Quant

Question 1

coefficient of variation

Answer 1

CV = (σ/mean) –> standard deviation / mean

Express how much dispersion exists relative to the mean and allow for comparison of dedree of dispersion

Choose investment with lower CV

Question 2

calc a confidence interval

Answer 2

step 1 - calc the standard error of the mean = standard deviation / sq rt of the sample size

step 2 - calc confidence interval

This is the confidence interval range.

1. 645 for 90% confidence intervals (the significance level is 10%, 5% in each tail).
2. 960 for 95% confidence intervals (the significance level is 5%, 2.5% in each tail).
3. 58 for 99% confidence intervals (the significance level is 1%, 0.5% in each tail).

Step 3 calc the confidence interval. For example, mean of 25, w 95% conficence interval, standard error is 2

Sample Mean +/- (standard error * 1.96)

Lower tail: 25 - (2 * 1.96) = 21.08
Upper tail: 25 + (2 * 1.96) = 28.92

Question 3

Money Weighted Return

Answer 3

Concept here is you’re looking for IRR based on cash into (+ buys) and out of (- divds and sells) of the account.

Use cash flow function on calculator.

Question 4

Time Weighted Return

Answer 4

Concept here is this is the geometric mean of each holding period return. Time weighted is not affected by the timing of cashflows

step 1 - calc holding period return for each period.
([price + divd) / purchase price] - 1

step 2 - use geometric mean to get TWR
When calculating the geometric mean for a returns data set: (1+R1) * (1+R2) * (1+Rn)^1/n

The time-weighted rate of return is the preferred method of performance measurement, because it is not affected by the timing of cash inflows and outflows.

Question 5

How to Calc Continuous Compound Returns - Given a $ amount or Rate

Answer 5

Use LN button on calculator

If given $ amount –> ln(price/purchase price)
e.g. LN(120/100) = LN(1.20) = .1823 = 18.23%

If given a rate –> ln(1+rate)
e.g. rate is 20% = ln(1+.20) = .1823 = 18.23%

Question 6

Describe unbiased, consistent and efficient estimators.

Answer 6

An unbiased estimator has an expected value equal to the true value of the population parameter.

A consistent estimator is more accurate the greater the sample size.

An efficient estimator has the sampling distribution that is less than that of any other unbiased estimator.

Question 7

Covariance of a 2 security portfolio

Answer 7

Sum of: [(return on Asset 1 in period t - mean return on Asset 1) * (return on Asset 2 in period t - mean return on Asset 2)] / # of periods

Covariance measures the extent to which two variables move together over time. Same rules as correlation

Question 8

Correlation of 2 stock portfolio

Answer 8

Remember correlation symbol looks like a little p

= covariance of asset 1 & 2 / (standard deviation of asset 1 * standard deviation of asset 2)

Note covariance can then be expressed as: = correlation * standard deviation of asset 1 * standard deviation of asset 2)

Question 9

Calc the variance and standard deviation of a portfolio

Answer 9

variance = (weigh of asset 1^2 * variance of asset 1) + (weigh of asset 2^2 * variance of asset 2) + 2 * weight of asset 1 * weight of asset 2 * the covariance of asset 1 & 2.

Note: the covariance of asset 1&2 is also = correlation of asset 1&2 * standard deviation of asset 1 * standard deviation of asset 2

Note: the variance of asset 1 is the standard deviation of asset 1^2. think of the symbols.

Standard Deviation of the Portfolio = square root of the portfolio variance.

Question 10

steps for hypothesis testing

Answer 10

1 - Stating the hypotheses.
2 - Identifying the test statistic and its probability distribution.
3 - Specifying the significance level.
4 - Stating the decision rule.
5 - Collecting the data and performing the calculations.
6 - Making the statistical decision.
7 - Making the economic or investment decision.

Question 11

covariance of 2 stock

Answer 11

first calc the mean return for both

covariance = sum of: {(return on X period 1 - Mean of X) * (return on y period 1 - mean of y)] + {(return on X period 2 - Mean of X) * (return on y period 2 - mean of y)] / (n - 1)

Question 12

The effective annual rate, based on continuous compounding for a stated annual rate of %, can be calculated from the formula:

Answer 12

effective annual rate = e^x [calc button] - 1

Based on a stated rate of 10%, the effective rate with continuous compounding is .1 (2nd LN for e^x] - 1 = .10517 or 10.517%.

Question 13

what does the “sampling error” represent?

Answer 13

The difference between the true population parameter (i.e. mean index return) you’re trying to estimate and the sample statistic calculated is called the sampling error. The arithmetic mean is the appropriate estimator of the next period’s return.

Question 14

Geometric Mean

Answer 14

DON’T FORGET TO MINUS THE 1. The geometric mean is always less than or equal to the arithmetic mean. The only time the two means will be equal is when there is no variability in the observations.

frequently used to average rates of change over time or to compute the growth rate of a variable. we frequently use the geometric mean to average a time series of rates of return on an asset or a portfolio, or to compute the growth rate of a financial variable such as earnings or sales.

Rg = {[(1+R1) * (1+R2) * (1+Rn)] ^ 1/n} - 1

The greater the variability of returns, the greater the difference between this and arithmetic mean. Arithmetic mean will always be greater

Question 15

F - test

Answer 15

Used to compare the variances of 2 populations

Question 16

Define a Type I Error

Answer 16

Rejecting the a true null. The probability of this is the significance level. You’re 95% confident the bull is false, so your 5% significance is that the null is true

Question 17

The II error

Answer 17

Failing to reject the null when it is false

Question 18

Power of the test

Answer 18

The probability of correctly rejecting the null

Question 19

P value

Answer 19

The smallest level of significance at which the null can be rejected. The smaller the p-value, the stronger the evidence against the null.

Question 20

Bayes Formula

Answer 20

Used to update probability given new info.

P (Event | New Info) = {P (New Info | Event) / (New Info)} * P(Event)

Question 21

Z score

Answer 21

(Observation - population mean) / standard deviation

Question 22

Continuous compounding

Answer 22

Continuously compounded rate from stated rate:
= ln(S1/So) # ln (1+HPR)

Effective annual rate from continuously compounded rate:
= e^r - 1

OR

deposits 2,000 into an account that pays 6% per annum compounded continuously. Value after 4 years is

.06 * 4 2nd e^x * 2000 = 2,542.25

Question 23

cross sectional data

Answer 23

Data on some characteristics of multiple companies at a single point in time are cross-sectional data.

Question 24

Monte Carlo Simulation

Answer 24

Monte Carlo simulation is better suited to hypothetical “what if” analysis than historical simulation. Monte Carlo simulation is not an analytical method that can provide great insights into cause and effect relationships.

Monte Carlo simulation is used to:

• Value complex securities.
• Simulate the profits/losses from a trading strategy.
• Calculate estimates of value at risk (VaR) to determine the riskiness of a portfolio of assets and liabilities.
• Simulate pension fund assets and liabilities over time to examine the variability of the difference between the two.
• Value portfolios of assets that have non-normal returns distributions.

Question 25

Statistically significant vs economically meaningful.

Answer 25

A statistically significant result might not be economically meaningful after an analyst accounts for the risk, transaction costs, and applicable taxes.

Question 26

standardize a random vairable

Answer 26

X - mean of X / standard deviation of x

this is the z formula z = (x - u) / standard deviation

Question 27

Test statistic

Answer 27

(sample mean - pop mean) / standard error

Standard error is standard deviation / square root of sample size