When Big Numbers Attack: Corporate Defined Benefit Plans are Not the Problem

I started my career working closely with corporate pension plans, thus when I saw the following article in my twitter feed causing alarm I thought there might be an interest in some context and a reality check into the supposed corporate pension crisis. Note that state and local pensions are a completely different story.

Let's go to Bloomberg's article titled 'S&P 500’s Biggest Pension Plans Face $382 Billion Funding Gap':

People who rely on their company pension plans to fund their retirement may be in for a shock: Of the 200 biggest defined-benefit plans in the S&P 500 based on assets, 186 aren’t fully funded. Simply put, they don’t have enough money to fund current and future retirees.The situation worsened for more than half of these funds from fiscal 2015 to 2016. A big part of the reason is the poor returns they got from their assets in the superlow interest-rate environment that followed the financial crisis. It’s left a hole of $382 billion for the top 200 plans. 

The reality is corporate pension plan participants are completely fine and the article simply regurgitates a straw man argument that has cost employees the security that a defined benefit "DB" pension provides.

HOW DO CORPORATE PENSION PLANS WORK

I'm going to oversimplify things a bit, but at a high level corporate pensions have assets (straight forward - they are what they are) and liabilities which are the benefits that participants have earned and are owed. These liabilities are a bit more complex because even if you know roughly what is owed in the future, you don't know exactly what those liabilities will cost in today's dollars. 

The way a corporate pension backs into this value is through a discount rate. The end result is liabilities are worth less today than in the future given the present value of a dollar today is worth more than in the future. An example... assuming liabilities for a plan are $100 / year for 25 years discounted at 4.3% (more on that later), they are worth $1614 (less than $100 x 25 = $2500) as seen below.

Cash Flows Discounted Back to a Present Value at a 4.3% Discount Rate Each Year

Total value of 25 years of $100 / year discounted back at 4.3%

BUT THAT BIG NUMBER IN THE HEADLINE IS SCARY

$382 billion!!!! 

That number seems big, but notice there is no mention of the relative scale of that. According to P&I as of 9/30/16:

Among the 200 largest retirement plans, assets totaled $6.79 trillion as of Sept. 30, up 6.2% from the year earlier. Of this, $4.83 trillion belonged to DB plans (up 5.5%) and $1.96 trillion to DC plans (up 8%).

So that big $382 billion number was ~8% of total plan assets as of 9/30/16 (global stocks have also happened to go up ~17% since that time so the funded status has likely improved quite a bit since). 

BUT PLANS WOULD NEVER USE A 4.3% DISCOUNT RATE... MORE LIKE 10%, RIGHT?

Corporate pensions are required to discount liabilities at a rate roughly equal to a corporate bond of similar duration as their pension liabilities. The rationale being that's the rough rate a debtor would require, but also because when a plan is fully funded (i.e. 100% assets to cover future liabilities at this discount rate) the plan could simply invest the proceeds in long corporate bonds and call it a day (it's more complex than that, but close enough for this post - it also happens to be the basis of liability driven investing "LDI" and why pensions own a lot of long bonds). The discount rate is extraordinarily low right now given where market rates and spreads are and can be thought of how much it would cost a corporation to fund their underfunded status. So a big part of the reason some plans are underfunded hasn't been due to their asset performance in the "superlow interest-rate environment that followed the financial crisis" per Bloomberg, but rather because their liabilities have increased in present value terms due to the superlow interest-rate they are discounted by.

Looking at Intel's latest annual report (the poster child in the article as they are the most underfunded plan in % terms), we see they used a 4.3% discount rate at year-end. 

This rate has huge implications for the liability calculation. Assuming a move up in rates to just 5%, we can see that the present value of liabilities in the previous examples goes down more than 6%. In reality, assuming pensions have a duration of ~20 years, a ~40 bp higher rate as of 9/30/16 would have pushed the underfunded status of pensions to $0 without a change in asset valuations.

POOR ANECDOTES DON'T HELP

Back to Bloomberg:

Last month, the 70,000 participants in the United Parcel Service Inc. pension plan learned they won’t earn increased benefits if they work after 2022. Late last year DuPont Co. announced it would stop making payments into its pension plan for 13,000 active employees, and Yum! Brands Inc. offered some former employees a lump-sum buyout to offload some of its pension liabilities. General Electric Co. has a major problem. The company ended its defined benefit plan for new hires in 2012, but its primary plan, covering about 467,000 people, is one of the largest in the U.S. And at $31 billion, GE’s pension shortfall is the biggest in the S&P 500.

Now the reality of what this means...

• UPS / DuPont: these moves have nothing to do with past pension liabilities or risk to participants. That has to do with corporations de-risking their balance sheets by moving future benefits from defined benefit (they have the obligation to pay an amount) to defined contribution (a one off payment into a 401k). Benefits that have already been earned are not changed.
• Yum! Brands: this is an option for employees to leave their plans at the current present value of their liabilities. Options have positive values for option holders, so this is a good thing.
• GE: $31 billion is certainly GE's problem, but it is not their employees issue unless the company goes bankrupt, cannot make the payment in bankruptcy, and the participant is above the threshold guaranteed by the PBGC (a government agency that backstops corporate pensions for a fee - and is required). None of this likely matters as GE has an equity cushion for participants of $222 billion (i.e. their market cap) and if GE wanted, they could simply add $31 billion in debt to fund their plan and make this optical issue go away (something they may be forced to do down the line in increments given rules)

As for Intel (the poster child as the least funded pension), they have unfunded obligation of $2 billion or less than one quarter of earnings.

