# On variable annuities

Its been a while that I haven’t looked at variable annuity products, so I am writing this post to refresh my memory tool!

A variable annuity products is a insurance product, it is most of the time a life insurance products. People invest and are supposed to recieve some fixed coupons amount based on the valuation of the portfolio. Let;s assume Mr A has bought a variable annuity instrument from a life insurance, The insurance purchase a basket of Equity and bond and money market instrument on behalf of Mr A. The basket can be fixed or be reblanced on a periodic basis , this depends if the variable annuity product has a policy to keep a fixed weight ( in dollars) among different asset. The insurance will pay coupon based on the performance of the basket each year until death happens. At the event of death the insurance pays the basket amount to the beneficiaries of Mr A. However the insurance guaranties that the coupon levels will be higher than a certain amount. It also guaranties that the guaranteed amount would be higher than a certain level. So the insurance cover the risk of Mr A against losing a big revenue and covers the risk of beneficiaries of Mr A in case of death. On the other hand the client has the right to exit at his own discretion and will recieve a lump sum, this lump sum is normally hair cutted, it is only a percentage of the total investment. But this lump sum can be also floored, so the client will recieve a minimum amount of its initial investment.

So Mr A having invested on variable annuities can recieve 3 type of income:

A fixed retirement income , variable depending on the portfolio level

The guaranteed lump sum in case of death

A hair cutted lump sum in case of an exit

The lump is sum is normally calculated based on a maximum drawdown. It is a weighted lookback , a level which depends on the maximum and average value of the variable annuity protfolio since inception

These life insurance products are generally in demand because of many reasons, one reason is an extra pension. The other is related to covering the cost of inheritance tax for the beneficiaries. The above explanation is a very simplistic one, There are mainly three risks associated with the variable annuities, the client exit risk, and the life risk the market risk. The two first are mostly called actuarial risk. The market risk in itself is a complicated structure product.

The insurance normally contact a bank in cover its market risk, that being said the risk that the portfolio income can not cover the floored level or the lump sum. Both death and client exit can be simulated via deterministic or stochastic models. In case of the deterministic model the risk is calculated based on actuarial assumptions.

One of risk of the variable annuity product is the sensitivity to the bond and equity correlation. When rates goes high, they normally have slightly negative correlation to the equity and they do have strong negative correlation to the bond value. The bond being fixed at a predefined yield is no more interesting and the bond portfolio value decreases. So in case of a positive move on rates both the equities and the bond porfolio goes down. This will double the effect of the devaluation of the portfolio and needs to be taken into account while pricing the variable annuity put contract.