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Exam FM/2 Review Cash Flows, portfolios, duration, & immunization

Exam FM/2 Review Cash Flows, portfolios, duration, & immunization. Cash Flows. Net Present Value method = Calculate present value of cash flows; interest rate is given Internal Rate of Return = Interest rate where Net Present Value is zero. Interest Measurements.

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Exam FM/2 Review Cash Flows, portfolios, duration, & immunization

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  1. Exam FM/2 ReviewCash Flows, portfolios, duration, & immunization

  2. Cash Flows • Net Present Value method = Calculate present value of cash flows; interest rate is given • Internal Rate of Return = Interest rate where Net Present Value is zero

  3. Interest Measurements • Dollar Weighted Return – Return assuming simple interest • Time Weighted Return – Return using growth factors

  4. Example 1 Find the time weighted and dollar weighted yields if the original deposit of 100,000 dropped to 90,000 at mid-year but the deposit made at that point was 10,000 and the final amount in the fund was 110,000. Ans: Time: -1% Dollar: 0%

  5. Portfolio Methods • Portfolio method • Everybody receives same interest every year • Read down the final column • Investment year method • Interest rates are based on the investment year, then move to the portfolio rate • Read across the row and then down the final column

  6. Example 2

  7. Rates • Spot Rate - yield rate for zero coupon bond bought now • Forward Rate - yield rate for bond bought in the future • Inflation Rate • Consider it a negative interest rate • Just divide by (inflation rate)

  8. Duration • Duration is a weighted present value of cash flow times • Macaulay duration, or just duration • Weight times using PV of cash flow (current price) at those times • Also the relative change in price due to changes in force of interest • Modified duration • Simply v times the Macaulay duration • Relative change in price due to changes in i

  9. Convexity • Convexity • Relative second derivative of price, with respect to interest rate • Approximating Price changing using application of Taylor Series

  10. Immunization • Immunization – protect large price changes from changes in interest rates • Cash Flow Matching (Exact matchingor Dedication) • Match each liability with an asset • Redington immunization • PV(Assets) = PV(Liabilities) • MacD(Assets) = MacD(Liabilities) • Convexity(Assets)>Convexity(Liabilities) • Full immunization • PV(Assets) = PV(Liabilities) • ModD(Assets)=ModD(Liabilities) • Assets straddle the Liabilities

  11. Problem 1 • You are given this information about the activity in two different investment accounts. During 1999, the dollar weighted return for investment account K equals the time weighted return for investment account L, which equals i. Calculate i. ASM p.273 Answer: 15%

  12. Problem 2 • A person deposits 1000 on January 1, 1997. Let the following be the accumulated value of the 1000 on January 1, 2000:P: under the investment year methodQ: under the portfolio yield methodR: where the balance is withdrawn at the end of every year and is reinvested at the new money rateDetermine the ranking of P, Q, and R ASM p.284 Answer: R>P>Q

  13. Problem 3 • The one-year forward rate for year 2 is 4%. The four-year spot rate is 10%. The expected spot rate at the end of year two on a zero-coupon bond maturing at the end of year 4 is 7%. Determine the one-year spot rate. ASM p.435 Answer: 22.96%

  14. Problem 4 • The real rate of interest is 4%. The expected annual inflation rate over the next two years is 5%. What is the net present value of the following cash flows? ASM p.433Year 0 1 2Cash Flow -300 160 160 Answer: -19.30

  15. Problem 5 • A $100 par value bond with 7% annual coupons and maturing at par in 4 years sells at a price to yield 6%. Determine the modified duration of the bond. ASM p.452 Answer: 3.43

  16. Problem 6 • An annuity-immediate has payments of $1,000, $3,000, and $7,000 at the end of one, two and three years, respectively. Determine the convexity of the payments evaluated at i=10%.ASM p.472 Answer: 7.63

  17. Problem 7 • A company must pay a benefit of $1,000 to a customer in two years. To provide for this benefit, the company will buy a one-year and three-year zero-coupon bonds. The one-year and three-year spot rates are 8% and 10%, respectively. The company wants to immunize itself from small changes in the interest rates on either side of 10% (Redington immunization). What amount should it invest in the one-year bonds?ASM p.472 Answer: 420

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