean and value of NEXT observation (eg next year’s return; use geometric mean for estimating multi-year returns). The sum of actual deviations from the arithmetic mean is ZERO.
Mean (Weighted)
Sum of (weight * observed value) of all observations
Mean (Geometric)
(1+observed value A * 1+observed value B * …)^[1/n], then - 1
ie the nth root of (observed value A * observed value B * …)
When calculating for returns, must add 1 to each value under the radical and then subtract 1 from the result.
Used for multiple periods or when measuring compound growth rates. Geometric mean return shows the rate that would have to be compounded over n periods to get the same observed returns. Preferred number to estimate multi-year returns (eg next 3 years).
Mean (Harmonic)
N / (1/observed value A + 1/observed value B)
Used for stuff like avg cost of shares over time.
Median
Midpoint of data set. If even number of observations, then it is the mean of the two middle observations.
Mode
Most occurring value. Can have unimodal, bimodal, trimodal, etc, if more than one value appears frequently.
Quantile
Value at or below which a states proportion of data lies.Ly = (n + 1) * (y/100)
y = percent
Eg, what is third quartile for 10 observations? It’s the point below which 75% of observations lie.
(10 + 1) * (75/100) = 8.25
Once you have the quartile, eg 2.8 (between funds 2 and 3) out of 13 funds, you can use linear interpolation to get the value of the quartile.
Approx. value of quartile ≈ X2 + (Computer quartile - y/100) × (X3 – X2),