III. Portfolio Management Type Questions :

The remaining questions are related to each other and also use time value of money for solutions.

Part $1$:

$17.$ A new client allocates $$100$ million to your investment management firm. The client wants you to create a long$-$term fixed income portfolio and agrees to bonds with a $20-$year average term. To simplify, assume all the bonds are identical with $20-$year terms, coupon rates of $5\mathrm{.}75\%[$payable semi$-$annually$],$ AA credit ratings, and exactly $6$ months to the next coupon date. If the bonds are trading at par and are purchased at par, what is their yield to maturity? Round to $1$ basis point.

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$18.$ To form the $$100$ million portfolio, how many bonds would be purchased? Round to $1$ whole bond.

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$19.$ One year later, when the bonds mature in $19$ years, the yield to maturity on the bonds decreases to $5\mathrm{.}20\%.$ What is the price or value of one of the bonds? Round to one cent. Refer to the comments in question $15.$

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$20.$ What is the total value of the bonds in the portfolio assuming none of the bonds were upgraded or downgraded? Round to $$1.$

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$21.$ What is the total capital gain or loss of the bonds in the portfolio since inception? If a capital loss, write your answer as a negative number and round to $$1.$

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$22.$ Reviewing the results over the first year $$ i$.$e$.$ doing a performance evaluation, how much $$income$$ in the form of coupon receipts was generated by the portfolio. Round to $$1.$

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$23.$ Assume the coupons collected from the first coupon payments $[6$ months after acquiring the bonds$]$ are reinvested at $3\%[$on an annual basis$].$ How much additional income was generated by the reinvestment for the $6$ months? Round to $$1.$

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$24.$ Including the coupon receipts and the reinvested income, what is the total income generated by the portfolio during the first year? Round to $$1.$

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$25.$ Including the total income and the capital gain or loss on the portfolio, how much did the total value of the portfolio change during the first year? Assume no funds were withdrawn from or invested in the portfolio and if a loss, write your answer as a negative number and round to $$1.$

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$26.$ Knowing that $$100$ million was initially invested in the portfolio, what was the $$total return$,$ which includes both income and capital gain or loss and is expressed as a percentage, on the portfolio during the first year? Round to $1$ basis point.

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