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Test 2 Review

Test 2 Review - FINA 4326 Test#2 Review Sarah DeVito...

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FINA 4326 – Test #2 Review Sarah DeVito Current Events Fed accepts the Mortgage Backed Securities and gives treasuries in return Mortgage-backed securities now have no face value because they have no perceived value Bear Stearns Inc – leading global investment bank, securities trader, and brokerage firm – loses half of its value o JP Morgan buys it for 10$ a share o JP Morgan essentially picks up a prime brokerage division in the midst of bailing out Bear Stearns Fed recently lowered the discount rate to 3.25% and opened the discount window to investment banks (has not been done since the great depression) Bond investors of Bear Stearns are happy because they basically hold JP Morgan bonds Bear Stearns’ price fluctuations on the market are due to open market purchases of BSC shares to approve the merger of JP Morgan and BSC Duration Duration: the weighted average maturity of a bond’s cash flows or of any series of linked cash flows Duration of a zero coupon bond with maturity period of n years is n years If there are coupon payments, the duration will be less than n years Higher duration signifies more volatility and therefore, more interest rate risk MODIFIED duration is approximately proportional to the % change in price for a given change in yield Two ways of calculating duration o Modified o Macaulay Modified vs. Macaulay EXAMPLE Scenario: Interest rates go down across the board Bond A Bond B Coupon 10% semi-annual 15% semi-annual Maturity N=3 N=4 YTM 10% 10% Price $1,000 $1,000 MACAULAY’S DURATION : the weighted average of bond cash flow – weights are the time periods of the cash flow Bond A 1. Calculate the present value of cash flows Period Payments Present Value Calculations 1 50 50/1.05 47.61904762 2 50 50/(1.05) 2 45.35147392
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3 50 50/(1.05) 3 43.19187993 4 50 50/(1.05) 4 41.13512374 5 50 50/(1.05) 5 39.17630832 6 50 1050/(1.05) 6 783.5261665 2. Weight the future value of the cash flows Year PV of Cash Flows Weighted PV of CF .5 47.61904762 23.8095235 1 45.35147392 45.3514739 1.5 43.19187993 64.7878199 2 41.13512374 82.27024748 2.5 39.17630832 97.9407708 3 783.5261665 2350.5785 = 2664.70 3. Divide by the current price 2,664.70/1,000 = 2.66 years (years denotes Macaulay’s duration) ** 2.66 years is the effective maturity (meaning the longer Macaulay duration = ↑interest rate risk) MODIFIED DURATION Modified duration = Macaulay’s Duration/(1+Y) Y = YTM if coupon payments are annual Y = YTM/2 if the coupon payments are semiannual SO, Modified duration of Bond A = 2.66/[1+(.05/2)] = 2.53 Modified duration of Bond B = 3.15/[1+(.15/2)] = 2.93 If interest rates drop by 1%, price of Bond A will go up by an average of 2.53% - modified duration If interest rates increase by 1%, price of Bond A will go down by 2.53% - modified duration Duration properties o ↑duration, ↑interest rate risk o ↑bond maturity, ↑duration o ↓coupon, ↑duration o ZERO COUPON BOND: maturity = Macaulay’s duration
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Test 2 Review - FINA 4326 Test#2 Review Sarah DeVito...

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