1 / 17

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.

tanika
Download Presentation

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

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related