Eliat Karlin is a 35-year-oid bank executive who has just inhented a large sum o

Question

Eliat Karlin is a 35-year-oid bank executive who has just inhented a large sum of money Haing spent several years in the bank's inwestments department, he's wel aware of the concept of duratian and dec des bo apply it to his bond portfolia. In partioular, Elat intends to use $1 milian of his inhertance to gurchaae 4 U.S. Treasury bonds: 1 . An 869%, 13-year bond that's priced at $1, 101.25 to yiuld 7.46%. 2. A 7.761%, 15-year bond tnat's priced at $1015.16 to yield 75e% 3. A 20-year strp00d Treasury (zero coupon> nat's prced at $198.52 to yi0d 825%. 4. A 24-year, 7.46% bond that's onced at $95401 to yeld 789%. Note that these bonds are semiannual compounding borda a. Find tne duration and te modned duraton of each bond. b. Find the duration of the whole bond portiolio if Eliat puts $250,000 irto each of the 4 US. Treasury bonds c. Findre duration ofthe portfoloEi0l puts $350,000 each into bonds 1 and 3 and $150,000 ea? bonds 2 and 4 d. Which portfolia-borchould Eliot select he thinks rates are about to head up and he wants to avcid as much price voatlty as poss ble? Explain. From which portfolio does he stand to make more in annual inturest income? Which portfolio would you recommend, and why? Bond 1: 13 years, B e9%, priced to yield 746%. The duraton of this bond is yoars Round to two docimal places.) The modified duration of this bodyuars (Rcund to two decimal pacus.) Bond 2 15 years, 7.761% onced to yield 7.50%. The durat on af this bond is years (Round to two decimal places.) The modified duration of this bond years. (Round to two decimal paces.) Bond 3. 20 years, zero coupon, priced to yield 8.25%. The durat on of this bond is years Round to two decimal places.) The modified durton of this bond s years. (Round to two decimal pieces.) Bond 4-24 years, 7.46%, priced to yield 7.89%. The duraton of this bond isyoars IRound to two decimal placae.) The mod fied duration of tris bondeers(Round to two decimai pleces) b. Find the duration of the whole bond portiolio if Eliat puts $250,00O irto each of the 4 US. Treasury bonds The duraton of this portbio is yeare Round to two decimal places) e. Find the duration of the pontolo if Eliot puts $350000 each into bonds 1 and 3and $150,000 each into bonds 2 and 4 The duration of this portolo is years. (Round to two decimal places)

Explanation / Answer

Period calculation

Duration =(1+RATE)/(RATE*NOP)-(1+RATE+T*(CR/NOP-RATE))/(CR*((1+RATE)^T-1)+RATE*NOP)

NOP (number of payment ) , assumed = 1(per year)

Modified Duration = Duration /(1+Rate)

Bond 1)

Bond 2)

Bond 3)

Bond 4) a

Bond 4) b To calculate further ,we should calculate average coupon rate and yield of the invesment by method of weighted average return using formula

Coupon rate of portfolio = w1 * C1 + w2 * C2 +........+ wn * Cn

Yield of portfolio =w1 * Y1 + w2 * Y2 +........+ wn * Yn

Maximum holding period of the portfolio = maximum maturity period of bond in portfolio = 24 years of bond 4.

C)

Duration 8.50 Modified Duration 7.91

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