$1.(12$ points$)$ Imagine that you have some funds available for investment for a $3-$year period.$$ You believe that a fixed$-$income instrument is appropriate for a relatively short time horizon. Unfortunately, the $3-$year maturity sector of the fixed income market look particularly unappealing to you at the present time.$$ You have, however, found a $7-$year maturity bond priced rather attractively.$$ The bond you have your eyes on has the following characteristics;

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$7-$year term to maturity

$6\%$ coupon rate, paid semiannually

$$ Selling to yield $12\%$ annually

$$ Priced at $$72\mathrm{.}1150$ per $$100$ of par

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Currently, the Treasury spot rate curve is given as the following, where the spot rates are expressed in annual figures.$$

Period

Years

Annual Par YTM

Price

Spot Rate

Semiannual

$1$

$0\mathrm{.}5$

$3\mathrm{.}00\%$

$$

$3\mathrm{.}0000\%$

$1\mathrm{.}5000\%$

$2$

$1\mathrm{.}0$

$3\mathrm{.}30\%$

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$3\mathrm{.}3000\%$

$1\mathrm{.}6500\%$

$3$

$1\mathrm{.}5$

$3\mathrm{.}50\%$

$100$

$3\mathrm{.}5053\%$

$1\mathrm{.}7527\%$

$4$

$2\mathrm{.}0$

$3\mathrm{.}90\%$

$100$

$3\mathrm{.}9164\%$

$1\mathrm{.}9582\%$

$5$

$2\mathrm{.}5$

$4\mathrm{.}40\%$

$100$

$4\mathrm{.}4376\%$

$2\mathrm{.}2188\%$

$6$

$3\mathrm{.}0$

$4\mathrm{.}70\%$

$100$

$4\mathrm{.}7520\%$

$2\mathrm{.}3760\%$

$7$

$3\mathrm{.}5$

$4\mathrm{.}90\%$

$100$

$4\mathrm{.}9622\%$

$2\mathrm{.}4811\%$

$8$

$4\mathrm{.}0$

$5\mathrm{.}00\%$

$100$

$5\mathrm{.}0650\%$

$2\mathrm{.}5325\%$

$9$

$4\mathrm{.}5$

$5\mathrm{.}10\%$

$100$

$5\mathrm{.}1701\%$

$2\mathrm{.}5851\%$

$10$

$5\mathrm{.}0$

$5\mathrm{.}20\%$

$100$

$5\mathrm{.}2772\%$

$2\mathrm{.}6386\%$

$11$

$5\mathrm{.}5$

$5\mathrm{.}30\%$

$100$

$5\mathrm{.}3864\%$

$2\mathrm{.}6932\%$

$12$

$6\mathrm{.}0$

$5\mathrm{.}40\%$

$100$

$5\mathrm{.}4976\%$

$2\mathrm{.}7488\%$

$13$

$6\mathrm{.}5$

$5\mathrm{.}50\%$

$100$

$5\mathrm{.}6108\%$

$2\mathrm{.}8054\%$

$14$

$7\mathrm{.}0$

$5\mathrm{.}55\%$

$100$

$5\mathrm{.}6643\%$

$2\mathrm{.}8322\%$

$15$

$7\mathrm{.}5$

$5\mathrm{.}60\%$

$100$

$5\mathrm{.}7193\%$

$2\mathrm{.}8597\%$

$16$

$8\mathrm{.}0$

$5\mathrm{.}65\%$

$100$

$5\mathrm{.}7755\%$

$2\mathrm{.}8878\%$

$17$

$8\mathrm{.}5$

$5\mathrm{.}70\%$

$100$

$5\mathrm{.}8331\%$

$2\mathrm{.}9166\%$

$18$

$9\mathrm{.}0$

$5\mathrm{.}80\%$

$100$

$5\mathrm{.}9584\%$

$2\mathrm{.}9792\%$

$19$

$9\mathrm{.}5$

$5\mathrm{.}90\%$

$100$

$6\mathrm{.}0863\%$

$3\mathrm{.}0432\%$

$20$

$10\mathrm{.}0$

$6\mathrm{.}00\%$

$100$

$6\mathrm{.}2169\%$

$3\mathrm{.}1085\%$

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a$.$ What yield does the market appear to expect on $4-$year bonds $3-$years from today?$$ In other words, $3$ years from now, what does the market expect the yield on a $4-$year bond to be$?$

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b$.$ If the market$$s expectations around this future yield prove correct, at what price would we expect to be able to sell this bond for in $3$ years$$ time?$$ For simplicity, use this single rate from part $($a$)$ as the discount rate for calculating the future selling price.$$

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c$.$ If we forecast the selling price computed above, what annualized yield to maturity do we expect to earn over the holding period?$$

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d$.$ Identify $2$ reasons why you might be skeptical of actually earning the computed YTM over the next $3$ years.$$

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