VaR & ES for Pension Funds vs. Day Traders: Autocorrelation, Normal Distribution & Flash Crash

(i) When there is autocorrelation of returns:

• Pension funds: Autocorrelation of returns means that there is a relationship between past and future returns. Pension funds, with their long-term investment horizon, should take this into account when calculating VaR and ES. They should consider the persistence of returns and the potential for clustering of extreme events. This means that pension funds should use models that incorporate the autocorrelation of returns to better estimate the potential losses they could face.
• Day-traders: Day-traders, with their short-term investment horizon, may not need to take into account autocorrelation of returns when calculating VaR and ES. Since they are focused on daily trading, they may assume that returns are independent and identically distributed each day. Therefore, they can use simpler models that do not incorporate autocorrelation.

(ii) When returns are normally distributed, independent with a mean of zero:

• Pension funds: In this scenario, pension funds can use traditional VaR and ES calculations based on the assumption of normal distribution. They can assume that returns are independent and identically distributed, and use historical data to estimate the mean and standard deviation of returns.
• Day-traders: Similar to pension funds, day-traders can also use traditional VaR and ES calculations based on the assumption of normal distribution. However, since they have a short-term investment horizon, they may need to update their calculations more frequently to reflect changing market conditions.

b) The flash crash episode on May 6, 2010, where the DJIA index dropped significantly within minutes and then recovered, can be connected to the mechanism of algorithmic trading. Algorithmic trading involves the use of computer programs that execute trades based on pre-defined rules and algorithms. During the flash crash, there were a large number of sell orders triggered by algorithmic trading programs, which led to a rapid decline in prices.

The type of traders involved in this episode were likely day-traders or high-frequency traders who heavily rely on algorithmic trading strategies. These traders aim to exploit short-term market movements and capitalize on small price discrepancies.

It is possible to envisage a similar episode in reverse, where prices would go up quite a lot and then go down back to normal levels in a matter of minutes. This could occur due to a sudden surge in buying pressure triggered by algorithmic trading algorithms or a large influx of buy orders. As prices rise rapidly, other traders may join the buying frenzy, causing a further increase in prices. However, once the buying pressure subsides or reverses, prices can quickly plummet as traders rush to sell, resulting in a sharp decline back to normal levels.