Formulas

Question 1

Cash Dividends

Answer 1

close price - dividend value

Question 2

Stock dividends/stock splits

Answer 2

close price/number of shares increase

Question 3

VWAP

Answer 3

sum(prices x price volumes) / sum(volumes)

Question 4

TWAP

Answer 4

sum(prices x time duration of prices) / sum(total time duration)

Question 5

Implementation Shortfall

Answer 5

(Execution Price - Benchmark Price) x Quantity

Question 6

Simple return

Answer 6

p(t) - p(t-1) / p(t-1) = (p(t) / p(t-1)) - 1

Question 7

Log return

Answer 7

log(p(t)) - log(p(t-1))

Question 8

Simple to log

Answer 8

log(1 + simple value)

Question 9

Log to simple

Answer 9

(e^log return) - 1

Question 10

Simple aggregate return

Answer 10

product(returns + 1) - 1

Question 11

Log aggregate return

Answer 11

sum(returns)

Question 12

Sharpe

Answer 12

mean(returns - interest rate or risk free rate) / sd(return - risk free rate)

Question 13

Information

Answer 13

mean(returns - benchmark returns) / sd(returns - benchmark returns)

Question 14

Sortino

Answer 14

mean(return - MAR) / downside deviation(return, MAR)

Question 15

Maximum Drawdown

Answer 15

Maximum loss from peak to trough.

Question 16

Calmar Ratio

Answer 16

Final cumulative result / maximum drawdown.

Question 17

Simple Moving Average

Answer 17

sum(prices) / n

Question 18

Weighted Moving Average

Answer 18

sum(prices x weights) / sum(weights)

Question 19

Exponential Moving Average

Answer 19

EMA(t) = (SmoothingFactor x price) + (1 - SmoothingFactor) x EMA(t - 1)

Question 20

Smoothing Factor

Answer 20

2 / n+1

Question 21

Combinations

Answer 21

n! / r! x (n-r)!