Question $1$ Value at Risk $($Delta$-$Normal Method$)$

Suppose ABC company invest $$100,000,000$ portfolio of securities with a daily volatility $($standard

deviation$)$ of $2\mathrm{.}5\%.$ Assume the risk satisfies delta normal method assumptions, that is

$r_{t}i.i.dN(0,2\mathrm{.}5\%{?}^2)$

Step $1$: Please determine the VaR at $95\%$ confidence level over the next day. $($First find the critical value

of the standard normal at $Z_{}$ where $=5\%,$ VaR$=$mean$+$sd$*Z_{}$ to calculate the Value at Risk. But if you

use each $=95\%,$ and the VaR$=$ mean$-$sd$*Z_{}.$ Either way will give you the same results. Make sure you

choose the right $$ and use the right sigh of VaR function.$)$

Step $2$: Please interpret the meaning of the VaR at $95\%$ confidence level over the next day.

Step$3$: Please determine the VaR at $95\%$ confidence level over the next $10$ days.

Step $4$: Please interpret the meaning of the VaR at $95\%$ confidence level over the next $10$ days.

Question $2$ Value at Risk $($Historical Data Method$)$

Suppose ABC insurance company invests $$500,000$ in the S&P $500$ index in the period Jan $1,2007$ to

December $31,2008(2008$ Financial Crisis time$).$

Step $1$: Please go to Yahoo Finance website, get the daily adjusted close price.

Step $2$: Please calculate the daily return: $r_t=\frac{P_{t+1}-P_t}{P_t}$

Step $2$: Please calculate the daily return: $r_t=\frac{P_{t+1}-P_t}{P_t}$

Step $3$: Please determine the daily gains and losses using the daily return derived from previous step.

Step $4$: Please find the minimum, maximum, mean, standard deviation, skewness and kurtosis for daily

returns. Please explain whether daily gains and losses fit into a normal distribution based on the

statistical coefficients you just calculated. $($Hint: normal distribution's skewness coefficient is $0$ and the

kurtosis coefficient is $3$ and excess kurtosis coefficient is $0.)$

Step $5$: Please find the VaR at a confidence level of $95\%,99\%$ and $99\mathrm{.}5\%.($Hint: You can directly apply

percentile function on the daily gains and losses data generated in step $3.$ When you apply the

percentile function, the $"kth"$ parameter should be $"1-$confidence level".$)$

Question $3$: Total Risk and Systematics Risk

The data file "Total Risk and Systemic Risk.xlsx$"$ shows the monthly adjusted close price for Google,

Weight Watcher and NYSE composite index from $2008$ to $2018.$

Step $1$: Please find the mean, variance, standard deviation, and coefficient of variant for the monthly

adjusted close price of Google, Weight Watcher and NYSE, respectively.

Step $2$: Based on the results you calculated in step, please explain which stock or index have the highest

monthly price volatility.

Step $3$: Please determine the monthly return for Google, Weight Watcher and NYSE, respectively. $($Recall

$r_t=\frac{P_{t+1}-P_t}{P_t},$ here the period is month.$)$

Step $4$: Please determine Beta for Google, Weight Watcher and NYSE, respectively. $($Hint: Beta $=$

$\frac{\text{C}\text{o}\text{v}(r_i{r}_m)}{\text{V}\text{a}\text{r}(r_m)},$ where $r_i$ stands for the return of individual stock, $r_m$ stands for the return of market portfolio.

Here we assume NYSE return represent the return of market portfolio$)$

Step $5$: Please compare the Betas from step $4,$ and explain which stock has the highest systematic risk.

Question $4$: Forward Price

Suppose the current stock price is $$200$ per share. The risk$-$free interest rate is $5\%.$ What will be the

forward price on a contract that expires in three months $($a quarter of a year$)?$ Suppose there is no

dividends paid over the three months.