Иммунизация облигаций

Иммунизация облигаций

Иммунизация 

• Инвестиционная  стратегия, которая помогает защитить ожидаемый доход по ценной бумаге или портфелю ценных бумаг, когда  приобретаются такие ценные бумаги, чья дюрация соответствует продолжительности  планируемого инвестором периода владения.

  

• Если средняя  дюрация равна желаемому периоду  владения инвестором ценной бумаги, эффект состоит в том, что общий доход  инвестора постоянен независимо от того, растут ли процентные ставки или  нет.

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.

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%.

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.

Example: Case 1 

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

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.

Example: Case 2 

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

Immunization and Duration 

• The investor’s 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.

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 bond’s market price will rise to $1,001.60 due to the drop in interest rates.

Example: Case 1 

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

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 bond’s market price will fall to $998.40 due to the rise in interest rates.

Example: Case 2 

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

Conclusion 

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

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.