Wednesday, December 18, 2013

Mei's Monte Carlo Adventure

"As you know Mei the company decided to move from a DB plan to a DC plan...even though it was hotly debated." Aisha, VP of Human Resources, told Mei as they walked from the cafeteria. "However, now that its done we need to manage the transition and understand the implications. Can you help us with that? I know you had mentioned Monte Carlo simulation before"

"Absolutely!" Mei replied. For quite awhile she had thought such an approach might help quantify impacts of such a change.

"There are a still a lot of questions" Aisha continued. "How will the company go about funding this change in benefit? And what does this change mean for employees compared to where they are currently?"

"Those are great questions" Mei replied. "It is a complicated topic..."

"It is!" Aisha emphatically agreed. "That's why I am trying to get as much clarity as possible."

"Well, I did something similar a while back, and so half the work is already done." Mei said. "Let's set up a time to talk tomorrow...I should have something for you by then."

"OK, that'll be great!" Aisha responded, a grin slowly appearing on her face. "Of course, I could always have my people get a hold of your people..."

Mei smiled. "I think it might be quicker if we just say 2 o'clock!" They both laughed.

"OK, two it is!"

Retirement planning (any financial planning for that matter) can be a difficult undertaking.

For all the reasons we have enumerated before (for example "Why Your Cash Flow Forecast Will Always Be Wrong") forecasting the future is impossible to do. There are simply too many unknowns.

One of the advantages to a technique like Monte Carlo simulation is that it can let you glimpse some of the possible outcomes the future may hold - good or bad.

While our last post - Pension Potholes: Mei and the Curse of Exponentiation - focused on the accounting side of retirement plans, in this post we will look at the economics to both the company and the individual.

Portfolio Differences

There are a number of fundamental differences to be considered when we make a comparison between a Defined Benefit plan (DB) and Defined Contribution plan (DC).

One of these is the investment portfolio. In a DB plan, the company assumes responsibility for managing the portfolio (usually with the assistance of consultants and investment managers). In most DC plans, the individual directs the investments.

A company, with many employees, some new and some near retirement, enjoys the benefits of the the pooling principle when constructing its investment portfolio. The portfolio can remain relatively constant through time, because in any given year only a small fraction of the assets are needed to pay out benefits.

For the individual employee, the makeup of the investment portfolio will change over time. Why? Because the closer one gets to needing the funds, the less risk one can take with them. If we are going to need $100 next year, investing them in an asset that could decline by 50% over that time is not wise, as we run the risk of only having $50 when we needed $100.

On the other hand, if we don't need that $100 for 40 years, a 50% blip...or two...or three, won't matter much as there is a lot of time for recovery and high returns to make up for it.

Because of this, a typical investment pattern through a person's lifetime begins with a large portion of higher return / higher risk securities like stocks. As time goes on, these securities are gradually replaced by lower risk (and lower return) securities like bonds.

Figure A
The percentage of high risk securities that make up the portfolio decreases over time in order to reduce potential variation

Figure A shows how this mix changes over time. Because of the downward slope of the line, it is sometime referred to as the investment or portfolio "glidepath".

The Burden of Uncertainty

Another major difference between the two plans is who bears the burden of uncertainty.

An employee who has saved $1 million has saved too much if they die the following year, while another will have saved too little if they live to be 103. The answer to the question "have I saved enough?" is unknown until life has played out.

In a DB plan this uncertainty is borne by the pension sponsor. With many participants, this risk is tempered by the the pooling principle. Some will grow old while others will die young, with the result that it tends to average out from year to year, and also between years.

Another source of uncertainty is counterparty risk, and here the DC participant has the advantage. The employee receives a contribution every year and can invest it at their own direction. They can ensure that they diversify their counterparty risk by investing in a number of different funds from a number of different management companies. Should Vanguard go under, for instance, only a portion of their assets will become ensnared in the quagmire.

The DB participant relies on the employer. Should the employer go under, support of the plan will cease, and the future of any benefit payments becomes questionable. There are 'backstops' in the US, such as the Pension Benefit Guaranty Corporation (PBGC), but these are imperfect. For one, the PBGC only guarantees a minimum amount of the benefits, so the remainder will be lost. In addition, being a Federal agency, its future is always a bit uncertain as well, subject to the vagaries of dysfunctional political processes. The US seems to struggle these days with what it can afford and what it is willing to pay for, so there is always the danger that the PBGC goes the same way itself as those it has had to guarantee.

What Needs to Get Funded?

Mei stopped by the office of Enrique, who worked in HR.

"Hi Enrique, I'm helping Aisha with a project and wondered if I could pick your brain for a moment?"

"Sure", said Enríque "What do you need?"

"With the company moving to a DC plan, we want to understand the financial implications in order to design things in the best way. Part of that involves looking at how we may make funding contributions to the retirement plans."

"I'm not sure how much help I can be for financial're the company's recognized expert at that Mei!" exclaimed Enrique.

Mei blushed. She tried hard to do great work and was always happy to hear that she had been successful, but in her mind that was simply attempting to be the best she could be and giving the company all she got. Doesn't everyone do that?

"Don't sell yourself short, Enrique", she replied. "One perspective we are going to take is to look at how funding a single employee through their life time changes based on the change in plan - so I was hoping you could tell me how we might simulate that process."

"Well, under the DB plan an employee would get a pension payout for as long as they lived based on a formula of 2% of their final salary times the number of years of service"

" when an employee starts, we need to know a way to project their final salary. What's the best way to do that, Enrique?" she queried.

"Well, generally we try to make sure it increases at least at the rate of inflation. Right now that seems to be around 2 1/2%"

Mei's brow furrowed as she processed what Enrique had said. "So.." she began, "If I have a beginning and ending year, and their initial salary, I can use that rate to get to the final value. Does someone starting at age 25 and working until retirement at age 65 seem reasonable to you? And if so, what starting salary should I use?"

"That obviously depends on the position and role, but I think $50,000 is a safe assumption."

Mei smiled. "OK, I think we got what I need." She looked directly into his eyes "Thank you for your help Enrique"

"Sure thing Mei, you've done the same for me before"

"Oh, I almost forgot, what are your kids going to be for Halloween?"

It was Enrique's turn to smile. "One is going to be a magician, with a black top hat and all that, and our youngest is going to be a big pumpkin! They're both so psyched!"

Figure B
Payout Calculation and NPV

Prior to funding a commitment, we need to know what the value of that commitment is - the end goal. For a pension obligation, this is the payout the employee will receive over their life expectency based on a 'payout formula'.

Using the one Mei discussed, Figure B shows the calculation of the final salary and the annual payment to be received.

Figure B also calculates - assuming 25 years of retirement (being paid at the beginning of each year), and using a 5% rate of return (the current expected return on long-term quality bonds for the sake of this post) - the net present value of these payments at the time of retirement.

Funding Considerations

With the calculation in Figure B, we now know what needs to be funded. The next question we need to ask is how do we get to this $1,629,144.90 number?

We can adopt a number of different strategies:

    ::Fund the entire obligation up front
    ::Fund through time in direct proportion to service cost
    ::Fund through time at a constant percentage of salary
    ::Fund through time as a "levelized" payment
    ::Fund through time at a "target percentage"

Using some of the worksheets from the last Treasury Cafe post ("Pension Potholes: Mei and the Curse of Exponentiation"), Figure C shows the annual funding amounts required under each scenario during the employee's career. From this graph "The Curse of Exponentiation" is apparent, as the approaches that start low increase over time at an increasing rate by the end of the employment term.

