## Gratuity Valuation – A Simple Example Continued – Sensitivity Analysis

*in*Actuarial Concepts

# Sensitivity Analysis

The results of the gratuity valuation need to be tested for their sensitivity to key actuarial assumptions. Continuing with our simple example, we have carried out a sensitivity analysis on the Discount Rate and Salary Increase assumptions below.

Firstly, we re-calculate the actuarial liability by varying the assumptions one at a time while keeping all other assumptions unchanged and see the impact on the funded status of the plan (as mentioned above, for illustration purposes, we are only considering two key assumptions in our analysis both of which relate to the liability calculations). The result of this exercise is give below:

Assumptions | Existing | i | i | s | s |

Discount rate (i) | 13% | 14% | 12% | 13% | 13% |

Salary increase factor (s) | 8% | 8% | 8% | 9% | 7% |

Actuarial Liability as at 31-12-2010 | 10,454.09 | 8,096.93 | 13,528.15 | 13,657.32 | 7,982.28 |

Fair Value of Plan Assets as at 31-12-2010 | 10,000.00 | 10,000.00 | 10,000.00 | 10,000.00 | 10,000.00 |

Surplus (deficit) | -454.09 | 1,903.07 | -3,528.15 | -3,657.32 | 2,017.72 |

We have assumed a 1% change over the existing assumptions. The existing position shows an actuarial deficit of 454. When the discount rate is increased by 1%, all other factors kept unchanged, it results in an actuarial surplus of 1903.07. On the other hand if the discount rate were to decrease by 1% it would result in a much larger deficit.

When the salary growth rate is increased by 1% the deficit increases eight-fold whereas a 1% decline in the growth rate results in a decline in the actuarial liability and consequently a significant surplus. The sensitivity of the actuarial liability and hence surplus appears to be greater for the salary increase assumption than the discount rate.

In order to assess the extent of a 1% change in the discount rate (or salary growth rate) on the actuarial liability we will calculate the duration and convexity of the liability. Using the derived duration and convexity we then calculate the approximate change (%) in liability. The methodology for determining duration, convexity and approximate change (%) is discussed in the following course:

Duration & Convexity Calculation Example

The results of this analysis are given below:

Discount Rate (i) | 0 | – | + |

i | 13.00% | 12.00% | 14.00% |

Actuarial Liability | 10,454 | 13,528 | 8,097 |

Duration | 25.98 | ||

Convexity | 342.88 | ||

Approximate liability change (%) | |||

due to duration | 25.98% | -25.98% | |

due to convexity | 3.43% | 3.43% | |

Total change in liability (%) | 29.41% | -22.55% |

Salary Increase (s) | 0 | – | + |

s | 8.00% | 7.00% | 9.00% |

Actuarial Liability | 10,454 | 7,982 | 13,657 |

Duration | (27.14) | ||

Convexity | 349.83 | ||

Approximate liability change (%) | |||

due to duration | -27.14% | 27.14% | |

due to convexity | 3.50% | 3.50% | |

Total change in liability (%) | -23.64% | 30.64% |

The 0, – and + signs in the first row, represent the existing position of the assumption, a 1% decline in the assumption and a 1% increase in the assumption respectively.

A 1% decrease in the Discount Rate assumption leads to a 29.41% increase in the actuarial liability all other factors kept unchanged, whereas a 1% increase in the assumption leads to a 22.55% decline in the actuarial liability, all other factors kept unchanged.

A 1% decrease in the Salary Increase assumption leads to a 23.64% decrease in the actuarial liability all other factors kept unchanged, whereas a 1% increase in the assumption leads to a 30.64% increase in the actuarial liability, all other factors kept unchanged.

As can be seen the actuarial liability is the most sensitive to an increase in the salary growth assumption, all other factors kept unchanged.