Question: a assume daily returns that are normally distributed with constant...
(a) Assume daily returns that are normally distributed with constant mean and variance, i.e. they are given by
where the time increment t + 1 is 1 day. Derive the following formula for the Value-at-Risk at the α% (VaR) critical level and 1-day horizon.
where Φ is the standard normal cumulative density function.
(b) The expected shortfall at the critical level α% and 1-day horizon can be defined as
Using the V aR formula from part (a) derive the following formula for the 1-day expected shortfall at critical level α
where φ is the standard normal probability density function. Hint: From the properties of the normal distribution we know that if Z is normally distributed