Figure C
Funding Strategies
Funding at Service Cost minimizes upfront payments but increases exponentially. Funding at a percentage of salary shows a similar but less severe pattern. Levelized funding does not change through time.

Note that the percentage of salary method is essentially equivalent to the DC plan approach, since in most cases employers contribute (or in some cases "match" a 401k contribution) to employee's retirement plans on this basis.

Now that we know what the obligation is and alternative ways to fund it, we next need to consider how these funds will be invested prior to the time that they need to be paid out.

Setting Up The Investment Portfolio

Funds that have been set aside in order to satisfy a target obligation are not shoved under a mattress. They are invested in order to earn a return until the time they are needed.

For the simulation in this post we will assume that the company is able to invest in 4 asset classes: short-term fixed income, long-term fixed income, equity, and alternatives (e.g. hedge funds, private equity, venture capital, etc.).

Figure D
Risk and Return Assumptions
As risk, measured by standard deviation increases, so does expected returns

For the DC alternative, we will assume the short-term fixed income, long-term fixed income and equity are the sole options, since individual investors do not generally have access to good alternatives classes unless they are already quite "well off".

Figure D shows R output (R is an open source statistical software) for each of our asset classes expected return and standard deviation, while Figure E shows the correlation between these securities.

Figure E
Correlation Between Asset Classes

As we mentioned earlier, individuals will need to follow a "glidepath" approach to their investment portfolio while the company will be able to keep its portfolio constant through time. How will we model this glidepath process?

In a prior post ("Should You Rebalance Your Investment Portfolio?") we used an "efficient frontier" approach using a minimum variance target to determine the asset make-up of the portfolio. We can use this concept for this problem by assuming that the DB plan maintains a consistent variance target while the DC participant uses a decreasing target variance over time. The investment firm BlackRock identifies a variance glidepath in this research article which we can use as a guide.

Figure F shows a comparison between the variance targets of the DB and DC plans.

Figure F
Equity and Alternatives Investment Allocation
DB allocation remains constant at 9%. DC allocation goes from 12% to 4% as employee moves from 25 yrs. old to 90 yrs. old.

We can also use an assumption based on target asset allocation percentages. For the DB plan case, we will assume a 50% equity, 40% LT fixed income, and 10% alternative investment composition (these percentages are 'in the ballpark' for corporate pension plans in the US). For the DC case, we will assume that the portion of equity begins at 90% and is lowered to 40% as time progresses. The percentages used are an appoximation based on those found in Vanguard's Target Date Funds. We will also assume the fixed income component shifts from long-term to short-term proportionally once the person reaches 60 until 90.

Figure G shows a comparison between the equity and alternatives targets of the DB and DC plans.

Figure G
Equity and Alternatives Investment Allocation
DB allocation remains constant at 60%. DC allocation goes from 90% to 40% as employee moves from 25 yrs. old to 90 yrs. old.

Why Multiple Approaches?

We now have two different approaches to determine the portfolio composition. Why don't we figure out which one is "best" and simply use that one?

There are several issues to consider.

First, a lot of the data we use comes from historical market performance, which contains a lot of "noise" - correlations do not stay constant over time, volatility is itself volatile, theories about how the market works vary, etc. Using one approach could be akin to the old story about the person building their house on the sand.

Using two different approaches let's us deploy the triangulation process (see "Does Your CFO Got What it Takes?" for a description of the triangulation process) in our analysis. The more a conclusion shows up in the different methodologies, the more confident we can be in it. The more varied the results, the less definitive are the conclusions that can be drawn.

In addition, it forces us to reconcile the results of the different methods. This reconciliation process can identify inadvertent mistakes in the simulation set-up, such as coding or math errors. But even better, it creates additional data which we can analyze allowing for deeper, more granular insights than if we used just one method.

Establishing Our Process

"The thing with stock prices is that they are lognormal" Biff Tarplin told Mei over the phone.

Biff was the company's primary consultant for the pension investment portfolio. "But to model them you generally need to use normal factors, since most statistical software calculations, from Excel to R, use these in the calculation rather than lognormal variables" he continued.

"So Biff, am I correct in saying that if I have a return calculated from the stock price, such as 8%, then that return is lognormal and needs to be converted to normal in order to arrive at the correct distribution?"

"You're spot on, Mei. That's exactly what you need to do. But also keep in mind that in order to tie amounts through time you want to focus on the geometric average, not the arithmatic one."

"I remember something about that, the geometric will be lower due to the ups and downs in any given year?"

"Exactly, the focus is on final values, not annual averages."

"Thanks Biff, this was helpful" Mei sometimes wondered what Biff's professional life was like, breezing in and out of different companies on a regular basis. The variety was probably profoundly interesting, but she suspected that all the fun work was performed elsewhere in the firm and not by Biff himself.

Figure H
Simulation Equations
The ending stock price of a security is the exponential value of the normally distributed price, which changes as a result of average return and standard deviation.

Mei turned to her computer. Since the information in Figure D was lognormal, she would need to convert these to normal parameters.

For this process she used a method using the equations shown in Figure H. She used the normal parameters (which are the natural logarithm values of the Figure D parameters), added these to get a normally distributed ending stock price, and then took the exponential value of this to represent the ending stock price one would see quoted in a daily paper or internet site.

Figure I
Simulation Results vs. Expected
The results of simulated stock values and returns vs. those expected are very close.

In order to calibrate this procedure, she ran 10,000 simulations. The results shown in Figure I compare the Monte-Carlo output with the theoretical expectations, which are all quite close. This indicated that the model was performing the calculations correctly.

So far so good.

A Monte Carlo analysis requires that we program a series of steps. We might do this by writing code in R, or VBA in Excel, or use software where some of these steps have been programmed for us by the developer.

Figure J
Ending Stock Price Comparison
Actual simulated ending prices (the red circles) track closely to the theoretical median values (the blue line).

No matter the source, if we are to rely on the results of the analysis, it is important to create tests that ensure that the programs we have created are working right.

Figure I is therefore a critical step in the process.

Another way to validate our model is to examine items visually. For example, Figure J compares the median stock price simulated for each year of the 100 year period, and compares it to the theoretical value using the methodology from page 300 of John Hull's book "Options, Futures, and Other Derivatives".

Figure K
Ending Stock Price Comparison
Actual simulated ending prices (the red circles) track closely to the theoretical mean values (the blue line).

Figure K compares the mean values of the ending years' stock prices with those that would theoretically occur using the normal to lognormal conversion equations from the Treasury Cafe post Simulating ROI (Return on Investment): or What's So Normal About Logs?.

Figures J and K provide an indication as to the magnitude of differences we encounter when dealing with lognormal distributions. In Figure J, the y-axis goes to about 2000, indicating that in 100 years the median value is around that number. The mean value, the subject of Figure K, is almost 10000, or close to 5 times the median. Since the median and the mean are both termed "averages", yet significantly different, we need to be clear what is meant when that term is used.

Figure L
All Asset Classes Simulated Returns and Standard Deviations
Simulated results are fairly close to those expected

At this point we can feel pretty comfortable that our simulation of a stock price series has been programmed correctly.

