Immunization (form of investment matching)

Question 1

Immunistaion - approximate liability matching

Answer 1

• Investment of assets such that the present value of assets less liabilities is immune to
  general small changes in interest rates
  𝑘
• DMT = ∑ 𝐶𝑘∗𝑣𝑡𝑘 ∗𝑡𝑘/
  ∑ 𝐶𝑘
  𝑘 ∗𝑣𝑡𝑘
• Convexity = second derivative with respect to the effective interest rate/ Pv of assets /
  liabilities ( sensitivity of volatility of the cashflows to change in interest rate)
• Volatility = DMT * v
• Purpose : similar to matching, which is to reduce the risk of failing to meet liabilities as they
  fall due , arising from changes in investment conditions
• Used when pure matching is not possible
• Ensures that PV of assets is never less than that of liabilities , rather than matching the
  timing and amounts of individual cashflows

Question 2

Conditions of immunization

Answer 2

• PV ( Assets ) = PV ( Liability outgo )
• DMT ( Assets ) = DMT ( Liabilities )
• Convexity ( Assets ) > Convexity ( Liabilities ) / spread

Question 3

Limitations of the classical immunization theory

Answer 3

• Generally aimed at fitting monetary liabilities , and many investors need to meet real
  liabilities
• The possibility of mismatching profits as well as the losses is removed apart from a small
  second order effect
• Theory rely in small changes in interest rates , the fund may not be protected or hedged
  against large interest rate changes
• The theory assumes a flat yield curve and requires same change in interest rates at all terms
  o In practice , the yield curve does change shape from time to time
• In practice , the portfolio must be rearranged constantly to maintain the correct balance of
  o Equal DMT and
  o greater spread of assets proceeds
  o therefore the theory ignores the dealing costs of daily or monthly arrangement of
  assets
• Assets of a suitably long DMT may not exist
• The timing of assets proceeds and liability outgo may not be known