Increasing The Range Of Irrelevance Of r*

Eric Lonergan wrote an interesting article recently: "r* and the range of irrelevance." I largely agree with his points, but in my view, he is far too sympathetic to economist's theories about the "natural real rate" (r*; although economists have switched to referring it to as r* to avoid the hangups around the word "natural rate.") I just wanted to expand on one topic he touches in the first sentence; it seems unclear to me that the risk free rate is extremely influential in all financial asset markets.

(Also: Happy New Year!)

Eric Lonergan's lead sentence is:

Despite the fact that interest rates determine all asset valuations [emphasis mine - BR], there is nothing close to a general theory of interest rate determination. 

My concern here is the first part of the sentence; I think "determine" is too strong a word. Please note that my discussion largely diverges from Lonergan's arguments from this point; I largely agree with what he wrote. Instead, parts of his discussion just triggered some arguments that I had been thinking about earlier.

What is an "Interest Rate"?

For fixed income instruments, we can either quote market prices in terms of a yield, or a price. There is a fixed convention (that depends upon the instrument and market) that converts between the two. For these instruments, it is trivially true that the yield determines the price. However, what I am aiming at is the notion that "interest rates" determine the appropriate valuation of financial assets. In the case of corporate bonds, what will the quoted yield be?

One of the basic problems with economic theory is that most discussions do not take into account the advances of fixed income analysis that have taken place over the past four or five decades. We need to distinguish between a theoretical fitted curve, and the actual quoted prices of instruments.

Take the "10-year Treasury yield" from the Federal Reserve H.15 report. Even though it may be recorded as x% on a given day, it is entirely possible that not a single Treasury trade will have gone through at x% on that day. The benchmark 10-year Treasury Note may be trading at yield below x% (since there is usually a benchmark premium that relates to liquidity and special repo financing rates), and off-the-runs may be trading with yields above x%.

In order to make sense out of the multitude of price quotes, fixed income analysts have to work with these fitted curves. There is no guarantee that we can transact at exactly those levels, but the idea is that we should be at least close. Furthermore, the curves themselves are expected to evolve in ways that are predicted by financial theory, such as in option pricing models, or affine curve structure models.

Once we realise we are dealing with a fitted curve going from overnight to perpetual maturities (consols),  debates about what maturity we are supposed to be talking about are moot. In financial theory -- as well as in the dreaded Dynamic Stochastic General Equilibrium models -- central banks are supposed to pin down the entire cure through the influence on rate expectations (modulo the term premium).

Pretty much by definition, all credit risk-free instruments (currency in circulation, bank reserves, Treasurys, OIS, Fed Funds, ...) are supposed to trade near the theoretical risk-free curve. So yes, for these instruments, the fitted curve matters.

In the rest of this article, I use the risk-free curve to stand in for "interest rates." How much does it matter?

Case: Credit Instruments

The usual situation is that instruments with credit risk trade at a positive spread to the theoretical risk-free curve. (There are exceptions, such as in the tax-free municipal market in the United States, or when the central government is viewed as posing default risk.)

If we assume that credit spreads are fairly stable, the risk-free interest rate curve is going to be a major driver of observed credit spreads. However, in a low interest rate environment (such as we have seen in most developed countries in the past decade), credit spreads may be more volatile than the risk-free curve. Since credit spreads typically move in a counter-cyclical fashion, it may be quite difficult to guess how the yield on a corporate bond will evolve if the only available data we have is the yield on a comparable maturity risk-free bond. However, if we are looking at sub-investment grade ("junk") bonds, the relationship may be very tenuous.

Central banks can attempt to influence credit spreads. The classic example was the massive purchases of non-Treasury instruments by the Federal Reserve as part of the response to the Financial Crisis. However, since they acted like pseudo-Monetarists and only worried about the quantity of purchases, and not the pricing (spread), there is no reliable guide for pricing by other agents. (The lack of a price signal was why the Treasury purchases during Quantitative Easing was a massive theoretical fail.)

In summary, the risk-free curve obviously matters for credit instruments, but the effects get fuzzy.

Currencies: Whatever

The pricing of currency forwards is obviously related to interest rate differentials (and the basis). Forward basis swaps are for intents and purposes a funding instrument, and are traded by fixed income investors. However, the determination of the spot currency rates seems to driven by whatever random meme that currency investors are herding around at the moment.

Real Estate: Not so Much

Commercial real estate is typically approached in a fashion that looks similar to fixed income investing. The cap rate is a key metric, and is often compared to corporate spreads.

However, real estate is a long-lived asset. Although commercial leases are fixed for a period, they can be revised upward or downward based on market conditions. The direction of those potential revisions is a major factor in determining the fair value of the property.

Once we start looking at residential properties, it is clear that interest rates are not a major determinant of prices; housing markets globally have entered and exited bubbles repeatedly.

Since most real estate is purchased using debt, interest rates obviously matter, eventually. That said, it is unclear what level of interest rates is needed to choke off a real estate boom.

Equities: Theoretical Link, at Best

If equity investors were the rational people of financial theory, they are supposed to be valuing equities using discounted cash flow analysis. That said, it is unclear whether observed price movements can be explained by changes in the net present value of cash flows, other than by the trivial step of backing out the inputs to discounted cash flow analysis from the observed price.

Even if we accept the premise that valuations depend upon discounted cash flow analysis, we run into problems.

• It makes no sense to discount risky corporate cash flows at the risk-free rate. We should be using a corporate curve as our base curve, and that corporate spread will vary from the risk-free rate in a fashion that is discussed earlier.
• The projected cash flows depends upon the state of the economy. Under most scenarios, they will rise when expected nominal growth is higher, which is associated with higher nominal interest rates.
• Based on historical experience and financial theory, the equity risk premium should be large and variable. Its movements will dwarf the movements of the risk-free curve.

(Lonergan's article has a discussion about the rate of return on capital. He unfortunately follows the lead of mainstream economic models, which do not take accounting identities seriously. Realised aggregate profitability is largely a question of wage bargains and accounting identities, as per the Kalecki Profit Equation. The relationship between realised profit and the beliefs of equity market participants is not obvious.)

Concluding Remarks

Although a risk-free interest rate curve is an input into standard financial valuation models, it's importance to anything other than high-grade debt is questionable. That is, movements in the risk-free curve may tell us very little about the valuation changes in riskier assets.

The tendency to blame all movements in financial markets on central banker's actions tells us more about the psychology of financial market commentators than it does about asset valuations.

(c) Brian Romanchuk 2018