Since we need to simulate 4 separate price series, we will need to replicate this base methodology, but with the added wrinkle that the price series need to exhibit the correlation patterns shown in Figure E.

We can ensure that this occurs by using the Cholesky Decomposition.

What the Cholesky process does is ensures that the 4 random numbers impact each of the 4 asset classes in a manner that allows the correlation to be maintained (note: I thought I had gone through an explanation of the Cholesky process in prior blog posts but found I have not - once I actually write what I thought I had already wrote I will put the link here!).

Figure M
Simulated Correlations
Simulated correlation of returns is consistent with those in Figure E

Under the "make sure our model works as intended" objective, we need to compare the returns and correlations that have been simulated to the ones we intend to simulate. Figure L shows the simulated returns for all the equity classes, on both a normal and lognormal basis. Figure M shows the correlations, which are very close to the ones shown in Figure E.

Focus on the Results

"What are the pieces of information that you really want to see?" Mei asked Aisha over the phone. "I want to make sure the Monte Carlo captures the critical items"

There were a few moments of silence as Aisha thought through her answer. "Well, from the company's point of view, I think we want to know what is the outflow of cash under the new approach vs. the old one."

Mei waited as Aisha thought some more.

Aisha continued "And from the employee's perspective, we know that under the DB plan they receive a payment for as long as they live. As an employee I would want to know what the chances are that I do not have enough funds for retirement. Does that make sense?"

It was Mei's turn to pause and process. "Yes, that does. There may be other items of interest, such as earnings impacts, that might be considered, but this would require another layer of analysis which would take some time."

"Well let's hold off on that then, Mei. We can get to that in another round, right?"

"Oh yes. It's just a tricky calculation, with things amortizing in and out, that requires a lot of additional variables that need to be set up and tested. It's really a timing thing, and I know we are meeting tomorrow..."

"Absolutley, let's do this one step at a time. If we have some information, it might help us to figure out what the next direction is without going down blind alleys."

"Good point. See you tomorrow at 2!"

A Monte Carlo analysis can be used for many things. As the dialog above suggests, it is important to define the questions we want answered.

We can go down a lot of rabbit holes otherwise.

The reason for this goes back to the programming element we discussed in the last section. The more information we want to capture, the more programming will be required to do it...meaning more time will need to be spent.

Thus, if we have deadlines, we need to make sure we get the information that is required while preserving the ability to get more later if we so choose.

In addition, like a lot of business issues, the process will be iterative. Do not think that our Monte Carlo analysis is a "one and done" thing. The information generated will spur additional questions. Distributing the information to a wider group of people will spur additional questions. As we go through the process of setting up the analysis it will spur additional questions.

Some of these questions may warrant further investigation, but that need will evolve over time and cannot be immediately known up front.

That being said, to the extent it is not too cumbersome we should capture the information to answer questions we may already suspect will come up. Having an immediate answer enhances the confidence people will have in the results.

And this is especially important for a Monte Carlo analysis, because most do not trust a "black box". Answering questions, and showing this in an understandable way, is one way to remove some of the mystery surrounding the process.

For Mei, the critical questions are:

    ::How much cash will the company need to contribute?
    ::How likely is it that employees will not have enough funds for retirement?

With these ends in mind, we can begin generating the data we require.

Feeding the Beast

Using the asset price model she had developed, Mei turned to the task of modeling the investments in those assets.

Based on the allocation methods derived from the data underlying Figures F and G, she taught the program how to allocate funds in the correct proportion, and then programmed the calculation of the results.

All systems go. She pushed the button on her computer. The indicator on the machine told her the process was underway.

She knew it would take a little while.

"Might as well get something to eat while I can" she thought, as she pushed the chair away from her desk.

The beginning of the simulation can often be the most anti-climactic moment of the whole proess.

The program is in the process of doing everything we have told it to do, and the results are the only item that remains.

Depending on the complexity of the calculations and the number of iterations, we can wait anywhere from a minute to a day for the results to be made available to us.

Yet pushing the button does not signify the ending of our task. We will have spent a lot of time getting to this point in the process, but it is not over yet. What remains is for us to get the results, examine them, understand what has occurred, and present them to others in an understandable way.

We ain't out of the woods yet!

Interpreting the Results

Mei was happy to see upon her return that the processing was complete. With eager anticipation she began to investigate the outcomes of the procedure.

Figure N
DB Allocation Strategies at Retirement
Vertical lines represent mean average results for each strategy compared to target (the black vertical line). All strategies have higher mean averages than the funding target.

She decided first to look at funding the plan from the company's point of view using the 40-50-10 investment allocation, and made a graph of the distribution of outcomes at the point of the employee's retirement comparing three of the funding alternatives: up front, percentage of salary, and levelized. This is shown in Figure N. The statistics themselves are shown in Figure O.

All of the strategies had a mean average that was higher than the target (i.e. a little over $1.6 million), making them all potentially viable alternatives.

Figure O
DB Allocation Strategies at Retirement (in $Millions)

Mei noticed that the distributions were such that one could almost imagine putting their hand on the green line and squishing it down, with the end result being the gold line - lower 'hump' and more extreme values. This is due to the standard deviation of the Up Front funding strategy being larger than the other strategies.

Figure P
Weighted Average Years Invested Formula
The weighted average years of investment is the sum of each years investment, adjusted by the investment rate, as a percent of the total, multiplied by the number of years of that investment.

"Interesting," she thought. "There seems to be a relationship between standard deviation and the amount of time the investments were made. Since the Up Front strategy is funded 100% at the start, it had the longest time in the market."

Mei calculated the weighted average time an investment was in the market using the formula in Figure P. She then used this to divide each of the strategies standard deviations, with the results shown in Figure Q.

This showed that the standard deviation of each strategy was essentially the same once the number of years in the market was taken into account.

Figure Q
Standard Deviation per Invested Year (in $000)
The standard deviation of the ending value is proportional to the number of years invested in the market.

Clearly there were a number of factors at play here. The company could fund all at once, be done with it, but would then face more volatile end results. The more it funded through time, the less volatile the results in the plan. In theory, the volatility associated with this return would simply occur outside of the pension portfolio rather than in it.

Figure R
DC Funding Stats

Mei then turned her attention to the DC style contribution and the difference with the DB. She had modeled each of the funding scenarios, though the only practical option was the Percentage of Salary method.

The major difference between these two scenarios was the glidepath that individual investors would execute (as shown in Figure F), and differences in the portfolio value at the time of retirement would be determined primarily by this difference.

Figure S
Rate of Change in SD/Mean Ratio
The change in the ratio of standard deviation to mean becomes lower for the DC funding as the investment mix becomes more conservative.

"Interesting", she thought. "The mean is higher for the DC than for the DB, but so is the standard deviation. The medians, on the other hand, are about the same. What does this mean?"

She reflected further. "Since standard deviation is higher, this will push the mean further out, just as was shown in Figure N."

"Why would standard deviation be higher?" she mused. "Well, since there is a 90% allocation to equities the first 16 years, compared to a lower amount for the corporate plan, this could be a reasonable explanation."

Figure T
Portfolio Value at Time of Retirement

In order to test this explanation, she compared the change in the standard deviation as a percentage of mean value for the DB and DC investment allocations, with the results in Figure S showing that the rate of change does become lower as the asset allocation percentages were changed through time.

