Asset liability modeling: Understanding the basics
22 August 2006

To fully understand what asset liability modeling (ALM) is and how it works, we’ll need to go back to basics.

In general, people don’t work continuously until they die but eventually reach an age when it’s either impossible or unfeasible for them to carry on working. Once they have stopped working, most people still have many years to live, and with that come the associated needs, wants and responsibilities of everyday life. People still need to, for example, eat and have a place to live, etc and therefore require an income or some sort of savings to afford this.

In an ideal world, everyone would save enough money in their working years to provide for the period in their lives when they won’t earn a living. However in reality most of us don’t have the discipline to save continuously or the skills required to invest our savings so as to achieve the best possible returns with the lowest possible risk. It is really because of this that the pension fund industry was born. 

By belonging to a pension fund, members enter into a contract whereby the fund commits to paying them an amount of money at retirement based on an agreed upon formula. This payment is used to fund their income needs in retirement and can be thought of as a “retirement salary”. 

Pension Fund Liabilities

In order to meet their commitments, funds must work out what members’ expectations are regarding the amount they will be paid in retirement. For example, members will probably want to be paid a retirement salary that allows them the kind of lifestyle they have become used to during their working years. They will therefore most likely expect a pension income similar to their salary before retirement.

These amounts, which will provide for the members’ income in retirement, are known as the fund liabilities. In order to retain their real value into the future in relation to the rising cost of living and the members’ expectations regarding their spending power, the fund liabilities are not fixed. They are expressed in “real terms” and are either a function of an employee’s salary close to retirement, linked to a Consumer Price Index or the growth rate of the assets, or a combination of these three factors.

Pension Fund Assets

In order to save enough money for their retirement, members and (in some cases) their employers make ongoing contributions to their pension fund during their working lives – the contributions are typically a percentage of the member’s salary while employed. All these contributions are pooled together and invested by the pension fund on the members’ behalf. The assets of the fund are therefore comprised of member and employer contributions as well as any investment returns achieved on the steady build up of assets.

The Goal of Asset Liability Modeling

The goal of an ALM process is to ensure that the assets of each member and hence the fund as a whole, will be sufficient to cover the expected liabilities of the fund/member in the future. Let’s consider the graph below relating to a fictitious pension fund member, Mr X. At age 25, Mr X joins the fund with zero fund credit. At that point he is being paid a salary of 1 unit, 15% of which he contributes to the fund until age 60 at which point his contract stipulates he must retire. The blue bars below represent Mr X’s contributions, between age 25 and age 60. Note that we assume inflation remains at 3.5% pa for the entire period and hence his salary increases by this amount until he reaches the age of 60. The sum of his contributions as well as the investment growth thereon (i.e. his assets, which we assume will grow at a constant growth of 7.7% per annum for the entire period) is represented by the yellow area.

We assume Mr X retires at 60 and receives pension payments equal to 80% of his final salary until he dies, which we assume is age 80. Each year his pension payments increase in line with inflation. In the below graph, these pension payments are represented by the red bars, and are the liabilities of Mr X’s fund. Matching his assets to his liabilities involves ensuring that at all times, the projected height of the yellow area (i.e. the value of Mr X’s fund assets) is sufficient to cover the sum of the red pension payments from that point until his projected death. The final payment to Mr X, just before his projected death at age 80, would pay out the remaining assets of his portion of the fund.

Why model the assets and liabilities?

Pension fund trustees are bound by a fiduciary duty to act in the best interests of the fund members whose assets they are in charge of. The most important part is ensuring that the members’ expectations regarding what they will be paid during retirement are met. If a member’s assets are not sufficient to cover their liabilities, the fund may face a number of issues ranging from member disappointment and possible lawsuits, to the need to raise the contribution rate or even having to bolster the shortfall from the coffers of the employer/company. (This will depend on the nature of the guarantees provided by the fund, and whether the fund is a defined benefit or defined contribution scheme.) None of these situations are desirable for the fund and can be avoided (though perhaps not prevented) by regularly modeling the fund’s assets and liabilities.

How are the assets and liabilities modeled?

To explain how the assets and liabilities are modeled, let’s revisit the example of Mr X above. In this example we have estimated what will happen to Mr X based on a set of assumed variables that will determine the size of Mr X’s assets and liabilities in the future. The growth rate of his assets, his contribution rate and the age at which he will retire, are assumptions used to determine the size of Mr X’s assets at some point in the future. The inflation rate and the age at which Mr X will die are assumptions used to determine Mr X’s liabilities. A deterministic model such as this is highly dependant on the accuracy of these assumptions, which if incorrect will mean that the predicted level of assets and liabilities is also not correct.            

To improve on the potential inaccuracies that a deterministic model can introduce, most ALM’s use stochastic modeling. In simple terms, some stochastic models also make assumptions about the future based on what happened in the past, but each assumption has a range of possibilities with its own probability of occurring. The model therefore builds a range of possible scenarios for the future with an attached probability of each of those scenarios taking place. To illustrate, let’s use the example of Mr X. In the deterministic model above, we assumed that Mr X would die at age 80. The stochastic way of modeling his mortality would be to say that we assume that Mr X will die somewhere between the ages of 25 and 100, with a high likelihood of his death occurring around age 80 and a small likelihood of it happening before or after then. History, and careful actuarial modeling, has shown that for a typical 25-year-old male, the mortality probability looks something like the graph below.

When applying stochastic modeling to a member’s assets, one can arrive at a range of possible asset returns. So instead of assuming that Mr X’s asset returns will be 7.7%, we could work out a range of possible returns and attach likelihood to each of those possibilities. The answer may look something like the graph below.

Members’ fund assets are usually invested in a variety of different assets classes (e.g. cash, equities, bonds, etc). Each of these asset classes has different risk return characteristics and understanding this is fundamental to formulating an asset mix that is most appropriate for the member. The asset mix will determine what the member’s assets will be worth at a point in the future (e.g. retirement), and if modeled stochastically, we can determine what the likelihood is of achieving that value. We can then get an idea of the probability of meeting the member’s liabilities.

Members of differing age will require a different mix of asset classes, allowing them to take advantage of their associated risk and return characteristics.  For example, a young member, like Mr X above, will be contributing to and growing his asset base over the next 35 years until retirement, and can afford to take some risk to potentially achieve higher returns. A member close to retirement on the other hand, should be much more risk averse, needing to preserve their asset base with respect to the cost of a pension, therefore preparing for retirement. They would therefore require a more conservative, low risk mix of assets.

Even after retirement, pensioners should pay attention to their asset mix as a measure of growth is still necessary to preserve the “real” value of their assets. This is well illustrated in the example of MR X who even after retirement, still manages to grow his assets for a few years.

Once the risk and return characteristics of the asset classes have been modeled, and an asset class mix that will most likely result in the modeled liabilities of that member being met, has been decided upon for each member, the ALM process is complete. The next step is deciding how to implement this asset allocation across the fund. We will cover this process in next month’s article.

ENDS
For more information:
Dianne Lea - Marketing Manager - (021) 683 111 or 083-650 0027