I. Understanding Longevity and Interest Risks Under a Defined Contribution System

As a provident fund, the primary mission of CPF Board is to provide secure retirement. However, designing a payout phase on how and when to drawdown the accumulated savings become very intricate. Mandatory annuitization of CPF savings, which provides a fixed payments in exchange for an initial lump sum, helps to mitigate longevity risks.

For the cohort turning age 55 in January 2021, to receive a full monthly payout for life from age 65, they need to set aside $186,000 in their full retirement account. The estimated monthly payouts based on the CPF LIFE standard plan at age 65 in 2031 are in the range of $1430 and $1530.

Suppose CPF members (John and Mary) can use their CPF monies to buy private annuity products at age 55, with the first payout deferred to age 65. Suppose both John and Mary have the same birthday on 1 January, and both want to use their entire CPF monies in their basic retirement account ($186,000) to buy an annuity. Assume that the committed sum will continue to earn the annual interest rate (monthly compounded) until the payout age of 65.

[1] Consider a term annuity, with the term pegged to the life expectancy at age 65, namely, 20 years for male and 23 years for female.

a. What will be the monthly annuity payouts for John and Mary at age 65 if the annual interest rate is 3.5% and that both John and Mary receive the payouts at the end of each month?

b. What will be their annuity monthly payouts if the annuity provider uses different interest rates (5% and 2%) in the annuity payout formula in response to the interest rate environment? What risks do John and Mary face when buying annuity products?

[2] Besides interest rate risk, John and Mary are well aware of longevity risk, that they will outlive their retirement savings. Both see the possibility of outliving their expected lifespan as both consciously adopt healthier lifestyles. To hedge against longevity risk, they consider using $186,000 to buy a life annuity, which also has an annual interest rate fixed at 3.5%.

a. What will be average monthly payouts for John and Mary for a life annuity?

b. Analyze and provide possible reasons why the computed payouts are different from the estimated CPF LIFE payouts.

Hint: First compute the annual life annuity since the life table gives age in years and not in months. Use the 2018 complete life tables for Singapore male and female residents to compute the survival probability (the probability of surviving to age x+t) from age x =65 to 100+ for John and Mary.

Let _t p_x be the probability that someone aged exactly x will survive for x+t more years, i.e. live up to at least age x+t years.

_t p_x = l_x+t /l_x

The conditional probability of survival at age x is given by _t p_x= 1- _t q_x