Mei turned her attention to comparing the DB plan to the new DC plan. The distributions were very similar, with only slight variations, as shown in Figure T.

Figure U
Required Percentage of Salary Contributed
The contribution percentage is a function of the target future value divided by the sum total of the salary increase and investment return assumptions scaled by the initial salary.

She again paused to think about this conclusion. The amount of funds in each was the same. She had calculated the required percentage of salary analytically by using the equation shown in Figure U. The major news would be if there were a major difference. Since there wasn't, this provided greater confidence in the results she was examining.

In addition to the distribution of the ending value, she directly calculated the percentage of times the ending portfolio value at the time of retirement was lower than the target, and the percentage of times the ending value at age 90 was less than zero. This table is shown in Figure V.

Figure V
Underfunding Frequency
The chance of not meeting targets at retirement age (first 3 columns) are greater than at age 90 (last 3 columns).

Between the two scenarios - allocating the DB and DC investments in a strategy where contributions were made as a percentage of salary, the DB had about a 37.5% chance of being underfunded, while the DC had a 39.5% probability - at about 2% not dramatically different.

By the time the retiree reached age 90, this difference had tripled to about 6%, due to the more conservative investment allocation of the retiree compared to the company.

Figure W
Standard vs. Target Variance Allocation
The target variance approach keeps ending values in a much tighter range.

Mei then turned her attention to the differences of portfolio composition within each strategy. In the first DB pass, a fairly standard 0-40-50-10 allocation was made. In the second DB pass, the portfolio allocation was determined by targeting a variance level and optimizing the highest return that would maintain that level.

Figure W shows a comparison of the ending values at retirement between these two approaches for the DB Pct Salary method. The Target Variance method shows a much tighter range, though the data in Figure V show that the chance of not hitting the retirement value is 17% greater.

Figure X
Sharpe Ratio Comparison
The Sharpe ratio of the optimized portfolio is consistently higher.

Mei concluded that the explanation for this was likely that the Standard Allocation had a much higher standard deviation than the Target Variance. However, the Standard Allocation does not explicitly optimize for return given risk. She wondered if, controlling for risk and return, the Target Var pattern was superior.

In order to answer this question, she calculated the Sharpe ratios for each year of the investment up until the retirement date, with the results shown in Figure X. While the Standard Allocation strategy had higher mean and higher liklihood of meeting the funding target, it was not as optimal as the Target Variance method in terms of 'bang for the buck'.

Since pension investments are 'stranded' in the plan, in order to retain optionality on the funds a company is wise to delay contributions as long as possible. This optionality is lost when moving to a DC plan. Mei decided to see how much value had been given up by the company in order to move to the DC plan.

She added some funding logic to her previous model, essentially running the results through a test. If the value of the portfolio at the end of the year was higher than where the target value of the portfolio should be for that year, the amount funded would be limited to that required to get funding back up to target, rather than the full percentage of salary amount.

Figure Y
Contribution NPV Scenarios
The funding optionality in the DB plan reduces the present value of the contribution cost compared to the DC alternative.

Secondarily, any value in a DB portfolio can be used to fund other employees, which the company loses when it defines its contribution.

Figure Y shows the present value of the contributions assuming one or both of these scenarios, comparing it to both portfolio asset allocation methods. By simply allowing contributions to be limited to full funding, the company reduces the cost by about 2% to 10%. When incorporating the return of excess funds to others within the plan, the cost was reduced by about 10% to 50%!

Mei let out a low whistle. "That's a lot of money we've decided to spend!" she thought.

What Can We Do?

An analysis such as we have done here is not a 'be-all, end-all' type of thing. We have added information and examples to the pool of knowledge and meaning, but there is always more that can be done.

Each time we complete an analysis, a number of questions can be asked:

    ::What are the actions we can take based on this information?
    ::What type of follow-up information is desirable?
    ::Are there specific pieces within the analysis that we would like to 'drill down' and study more thoroughly?
    ::How does this reconcile with other analyses that have been performed, and what can we learn or conclude from the similarities and/or differences?

The list goes on......

Some of these items are:

Figure Z
Variance of Normal and Lognormal Results versus Expected Results
Variation in lognormal parameters vs. those expected is much more pronounced than normal ones

Make Allowances for Inprecision - Because normal variables come from a symmetric distribution, simulations using them produce much "tighter" results compared to expectations than do lognormal variables. This is due to the non-linear assymetry of the lognormal distribution. Figure Z shows the differences between the simulated and expected values of each of the 4 asset class parameters means and standard deviations. There is a much wider range of difference from the lognormal side. Since we live in a world where asset returns are lognormal, we need to take this inprecision bias into account when interpreting or making decisions based on our analytical results.

Don't Drop the Investment Ball - Figure V showed the percentage of times the target value (either at $1.6 million or zero) was not achieved. In almost all cases, this percentage was lower at age 90 than at retirement. This indicates that the performance of the investment portfolio during retirement - a time when it is being drawn down and depleted - is still a significant factor. One is not done once the payments begin, and the decisions during this time will be important. Don't fall asleep at the switch!

DB Plans Have an Advantage - because DB plans can keep investing at higher levels of risk (modeled in this post by haing access to higher returning investments) they reduce the probability of funding shortfalls. In addition, since they are pooling individuals, the law of large numbers works for them where it does not for the individual. Clearly employees are worse off when a company moves from one type of plan to the other.

Removing Uncertainty is Valuable - given the compelling economic advantages of the DB plan over the DC - up to 50% as shown in Figure Y, the fact that companies continue to move away from these plans to ones that are economically more expensive shows just how willing they are to remove volatility from their income statements and balance sheets. If markets were efficient, one would assume that this type of 'mirage' would be seen through by others, but perhaps because the accounting is complex, the horizons are long, and it takes time and discipline to see the results, clouds the situation enough that the inefficiencies are never exploited.

Portfolio Composition Matters A Lot - in this analysis we looked at two different methods to construct a portfolio. One was based on allocation percentages to certain asset classes based on target date funds. The other was to look at reducing variance through time and then using portfolio math to create a portfolio to achieve it. The chance an employee would not have enough funds to last their lifetime increased by 45% between the two approaches! Decisions about portfolio construction can make or break you.

That's a Wrap

Mei sat across from Aisha at the conference table in the VP's office.

After a brief exchange of pleasantries, she began to discuss the results of her analysis.

"We ran a comparison of 3 different funding strategies through 2 different types of portfolio construction methods, all from a DB and DC plan perspective, for a total of 12 different scenarios. Some of these are relevant and some are not. For instance, fully funding a DC participant's benefit likely does not make a lot of sense since they may never work at the firm all the way to retirement."

"You wanted insight into two different questions. The first was how we should fund the benefit going forward. I would recommend that we use a percentage of salary method for a couple of reasons. The first is that this is a fairly common approach in the industry so we will not appear as an outlier. The second is that the approaches that delay investments into the plans reduce the range of outcomes, so employees will be less likely to experience financial distress due to insufficient balances."

Mei showed Aisha the data contained in Figure V, pointing out the lower occurrances of not meeting target levels under this approach than the others for all but the DC Target Var approach.

"Using the percentage of salary approach also works in factors such as inflation, doesn't it Mei?" Aisha asked.

"Yes" Mei replied. "I think using a level approach would be problematic. So many things can change in 40 years, such as your point about inflation, that it is probably not..." she struggled to find the right phrase "...realistically plausible."

