Quantitative (12%) Flashcards
P(AB)
P(A|B) * P(B)
P(A or B)
P(A) + P(B) - P(AB)
Probability
to
Odds
P(E)
—————
1 - P(E)
Expected Value
E(x)
Σxn*P(xn)
Weighted average of the possible outcomes of a random variable, where the weights are the probabilities that the outcomes will occur.
Degrees of Freedom
n - 1
Combination
n!
——————
(n - r)! r!
Permutation
n!
——————
(n - r)!
Percentile
(n + 1)*(y/100)
Money-Weighted
Rate of Return
The internal rate of return on a portflio, IRR
The rate of return where NPV = 0
Time-Weighted
Rate of Return
For periods less than one year
(1 + HPRn) - 1
For periods greater than one year (geometric mean)
(1 + HPRn)1/n - 1
geom always less than arith
The rate at which $1 compounds over time.
1.21903 [ENTER] 3 [1/x]
HPR
(P1 + D)
———— - 1
P
Harmonic Mean
1
———————
Σ(1/Pn)
Average cost of shares purchased over time.
(Dollar cost averaging)
Population Variance
Σ(x - µ)<span>2</span>
—————
n
Sample Variance
Σ(x - µ)<span>2</span>
—————
(n - 1)
MAD
Σ|x - µ|
—————
n
Z or T
(x - µ)
————
σ
Standard Deviation
σ
SQRT of the Variance (σ2)
SQRTσ2
Standard Error
σ
————
SQRTn
- in stats the sample mean deviates from the population mean. This deviation is the standard error.
Z Score for 90%
1.65
Mean+-1.65σ
Z Score for 95%
1.96
Z Score for 99%
2.58
Confidence Interval
X(+/-) Zσ
or
X(+/-) Z(Standard Error)
7 Steps in
Hypothesis Testing
- State hypothesis
- Select test statistic
- Specify level of significance
- State decision rule
- Collect sample, calculate sample statistic
- Make a decision based on hypothesis
- Make a decision based on results
Hypothesis Test Statistic
(x - H0)
————————
Standard Error
Coefficient of Variation
CV
S
———
X
Excess risk per unit of return.
(Lower is better)
Sharpe Ratio
E(Rp) - Rrf
——————
σp
Excess return per unit of risk.
(Higher is Better)
Chebyshev’s Inequality
The percentage of observations that lie within k standard deviations of the mean is at least
1 - 1/k2
for all k > 1 regardless of the shape of the distribution.
Roy’s Safety First Criterion
E(Rp) - RL
——————
σp
Probability that the portfolio expected return E(Rp) will be greater than the threshold RL.
(Higher is Better)
APR to EAR
(1 + APR/n)n - 1
EAR to APR
[(1 + EAR)1/n- 1]n
EAR to HPR
(1 + EAR)n/365 - 1
HPR to EAR
(1 + HPR)365/n - 1
HPR to r<span>mm</span>
HPR(360/n)
EAR with
Continuous Compounding
er - 1
or
(rex - 1)
Perpetuity
PMT
P = ———
r
What does it mean to be a discrete distribution?
finite number of outcomes.
IE. rolling a dice.
What is a univariate distribution?
distribution between 1 variable.
What is the multivariate distrbution? Explain how it can be both continuous and discrete?
probabilities between a group of variables. The behaviour of one variable is tied into the other.
- When discrete you can explain probability using joint prob tables.
- When continuous use normal distribution.
What is the binomial distribution?
- Also called bernoulii experiment.
- discrete prob distribution in which yes/no experiements each of which has prob p
Describe properties of the central limit theorem.
- sample size is large, n>30
- mean of population, and mean of sample are equal
- variance = σ2/n
When do you use t vs. z stat?
When sampl from small sample large sample
Normal dis, known σ2 z-stat t-stat
Normal, unknown σ2 t-stat t-stat*
nonnormal, known σ2 N/A z-stat
nonnormal, unknown σ2 N/A t-stat*
- z-stat theoretically works, but t-stat more conservative.
- NO test, if non-normal, variance unknown, and small.
A low put/call ratio is a sign of what type of mkt?
bullish
What is subjective probability?
What is joint probability?
What is empirical probability?
What is conditional probability?
probability based on judgement.
prob that two or more events happen concurrently.
prob calced based on historical data.
prob of one happening given the other occurs.
What is the sampling error?
sampling error of mean = sample mean - pop mean
x - ü
Desirable properties of estimators should be?
- unbiased
- expected value =parameter you are trying to estimate
- efficient
- if varince of unbiased estimator is smaller than all other unbiased estimators or parameters you are trying to esimate.
- consistent
- accuracy of sample size increases as sample size increases. As sample size increases, SE approaches 0.
What do total capitalized costs include?
fixed production costs, direct conversion costs of material and labor, and storage costs part of production. Do not include waste costs.
When is DPS antidilutive?
When it exceeds EPS. If it does then you use EPS.
Cash flow debt coverage ratio?
CFO/total debt
Interim report?
Interim reports, either quarterly or semi-annual, contain updated information on a company’s performance and financial position since the last annual report.
Impairment using IFRS
Under IFRS, an asset is considered to be impaired when its carrying amount exceeds its recoverable amount (the higher of fair value less cost to sell or value in use).
Fair value less costs to sell: 480,000 – 50,000 = 430,000 Value in use = 440,000 Recoverable amount (higher value of the above two amounts) = 440,000 Impairment loss under IFRS = Carrying value (net book value) – recoverable amount Impairment loss = 500,000 – 440,000 = C$60,000
double declining balance
2*SL rate
*do not take out residual value, yo.
longitudal data?
observations over time of multiple characteristics of same entity (GDP, unemployement), over 10 years
panel data
multiple characteristics, multiple companies, over time.
p value
smallest level of significance in which hypothesis can be rejected.
standard deviation
You can do in calc.
SE= Divide this by sqrt n
FV of continuous compounding?
PV * Er*t
Nominal rate =?
RFR+inflation premi + risk premiums (default, liquidity, maturity pref)
Two populations, variances equal, What is the t-stat to determine whether two population means are equal?
(
