Quants Flashcards
Bank Discount Yield formula
= (D/F) * (360/T)
Geometric Mean formula
= (1+R1)(1+R2)(1+Rn…) [yx] n [1/x] - 1
P(AorB) formula
= P(A) + P(B) - P(AB)
P(A/B) formula
= P(AB) / P(B)
P(AB) formula - dependent events
= P(A/B) * P(B)
P(AB) formula - independent events
= P(A) * P(B)
“compound rate of return of the portfolio” aka…
geometric mean
“portfolio average return” aka…
geometric mean
Bayes formula
Updated Probability of Event Given Info = (Prob of Info Given Event / Unconditional Prob of New Info) * Prior Prob of Event
Money Weighted Return is sensitive to…
the additions and withdrawals of funds over the course of the investment
HPR formula
= Ending-Beginning / Beginning
MWR formula
= IRR
empirical probability
probability estimated from data as a relative frequency of occurrence
subjective probability
probability drawing on personal/subjective judgement
priori probability
probability obtained based on logical analysis
Bayes formula - P(Event/Info)
= P(Event/Info) = [ P(Info/Event) / P(Info) ] * P(Event)
coefficient of variation (CV) formula
= sd / mean
permutation formula
nPr = n! / (n-r)!
order DOES matter
the arithmetic sum of deviations around the mean will always…
equal zero
the mean absolute deviation will always…
be less than or equal to the standard deviation
Time Weighted Return TWR
= (1+HPR1)(1+HPR2)(1+HPRn…) - 1
Effective Annual Rate (EAR) formula
= (1+periodic rate)^m - 1
periodic rate is stated annual rate divided by # of compounding periods (m)
if the P-value is less than the specified level of significance…
the null hypothesis is rejected
P-values are never…
negative
t-test statistic formula
= (d-h) / (sd/square root of n)
where d= the mean difference, h= hypothesized difference of the means
Z statistic formula
= (h-mu) / popSD
where h= hypothetical value. then use Z to find probability of a Z value. If negative, 1-P(Z)
discrete random variable
a random variable that can take on at most a countable number of possible values. ex. number of days
continuous random variable ex.
percentage changes, returns
a statistically significant result might not be…
economically meaningful after accounting for risk, transaction costs, and taxes
Central Limit Theorem
given a pop that has finite variance and large sample size, the distribution of the sample will be normal, will have a mean equal to the pop mean, and will have a variance equal to the pop variance
central limit theorem holds without regard to…
the distribution of the underlying pop
Standard Error of the Sample Mean formula
= sd/square root of n
Confidence Interval for the Pop Mean formula
= X bar +/- t (sd/square root of n)
do not divide t by 2
Type II Error
double negative. fail to reject the null
Type 1 Error
reject a true null
if the P-value exceeds the stated level of significance…
the null hypothesis cannot be rejected
Resistance
a price range in which selling activity is sufficient to stop the rise in price
Support
low price range in which buying activity is sufficient to top the decline in price
change in polarity
refers to support, when breached, becomes resistance; resistance, when breached, becomes support
as the degree of confidence is increased…
the confidence interval becomes wider. a larger sample size decreases the width of the confidence interval
use Z-statistic when…
sample has normal distribution with known variance. does NOT use degrees of freedom
nonparametric tests
primarily concerned with ranks, signs, or groups
Bollinger Bands
price volatility
