Duration and Portfolio Immunization

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Duration and Portfolio Immunization
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Portfolio Immunization

• Portfolio immunization
• An investment strategy that tries to protect the
  expected yield from a security or portfolio of
  securities by acquiring those securities whose
  duration equals the length of the investors
  planned holding period.

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Portfolio Immunization

• If the average duration of a portfolio equals the
  investors desired holding period, the effect is
  to hold the investors total return constant
  regardless of whether interest rates rise or
  fall.
• In the absence of borrower default, the
  investors realized return can be no less than
  the return he has been promised by the borrower.

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Example

• Assume we are interested in a 1,000 par value
  bond that will mature in two years.
• The bond has a coupon rate of 8 percent and pays
  80 in interest at the end of each year.
• Interest rates on comparable bonds are also at 8
  percent but may fall to as low as 6 percent or
  rise as high as 10 percent.

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Example

• The buyer knows he will receive 1000 at
  maturity, but in the meantime he faces the
  uncertainty of having to reinvest the annual 80
  in interest earnings at 6, 8, or 10.

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Example Case 1

• Let interest rates fall to 6.
• The bond will earn 80 in interest payments for
  year one, 80 for year two, and 4.80 (80 x
  0.06) when the 80 interest income received the
  first year is reinvested at 6 during year 2.

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Example Case 1

• How much will the investor earn over the two
  years?
• First years interest earnings Second years
  interest earnings Interest earned reinvesting
  the first years interest earnings at 6 Par
  value of the bond at maturity.
• 80 80 4.80 1,000 1,164.80

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Example Case 2

• Let interest rates rise to 10.
• The bond will earn 80 in interest payments for
  year one, 80 for year two, and 8.00 (80 x
  0.10) when the 80 interest income received the
  first year is reinvested at 10 during year 2.

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Example Case 2

• How much will the investor earn over the two
  years?
• First years interest earnings Second years
  interest earnings Interest earned reinvesting
  the first years interest earnings at 10 Par
  value of the bond at maturity.
• 80 80 8 1,000 1,168.00

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Immunization and Duration

• The investors earnings could drop as low as
  1,164.80 or rise as high as 1,168.
• But, if the investor can find a bond whose
  duration matches his or her planned holding
  period, he or she can avoid this fluctuation in
  earnings.
• The bond will have a maturity that exceeds the
  investors holding period, but its duration will
  match it.

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Example Case 1

• Let interest rates fall to 6.
• The bond will earn 80 in interest payments for
  year one, 80 for year two, and 4.80 (80 x
  0.06) when the 80 interest income received the
  first year is reinvested at 6 during year 2.
• But, the bonds market price will rise to
  1,001.60 due to the drop in interest rates.

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Example Case 1

• How much will the investor earn over the two
  years?
• First years interest earnings Second years
  interest earnings Interest earned reinvesting
  the first years interest earnings at 6 Market
  price of the bond at the end of the investors
  planned holding period.
• 80 80 4.80 1,001.60 1,166.40

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Example Case 2

• Let interest rates rise to 10.
• The bond will earn 80 in interest payments for
  year one, 80 for year two, and 8.00 (80 x
  0.10) when the 80 interest income received the
  first year is reinvested at 10 during year 2.
• But, the bonds market price will fall to 998.40
  due to the rise in interest rates.

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Example Case 2

• How much will the investor earn over the two
  years?
• First years interest earnings Second years
  interest earnings Interest earned reinvesting
  the first years interest earnings at 10 Par
  value of the bond at maturity.
• 80 80 8 998.40 1,166.40

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Conclusion

• The investor earns identical total earnings
  whether interest rates go up or down.
• With duration set equal to the buyers planned
  holding period, a fall (rise) in the reinvestment
  rate is completely offset by an increase (a
  decrease) in the bonds market price.

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Conclusion

• Immunization using duration seems to work
  reasonably well because the largest single
  element found in most interest rate movements is
  a parallel change in all interest rates (explains
  about 80 of all interest rate movements over
  time).
• So, investors can achieve reasonably effective
  immunization by approximately matching the
  duration of their portfolios with their planned
  holding periods.

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Opportunity Cost

• Duration is not free. There is an opportunity
  cost.
• If the investor had simply bought a bond with a
  calendar maturity of two years and interest rates
  rose, he or she would have earned 1,168.
• The opportunity cost of immunization is a lower,
  but more stable, expected return.

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Limits of Duration

• In reality it can be difficult to find a
  portfolio of securities whose average portfolio
  duration exactly matches the investors planned
  holding period.
• As the investor grows older, his planned holding
  period grows shorter, as does the average
  duration of his portfolio, but they may not
  decline at the same rate.
• Portfolio requires constant adjustments.

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Limits of Duration

• Many bonds are callable so bondholders may find
  themselves with a sudden and unexpected change in
  their portfolios average duration.
• The future path of interest rates cannot be
  perfectly forecast therefore, immunization with
  duration cannot be perfect without the use of
  complicated models.