Actuaries Scrutunized!

[Kenshiro]

Originally Posted by Emily

Because they already accrued the cost before the salary increase. They couldn't have gotten out of it. It wouldn't be reasonable to assume people keep working without salaries at least keeping up with inflation. There is an inflation component in the discount rate, why take it out of the liability stream.

This is an accounting issue, not a valuation issue. I could see either being reasonable, but you would want the treatment to be the same across entities. If public sector salary increases are tied directly to inflation (which they may be), I think the argument for PBO is stronger. I wouldn't really object to it.

[WWSituation]

The reason to use the risk free rate is to know how much cash it will take in today's market to replicate a position (from a market risk perspective). In a no-arbitrage world, this is the MINIMUM value a stream of cash flows can take to ensure no-arbitrage. The underlying source of the position is irrelevant (i.e. actives, inactives, whatever).

Whether you want to build inflation into your benefit is another matter, and there are risk-free benchmarks for replicating those positions as well.

Whoever said that plan sponsors in the corporate sector gets this is thinking very wishfully, though there are a few that seem like they do after being force-fed the concept for all of these years.

[Jeremy Gold]

It is difficult to agree on an answer when several different questions are being asked. Most economists would probably ask what does the employee acquire, when does s/he acquire it, and what's its value?

Clearly salary is acquired pretty contemporaneously with its payment. Along with salary, the public employee acquires promises of future cash flows. In the simplest case, it seems that the promises are acquired in an accrued benefit (rather than a projected benefit) pattern. This should be our first answer and it will generally lead to good decision making by employees (whether to take the job, when to stay and when to leave), by taxpayers (how much value are our employees acquiring each year -- pay and promises), and by the negotiators (unions for the employees and elected officials, weakly, for the taxpayers).

When benefit payments are certain to be made (zero or near zero probability of default or reneging) the discount should be at or near default free as well.

It seems pretty clear that the acquired benefit cannot be less than the accrued since the employee can take that at will. And thus the liability cannot be less than the accrued benefit valued at default free rates.

BTW, I like several comments in this thread such as:

Why would you want to account for something before the service has been performed?
You're paying these guys salaries too. Do you think you'd put your expected future payroll on the books too?
Using PBO because the benefits are protected from cutback just confuses the accounting.

I think that Emily and others who defend the traditional actuarial practice want to use models that best predict what will happen in all aspects of the plan's operation -- benefit accrual, salary increases (usually viewed as exogenous, where an economist would generally design an endogenous model), expected rates of return on assets, etc.

So it may be that the distinction is this -- traditional actuaries believe our job is to predict (and this may be pretty useful for budgeting and for planning) while pension finance actuaries think our job is to price (synonym of value in this context) benefit promises as they are made by the employer and acquired by the employee (and this may be pretty useful for financial reporting and decision making (in re: benefit improvements and pay increases).

But could the liability be greater than the ABO?

In the private sector situation, I have argued that a liability with respect to future service exists if the employee will be paid more than s/he is worth in the future and the employer is committed to pay more than the value of the services rendered. In the private sector, I argue that we do not account for future salaries because pay will be kept commensurate with value delivered by competitive forces. By extension, since total comp should be more competitively disciplined than cash pay, there is no reason to account for pensions based on future pay.*

Note that a contract that called upon an employee to perform well for five years and then to hack it for the next five (think sports, think entertainment) while receiving pre-negotiated pay for the whole ten years might leave the employer with a liability after five years. But the necessary condition for a liability is the existence of a contract that is competitive over the whole period but pays less than the employee is worth at first and more later.

A well administered pay scheme in the private sector should not generate liabilities beyond accrued benefits -- at least not for a cohort. We might overpay some and underpay others but competition should keep us in line.

But in the public sector competitive forces may be inadequate to discipline the total compensation system. Just for example, in many localities public sector employees vote their pocketbooks and politicians respond.

So I am comfortable with ABO in the private sector (should be adjusted for default risk, if any, think about unfunded SERPs promised by airlines and steel companies) and I am comfortable with ABO in the public sector -- as (1) the minimum liability and (2) a key decision influencing tool that, if disclosed and monitored, may discipline negotiations in such a way that total future compensation should not be too much greater than the value of services to be rendered.** Without decent measures, how can we expect politicians to ever try to balance total compensation and services rendered.

The key issue for an economist is the contract (explicit or implicit) and how understanding the contract helps to answer what the employee gets, when, and what is its value.

* http://www.soa.org/library/journals/...naaj0501-6.pdf

** i.e. with ABO disclosed, the excess of the economic liability over the ABO will be held in check -- more so, at least, than it appears to be in some systems today.

