The fractal nature of asset-liability matching

What type of asset-liability matching am I talking about

Asset-liability matching means different things to different people, even when you think you’re dealing with a specific situation and therefore talking about the same thing.

Painting with broad strokes, there’s asset-liability matching (ALM) when managing a pension fund, an insurance business, or a corporation’s balance sheet. The first two typically deal with neutralizing fluctuations in market value (i.e., PV of cash flows) of assets and obligations, while the third has to do with a corporation’s cash investment strategy relative to its floating-rate debt.

This post refers to the third type: ALM when managing a corporation’s investments and debt.

Objective: protect the income statement

What’s the objective of this type of ALM? The objective here is to reduce the impact of interest rate fluctuations to the company’s income statement (a.k.a. P&L). This may be a case of “accounting over economics” because changes in market value of debt and investments do not normally hit the income statement. Only interest earned and interest owed in a period are recorded in the income statement under the other income & expense section and that’s all what some management teams care about.

They’re busy running the business and they don’t want to explain why the results for the quarter look bad because other income & expense screwed things up.

Investment portfolio (asset): what’s “floating-rate”?

I once managed an investment portfolio that looked like this:

Yes, it was $40 billion with a “B”. As you can see in the table, we had approximately $4B invested in money market funds, commercial paper, and short-term treasuries. In addition, we estimated that about $3B of the other investment strategies had, at any given time, a maturity of less than 1 year or was subject to portfolio turnover as benchmarks reset each month.

In practical terms, this represented $7B of “floating-rate” investments because they would all “reset” to ongoing rate levels within one year. Moreover, the average maturity of these investments was 90 days.

Debt portfolio (liability): what’s floating?

Now, imagine that after looking at our investment portfolio and concluding that we had $7B in floating-rate investments, we turn to our debt portfolio.

We only have $0.5B in commercial paper. The rest is all fixed-coupon long-term debt with various maturities.

Therefore, there’s an asset-liability mismatch: $7B on the asset side, $0.5B on the liability side.

(To be clear, we’re concerned only about the front-end (that is, the floating portion of both portfolios) because our objective is to reduce volatility in the other income & expense line.)

Use swaps to transform debt from fixed-coupon to floating-coupon

We make our case to management that we should adopt a risk-neutral stance by increasing our floating-rate debt.

“This will immunize our income statement from fluctuations in rates”, we say, “and there’s no need to go to the debt markets or obtain a bank loan, we can achieve our objective by picking up the phone and executing interest rate swaps.”

“Bingo!” says the CFO.

Off we go. Call a few banks and execute $4.5B notional in interest swaps in which we pay 3-month SOFR and receive a fixed rate.

Now, we’re asset-liability matched.

If the central bank cut interest rates by 100 basis points (bps) and we were mismatched, the net impact to the income statement in the next year would be approximately (of course, all else equal) -$65 million.

• Assets: $7B x (-100bps rate cut) = -$70 million
• Liabilities: $0.5B x (-100bps rate cut) = -$5 million
• Net → Assets – Liabilities = -$70M – (-$5 million) = -$65 million

With matched portfolios, the impact is zero.

• Assets: $7B x (-100bps rate cut) = -$70 million
• Liabilities: $7B x (-100bps rate cut) = -$70 million
• Net → Assets – Liabilities = -$70M – (-$70 million) = 0

Caveats, of course

Of course, in the real world, there are nuances that will make the net impact diverge from zero. One of the sources of divergence is, for example, the inability to invest in the liability rate. In this case, our swaps use SOFR as the reference rate, but we do not invest in SOFR, we invest in other products (commercial paper, etc.). The relationship between these rates has a beta of 1 (or close to 1) but of course there’s an error bar around them.

In any case, for all practical purposes, the portfolios are immunized… aren’t they?

Enter the fractal universe

Let’s say we have both sides at $7B floating and we go on about our lives. Quarters come and go, interest rates continue to fluctuate, and other income & expense doesn’t get much attention from management nor investors because its volatility has been muted thanks to the great work we’ve done.

Then one day, circumstances change for whatever reason, and we find ourselves in a reality where there’s high sensitivity to changes in income & expense in any given quarter. In other words, we originally reduced volatility from +/- $20 million in any given quarter to +/- $5 million. And in the new reality, +/- $5 million causes heartburn to management and we’re told that we’re failing: “you told us our portfolios were immunized and yet we see $5 million swings.”

In our defense, we show them the bar chart again.

“Look it’s all matched. It’s ALM by the book!” We say.

“Well, it’s not working.” They say.

Increase the resolution

We go out for a walk to think about things.

After a while, we realize what’s happened: it’s not only management’s sensitivity that has changed. We have increased the resolution (or the frequency) of our timeline. We used to think in year-long periods, but now we’re looking at the income statement by month or by quarter.

If we zoom in the front end of our portfolios.

This is what we find:

Asset-liability mismatch at the monthly level. That’s why I call it fractal and that’s what can create heartburn when measuring results in a higher frequency.

What to do?

You can decide to match things at this level or keep them as they are and instead educate stakeholders about the possible outcomes of the micro mismatch.

I’d choose the latter because matching at the micro level is operationally burdensome and can also give rise to false expectations again (e.g., you match to the month, and then SOFR and CP markets do not move in lockstep for a couple of months in a row… more explaining to do…).