Question $4.$ You gather the following from reading the Pillar $3$ Reports of Elon Musk's bank regrading

implementation of the value at risk method.

Internal model approach Value$-$at$-$Risk and stressed Value$-$at$-$Risk

The following table provides information on the mean, minimum and maximum VaR over the reporting

period and at period end. VaR is based on a $10-$day holding period.

Notes on Back$-$testing

VaR estimates are back$-$tested regularly for reasonableness. Back$-$testing is a process that compares

the Group's daily VaR estimates against both actual and hypothetical daily profit or loss $($P&L$)$ to

ensure that model integrity is maintained.

The results of back$-$testing are reported to senior management, risk committees and regulators. In

addition to back$-$testing, the risk measurement model and all pricing models are subject to periodic

reviews and independent validation at frequencies specified by the Group Model Risk Policy.

Back$-$testing, carried out by comparing the Group's daily VaR estimate against actual P&L$,$ identified

no exceptions during the six months ended $30$ September $2023$ or the six months ended $31$ March

This remains within the model parameters and indicates acceptable operation of the VaR model

within APRA's guidelines.

Answer the following questions.

$($a$)$ From your understanding of the VaR model what proportion of exceptions $($i$.$e$.,$ total backtest fails$)$ as

a percentage expect to be reported by the bank in future? Why?

$($b$)$ As you increase the backtest period, what do you expect to happen to the number of backtest fails?

Justify your answer.

$($c$)$ Why is Expected Shortfall considered to be an improvement over VaR? Ensure you refer to your

knowledge of distributions and tails. $($Note $-$ you are not expected to specifically calculate Expected

Shortfall$).$

Answer A B and C please I've been struggling to do these questions.