[Dan Moore]

One new term is introduced by the model: present value of future (sponsor) contributions, or PVFC. PVFC is a simplified risk-adjusted calculation of a discounted set of projected sponsor contributions to the plan:

• Demographic and economic assumptions (including mandated assumptions) that are subject to variation that would significantly affect contributions (variable assumptions) will have a normal distribution imposed on them, and contributions will be forecasted at three levels for each variable assumption: the mean, and the mean plus & minus one standard deviation. These three values are approximately at the centroids of the middle one-third and the two tail one-thirds of the distribution, and are intended to account for the risk of the experience differing from the mean. If there are 2 variable assumptions there would be a total of 3^2, or 9, contribution forecasts.
• For simplicity, the assumed demographic, trend, and salary scale experience used in the forecasts is also the assumption used in the forecast actuarial valuation (if a valuation is needed).
• If the variable assumptions are deemed to be uncorrelated, the unweighted average of all the forecasts would be used. If two variable assumptions are deemed to have a correlation of -0.5, for example, then the results from the (+-) and (-+) corners are weighted 1.5, and (++) and (--) are weighted 0.5; the other 5 weighted 1.0.
• For a US qualified pension plan, there would likely be at least 2 variable assumptions; return on assets, and PPA 06 segment rates. In addition, for a pension plan, salary scale and retirement rates may be deemed to be variable assumptions. For a postretirement medical plan, medical inflation trend would be a variable assumption.
• Selected forecasts, including the worst case, and interpolation of results could be used to cut down on the number of forecasts needed.

Before continuing to discuss the details of PVFC, I will peek ahead to show where I’m going with this. The question posed by FAS 157 is: what price is the DB plan sponsor willing to pay to settle the liabilities. The answer given by this model is that the maximum price they would pay is the price that keeps the PVFC unchanged. That is, the DB plan sponsor won’t settle liabilities if that results in an increase in the PVFC.

As to the MVA of plan assets, the plan sponsor considers that (in most cases) to be already gone, in that there is no expectation of ever getting it back. Its value is in reducing future sponsor contributions. The plan sponsor views the PVFC as its debt for the DB plan.

Consider the equation:

MVA + PVFC = PVFB + PVFE

The last 2 terms are present value of future benefits and present value of future expenses. PVFE should be included because plans do have expenses and including it will slightly lower the resulting discount rate for a funded plan where the funding of expenses is deferred (as under PPA 06). (Expenses would also be reflected in the projected assets used in the forecasts.) To simplify this description, however, I’m dropping this term, so we have:

MVA + PVFC = PVFB.

PVFB is the regular PVFB, calculated using non-variable assumptions (set at the mean). The discount rate produced by the model is the one that makes the equation true when it’s used to calculate PVFB.

To see why this is, say the sponsor wished to settle the entire PVFB. He would be willing to pay MVA + PVFC; his immediate out-of pocket cost is PVFC, so PVFC hasn’t changed.

Say he wanted to settle a fraction k of the PVFB, leaving (1-k) * PVFB remaining. He would be willing to pay k *(MVA + PVFC). You have (1-k)* MVA + (1-k)*PVFC = (1-k)*PVFB. His remaining present value of future contributions PVFC’ = (1-k)*PVFC + k*PVFC = PVFC, whether k*PVFC of the settlement is paid out of plan assets or outside the plan.

The reason PVFB is not explicitly risk-adjusted is that the PBO (or ABO) you will calculate using the resulting discount rate is not explicitly risk-adjusted either; all the risk adjustment occurs in the calculation of PVFC.

[Kenshiro]

Originally Posted by Dan Moore

One new term is introduced by the model: present value of future (sponsor) contributions, or PVFC. PVFC is a simplified risk-adjusted calculation of a discounted set of projected sponsor contributions to the plan:

• Demographic and economic assumptions (including mandated assumptions) that are subject to variation that would significantly affect contributions (variable assumptions) will have a normal distribution imposed on them, and contributions will be forecasted at three levels for each variable assumption: the mean, and the mean plus & minus one standard deviation. These three values are approximately at the centroids of the middle one-third and the two tail one-thirds of the distribution, and are intended to account for the risk of the experience differing from the mean. If there are 2 variable assumptions there would be a total of 3^2, or 9, contribution forecasts.
• For simplicity, the assumed demographic, trend, and salary scale experience used in the forecasts is also the assumption used in the forecast actuarial valuation (if a valuation is needed).
• If the variable assumptions are deemed to be uncorrelated, the unweighted average of all the forecasts would be used. If two variable assumptions are deemed to have a correlation of -0.5, for example, then the results from the (+-) and (-+) corners are weighted 1.5, and (++) and (--) are weighted 0.5; the other 5 weighted 1.0.
• For a US qualified pension plan, there would likely be at least 2 variable assumptions; return on assets, and PPA 06 segment rates. In addition, for a pension plan, salary scale and retirement rates may be deemed to be variable assumptions. For a postretirement medical plan, medical inflation trend would be a variable assumption.
• Selected forecasts, including the worst case, and interpolation of results could be used to cut down on the number of forecasts needed.

Before continuing to discuss the details of PVFC, I will peek ahead to show where I’m going with this. The question posed by FAS 157 is: what price is the DB plan sponsor willing to pay to settle the liabilities. The answer given by this model is that the maximum price they would pay is the price that keeps the PVFC unchanged. That is, the DB plan sponsor won’t settle liabilities if that results in an increase in the PVFC.