The Case for the Harmonic Mean P/E Calculation

The most recent "analysis" seemingly spreading like wildfire across the perma-bear community was performed by Horizon Kinetics in their most recent quarterly commentary. Their claim is that the price-to-earnings of the Nasdaq (or any index really) is much higher than reported because we are being fed a manipulated harmonic mean rather than arithmetic mean for the price to earnings ratio (don't worry, I'll explain the difference). While the piece also claims excluding non-earners from the calculation is wrong (something I also don't agree with), I'll ignore that portion for now* as it is more nuanced, a separate argument in their piece, and because their specific argument for the arithmetic mean is so clearly wrong.


CASE STUDY #1

Let's start with a case study Horizon Kinetics provides outlining how they believe the P/E for an equal weighted three stock portfolio (with an investment of $1 million to each) should be calculated.

One business earns $100,000 per year, so it has a price‐to‐earnings ratio of 10x; the second earns $50,000, for a P/E ratio of 20, and the third earns only $20,000 and so has a P/E of 50. This last one is probably situated on a high‐ growth street corner. Averaging the three P/E ratios of 10, 20 and 50 means that the average P/E of the 3‐ company portfolio is 26.7x. So far, so good.

Not a good start...

The 3-company portfolio clearly does not have a P/E of 26.7x when you take a step back and think about what you as an investor own in aggregate. The companies in the case study earn $100,000 (10% yield on $1 million) + $50,000 (5% yield on $1 million) + $20,000 (2% yield on $1 million) = $170,000, which is a 5.7% yield on $3 million total investment. A $3 million total investment divided by $170,000 of earnings = (1/ 5.7% yield) = a P/E of 17.65x, which is 66% LOWER than their calculation.

The easy way to view the correct harmonic mean calculation is to think about what you own in terms of earnings yield (getting to an average earnings yield and then backing into the P/E is the harmonic mean calculation). In this example:

• Company A: 10x P/E = 10% earnings yield (1/10)
• Company B: 20x P/E = 5% earnings yield (1/20)
• Company C: 50x P/E = 2% earnings yield (1/50)

(10% + 5% + 2%) = average yield of 5.67%. 1/5.67% = the correct 17.65x aggregate P/E.

Visualizing this makes it clearer. The left-hand chart shows the earnings yield for each company, while the right hand chart shows the contribution from each company in total (the earnings of each company divided by the whole $3 million investment - then stacked). We'll revisit the right hand chart to show how an extreme multiple can overly influence the arithmetic mean of the P/Es when we review their second case study.

CASE STUDY #2

Horizon Kinetic's next case study is worse because the error in the result is so obvious as it includes a company with an extreme high P/E ratio.

Observe the following hypothetical equal‐weighted 4‐stock portfolio consisting of a range of low, somewhat high and egregiously high‐valuations, ranging from 10x to 300x. A simple average results in a portfolio P/E of 90x.

• Company A: 10x P/E or 10% yield
• Company B: 20x P/E or 5% yield
• Company C: 30x P/E or 3.3% yield
• Company D: 300x P/E or 0.33% yield

An average P/E of (10x + 20x + 30x + 300x) / 4 = 90x implies an earnings yield of just over 1% (1/90). Compare this to the average earnings yield of 10% + 5% + 3.3% + 0.33% = 4.67% average, which gets you to a correct aggregate portfolio P/E of 21.4x (1 / 4.67%).

Visualizing this case study again shows their error more clearly. On the right hand side we can see that the earnings contribution of a 25% weight to the first three stocks alone yields more than 4.5% (10% x 25% + 5% x 25% + 3.3% + 25% = 4.575%), so by their rationale the earnings of company D contributes -3% to the overall portfolio (i.e. something akin to company D losing $140,000 on their $1,000,000 investment instead of having small, but positive earnings).

And of course, their ridiculous conclusion.

That completes the strange journey of transforming a fairly understandable, if alarming, P/E of 90x into the more comforting Harmonic Mean P/E ratio of only 21.5x.

And the even more bearish takeaway of an investment in the Nasdaq 100.

No active manager would be permitted to manage a concentrated, high‐P/E portfolio for an institutional client.

* you are paying a price to own the lack of historical earnings (which is a case for including these companies), but the fact is these non-earners have often been the fastest growing companies in the Nasdaq, thus including their negative historical earnings ignores their future potential (a case for excluding these companies from the valuations calculation)

EconomVIX...A Summary of Past VIX Posts

RCM Alternatives has a great piece (HT Tadas) outlining what the VIX is, the market for VIX related products, and how to think about volatility as an asset class. It also happens to contain my new favorite quote for anyone thinking about trading volatility:

Still, if you cannot see the VIX futures curve in your head, burning $100 bills is probably more profitable than trading them.

I'll piggyback on the RCM piece given the interest in volatility trading strategies (due to the remarkable run of some of the short VIX ETPs) and link to old posts that I've previously done on the subject that I thought might be helpful.



What Exactly Does the VIX Tell Us?

How a Low VIX Can Remain an Expensive Hedge

A Framework for a Short VIX Allocation

Breaking Down Volatility of the VIX

Utilizing the Money Sucking $UVXY to Improve Risk Adjusted Returns

Using the VIX Futures Term Structure to Reduce Equity Exposure

Adding a VIX Signal to Momentum

The Case for a Steady Volatility-State Managed Portfolio