The real interest rate and why it governs everything

A Swiss savings account paying 1 percent looks better than one paying 0.25 percent. Whether it actually is depends entirely on a number the bank does not print on the statement. If prices are rising at 2 percent, the 1 percent account is destroying purchasing power at roughly 1 percent a year; if prices are flat, it is genuinely adding to it. The nominal rate is a promise about francs. The real rate is a promise about what those francs will buy. Almost every serious mistake in personal and institutional finance comes from confusing the two.

This distinction is not an accounting nicety. The real interest rate is the price of shifting consumption across time, and because every financial asset is a claim on future consumption, it is the single variable that sits underneath valuations, corporate investment decisions, currency flows, and the sustainability of government debt. When the real rate moves, everything reprices — not by sentiment, but by arithmetic.

The Fisher relation, and the two versions of it

The standard shorthand, associated with Irving Fisher, is that the nominal interest rate equals the real rate plus expected inflation: i ≈ r + π. The exact form is multiplicative, because compounding does not add:

(1 + i) = (1 + r) × (1 + π)

Take a Swiss term deposit at 1.00 percent with inflation at 2.00 percent. The approximation says the real return is −1.00 percent. The exact calculation is (1.0100 / 1.0200) − 1 = −0.98 percent. At these levels the shortcut is fine. At Turkish or Argentine levels it is not: with 60 percent inflation and a 70 percent deposit rate, the approximation says +10 percent real while the truth is (1.70 / 1.60) − 1 = +6.25 percent. Use the exact form whenever either number is large.

The more important split is between the ex ante real rate and the ex post real rate. Ex ante is the rate you believe you are locking in: today's nominal rate minus the inflation you expect. Ex post is what you actually got: the nominal rate minus the inflation that actually happened. Only the ex ante rate influences decisions, because it is the only one available when you decide. Only the ex post rate determines who is richer afterwards. The gap between them is where wealth quietly changes hands, and the next lesson in this course is devoted to it.

Wicksell's natural rate, and why the policy rate is not the stance

Knut Wicksell, writing at the end of the nineteenth century, distinguished the market rate of interest set by banks from the "natural" rate that would equate desired saving with desired investment at full employment. Modern macroeconomics calls the latter r-star (r*). It is unobservable, it drifts over decades, and it is driven by real forces: demographics, productivity growth, the global appetite for safe assets, and the propensity of households and governments to save.

The mechanism that makes this matter is simple. If the central bank holds the real policy rate below r, borrowing to invest is profitable at the margin for more projects than the economy can supply resources to, demand runs above capacity, and inflation rises. Hold it above r, and the reverse. Policy is therefore never "tight" or "loose" because the nominal rate is high or low in absolute terms. A 15 percent policy rate with 25 percent inflation is stimulative. A 0 percent policy rate with 2 percent deflation is restrictive — which is exactly the trap Japan spent decades in, and the reason the Swiss National Bank pushed its policy rate below zero in the years after 2014: with inflation flirting with negative territory and the franc under enormous appreciation pressure, a nominal floor of zero would have delivered a positive and unwanted real rate.

Two implications follow. First, you cannot judge monetary policy from the headline rate alone. Second, the central bank controls the short-term nominal rate directly and the short-term real rate only to the extent that expected inflation is sticky in the near term. Over long horizons, real rates are set by savings and investment, not by a committee.

Why the real rate is the discount rate that prices everything

An asset is a bundle of future cash flows. Its value is those flows discounted back to today. The discount rate is a real rate plus whatever risk premium the flow deserves, and the arithmetic is unforgiving over long horizons.

Consider a single payment of CHF 1,000,000 due in 20 years. Discounted at 1 percent, it is worth 1,000,000 / 1.01²⁰ = CHF 819,544. Discounted at 3 percent, it is worth 1,000,000 / 1.03²⁰ = CHF 553,676. A two-percentage-point change in the discount rate — small in absolute terms — removes about 32 percent of the present value.

The same mechanism operates on bonds. A 30-year zero-coupon bond yielding 2 percent trades at 1 / 1.02³⁰ = 55.2 percent of face value. Move the yield to 3 percent and it trades at 1 / 1.03³⁰ = 41.2 percent — a fall of just over 25 percent, with no default, no downgrade, and no change in the promised cash. This is duration, covered properly in the fixed-income course, but the driver is the real rate underneath the nominal yield.

It also explains a pattern that is often described as a mood swing and is really arithmetic. Long-duration assets — profitless growth companies, venture portfolios, thirty-year bonds, real estate valued off a capitalisation rate — have most of their value in cash flows far in the future. Their present value is therefore hypersensitive to the discount rate. When real rates rise, these assets fall the hardest, not because investors became pessimistic about the business but because the same future francs are now worth fewer present francs.