As to the MVA of plan assets, the plan sponsor considers that (in most cases) to be already gone, in that there is no expectation of ever getting it back. Its value is in reducing future sponsor contributions. The plan sponsor views the PVFC as its debt for the DB plan.

Consider the equation:

MVA + PVFC = PVFB + PVFE

The last 2 terms are present value of future benefits and present value of future expenses. PVFE should be included because plans do have expenses and including it will slightly lower the resulting discount rate for a funded plan where the funding of expenses is deferred (as under PPA 06). (Expenses would also be reflected in the projected assets used in the forecasts.) To simplify this description, however, I’m dropping this term, so we have:

MVA + PVFC = PVFB.

PVFB is the regular PVFB, calculated using non-variable assumptions (set at the mean). The discount rate produced by the model is the one that makes the equation true when it’s used to calculate PVFB.

To see why this is, say the sponsor wished to settle the entire PVFB. He would be willing to pay MVA + PVFC; his immediate out-of pocket cost is PVFC, so PVFC hasn’t changed.

Say he wanted to settle a fraction k of the PVFB, leaving (1-k) * PVFB remaining. He would be willing to pay k *(MVA + PVFC). You have (1-k)* MVA + (1-k)*PVFC = (1-k)*PVFB. His remaining present value of future contributions PVFC’ = (1-k)*PVFC + k*PVFC = PVFC, whether k*PVFC of the settlement is paid out of plan assets or outside the plan.

The reason PVFB is not explicitly risk-adjusted is that the PBO (or ABO) you will calculate using the resulting discount rate is not explicitly risk-adjusted either; all the risk adjustment occurs in the calculation of PVFC.

Before I point out any problems with your model (and there are several), I want to just ask...why? What problems with the current or FE model are you trying to fix?

Emily, would you support this model?

[Emily]

Originally Posted by Kenshiro

Emily, would you support this model?

Looks promising. It's contributions that public plan sponsors are concerned with, not arbitrary measures of liability.

[JMO]

Originally Posted by Emily

Looks promising. It's contributions that public plan sponsors are concerned with, not arbitrary measures of liability.

[Kenshiro]

Originally Posted by Emily

Looks promising. It's contributions that public plan sponsors are concerned with, not arbitrary measures of liability.

Originally Posted by JMO

Et tu, JMO?

[short & sweet]

Originally Posted by Dan Moore

One new term is introduced by the model: present value of future (sponsor) contributions, or PVFC. PVFC is a simplified risk-adjusted calculation of a discounted set of projected sponsor contributions to the plan

I'll throw in two cents, acknowledging there are a diverse range of perspectives and I haven't absorbed everything.

The discount model using PVFC would be intended as just a mathematical funding perspective where the calculated fund balance is not intended to reflect funding security for accrued benefits.

An observer might say that PVFC represents the extent to which the plan is underfunded, but since the liabilities being funded in the calculation include future pension accruals based on future salary increases, the results are not really intended to say anything about the adequacy of the funding security for accrued benefits.

[Dan Moore]

More details on the calculation of PVFC:

• Return on assets is calculated in the forecast based on the plan’s investment allocation and the expectation and standard deviation of return for each investment category. Current FE does not dispute that equities can have a higher expected return than bonds; merely that the higher expected return is deemed irrelevant to the liability pricing. For PVFC, it’s not irrelevant.
• A funded plan’s projected future investment allocation is assumed to be the same as at present.
• Expected returns on equities should be adjusted to reflect current P/E levels vs. an average PE over the last 20 – 40 years. For me to accept that P/E levels have reached a permanently higher level will require many years of evidence. Assuming we will be able to calculate a relevant P/E in the future, of course.
• The general rule about forecasting contributions is that they are forecasted at the minimum required level. An exception would be made for a private or public sector postretirement plan not subject to minimum funding where the sponsor has made a written commitment to fund the plan at a certain level. If the sponsor reneges on the funding, it’s back to pay-as-you go forecasting until the shortfall is made up.
• For a funded plan, you need only forecast out to the point where the contributions end, starting with the worst case, if there is such a point.
• New entrants shouldn’t be included in the forecasts for PVFC because they don’t appear on the right hand side of the equation (PVFB).
• A discount rate is required to calculate PVFC (different from the discount rate the model produces). This rate is representative of the sponsor’s debt to its employees, so it should be a rate that is senior to its regular bond rate. It should probably be close to a risk-free rate. The logic here is that a company can go into bankruptcy and default on its loans, and still continue in business. It can’t, however, default on its compensation to employees, and the DBs are akin to compensation. (This is (kind of) my area of agreement with Jeremy Gold!)
• For an overfunded plan, the equation breaks down because you can’t have a negative PVFC. The solution is to set a minimum discount rate for the model at the risk-free rate and for FASB to impose a cap on the pension asset similar to IASB, unless a surplus can be returned.