"OK, perfect."

"To your second question, I've already shown you [note: in Figure V] the liklihood employee's do not have enough to last during retirement. In the analysis this ranged from about 1/3 to close to 80%!"

"That seems pretty high" Aisha murmered.

"Yes, I thought so too" Mei responsed. "But remember this is an artifact of the simulation. The big driver of the difference was the portfolio construction. In one we used asset allocations representing percentages common in the field, while in the other we specified a target variance. The expected return from the second approach was lower than the first, which simply suggests that if we ran the Monte Carlo again we should increase the target in order to increase the return."

She paused for a moment, and looked to make sure Aisha was still following her train of thought. It seemed that she was.

Mei continued. "The critical conclusion is not the precise number but the fact that how employees create and manage their portfolios will be the decisive determinant of whether or not they have enough."

Aisha nodded. "Yes, that makes sense. But with all this target variance and stuff, that seems a little complex, doesn't it?"

"You're right, it does" Mei agreed. Though she loved doing this type of analysis, she also knew that others were not necessarily eager to do what she had done. She also knew that she was able to do this through a lot of specialized education and training - things that others were not going to have if they had not chosen this life's path.

Mei ensured she made eye contact with Aisha to drive her point home "They are going to need a lot of help"

Aisha nodded her understanding, and the faces of some of the thousands of people impacted by this decision flashed in through her mind.

"Yes they are, Mei....yes they are."

Key Takeaways

From a purely economic perspective, a DB retirement plan allows the company to perform better than it will under an equivalent DC style fund, due to its ability to invest in a wider range of investment alternatives, its ability to take advantage of the 'law of large numbers', and its analytical resources and capabilities. Accounting data does not always make this clear when viewed from a narrow slice of time. Because of this, firms may be willing to sacrifice the long-run advantages if the short-term ones are compelling enough.

You May Also Like
    ::Has your organization recently changed its retirement plan structure? What has been the effect?
    ::What 'next steps' would you recommend be taken to extend the analysis in this post?

Add to the discussion with your thoughts, comments, questions and feedback! Please share Treasury Café with others. Thank you!

Wednesday, November 27, 2013

A Blogful of Thanks - 2013

This is the 3rd year that Treasury Café has been in existence at Thanksgiving time. While I might mention a personal experience here and there, regular readers know that for the most part we focus on the topics at hand and try hard to deliver useful, informative, and empowering content.

However, in keeping with the tradition of this blog, today we make an exception with respect to topic, though our content objectives remain the same.

For Those Who May Not Know

In the US, the fourth Thursday in November is called Thanksgiving, and it is one of the national holidays. Wikipedia can explain its history better than I, but essentially its roots are in harvest festivals that many cultures hold.

Nowadays it is a holiday where families get together, often traveling in order to do so (in many US airports the busiest travel day is today), eat a large meal, watch football, and in general just hang out together.

I like Thanksgiving because of the low-key nature of it. Unlike other holidays, stores do not have rows and rows of merchandise to sell, and media advertising blitzes are minimal - at this stage they are already focused on if Thanksgiving did not exist. You might find that grocery stores play it up a bit, stocking up on turkeys, sweet potatoes, cranberry sauce, and pumpkin pie along with other things, but that's about it.

It's all about the people.

A Time For Gratitude

The primary emotion of Thanksgiving is gratitude. During the hustle and bustle of everyday life, we often get caught up in the pressures of too-long to-do lists, the various frustrations of daily life that arise and need to be dealt with, etc.

However, after taking a deep breath or two, and focusing our attention on higher order matters, we often realize that despite all that stuff going on we actually have a lot to be grateful for. It is important to remember this, as it keeps us humble and open to what the world has to offer.

This is no less true with respect to Treasury Café. Please allow me to tell you all about it.

Inside the Mind of a Blogger

A new blogger's primary fear is that we will write it and no one will come. Writing that first post takes a lot of time, effort and thought, for several reasons. First, we haven't done it before, so it is more conscious. Second, we don't entirely know what we are doing, so it involves a lot of concentration (think babies walking for the first time). Third, there is the technology aspect, which is all new as well.

So once the "Publish" button is hit, we kick back for a second and go "ahhh, I did it". That gratifying feeling lasts all of about two seconds, and is then swiftly replaced by a nagging question - "Is anyone going to read this?"

All of a sudden we are no longer in control. Some of us might call friends, or post on LinkedIn, Facebook, Twitter, etc. But the ball has been is in the potential reader's power at that point. We are at the mercy of the audience.

One of the most comforting things to a blogger, then, is to find out real people in real places are reading what we have posted. There's someone out there!

Comments Hall of Fame

The most noticeable way we know there are readers is when someone leaves a comment. This not only lets us know someone has read it, we also get to take the blog topic to a new level because there is another perspective now in the mix!

For this reason, my sincere appreciation goes out to the following:

Denisha Lacey is a returning member to the comments Hall of Fame. She and I met initially through her Treasury Café comments, and from there we have connected on other networks, and managed to meet in person for coffee or tea a few times. I am not sure how she was able to comment this year, as in this span of time she got married, started a blog, graduated college, moved halfway across the country and became a Certified Treasury Professional (CTP) to boot! She is an up and comer with a lot of fire in her belly and a desire to continue learning, improving and growing. For these reasons, there are probably no limits to what her future holds and the leadership roles she will fulfill in that future.

Samantha Gluck and I first met each other on Twitter, and after trading re-tweets and mentions I made my way to her blog and she made her way to mine for a little comment exchange. This is the classic maneuver that all those social media advisors keep telling you to do - build blog traffic and relationships by commenting on other people's blogs. In this case it worked (I will tell you more often than not it does not work). However, in our exchange I got the better end of the deal, because Samantha is a real live actual writer, and so my comments section benefits from her excellent craftsmanship.

Whitney Clark and I have interacted quite often through Twitter, though it is difficult for me to recall where or how that orginated. We have lots in common, as her firm manages money, which finance people like me think about often! People in her firm have also pioneered using Mind Maps in financial planning. While I have not used them for that, I am a fan of the technique for innovation purposes, writing, and other activities. By day she is the awesome social media manager for Wheaton Wealth, and by night she wishes that Chicagoland was below zero all year round!

Others to thank include ejones who I believe I may know, Anonymous (who seems to turn up in lots of places!), Ron , who I would like to tell that I put money in the Red Kettle today and sent a warm thought out about your brother, Brian Okello, who is learning about financial analysis, John Marc Thibault, a master of probability who kindly added to one of my analytical oriented posts, Blair, Kelly Boros, Mike Lehr, Otabek, Muaath, and Chris Farmand, who is an accountant interested in innovation, and therefore a man after my own heart!

Finally, the first blog comment after my first Thanksgiving post was from maddie, who was my first real social media friend. Here is what I said about her that year, when talking about my "firsts":

"My first E-mail dialogue was with maddie. However, to say that she was my first blog-generated e-mail correspondence really does her a disservice, because no matter what happens - in all the rest of my life - I will always have a special place in my heart for maddie.

I ran into maddie by way of another blog. Through that blog, she reached out to me with the wisdom and advice of someone who has "been there, done that" and really took me "under her wing". maddie is really the first one, and to some extent the only one, who provided the "somebody believes in me" feeling with respect to Treasury Café. And I tell you what, during the first couple months of blogging, you need that feeling! Thank you, maddie!".

