Hedging the unhedgeable longevity risk

Unexpected increases in longevity

Hedging the unhedgeable longevity risk

Considering the illiquid nature of these swaps, along with the imbalance between the buyers and the sellers, these are still early days for this market

Unexpected increases in longevity raise the costs for life insurance companies. Longevity risk occurs when people living longer than expected.

In the Netherlands the life expectancy of a 65 year old male in 1951 was 13 years and that of a 65 year old female was 14 years. Today, this has increased to 20 and 22 respectively. An annuity of EUR 10,000 for a 65 year old male in 2011 has a net present value (NPV) of EUR 140,000. This value is the present value of the estimated payments based on the expected survival for all future years discounted to present value terms. However if there were to be an improvement of one year in life expectancy, this value would increase to EUR 145,800 – that is almost a 4% increase in the actuarial value of the annuity. With the impending Solvency II regulations, and subsequently the risk based capital requirements, longevity risk becomes even more signifi cant.

More equity

Along with the solvency capital requirements (SCR) for longevity, Solvency II regulations also impose the risk margin in the value of liabilities known as the market value margin (MVM). The market value of liabilities according to Solvency II is the sum of the NPV of the liabilities and the MVM. The MVM is based on the cost of capital for all future capital that is to be held for all unhedgeable risks (that includes longevity risk). If longevity risk could be hedged, the solvency capital requirements would decrease and subsequently so would the MVM. The main aim of hedging would be to off set the hedging cost by a decrease in the MVM, as this would increase the shareholder’s equity along with reduced risk. For insurance companies there are limited options to reduce longevity risk. The ideal instrument for an insurance company would be an asset, whose returns are linked to longevity. A longevity swap is an agreement under which cash fl ows are exchanged that are on the one hand based on the mortality expectations at the start of the contract (fi xed leg) and on the other hand on the actual realized mortality (fl oating leg). The counterparties for such swaps are generally reinsurers who can hedge their mortality risk, or investment banks and hedge funds looking for risk diversification in their portfolio.

Premium

One of the first swaps entered into was by Lucida Plc, an insurance company in the UK. They entered into a 10-year swap with JP Morgan in February 2008 covering liabilities of GBP 100 million. Later in that year, Canada Life entered into a swap for 40 years with JP Morgan covering liabilities of £500 million. Since then, there have been a myriad of swap deals that have occurred between pension funds, insurance companies and investment banks, mainly in the UK. As these are still early days for this market, and considering the illiquid nature of these swaps along with the imbalance between the buyers and the sellers of these swaps, there is a premium that the buyers of longevity swaps have to pay. These premiums are expressed as a percentage of fi xed payments, which are to be paid in addition to the fi xed payments each period.

Example

Consider a homogenous portfolio of 65 year old Dutch males with total annuity rights of EUR 10,000, i.e. they receive EUR 10,000 for each year they are alive. The assets of the portfolio are all invested in a cash account, worth EUR 165,000 and perfectly hedged for interest risk. The portfolio is only exposed to longevity risk. The balance sheet of this portfolio looks as below:

To hedge the longevity risk of this portfolio a longevity swap matching the liabilities of the portfolio is to be designed. The notional of a longevity swap is based on the payments that are linked to longevity, in this case it is EUR 10,000, and therefore the notional is EUR 10,000. The underlying mortality for the swap would be based on that of a 65 year old Dutch male. The time length of the swap is as long as the liabilities. The premium for this swap is 3%. This would mean that the value of the swap is -EUR 4,200, as at the time of inception the mortality for the fi xed leg and the fl oating leg are the same. The capital requirements for longevity are reduced to zero due to perfect hedging and so is the MVM. This gives the balance sheet as below:

This hedge results in an increase in the shareholders equity by EUR 6,500, along with reduced risk as the SCR has fallen, shown by the MVM going to zero. However, had this premium been 8%, then the value of the swap would be -EUR 11,200. The MVM would still go to zero. The balance sheet with this higher premium is as follows:

With the higher premium, the cost of the hedge is EUR 500 more than the reduction in the MVM. This decreases the shareholder’s equity by EUR 500, although this scenario does still have reduced risk due to the hedge.

Longevity swaps have the capacity to hedge longevity risk and create a more risk-managed portfolio. And with the right premium, can also create value for the shareholders.