Estimated reading time: 3 minutes

## Preface

Below are FRM formulas for the level 1 Foundations of Risk Management segment.

You may download all our level 1 and 2 formulas **free of charge** on our website:

Please click here for our shop page.

## Correlation coefficient between two Securities:

Correlation coefficient =

(Covariance between Security A and Security B) /

(Standard Deviation of Security A * Standard Deviation of Security B)

## Variance of Two Securities

Variance =

(Weight_{A})^{2} * (Standard Deviation of A)^{2 } **+**

(Weight_{B})^{2} * (Standard Deviation of B)^{2} **+**

(2 * Correlation Coefficient_{AB} * Standard Deviation of A * Standard Deviation of B * Weight_{A} * Weight_{B })

## Perfect Positive Correlation

ρ = 1

## Perfect Negative Correlation

ρ = -1

## Standard Deviation

= (Variance)^{1/2}

## Risk Adjusted Ranking

Based on the Morningstar Rating System, an investment fund’s risk adjusted ranking may be calculated by:

(Fund Return / Average Peer Return ) – (Fund Risk / Average Peer Risk)

## Sharpe Ratio

= (R_{p} – R_{f}) / σ_{p}

Where:

R_{p }is the Portfolio Return

R_{f }is the Treasury-Bill Returns (or the Risk Free Rate)

σ_{p }is the Portfolio Standard Deviation of Return

## Sortino Ratio

= (Return on Portfolio – Minimum Accepted Return)** / **Standard Deviation of Returns Below Minimum Accepted Return

## Treynor Measure

= (Return on Portfolio – Risk free rate) / Portfolio Beta

## Jenson’s Alpha

= Return on Portfolio – CAPM predicted Return

## Information Ratio

= (Return on Portfolio – Benchmark Return) / Tracking Error

## A portfolio’s beta using the respective weightings:

Portfolio beta = w_{1}R_{1} + w_{2} R_{2} + w_{3} R_{3}

## Portfolio Expected Return

= R_{f} + R(R_{m} – R_{f})

## Expected Return

## Capital Asset Pricing Model, CAPM

We recall the CAPM formula:

Expected Return, ER = R_{f} + β*(R_{m} – R_{f})

Now the part of the formula “(R_{m} – R_{f})” is actually termed the “risk premium”

Thus, expected return on the security will be:

= Risk Free Rate + [ Security’s Beta *( Equity Risk Premium) ]

## Adjusted Exposure

= Outstandings + (Unused Portion of Commitments) * Usage Given Default

## Expected Loss

= AE * EDF * LGD

Where:

AE is the Adjusted Exposure

EDF is the Probability of Default

LGD is the Loss Given Default = ( 1 – Recover Rate %)

## Expected Loss is defined as:

Exposure * (1 – Recovery Rate) * (Probability of Default)

## Basis

Basis = Spot price of hedged asset – Futures price of contract.

## Market Coefficient of Variation

Market Coefficient of Variation = Standard Deviation of Market / Market Expected Return

## Standard Deviation of Market

Standard Deviation of Market = Market Coefficient of Variation * Market Expected Return

## Standard deviation of a two-stock portfolio

Standard deviation of a two-stock portfolio, we may use the formula:

s = [W_{A}^{2}σ_{A} ^{2} + W_{B} ^{2}σ_{B} ^{2} + 2W_{A}W_{B}σ_{A}σ_{B}r_{A,B}]^{1/2}

## Correlation Coefficient

For two assets ‘A’ and ‘B’

Correlation coefficient = Covariance_{AB} / [(Standard deviation_{A} * Standard deviation_{B})]

Rearranged, we have:

Covariance_{AB} = (Correlation coefficient) * [(Standard Deviation_{A} * Standard Deviation_{B})]

## Covariance

Covariance_{AB} = (Correlation coefficient) * [(Standard Deviation_{A} * Standard Deviation_{B})]

## Total Risk

Total Risk = Market Risk + Firm Specific Risk

or

Total Risk = Systematic Risk + Unsystematic Risk

Note:

Market risk can also be called Systematic risk or Undiversifiable risk

Firm Specific Risk can also be called Unsystematic risk

## Expected Return

Expected Return = Stock’s Alpha + (Stock’s Beta * % Market Movement)

## Excess Return

Excess Return = Expected Return – Risk Free Rate

## Correlation Coefficient

Correlation coefficient and covariance of two assets ‘A’ and ‘B’

Correlation coefficient = Covariance_{AB} / (Standard deviation_{A} * Standard deviation_{B})

## Standard Deviation of Market

Standard Deviation of Market = Market Coefficient of Variation * Market Expected Return

## Beta

The calculation of beta on a given Security A and the market

Beta = Covariance between Security A & the Market / Variance of Market Return

## Value at Risk

The Value at Risk (risk adjusted) performance measure can be stated as follows:

( Portfolio Return – RFR ) / (Portfolio Value at Risk / Initial Portfolio Value )

Where RFR = Risk Free Rate

## Capital Markets Line

The Capital Markets Line is from the given equation:

R_{F} + [E(R_{M}) − R_{F}] / σ_{M}

Where:

Intercept = R_{F}

Slope = [E(R_{M}) − R_{F}] / σ_{M}

## Expected Residual Return

Expected Residual Return = Information Ratio * Residual Risk

## Covariance for Markets A and B

Covariance formula for Markets A and B:

Cov (A, B) = β_{A,1} β_{B,1} σ^{2}_{F1} + β_{A,2} β_{B,2} σ^{2}_{F2} + (β_{A,1} β_{B,2} + β_{A,2} β_{B,1}) * Cov (F_{1}, F_{2})

## Equation of a Straight Line

The equation of a straight line: y = m(x) + c, also expressed as:

Y = Slope (x) + Intercept

## Summary

We hope that this post was useful! It’s the first in a series we have lined up.

Also, whenever you are ready, try the following links for more information:

Happy studying,

The QuestionBank Family