Unfortunately for me, maddie dropped out of social media right after her post-Thanksgiving comment on Treasury Café that year. Even though her blog site wouldn't even pull up anymore, I kept it on my blogroll for a year and half afterwards before I could bear to take it down...a very sad day for me. I miss her, and hope she is happy and doing well in her post-social life.

Shout Out Hall of Fame

The other big way for a blogger to know that others are reading is when people mention your blog in their blog, or in other social media settings. This has the added touch of attracting new readers to your site, who might come back in the future and/or leave comments.

For this reason, my sincere appreciation goes out to the following:

Wally Bock is someone who connected with me after I commented on his blog. He has had a longtime focus on leadership which I covered here on Treasury Café in "A Life's Worth of Leadership Lessons". Since a lot of the posts we cover here are about case studies of statistical distributions and financial strategies, replete with formulas, spreadsheet images and R output, mentioning Treasury Café would not seem to be a particular fit for his topic areas. However, on occasion we do cover issues with respect to managing the team, or being a valued partner, or working within the organization, and these have often been included in his "Midweek Look at the Independent Business Blogs" posts every Wednesday. Always willing to accept a challenge, he also found a way to work the Working Capital series into his Zero Draft blog about writing.

Rene Michau, from ANZ Bank, found me very early on in the life of Treasury Café. He was the first blogsite "member" and the first to include Treasury Café on a blogroll (which is yet another way of saying, "I read this and you should too"). He will often include Treasury Café posts in hisonline newspaper. You may have noticed that most of the connections I have made were through blog comments and Twitter, but early on Rene found me "out of the blue" somehow and thought I was worth staying in touch with.

Devan Perine, from EnMast, connected on Twitter in what amounted to a retweet contest - I'd retweet her, she'd retweet me, and so on over a long period of time. At some point she asked me to do a guest post for their site, which focuses on small business issues. I was happy to do so ( Hire for Fit, Not Just for Skills ), and learned through that process that the challenge in guest posts is that you cannot assume some level of past exposure, so you need to write something of interest to that audience while introducing any background as concisely as possible.

The Masters In Accounting website lists Treasury Cafe as one of the Top 50 Finance and Accounting blogs. The site is chock full of info on college programs from all over, so the fact that it made it on that list in the face of all that research is an honor. Note: there are a lot of other good blogs on that listing, you may want to put some into your Reader if you use one.

In the Twitter world, special thanks for unprompted Treasury Cafe tweets and retweets go to Zachary Jeans and Sandra Feinsmith.

In the print media world, thanks for mentions of Treasury Cafe and/or its author to Ira Apfel at the Association of Finance Professionals, Dan Bland at Corporate Treasurer, and Katharine Morton at Eurofinance. Writing print articles or serving as a source has been a new experience for me this year, so I am especially grateful as it has broadened my horizons.

And Finally

Thank you for reading this blog! One of the things that I have been most proud is the fact that Treasury Café has been read on every continent except Antartica (if you know someone there, please get them to visit!). It is amazing to me that we can reach out anywhere in the world, form connections and work together like we can these days.

I am very grateful for your visit, and the fact that you come back. I am very lucky to have you and to be living in these times.

Thank you!

    ::Who are you grateful for this year?

Add to the discussion with your thoughts, comments, questions and feedback! Please share Treasury Café with others. Thank you!

Thursday, September 19, 2013

Pension Potholes: Mei and the Curse of Exponentiation

"We need to do something about this pension plan" the CFO exclaimed. "It has created us a real problem in terms of hitting our performance targets and is causing us to lag our industry peers. I need you to look at this issue and make a recommendation as to what we should do about it. Can you get me something before our Board meeting early next week?"

"Of course" Mei replied.

Her mind was racing as she left the CFO's office...she had a lot of work ahead of her, without any indication of where it would end up.

What is Defined?

In general, there are two types of retirement plans that can be offered - Defined Benefit plans and Defined Contribution plans.

Emphasis on the word "defined".

A defined benefit plan is one that pays out a - you guessed it! - defined amount of benefits to the employee. The word "defined" in this context means "known with certainty". For example, should Marie be retiring tomorrow under a defined benefit plan she would know that she is going to recieve $400 every month for the rest of her life. Marie does not know (i.e. what is undefined) how much money the firm made in investments to produce this amount.

Figure A
Plan Comparison

Under a defined contribution plan, on the other hand, what is known is the amount placed into the plan. For example, Marie knows that every month the company paid into her retirement account 5% of her wages. What Marie does not know (i.e. what is undefined) is the amount of payments her retirement account will produce.

Figure A shows the comparison of the two plans and identifies where the certainty and uncertainty lies.

"A lot of companies are converting their DB plans to DC plans these days. Perhaps that would help your issue?" Stacy said. Mei had met her at a conference last year and they had stayed in touch since then.

Objective advice was always valuable.

"That seems like a pretty dramatic change!" Mei replied.

"It is for sure, but more and more seem to be doing it. The general consensus is that DB plans are going the way of the dinosaur."

If that were to be the solution, Mei decided she better check in with the Human Resources group and see what they had to say about this issue.

The Projected Benefit Obligation

An organization incurs a liability when it has a defined benefit plan because it is realizing the benefits of the employees' labor now in exchange for a payment that will be made later.

Figure B
Example Pension Payout Formula
According to this formula, a retiree will receive an annual payment equal to 2% multiplied by their final salary and years of service. The retiree in the example calculation will recieve 20,000 per year (2% x 50,000 x 20).

In order to achieve the matching principle - one of the pillars of the accounting process - there need to be methods and techniques to associate the current period's labor costs with this deferred obligation.

The Projected Benefit Obligation (PBO) is the measure of the current state of this liability.

Let's examine how this is calculated through an example.

We will assume that Joe's Agricultural Empire, LLC sponsors a defined benefit plan for their employees. The annual pension payout is determined by the formula shown in Figure B. The example shows an employee who will receive annual payments of 20,000. Note that applying the math to a single employee helps to make these factors more understandable, which is why we will use this approach in the blog post. In real life, we would apply these calculations to the entire employee group as a whole.

Figure C
Net Present Value Equation
The Net Present Value is equal to the sum of the n cash flows discounted at rate r

Knowledge of the annual benefit payment is the first step in being able to quantify the amount of the liability. In order to value these payments at a point in time, we also need to know the number of payments that will be made and a discount rate to apply to them.

For the sake of our example, let's say that Joe's employee is expected to receive 10 payments in retirement, and the current discount rate applicable to these is 10%. Using the Net Present Value formula (shown in Figure C), we can determine that the value of these payments at the employee's retirement date is 122,891 (see Figure D).

Figure D
Net Present Value Calculation
The Net Present Value of 10 payments of 20,000 discounted at 10% equals 121,891, verified using Excel's PV() function

At this point we have established the value of the payments made to the retiree at their retirement date. However, we have not dealt with the 20 years of employment the person works prior to that point.

In order to do that, we need to make a second series of NPV calculations, only now going back in time rather than forward. This second calculation needs to take into account the employee's actual years of service in order to assign the correct final value of the payments to the period when the labor was performed.

In the first year of employment, for example, the present value of the final amount is 1,005. The calculation of this amount is shown in Figure E.

