Quant 1 Flashcards
Periodic rate (PR)
= Stated annual rate (SAR)/n
where n = number of periods
Effective annual yield (EAR)
= (1+PR)^n - 1
where n = number of periods –> so if quarterly basis then n=4
- To convert back to PR –> (1+EAR)^1/n –> multiplied by n = SAR
NPV & IRR implications
When NPV = 0, IRR = WACC or MCC
PV of perpetuity
PV = PMT / r
Holding period yield (HPY)
= (Change in value + income) / beginning value
OR
= (1+EAY)^t/365 - 1
Effective annual yield (HPY)
= (1+HPY)^365/t -1
Money market yield (rMM)
= HPY x (360/t)
OR
= (360 x BDY) / 360 -(t x BDY)
Bank discount yield (BDY)
= (Discount/Face value) x (360/t)
Continuous compounding
= eAPR -1
Signifies that as n increases the rate of increase in the EAR slows down (increasing at a decreasing rate)
Required rate of return (I/Y)
= Nominal RF + default risk premium + liquidity risk premium + maturity risk premium
Bond equivalent yield (BEY)
= 2 x semiannual yield
or
= HPY x (365/n)
Time weighted return
(1+HPY x 1+HPY+…)^1/n -1
- Reflects the compounded (geometric) growth rate and should be used if the PM doesn’t have control of the flow of money
- When calculating HPY a deposit = income and a withdrawal = debit
Money weighted return
= IRR of a portfolio -Use the CF function on the TI CF0 = starting value (negative) CF1 = Contribution (negative), withdrawal or dividend = positive CF end = positive value
Measure of location
L = (n+1) x(y/100)
where y = percentile given
Note - if L is not a whole number then –> LB + (1-y)x(UB - LB) where LB equals lower bound of two numbers L is in between
Mean absolute deviation (MAD)
= sum(abs(Actual - EV))/n
Population variance (σ2)
σ2= (sum(A-EV)^2)/N
Always use a z value when dealing with population variance and std deviation
Sample variance (s2)
s2=(sum(A-EV)^2)/(n-1)
where n-1 = degrees of freedom and as the value of n-1 increases t value gets closer to approximating z value
Chebysev’s inequality
1/(1/k^2)
Standard normal z distribution
\+/- 1σ = ~68% confidence interval \+/- 1.645σ = ~90% confidence interval \+/- 1.96σ = ~95% confidence interval \+/- 2.58σ = ~99% confidence interval \+/- 1σ = ~99.7% confidence interval
Sharpe ratio
(ER - RF)/σ portfolio
A measure of the excess return per unit of risk - so a higher value is better b/c it indicates you are achieving solid returns relative to risk
Kurtosis
Degree to which a distribution is peaked or not peaked
Note - does not impact the ER or mean
Leptokurtic
Kurtosis > 3 = positive excess kurtosis - more peaked and greatest risk due to fat tails
Platykurtic
Kurtosis
Mesokurtic
Kurtosis = 3 and lowest level of risk
Coefficient of variation
= σ/M or S/x
Note - the lower the better because you want to reduce the risk (numerator) and maximize returns (denominator)
Correlation coefficient (r)
r = COV(A,B)/(σA x σB)
If r = ~1 –> σ portfolio ~= ER portfolio
If r = 0 –> σ portfolio σ portfolio = 0
Coefficient of determination
= r^2
Covariance (COV)
COV(A,B) = r(σA x σB)
OR –> COV(A,B) = P1 x (RA1 - ERA1) x (RB1 - ERB1) + P2 x (RA1 - ERA1) x (RB1 - ERB1)
If COV is negative diversification benefits are maxed
If COV = 0 then diversification risk exist
If COV is positive then there are little to none diversification benefits
Variance of 2 Asset portfolio
σ2 = (wa^2 x σ2a) + (wb^2 x σ2b) + 2(wa x wb x σa x σb x r)
Probability odds
= Pe/(1-Pe)
Odds for -> 1 to 7 = 12.5% means the odds against are 7 to 1 = 87.5%
Combination vs. Permutation
Combination - sequence of events doesn’t matter
nCr = n!/(n-r)r! where n is always > r
Permutation - order does matter
nPr = n!/(n-r)!
