A bond speculator currently has positions in two separate corporate bond portfolios: a long holding in Portfolio $1$ and a short holding in Portfolio $2.$ All the bonds have the same credit quality. Other relevant information on these positions includes:

Market Coupon Compounding Yield to

Portfolio Bond Value $($Mil$.)$ Rate Frequency Maturity Maturity

$1$ A $$12\mathrm{.}00\mathrm{.}0\%$ Annual $3$ yrs $9\mathrm{.}35\%$

B $4\mathrm{.}00\mathrm{.}0$ Annual $11$ yrs $9\mathrm{.}35$

$2$ C $16\mathrm{.}57\mathrm{.}5$ Annual $6$ yrs $9\mathrm{.}35$

Treasury bond futures $($based on $$100,000$ face value of $20-$year T$-$bonds having an $6\%$ semi$-$annual coupon$)$ with a maturity exactly six months from now are currently priced at $10712$ with a corresponding yield to maturity of $5\mathrm{.}393\%.$ The $$yield betas$$ between the futures contract and Bonds A$,$ B$,$ and C are $1\mathrm{.}11,1\mathrm{.}04,$ and $1\mathrm{.}02,$ respectively. Finally, the modified duration for the T$-$bond underlying the futures contract is $11\mathrm{.}881$ years.

Calculate the modified duration $($expressed in years$)$ for portfolio $2.$ Do not round intermediate calculations. Round your answers to three decimal places.

$4\mathrm{.}572$

$5\mathrm{.}682$

$3\mathrm{.}869$

$7\mathrm{.}215$

$8$ points

QUESTION $12$

A bond speculator currently has positions in two separate corporate bond portfolios: a long holding in Portfolio $1$ and a short holding in Portfolio $2.$ All the bonds have the same credit quality. Other relevant information on these positions includes:

Market Coupon Compounding Yield to

Portfolio Bond Value $($Mil$.)$ Rate Frequency Maturity Maturity

$1$ A $$12\mathrm{.}00\mathrm{.}0\%$ Annual $3$ yrs $9\mathrm{.}35\%$

B $4\mathrm{.}00\mathrm{.}0$ Annual $11$ yrs $9\mathrm{.}35$

$2$ C $16\mathrm{.}57\mathrm{.}5$ Annual $6$ yrs $9\mathrm{.}35$

Treasury bond futures $($based on $$100,000$ face value of $20-$year T$-$bonds having an $6\%$ semi$-$annual coupon$)$ with a maturity exactly six months from now are currently priced at $10712$ with a corresponding yield to maturity of $5\mathrm{.}393\%.$ The $$yield betas$$ between the futures contract and Bonds A$,$ B$,$ and C are $1\mathrm{.}11,1\mathrm{.}04,$ and $1\mathrm{.}02,$ respectively. Finally, the modified duration for the T$-$bond underlying the futures contract is $11\mathrm{.}881$ years.

What will be the approximate percentage change in the value of each if all yields increase by $80$ basis points on an annual basis? Do not round intermediate calculations. Round your answers to two decimal places.

$3\mathrm{.}66\%$

$-3\mathrm{.}66\%$

$-4\mathrm{.}26\%$

$4\mathrm{.}26\%$

$8$ points

QUESTION $13$

You work on a proprietary trading desk of a large investment bank, and you have been asked for a quote on the sale of a call option with a strike price of $$53$ and one year of expiration. The call option would be written on a stock that does not pay a dividend. From your analysis, you expect that the stock will either increase to $$75$ or decrease to $$36$ over the next year. The current price of the underlying stock is $$53,$ and the risk$-$free interest rate is $6\%$ per annum. What is this fair market value for the call option under these conditions? Do not round intermediate calculations. Round your answer to the nearest cent.

$$75\mathrm{.}12$

$$10\mathrm{.}74$

$$10\mathrm{.}50$

$$36\mathrm{.}25$

$8$ points

QUESTION $14$

Suppose ABC Mutual Fund had no liabilities and owned only four stocks as follows:

Stock Shares Price Market Value

W $1,000$ $$11$ $$11,000$

X $1,3001418,200$

Y $1,6002540,000$

Z $8001512,000$

$$81,200$

The fund began by selling $$53,000$ of stock at $$8\mathrm{.}00$ per share. What is its NAV? Do not round intermediate calculations. Round your answer to the nearest cent.

$$14\mathrm{.}56$

$$11\mathrm{.}98$

$$13\mathrm{.}58$

$$12\mathrm{.}26$

$8$ points