Return of Premium (ROP)

Return of Premium (ROP), as its name stated, is returning the premium that the policyholders have paid to them. The ROP can be paid upon death / surrender / maturity as the contract specified. In some jurisdiction (eg: India), there may be statutory requirement for insurers to paid a certain portion of ROP to the policyholders upon death or surrender.

The simplest formula, or the industry widely adopted formula for ROP is:

\begin{equation}
\begin{split}
BENEFIT\_PP _t & = ANN\_PREM × POL\_YR _t  × ADJ\_PC _t\\
BENEFIT\_OUTGO _t & = BENEFIT\_PP _t × NO\_STATES _t
\end{split}
\end{equation}

For example, if it is the 3 policy year for a whole life insurance policies, and the annual premium is 100. The contract states the policyholder can get 50% of ROP upon surrender. And it is expected 0.3 people will surrender at year 3. Then the surrender outgo is calculated by:

SURR_PP = 100 * 3 * 50% = 150
SURR_OUTGO = 150 * 0.3 = 45

Since premium may not be fixed (eg: for some guarantee renewal term products the premium can change every year), the above formula using constant "ANN_PREM" is flawed in this case. Some insurers therefore adopt the modified formula for these circumstances:

\begin{equation}
\begin{split}
BENEFIT\_PP _t & = \sum_{s = 1}^{t} PREM\_INC\_PP _s × ADJ\_PC _t\\
BENEFIT\_OUTGO _t & = BENEFIT\_PP _t × NO\_STATES _t
\end{split}
\end{equation}

I personally don't like this formula as well. I would suggest a more generic formula by treating cumulative paid premium as a balance (without interest credited to it). There is, creating a new variable to save the total premium paid and use it as a base for calculation, as below:

\begin{equation}
\begin{split}
ACCM\_PREM _t & = \sum_{s = 1}^{t} PREM\_INC\_PP _s \\
BENEFIT\_PP _t & =  ACCM\_PREM _t × ADJ\_PC _t\\
BENEFIT\_OUTGO _t & = BENEFIT\_PP _t × NO\_STATES _t
\end{split}
\end{equation}

This gives more flexibility and generalized the formula for any situation even there are twist on the premium payment formula.

Let's go through a practical example below:

We shall use the same double decrement model we have introduced in previous chapters. The annual premium is 100 and payable for 5 years. Assume the contracts stated that it will pay ROP upon death, surrender and maturity with the following percentages:

Year 1

ACCM_PREM(1) = ACCM_PREM(0) + PREM_INC_PP(1) = 0 + 100 = 100

DB_PP(1) = ACCM__PREM(1) * ROP_DTH_PC(1) = 100 * 120% = 120

DTH_OUTGO = DB_PP * NO_DEATHS = 120 * 0.000174 = 0.02

GCV_PP(1) = ACCM_PREM(1) * ROP_SURR_PC(1) = 100 * 30% = 30

SURR_OUTGO = GCV_PP * NO_SURRS = 30 * 0.099991 = 3.00

MAT_PP(1) = ACCM_PREM(1) * ROP_MAT_PC(1) = 100 * 0 = 0

MAT_OUTGO = MAT_PP * NO_MATS = 0 * 0 = 0

Year 2

ACCM_PREM(2) = ACCM_PREM(1) + PREM_INC_PP(2) = 100 + 100 = 200

DB_PP(1) = ACCM__PREM(2) * ROP_DTH_PC(2) = 200 * 120% = 240

DTH_OUTGO = DB_PP * NO_DEATHS = 240 * 0.000312 = 0.07

GCV_PP(1) = ACCM_PREM(2) * ROP_SURR_PC(2) = 200 * 40% = 80

SURR_OUTGO = GCV_PP * NO_SURRS = 80 * 0.044984 = 3.60

MAT_PP(1) = ACCM_PREM(2) * ROP_MAT_PC(2) = 200 * 0 = 0

MAT_OUTGO = MAT_PP * NO_MATS = 0 * 0 = 0

...

Year 10

ACCM_PREM(10) = ACCM_PREM(9) + PREM_INC_PP(10) = 500 + 0 = 500

DB_PP(10) = ACCM__PREM(10) * ROP_DTH_PC(10) = 500 * 120% = 600

DTH_OUTGO = DB_PP * NO_DEATHS = 600 * 0.000492 = 0.30

GCV_PP(10) = ACCM_PREM(10) * ROP_SURR_PC(10) = 600 * 100% = 600

SURR_OUTGO = GCV_PP * NO_SURRS = 600 * 0.007850 = 3.92

MAT_PP(10) = ACCM_PREM(10) * ROP_MAT_PC(10) = 600 * 100% = 600

MAT_OUTGO = MAT_PP * NO_MATS = 600 * 0.776870 = 388.43

A demonstration spreadsheet showing the calculation above can be downloaded here:

https://drive.google.com/file/d/0B4OirwHLcmE1c1hYQVQzU1cyNlk/view?usp=sharing