# FRM Level 2 Formulas – Market Risk Measurement and Management

## Introduction

We present the formulas for the Market Risk Measurement and Management segment.

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## Value at Risk, VaR

VaR  =   −μ + ( σ * Zscore )

or

VaR  =   μ − ( σ * Zscore )

## Sharpe Ratio

= (Rp – Rf) / σp

Where:

Rp   Portfolio Return

Rf    Treasury-Bill Returns (or the Risk-Free Rate)

σp    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

## Portfolio Beta

A portfolio’s beta using the respective weightings:

Portfolio beta = w1R1 + w2 R2 + w3 R3

## Portfolio Expected Return

= Rf + R(Rm – Rf)

## Hedging Relationships

FaceR  =  –  FN  X   (DV01N  / DV01R)  X  β

Where:

N is the Core

R is the Hedge

## Correlation for two assets ‘A’ and ‘B’

Correlation coefficient = CovarianceAB / [(Standard deviationA x Standard deviationB)]

Also:

Correlation coefficient =  ( Coefficient of determination ) ½

## Covariance for two assets ‘A’ and ‘B’

CovarianceAB = (Correlation coefficient) x [(Standard DeviationA x Standard DeviationB)]

## The Vasicek Model

dr  =  sdW

dr = [ k * ( q – r ) * dt ] + sdw

## Binomial Distribution

Binomial Distribution of Exceedances = ( x – pT ) / [ p ( 1 – p )T ] ½

Where:

T is the amount of trading days in the year

x is the amount of exceedances

## Forward Pricing

P( T* + T ) =  P(T*)  X  F( T* , T)