Corporate investment: the hurdle the real rate sets

A firm evaluating a project compares its expected real return on capital against the real cost of funding. If a Zurich manufacturer can earn 4 percent real on a new production line, that project is viable when the real cost of capital is 1 percent and marginal when it is 3.5 percent. Inflation itself is roughly neutral here — if the project's revenues and costs both inflate, the nominal return rises with prices and nothing changes in real terms. What changes behaviour is the real rate.

This is why a decade of very low and sometimes negative real rates left visible fingerprints: elongated project horizons, heavy share buybacks funded by cheap debt, private equity structures whose returns depended materially on financing costs, and property valuations supported by capitalisation rates that only made sense against a near-zero real discount rate. None of that was irrational. It was the correct response to the price of time, and it reverses when that price changes.

The Swiss saver: nominal rates, real losses, and a tax system that ignores the difference

Switzerland adds two frictions that make the real-versus-nominal distinction sharper than in most countries.

First, income tax is levied on nominal interest, not real interest. Second, most cantons levy an annual wealth tax on net assets, which is a charge on the stock of savings regardless of the return.

Work it through. You hold CHF 100,000 in a savings account paying 1.00 percent. Interest is CHF 1,000. Assume a marginal income tax rate of 30 percent across federal, cantonal and communal levels: tax of CHF 300, leaving CHF 700, a net nominal return of 0.70 percent. With inflation at 2.00 percent, the real after-tax return is (1.0070 / 1.0200) − 1 = −1.27 percent. Add a wealth tax of 0.3 percent — CHF 300 — and the net return falls to CHF 400, or 0.40 percent, giving a real after-tax return of (1.0040 / 1.0200) − 1 = −1.57 percent.

Compounded, that is not trivial. At −1.27 percent a year for ten years, CHF 100,000 retains 0.98726¹⁰ ≈ 0.880 of its purchasing power: about 12 percent of real wealth gone, with the statement showing a balance that only ever went up.

Two further Swiss specifics belong in the same frame. Interest paid by Swiss banks is subject to 35 percent withholding tax (Verrechnungssteuer), which Swiss residents reclaim through the tax return — a cash-flow timing issue rather than a real cost, provided the income is declared. And second-pillar occupational pensions in payment carry no automatic inflation indexation; only the first pillar (AHV/AVS) is adjusted, via the mixed index of wages and prices. A retiree's second-pillar pension is a long-dated nominal annuity, and its real value erodes at exactly the rate of inflation.

Measuring the real rate when nobody publishes it

In the United States, France or the United Kingdom you can read a real yield straight off an inflation-linked government bond. Switzerland does not have that instrument: the Confederation does not issue inflation-linked bonds, so there is no traded Swiss real curve. Practically, a Swiss-resident investor infers real rates by taking nominal Confederation yields or SARON-linked money-market rates and subtracting an inflation forecast — the SNB's quarterly conditional inflation forecast being the most obvious reference point, alongside KOF and SECO survey measures.

That inference carries error, and the error is the whole point. When you buy a nominal bond you are not buying a real return; you are buying a nominal return and taking inflation risk on top. Whether you are compensated for that risk is a question about the term premium and the inflation risk premium, which later lessons in this course take apart.

What to take away

• The real interest rate, not the nominal rate, is what determines whether saving preserves purchasing power, whether a project clears its hurdle, and whether monetary policy is actually restrictive.
• Use the exact Fisher form (1 + i) = (1 + r) × (1 + π) whenever inflation or rates are large; the additive shortcut understates the damage at high inflation.
• Because present value falls geometrically with the discount rate, a two-point rise in real rates can remove roughly a third of the value of a cash flow twenty years out — long-duration assets fall hardest for arithmetic reasons, not sentiment.
• Swiss tax is levied on nominal interest and on the stock of wealth, so a modest positive nominal deposit rate can still deliver a real after-tax return well below zero; compounded over a decade this is a double-digit loss of purchasing power.
• Switzerland has no inflation-linked government bonds, so the Swiss real rate must be inferred from nominal yields minus a forecast — which means the investor, not the market, carries the inflation error.

Sources

• Irving Fisher, The Theory of Interest (1930) — the original statement of the relation between nominal rates, real rates and expected inflation.
• Knut Wicksell, Interest and Prices (1898) — the natural rate of interest and the cumulative process linking rate gaps to the price level.
• Swiss National Bank, Quarterly Bulletin and the SNB's conditional inflation forecast, published with each monetary policy assessment — the primary Swiss reference for expected inflation.
• Swiss Federal Statistical Office (BFS/OFS), Swiss Consumer Price Index (LIK/IPC) methodology and releases.
• Bank for International Settlements, Annual Economic Report — recurring analysis of the global decline in real interest rates and its drivers.
• Federal Tax Administration (ESTV/AFC), documentation on Swiss withholding tax (Verrechnungssteuer) on interest and dividends.
• John H. Cochrane, Asset Pricing (revised edition, 2005) — the formal treatment of discount rates as the core object in asset valuation.