A bank holds a trading portfolio long position valued at 200

A bank holds a trading portfolio (long position) valued at $200,000. The distribution of the daily return on this portfolio is normally distributed with a mean zero and standard deviation of 3% What is the DEAR (in $) under 5-percent most adverse market movement scenario?

Solution

DEAR also known as Daily earning at Risk is the estimated potential loss of portfolio value over a one day unwind period due to adverse scenarios in Market for an example market volatility.

(For 5% we have z value equals to 1.65 as returns following normal distribution with mean 0 and std.deviation on daily basis is 3%)

Given standard deviation of 300 basis points at 5% level therefore movement can be calculated as 1.65*std.deviation=1.65×0.03=0.0495

DEAR= Portfolio Value× Adverse movement =$200,000×0.0495=$20×495=$9900