The amount of the final PV attributable to the current work period is known as the Service Cost.

Figure E
Service Cost Calculation
The amount of the final value of retirement pay attributable to the first year of service (i.e. Service Cost) is 1,005.

There is a slight twist in the second year. Using the same methodology as in Figure E (substituting 18 years until retirement for 19) will yield a Service Cost of 1,105. However, the amount of retirement pay the employee earned in the first year has not been paid out. Because it has been earned and not yet paid, we calculate an interest cost associated with this balance. At our 10% rate, interest on the first year balance of 1,005 is 100 (rounded amount).

Figure F
PBO Through Time
The PBO is increased each year by Service Cost and Interest Cost

With these two years calculated we can see how the Projected Benefit Obligation "rolls forward" through time. This is shown in Figure F.

Figure G shows the PBO calculation for each of the years of service, along with some of the intermediate values involved (e.g. percent of years of service completed, etc.). Figure H takes the service cost and PBO calculations, adds interest cost, and shows the PBO in "roll-forward" format.

Figure G
PBO Through Time
The underlying assumptions and intermediate calculations that generate the PBO. Note that as a check on our work the final amount of the PBO (122,891) is equal to the net present value of retirement payments we calculated earlier.

Figure H
PBO Through Time
The PBO in rollforward format. The ending value equals the beginning value plus the service cost plus the interest cost.

Since we are using a single active employee as our example, we do not see any reduction in the PBO. Naturally, as payments are made (i.e. the employee has retired and begins realizing the benefit) the PBO will be reduced by these amounts.

Because the PBO relies on a lot of actuarial assumptions (years in retirement, service years, final salary, etc) firms routinely engage professional actuarial firms who specialize in these assessments and calculations.

"According to this PBO data, our costs increase the longer the employee has been here, is that correct?" Mei asked.

On her way to HR she had stopped by the office of Scott, one of the company's accountants - the one who always found time to discuss issues and questions in a sincere attempt to help out. Mei liked it when she had the opportunity to discuss problems and situations with him because some new tidbit of knowledge or a deeper understanding always seemed to result.

"Yes. That is going to be due to the geometric nature of the calculation." he told her. "Since the PBO equation involves exponents in the formula, it will have an increasing effect. David Waltz, who writes the Treasury Cafe blog, calls this 'the curse of exponentiation'!"

"So that is one of the reasons why this is becoming a larger issue!" she exclaimed. "Our workforce is aging, so we are farther out the curve where the exponent effect really picks up."

"Exactly!" he beamed. Scott loved it when people understood what he was saying and they could share the insights. "And there are other factors too. For example, average lifespan has been increasing, so that increases the PBO as well since there will be more payments in retirement."

"Yes, that makes sense" said Mei. "I suppose any of the factors that we use the actuary for can increase it, higher wages due to higher inflation for instance?"

"Yes. There is a lot of uncertainty involved in the calculation."

"Doesn't make earnings any easier to predict, does it?"


Asset Returns

The PBO addresses the liability side of the pension equation. We now turn to the asset side.

In order to avoid large, "chunky" payment streams in later years, firms generally fund specific accounts that are held in trust for the sole purpose of making future payments to retirees. In the US certain levels of retirement plan funding are required for some entities.

Since investments earn returns, firms are also able to use these in the pension expense calculation.

Figure I
Pension Expense
Pension expense involves service cost, interest cost and assumed return on plan assets.

In order to determine this amount, an assumption about how much invested plan assets will earn is also required. For example, if Joe's Agricultural Empire were to place 1,000 into the trust account in year 1, and it assumed that 10% would be earned on these investments, then in year 2 expected returns of 100 (1000 x 10%) would be reflected in the pension expense calculation. Figure I builds on the prior PBO example and adds returns to come up with pension expense.

Mei ran into Miguel in the elevator. A long-time employee of the Treasury department, he was involved in investing the pension plan's assets and coordinated this activity both internally and with external parties such as consultants, investment managers and banks.

Another fortuitous encounter!

After explaining her project, Miguel opined "I can see why this is becoming a bigger issue. So long as the stock market was healthy, we were in a pretty good position with respect to funding our obligations. That has gotten a lot worse lately, so we are faced with raising a significant amount of cash to fund the plan."

"But the market has gotten better lately."

"Yes it has, but the effects of the past few years are catching up to us since we did not hit our return assumptions for several really bad years, and what is happening now will take a while to work its way into the financials. It is the difference between actual results and our assumed results that matter." he replied.

"Wait a sec, why do we use assumed returns? We know what they actually are, don't we?" Mei asked.

The Impact of Assumptions

In order to keep pension expense a little less volatile, the procedures involved with its calculation, on both the PBO side and the asset side, allow for changes to be "smoothed in" over a period of time (generally the remaining service years).

In addition, accounting rules do not require amortization of changes that are less than 10% of the PBO or the assets (whichever is larger). Only when the net changes are greater than this amount are amortizations required, and then only enough to get back within the 10% band.

Let's go back to the example in Figure F and Figure I. Let's say actual plan returns in year 2 were 0% rather than 10% (earnings were 0 vs. the assumed of 100). These differences are not immediately recognized anywhere. The amount of the beginning Year 2 PBO (from Figure F) is 1,005 and the beginning Year 2 Assets were 1,000. Since PBO is larger, we calculate the 10% "corridor" amount using that number, which equals a little bit more than 100. Since the return deficit compared to the 10% assumption is within (just barely!) the 10% corridor, no amortization is required.

Figure J
Amortization of Gains and Losses
Changing the discount rate from 10% to 8% results in a PBO that is higher by 550. In addition, investment returns were 100 lower than assumed. After adjusting for the 10% corridor, 550 will be amortized over the remaining service life.

Items such as asset returns, which replace an assumption because of the fact that time has passed, are called Experience Gains and Losses. Items that reflect changes in assumptions, such as the discount rate, are called Actuarial Gains and Losses.

All Experience and Actuarial Gains and Losses are combined when determining the amortization, and one net amount is added to the pension expense calculation.

For example, Figures F, G and H showed the calculation of PBO for one of Joe's Agricultural Empire, LLC's employees. At the beginning of year 2 the PBO, as shown in those figures was 1,005. Had we been calculating the PBO at the 8% rate from the beginning, the beginning PBO would be larger by 550. This is the amount that will need to be amortized over the remaining service life of the employee (which was 19 years at the beginning of the period).

Figure J shows the calculation of the amortization amount reflecting both the Actuarial Loss due to the discount rate change and the Experience Loss resulting from the investment performance of the assets.

The Balance Sheet

Up to this point we have considered expense, which is an income statement item. We now turn to the balance sheet perspective.

The offsetting entry to pension expense will be a liability account, such as Accrued Pension Cost, Benefits Payable, etc.

If the organization contributes cash into the pension trust during the year, the other side of the cash entry will be to the liability account mentioned in the previous paragraph, or if contributions have exceeded the liability, into an asset account (Prepaid Benefits, etc.).

Figure K
Balance Sheet Adjustments
The Accrued Pension Cost reflects the difference between the PBO and Assetsr

Finally, a comparison is made between the PBO and the value of the assets. If the PBO is greater, the liability is increased by this amount (net of tax) and the offsetting entry debits Other Comprehensive Income, which is in the Equity category. If the assets are greater, than the asset side is increased (net of tax) and the corresponding entry credits Other Comprehensive Income.

