Quant 1

Question 1

Periodic rate (PR)

Answer 1

= Stated annual rate (SAR)/n

where n = number of periods

Question 2

Effective annual yield (EAR)

Answer 2

= (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

Question 3

NPV & IRR implications

Answer 3

When NPV = 0, IRR = WACC or MCC

Question 4

PV of perpetuity

Answer 4

PV = PMT / r

Question 5

Holding period yield (HPY)

Answer 5

= (Change in value + income) / beginning value
OR
= (1+EAY)^t/365 - 1

Question 6

Effective annual yield (HPY)

Answer 6

= (1+HPY)^365/t -1

Question 7

Money market yield (rMM)

Answer 7

= HPY x (360/t)
OR
= (360 x BDY) / 360 -(t x BDY)

Question 8

Bank discount yield (BDY)

Answer 8

= (Discount/Face value) x (360/t)

Question 9

Continuous compounding

Answer 9

= eAPR -1

Signifies that as n increases the rate of increase in the EAR slows down (increasing at a decreasing rate)

Question 10

Required rate of return (I/Y)

Answer 10

= Nominal RF + default risk premium + liquidity risk premium + maturity risk premium

Question 11

Bond equivalent yield (BEY)

Answer 11

= 2 x semiannual yield

or

= HPY x (365/n)

Question 12

Time weighted return

Answer 12

(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

Question 13

Money weighted return

Answer 13

= 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

Question 14

Measure of location

Answer 14

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

Question 15

Mean absolute deviation (MAD)

Answer 15

= sum(abs(Actual - EV))/n

Question 16

Population variance (σ2)

Answer 16

σ2= (sum(A-EV)^2)/N

Always use a z value when dealing with population variance and std deviation

Question 17

Sample variance (s2)

Answer 17

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

Question 18

Chebysev’s inequality

Answer 18

1/(1/k^2)

Question 19

Standard normal z distribution

Answer 19

\+/- 1σ = ~68% confidence interval 
\+/- 1.645σ = ~90% confidence interval 
\+/- 1.96σ = ~95% confidence interval 
\+/- 2.58σ = ~99% confidence interval 
\+/- 1σ = ~99.7% confidence interval

Question 20

Sharpe ratio

Answer 20

(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

Question 21

Kurtosis

Answer 21

Degree to which a distribution is peaked or not peaked

Note - does not impact the ER or mean

Question 22

Leptokurtic

Answer 22

Kurtosis > 3 = positive excess kurtosis - more peaked and greatest risk due to fat tails

Question 23

Platykurtic

Answer 23

Kurtosis

Question 24

Mesokurtic

Answer 24

Kurtosis = 3 and lowest level of risk

Question 25

Coefficient of variation

Answer 25

= σ/M or S/x

Note - the lower the better because you want to reduce the risk (numerator) and maximize returns (denominator)

Question 26

Correlation coefficient (r)

Answer 26

r = COV(A,B)/(σA x σB)

If r = ~1 –> σ portfolio ~= ER portfolio
If r = 0 –> σ portfolio σ portfolio = 0

Question 27

Coefficient of determination

Answer 27

= r^2

Question 28

Covariance (COV)

Answer 28

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

Question 29

Variance of 2 Asset portfolio

Answer 29

σ2 = (wa^2 x σ2a) + (wb^2 x σ2b) + 2(wa x wb x σa x σb x r)

Question 30

Probability odds

Answer 30

= Pe/(1-Pe)

Odds for -> 1 to 7 = 12.5% means the odds against are 7 to 1 = 87.5%

Question 31

Combination vs. Permutation

Answer 31

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)!