1. Notional Amount Approach

2. Price Sensitivity Measures

3. Value at Risk (VaR)

(Measures of Market Risk)

Notional Amount Approach

What is it, and what are the Pros/Cons?

What it is:  The total underlying value of all securities

     ie. one option on 100 stocks, the notional amount is the value of 100 stocks)

Pros: 

• Simple

Cons:

• doesn't reflect the fact that different assets have different volatilities
• Doesn't reflect correlation risk
• Doesn't differentiate between long and short positions that might cancel eachother out (ie. hedging)

(Measures of Market Risk)

Price Sensitivity Measures

What is it, and what are the pros & cons?

What it is:  measures how sensitive a portfolio/security it is to changes in the pricing inputs; the Greeks

     ie. how does a 1% change in YTM affect the price of a bond?

Pros:

• Help traders monitor market positions
• Universal, easy(ish) to understand 

Cons:

• Reflect only partial measures of risk (partial derivatives)
• Not additive across price sensitivity groups (cannot obtain an overall measure of risk by adding them)

(Measures of Market Risk)

Value at Risk (VaR)

What is it and what are the pros/cons?

VaR calculates the worst expected loss over a given time horizon, at a given confidence interval, under normal market conditions

(Measures of Market Risk)

VaR

What are the 3 ways to calculate VaR?

1. Analytical (Parametric) VaR

2. Historical Simulations VaR

3. Mone Carlo Simulations VaR

(Measures of Market Risk)

VaR

What is the Formula for Parametric VaR?

(Measures of Market Risk)

Parametric VaR

What is the formula for the VaR of multiple securities?

(Measures of Market Risk)

Analytical (Parametric) VaR

What are the pros & cons of Parametric VaR?

Pros:

• Simplest method of computing VaR
• Easy to implement for a portfolio
• No pricing model Requires
• Easy to handle incremental Var

Cons:

• Assums normality of portfolio return
• not good for securities with non-linear payoffs
• If historical series have heavy tails then VaR will be over or under estimated (based on right or left tail)
• Requires estimations of volatilities and correlations
• Cannot be used to conduct sensitivity analysis
• Cannot be used to derive confidence interval for VaR

(Measures of Market Volatility)

Historical VaR

What is it?

What it is:

1st, calculates the returns of all assets in portfolio between a specific historical time period

2nd, the returns are then applied to current prices

(Measures of Market Volatility)

Historical VaR

What are the Pros & Cons?

Pros:

• No assumption on return distribution
• no need to estimate volatilities or correlations
• fat tails & extreme events captured if occured in data
• Measure can be aggregated across markets
• Allows calculation of confidence intervals of VaR

Cons:

• It completely relies of historical datasets
• Cannot accommodate changes in market structure
• may not be computationally efficient when there is a large number of instruments or they are complex
• cannot easily handle sensitivity analysis
• no theoretical foundation on the historical data

(Measures of Market Volatility)

VaR - Monte Carlo Simulations

What are they?

(Measures of Market Volatility)

VaR - Monte Carlo Simulations

What are the Pros & Cons?

Pros:

• Can accommodate any distribution of risk factors
• Can be used to model any complex portfolio
• Allows calculation fo confidence intervals for VaR
• Allows to perform sensitivity analysis and stress testing

Cons:

• Outliers are not incorporated into the distribution
• Computationally intensive

Stress tests & scenario analysis help us analyze the possible effects of extreme events that lie outside normal market conditions-

Purpose is to determine size (no frequency) of potential losses due to specific events

Evaluating portfolio vulnerabilities to a variety of extreme events

identifying unique vulnerabilities in the portfolio

Scenarios based on arbitrary combination of stress shocks, though many may be ruled out due to inconsistencies with the basic laws of economics

no theoretical foundation for the combination fo stress shocks

stress tests are static in nature, but market crises are dynamic