Figure K shows this calculation for year 1 using Joe's employee as the example. In this year no adjustment is required because the difference between the assets and the PBO is completely reflected in the accrued liability account (Accrued Pension Cost).

Figure L shows the calculation for year 2. With the impacts of the Actuarial and Experience Losses, the liability on the balance sheet does not initially reflect the entire difference between the PBO and the assets. For this reason, an entry is required to increase the liability, with the other side of the entry going towards the tax impact and equity (via Other Comprehensive Income).

Figure L
Balance Sheet Adjustments
The Accrued Pension Cost category does not reflect the entire difference between the PBO and Assets. An entry increasing this amount and reducing Equity via Other Comprehensive Income is required. This example assumes a 40% tax rate.

There are a couple of other items that can impact pension expense and its balance sheet impact which we are not going to cover since they are a little more 'esoteric'.

The first of these is called 'Prior Service Cost', which arises if changes are made to the pension benefit formula which is attributed retroactively. Say for example that Joe's changed their payout formula to 3% from 2%. The increase in the liability due to this change would be accounted for under this category. Another category relates to changes in accounting rules a few decades ago, which companies could amortize over a period of time (usually called 'Transition Costs" or something similar). Finally, there are specific accounting requirements when changes to the plan result in reduced benefits to some or all employees (usually termed 'Curtailment' or 'Termination'). These usually involve recognition on the financials of a lot of the items that are amortizing under normal circumstances.

Miguel continued "Our OCI has taken a hit because of this, which is a problem because that impacts our Debt to Equity ratios. It puts us in danger of breaking loan covenants - even if we've done everything by the book!"

A Cornucopia of Potholes

The consequences of the pension accounting methodology can create a wide array of problems and counter-intuitive results, many of which may lead to poor decisions being made. Among them are:

Valuation Confusion - an important point to keep in mind is that the pension accounting rules are designed to reflect proper accounting, not necessarily economic reality. If we are valuing our company, or determining the lifetime economic cost of an employee, then we are concered with the Net Present Value of our cash flows. These are not reflected in the income and expense items correctly until the point of retirement. In the Figure G example, we assume that the employee is going to work 20 years and retire. Because of this, we fully expect to incur the full dollar amount of the pension obligation on day 1 - the date of hire! Thus, we should reflect the NPV of our future outlays immediately, which would be 18,267 (the year 1 ending present value of 20,094 discounted an additional 10%). Simply looking at the income statement and balance sheet does not reflect our true expected obligation.

Figure M
Pension Expense at 2 Firms
Pension expense calculation favors the poorly managed company. Average annual salary increase of 3.72%, both employees beginning at 25,000. Employees at MBC finish the final 10 years at different firms.

Reward Bad Leadership - good leadership generally results in highly engaged employees who are motivated, causing them to want to stick around. Bad management, on the other hand, generally results in higher turnover. Many of our pension expense components, chief among them the benefit payout formula, relate to average service life. Consider two firms - ManageGoodCo (MGC) and ManageBadCo (MBD). MGC has an average service life of 20 years. MBC has an average service life of 10 years. Figure M shows the pension calculations at these two firms. MBC has lower pension expense! Because of this, activities such as benchmarking, valuation ratio comparisons based on earnings (such as PE), cannot be relied upon without adjusting for differences.

Figure N
Excess of Assets Over PBO
The amount of Assets at a level funding level always exceeds the PBO until the retirement year, peaking in year 13.

Management Discipline - since the NPV of the ultimate pension obligation can be calculated at the time of employment, it is possible for firms to evenly fund this obligation annually over the employee's career in order to prevent large funding requirements. In our Figure G example, an annual payment of 2,146 (assuming 10% returns, the same as PBO) will create a future value at the employee's retirement exactly equal to the PBO. However, the consequence of this is that the Assets of the plan will always exceed the PBO until the final year. The amount of this difference is shown in Figure N. Maintaining this payment level during the entire time will be extraordinarily difficult. It is quite easy to rationalize skipping a few payments in favor of 'more pressing' items such as an acquisition, a pet project, returning funds to shareholders, and a host of other things. Managers making these decisions in the early years are unlikely to be around to 'suffer the consequences' in the later years, increasing the likelihood that these types of decisions will be made.

Figure O
The Curse of Exponentiation
Using the Joe's employee as an example, we see that Pension Expense (Service Cost and Interest Cost) increases the longer the employee has worked there and the less Remaining Service Life there is.

Mismatched Timing - every industry progresses through various stages as time goes on, from introduction, then to growth, then to maturity, and finally decline. During the introduction and growth phases, the firms will need to hire more and more workers in order to accommodate market demand. This results in a lot of new workers, with long service lives ahead of them, and populating the very left hand side of the exponential curve (such as point A in Figure O). This translates into lower service cost, lower interest cost, and longer time frames to amortize experience and actuarial gains and losses. However, once the maturity stage is reached, worker attrition sets in, where hiring occurs only as those already employed leave. This moves the firm towards the right along the exponential curve (such as Point B in Figure O), resulting in higher service cost, higher interest cost, and reduced amortization periods (making these higher, for better or worse) as remaining average service life decreases. This all occurs at the same time as the firms need to become more cost conscious. Without rapid growth to offset costs, firms shift into optimizing expense at current levels and investigating ways they can reduce costs in order to maintain their current levels and avoid the decline phase as long as possible. Once the decline phase is reached, the pension expense factors become even more exacerbated. All at a time when they can least affort it.

Mei finally reached the office of Aisha, the VP of HR, and briefly explained her project.

"Wow, converting plans would be a big change. Morale is not the best around here right now anyway...this could hurt it even more! It makes it seem like the company is reneging on its promises."

"You mean because people have worked under that expectation for their entire time here and now they won't get it?"

"It's not quite as bad as that. Whatver they have earned up to this point has been earned, we can't go back in time and change things. But going forward we can. So someone who has worked here 16 years will be expecting to retire with 20 years in the payout formula, whereas if we change the plan it will only and forever be 16 years. So they will have less retirement payments than they expected."

"But if we replace it with a different form, such as a DC plan, won't that make them not care about the change?"

"Maybe, but it is very difficult to compare the one type to the other. There are a lot of factors - how financially savvy they are, how long they live, differences in salary levels used between the two options, a lot of other things..."

"Hey, maybe we should do a Monte-Carlo simulation of these differences. What do you think?"

"That sounds interesting and might be helpful, but I am not sure you have the time to do that prior to your recommendation deadline. I think you need to have a recommendation ready even if that is not done. Do you know what it would be?"

Key Takeaways

The calculation of a Defined Benefit plan's pension expense is a complex operation. The nature of the methodology creates long-term biases that are difficult to avoid when management has shorter term priorities. Due to the "Curse of Exponentiation", pension expense and funding become larger issues at exactly the wrong times. In order to correct for these factors, a long-term view of total value rather than accounting metrics can help correct for some of these drawbacks.

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For accounting "potholes" in other situations:

Cash Conversion Cycle: A Good Measure?

For NPV methodology and how it diverges from accounting treatment:

Does Your Accountant Speak Finance?

    ::What would you recommend if you were in Mei's shoes? Why?
    ::In what other ways does the "curse of exponentiation" manifest itself in the pension expense context?

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