The Mathematics of Credit Spreads: Why (1 + i)^x Matters More Than E=mc²

Book: Financial Stability: Fraud, Confidence and the Wealth of Nations by Frederick L. Feldkamp and R. Christopher Whalen
ISBN: 978-1-118-93579-8

Part Three of Financial Stability is where Feldkamp and Whalen stop telling stories and start proving their theory. Chapter 14 opens with a great anecdote. When a journalist asked Albert Einstein to name the most important mathematical formula in history, he did not say E=mc². He said: one plus i to the x. Compound interest.

The authors agree. And they use that formula to show why credit spreads, not base interest rates, are what really move markets.

Minimizing i and x

The theory of financial stability aims to minimize both the interest rate (i) and the time period (x) when applied to financial intermediaries’ assets and liabilities. That is how finance reaches equilibrium and maximizes equity and productivity growth across the economy.

But here is the tension. Financial stability minimizes the margin that banks use to pay their managers. Low margins are good for customers and the economy. They are terrible for bonus culture. This gap between management self-interest and institutional health is the foundation of moral hazard, off-balance sheet liabilities, and shadow banking.

The compound interest formula is the Rosetta stone. Table 9.1 in the book uses base rates and spreads to translate cash flow into debt and equity values. Over time, only cash flow supports economic valuation. Debt gets paid first under absolute priority. What is left belongs to equity.

What the Numbers Show

The results are striking. In a low-spread complete market, total value of constant cash flow rises 68.5 percent when base rates fall from 5 percent to 0 percent. With 50 percent leverage, equity rises 137 percent in the same scenario.

But spreads matter far more than base rates. At a 0 percent base rate, the difference between a normal market spread and the Armageddon spreads of 2008 produces a 55 percent decline in total value and a 78.6 percent decline in equity. Reverse the Armageddon effect and equity could rise 366.5 percent.

Compare the 2008 Fed response (0 percent base rates, liquidity injection) to the Depression-era liquidation approach (raising rates while blocking liquidity recycling). Using the Fed’s 2008 approach, total wealth ended up 41 percent higher and equity 625.7 percent higher than under liquidation.

The recovery hurdle tells the real story. Recovering from a Depression-style liquidation requires a 1,328.6 percent increase in equity values. Recovering from the 2008 approach requires only 98 percent. That is 13.56 times harder to come back from liquidation.

The 3-6-3 Bank

Feldkamp and Whalen run a thought experiment on a classic 1960s bank: borrow at 3 percent, lend at 6 percent, golf by 3. With $1 billion in loans, $900 million in deposits, and 2 percent operating costs, equity grows 13 percent per year. Over ten years, value compounds up 239.5 percent.

Now add defaults that wipe out asset earnings and credit spreads that push deposit costs up 200 basis points. That modest increase compared to 2008. The bank is insolvent in two years.

When leverage is good, it is very good. When it is bad, it is horrid. And since banks are essential and taxpayers ultimately insure their liabilities, reporting anything off-balance sheet is ridiculous.

Spreads and Defaults Move Together

Corporate default data correlates almost perfectly with credit spread graphs. When spreads rise from equilibrium to Armageddon levels, equity falls roughly 50 percent on average. Many marginal borrowers default at just a 50 percent decline. Without any change in base rates, equity falls about 75 percent.

The Fed sees little long-term impact from changing short-term rates because winners and losers offset over time as bonds mature. Spreads do not offset. They hit everyone at once.

My Reaction

I am not a quant, and this chapter is dense. But the core insight is accessible: compound interest plus leverage plus widening spreads equals catastrophe, and fast.

The moral hazard section resonated with me. Managers will always prefer high margins. Open markets and fraud enforcement are the only things that keep margins low. Mathematics does not care about your quarterly earnings call.

Henry Ford accelerating the 1933 banking crisis and J.P. Morgan profiting from the 1907 panic are dark reminders that some people benefit from deflation. The authors even wonder whether Morgan influenced the 1913 Federal Reserve Act to prevent the central bank from paying interest on reserves, preserving his crisis-buying opportunities.

Whether or not that conspiracy is provable, the 2008 Fed showed what happens when you remove that impediment. Liquidity returned. The math worked.

Chapter 14 is the proof that financial stability is not philosophy. It is arithmetic.

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