Question $5$

Suppose you have a portfolio with a long position of $$2$ million in BAA bonds and short $$1m$

in T$-$notes. Volatilities are $1\mathrm{.}58\%$ and $1\mathrm{.}90\%$ per month, respectively, with a correlation of

$0\mathrm{.}9654.$

Do not round intermediate calculations. Round your answer to the nearest dollar $($eg$.32).$

No commas. Use minus sign for negative numbers.

a$)$ Compute the $95\%$ monthly VAR for each position individually

BAA bond VAR

$

T$-$notes VAR

$

b$)$ Compute the $95\%$ portfolio VAR

Portfolio VAR

$

c$)$ Compute the diversification effect

diversification effect

$ The first number at each node in the tree below is the $0\mathrm{.}5-$year rate at that node. The second

number at each node is the price of $$1$ par of a $0\mathrm{.}5-$year zero at that node. The third number

$($if it appears$)$ is the price of $$1$ par of a $1-$year zero at that node. The fourth number $($if it

appears$)$ is the price of $$1$ par of a $1\mathrm{.}5-$year zero at that node.

The up move probability is $0\mathrm{.}5.$

Consider an $1-$year inverse floating rate note with a coupon equal to $12\%$ minus the $0\mathrm{.}5-$year

rate set $6$ months prior to the coupon date, with the additional provision that the coupon

cannot fall below $6\%($ie$)$ time $t$ coupon rate $(t),0\mathrm{.}06*$ par amount of the

note.

What is the price of the inverse floater at the up node at time $=0\mathrm{.}5($answer to four decimal

places$)$

s

What is the price of the inverse floater at the down node at time $=0\mathrm{.}5($answer to four

decimal places$)$

$

What is the price of the the inverse floater at time $=0($answer to four decimal places$)$Question $6$

Pacific Basin Bank $($PBB$)$ has outstanding a $$100,000$ face value, adjustable rate loan to a

company that has a leverage ratio of $90$ per cent $($defined as Current market value of debt

$/$Market Value of assets$).$ The current risk$-$free rate is $5$ per cent, and the time to maturity on

the loan is exactly $1$ year. The asset risk of the borrower, as measured by the standard

deviation of the rate of change in the value of the underlying assets, is $12$ per cent. Use the

KMV Merton model and the normal density function.

Do not round intermediate calculations.

d$1$

$($to six decimal places. No commas$)$

N$($d$1)$

$($to six decimal places. No commas$)$

d$2$

$($to six decimal places. No commas$)$

$N(d2)$

$($to six decimal places. No commas$)$

MV $($Debt$)$

$($to two decimal places. No commas$)$

credit spread $($interest rate on debt over risk free rate$)$

$\%($to four

decimal places. No commas$)$