Equity Stock Markets: Concepts, Instruments, Risks andDerivatives
Week 05 – Summary
Value-at-Risk
Value at Risk is a statistical method to quantify the level of financial risk (i.e., the maximum
potential loss) associated with any financial asset over a specified time frame. It is built around
the fundamental concepts in statistics of ‘normal distribution’ and ‘standard deviation’.
There are three methods to compute Value at Risk.
1. The Monte Carlo simulations (Based on hypothetical historic data)
2. The parametric model (which does not require data)
3. Historical Simulation (also refers to as “non-parametrical model” which is based
entirely on historic data)
The most commonly used VaR model is ‘Historic Simulation’.
Based on historic data and the day-to-day variation in that data, say for the last one year, the
average price (mean μ) as well as the standard deviation (σ) for the same one year period are
computed.
The daily volatility would be based on standard error as
, Equity Stock Markets: Concepts, Instruments, Risks and Derivatives
Prof. P C Narayan
Week 5
Where ‘n’ is the number of days/weeks/fortnight considered for the computation
At 95% confidence level:
The maximum value would be = μ + 2σ
The minimum value would be = μ – 2σ
At 99% confidence level:
The maximum value would be = μ + 3σ
The minimum value would be = μ – 3σ
This method is extensively used by financial institution to value their portfolio of loans and
investment, to determine the maximum likely loss in the event prices, interest rates and
exchange rates vary by 3 (+ or -) for each asset.
Shortcomings of VaR:
1. The assumption of ‘normality’ in the movements of prices, interest rate and exchange
rate in the market.
2. During times of extreme volatility, the Value at Risk model could fall terribly short
when estimating potential losses, because of the ‘normality’ assumption.
© All Rights Reserved. This document has been authored by Professor P C Narayan and is permitted for use only within the course "Equity
Stock Market: Concepts, Instruments, Risks and Derivatives" delivered in the online course format by IIM Bangalore. No part of this document,
including any logo, data, illustrations, pictures, scripts, may be reproduced, or stored in a retrieval system or transmitted in any form or by any
means – electronic, mechanical, photocopying, recording or otherwise – without the prior permission of the author.
Week 05 – Summary
Value-at-Risk
Value at Risk is a statistical method to quantify the level of financial risk (i.e., the maximum
potential loss) associated with any financial asset over a specified time frame. It is built around
the fundamental concepts in statistics of ‘normal distribution’ and ‘standard deviation’.
There are three methods to compute Value at Risk.
1. The Monte Carlo simulations (Based on hypothetical historic data)
2. The parametric model (which does not require data)
3. Historical Simulation (also refers to as “non-parametrical model” which is based
entirely on historic data)
The most commonly used VaR model is ‘Historic Simulation’.
Based on historic data and the day-to-day variation in that data, say for the last one year, the
average price (mean μ) as well as the standard deviation (σ) for the same one year period are
computed.
The daily volatility would be based on standard error as
, Equity Stock Markets: Concepts, Instruments, Risks and Derivatives
Prof. P C Narayan
Week 5
Where ‘n’ is the number of days/weeks/fortnight considered for the computation
At 95% confidence level:
The maximum value would be = μ + 2σ
The minimum value would be = μ – 2σ
At 99% confidence level:
The maximum value would be = μ + 3σ
The minimum value would be = μ – 3σ
This method is extensively used by financial institution to value their portfolio of loans and
investment, to determine the maximum likely loss in the event prices, interest rates and
exchange rates vary by 3 (+ or -) for each asset.
Shortcomings of VaR:
1. The assumption of ‘normality’ in the movements of prices, interest rate and exchange
rate in the market.
2. During times of extreme volatility, the Value at Risk model could fall terribly short
when estimating potential losses, because of the ‘normality’ assumption.
© All Rights Reserved. This document has been authored by Professor P C Narayan and is permitted for use only within the course "Equity
Stock Market: Concepts, Instruments, Risks and Derivatives" delivered in the online course format by IIM Bangalore. No part of this document,
including any logo, data, illustrations, pictures, scripts, may be reproduced, or stored in a retrieval system or transmitted in any form or by any
means – electronic, mechanical, photocopying, recording or otherwise – without the prior permission of the author.
