Please answer the following questions for the below:

David, a new hire at the risk management division of Citibank, questions his

company$$s risk management practices. He notices that the company allocates risks

equally across different divisions. His boss, Angela, explains that equal$-$weighting

helps reduce or reallocate different types of risks because of the correlation

structures across varying risks. However, he is self$-$centered and believes that

changing allocations across different divisions will not change the company$$s risk

exposures. He is asking for your help. You will use the excel file associated with

the VaR lecture to prove$/$disprove his arguments.

Hypothetically, let$$s assume the following value weights:

CEW CYB SPY AGG SPBO HYG

Weights: $0\mathrm{.}10\mathrm{.}10\mathrm{.}10\mathrm{.}50\mathrm{.}150\mathrm{.}05$

a$.$ Use the same data in the VaR excel file to compute the portfolio$$s value

weighted returns over time.

b$.$ Measure the sensitives to EACH individual risk factor $($ MKT$-$RF$,3-$Month, $10-$

Year$-2-$YearSpread, TED, OAS, OAS$\_$Corp, and USDRUBFX$).$ Identify risk

factors. Do you observe any changes in risk factors, compared to equalweighted portfolio returns?

c$.$ We discussed in class that risk factors may correlate, and as a result, one may

end up over$-$ or under$-$managing firm risks. Therefore, we should identify risk

factors in a multivariate setting. Use the multivariate regression to identify risk

factors? Compare your findings with what you find in part $($b$).$

d$.$ Now restrict risk factors to Fama and French five factors only. Do you observe

other equity risk factors besides the market factor $($MKT$-$RF$)?$

e$.$ Use the one$-$year historical returns until $9/30/2021$ to measure VaR at the $95\%$

and $99\%$ confidence interval. Interpret your results.

f$.$ Use the delta$-$normal method to measure VaR at the $95\%$ confidence interval.

g $.$Redo part $($f$)$ by using the t$-$student distribution with df$=6$ and df$=4($fat$-$tailed

distributions$).$

h$.$ From your results above, discuss whether David$$s statements is correct $$ i$)$

regardless of the weighting scheme, the company faces similar risk exposures.

II$)$ Equal$-$weighting risks across different divisions provides more risk reduction

than value$-$weighting.