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VaR can be defined as the worst loss that can happen under normal market conditions over a

specified horizon at a specified confidence interval level

LTCM use VaR, not only to report and compare risk, BUT as the basis to set minimum equity capital

The parameters must be chosen so that the probability of exceeding VaR is very low

Limits of VaRDefinition of Value at Risk

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VaR assumes same normal distribution for all assets types BUT financial assets do not exhibit normal

distribution.

- Stock markets: left skewed and fat tails

- The event far away from the mean would happen more often than the normal distribution

suggests

Limits of VaRVaR Assumption: Asset price follows a Normal Distribution

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Specified horizon should correspond to the period required to raise additional funds

VaRsspecified horizon used to set the amount of equity capital was a 10-day horizonsame as

Commercial banks (closely supervised by regulators)

The 10-day horizon was clearly insufficient for LTCM, especially when additional capital will be

needed precisely after the fund suffers a large loss.

Limits of VaRLTCM VaR specified horizon

same as Commercial Bank

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LTCM the portfolio [is] managed so that its target risk [is] no larger than the risk of an unleveraged

position in the S&P 500.

Beginning of 1998 - Fund Capital $4.8 billion - Daily dollar volatility $45 million

$45 $4.8

250

14.82%

The annual average volatility of S&P500 during 1978-1997 was 15%.

Limits of VaRLTCM VaR volatility: constant at market risk level

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LTCM the portfolio [is] managed so that its target risk [is] no larger than the risk of an unleveraged

position in the S&P 500.

What about liquidity risk?

LTCM overlooked the correlation and impact of volatility

Liquidity risk and solvency risk is not factored into VaR models as they assume that normal

market conditions will prevail.

VaR models have underestimated the probability of severe losses.

Traditional VaR methods assume that the fund is a price-taker

Limits of VaRLTCM VaR volatility: under normal market conditions