Formulas / Maths

Question 1

How to calculate standard deviation

Answer 1

Return - Average ^2
Sum
Divide by N-1
Square Root

Question 2

How to calculate covariance?

Answer 2

ReturnX - AverageX
ReturnY - AverageY
Multiply the products together
Sum
Divide by N-1

Question 3

Calculate a stock’s beta

Given Covariance and SD

Answer 3

CovarianceSM / SDm^2

Covariance between share and market divided by variance (SD squared)

Question 4

How to annualise a figure

Returns over multiple years

Answer 4

((V1/V0)^1/n) -1

Question 5

How to annualise a figure

Compounds multiple times a year

Answer 5

((V1/V0)^n)-1

Question 6

How to calculate VaR?

Answer 6

Annualised Return - Confidence Interval * Standard Deviation

Question 7

How to calculate CVar?

Answer 7

Average of returns that exceed VaR

Question 8

How do you calculate downside deviation?

For the Sortino Ratio

Answer 8

1) Set a minimum absolute return (e.g. 1, 0 or the Risk free rate)
2) Subtract MAR from all negative returns
3) Square each return
4) Sum the returns
5) Divide returns by (n-1) (this is all counts, not just negative returns)
6) square root
7) Annualise if need be.

Question 9

What is the formula to calculate equity beta?

Given unlevered Beta of 1 company & debt to equity of another

Answer 9

Beta(1+(1-Tax Rate)(Debt/Equity)

Question 10

What is the money weighted rate of return

Answer 10

Also known as the IRR
Measures the total return from start to finish taking into account cash flows

Question 11

What is the time weighted rate of return

Answer 11

Ignores cashflows / timing of cashflows
Measures returns in sub-periods which end with a cash flow

Question 12

What is time weighted rate of return useful for?

Answer 12

Comparing manager skill

Question 13

What is money weighted rate of return useful for?

Answer 13

Understanding the actual investment reurn received.