“I don’t know what a yield curve is, and at this point, I’m too afraid to ask”.
In the last few months, financial and social media have increasingly covered the current macroeconomic scenario making reference, among other things, to the so-called “yield curve”. In particular, the yield curve inversion has become a recurring argument that many analysts used to claim a recession is incoming.
If you feel daunted, fear not.
In this post, we will take a look at what a yield curve is, its relationship with recessions, and how to capture market expectations through the yield curve.
What is a yield curve?
The yield curve is a function that shows the relationship between market interest rates and the time to maturity of the instruments yielding those rates. The US yield curve is made of US Treasury bond interest rates for different maturities. The most liquid maturities are 2 years, 5 years, 10 years, 15 years, and 20 years. Interest rates represented in this yield curve are conventionally considered risk-free. This means that interest rates do not represent the opportunity cost of capital invested in risk-free assets.
In layman’s terms, the opportunity cost of capital is the return you are foregoing by choosing to invest your money in one asset instead of another one. Whatever “risk-free” investment you could think of, the US yield curve will always provide you with the returns you are giving up (and you are then expected to exceed) by putting your money in that more risky investment.
Normal and inverted yield curve
Finance textbooks teach us that yields are expected to be non-decreasing with respect to the time to maturity. Hence, investing money for 2 years should yield a higher interest rate than investing it for 1 year. Why is that? Because the longer your investment lasts, the higher your opportunity cost is for the capital you have invested.
What about the notorious “inverted” yield curve? In unusual situations in which yields decrease as time to maturity increases, the yield curve is called inverted. When the US government issues bonds for different maturities, investors could be increasingly unwilling to lend money for shorter terms because they could be worried about incoming economic turmoils. Hence, the US government is forced to decrease the price of short term bonds to make them more attractive to the markets. When a bond price decreases, its return (yield) increases. That’s how inverted yield curves originate.
What does an inverted yield curve anticipate?
Is it a recession incoming? Inverted yield curves could give (apparently) contradicting answers.
The table below shows how long it took for a recession to materialize after a yield curve inversion, measured as the spread between the 10-year and 2-year US Treasuries rate since 1976.
On the other hand, inverted yield curves have also anticipated quite juicy (on average) stock market returns if we consider S&P 500 as a proxy for the broad equity market.
Forward interest rates and market sentiment
Forward interest rates are interest rates on investment and loans that, instead of starting immediately as for spot rates, start at a future date, the settlement date, and last to a date further into the future, the maturity date. For instance, the rate at which I can invest / borrow money in 3 months from now and for the following 6 months is denoted as the 3m6m forward rate where the first number indicates the how distant in the future is the start of the investment and the second one indicates the time to maturity once the investment has started.
Why are forward rates important? They represent the expected future spot rates. This can be easily visualized with a practical example.
Suppose you can invest $100 for 6 months at 10% APR or for 12 months at 7% APR. You would find yourself with $105 after 6 months and $107 after 12 months in the first and second case respectively.
What if you reinvest the $105 you received after 6 months for another 6 months? Since the future 6-months spot rate is unknown, you cannot determine your future return upfront. However, you can compute what this rate should be to make you indifferent between investing for 6 months and reinvesting your proceeds for another 6 months and investing for 12 months straight away. The implied 6m6m forward rate, is the rate that makes these two alternatives equal in terms of return.
Market participants are then telling us they expect the future 6-month spot rate to be equal to 3.8% in 6 months from now. What if someone thinks this rate is too high and the correct 6m6m forward rate should be, say, 2%? In that case, one could try to profit from this misalignment by doing the following:
- Borrow $100 for 6 months at 10% APR
- Invest the $100 just borrowed for 12 months at 7%
- Repay the loan taken at step 1 by borrowing $105 for another 6 months at 2% APR (the expected future 6-month spot rate), costing $106.05 in total.
- Collect the $107 proceeds from the investment at step 2 and to repay the $106.05 loan at step 3 with a resulting profit of $0.95.
The example shown before depicts a situation in which the yield curve is inverted (the 12-months spot rate is lower than the 6-months spot rate). Markets are pricing in a reduction in the future spot rates (from 10% to 3.8% for the 6-months spot rate) that is likely to occur during recessions and / or periods of prolonged economic slowdown. As the example shows, when future rates are expected to decrease, the future borrowing cost is expected to fall as well. That’s why it is more convenient to:
- invest with longer maturities
- borrow with shorter maturities
The first would cause longer-dated rates to decrease because much more money will be lent compared to the borrowing demand, whereas the opposite would happen on shorter-dated rates where borrowing demand would outstrip lending supply. That’s how you end up with an inverted yield curve.
Yield curve in DeFi: the great absent (so far)
Money markets in the cryptocurrency industry are working great since the so-called “DeFi summer” of 2020. However, lending and borrowing activities are mainly executed on a continuous basis without fixed terms on both interest rates and maturities. Floating rates and maturity-less loans and deposits make it difficult to extrapolate a yield curve out of them.
The closest representation of a yield curve in DeFi could be provided by fixed lending and borrowing protocols like Notional Finance. The chart below shows a USDC and DAI yield curve that has been interpolated using three maturities (June 2022, September 2022, and March 2023).
The following table shows spot and forward rates derived from the USDC and DAI yield curves.
The USDC curve flattens out from September 2022 on, whereas the DAI curve is inverted in the June-September 2022 portion.
How to profit from this? A possible strategy could be to:
- Lend DAI choosing the Jun 27, 2022 maturity to earn 5.44% APR
- On Jun 27, 2022 swap the DAI proceeds to USDC to lend it until September 25, 2022 and earn an expected 5.65% APR
- On September 25, 2022 swap the USDC proceeds to DAI to lend it until March 24, 2023 and earn an expected 9.14% APR
Assuming that forward rates turn out to be equal to the actual ones, this strategy would result in a 7.56% APR against the highest achievable single investment APR which is 7.44% on DAI with maturity on March 2023.
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Disclaimer
The information provided in this article is provided for informational purposes only and does not constitute, and should not be construed as, investment advice, or a recommendation to buy, sell, or otherwise transact in any investment, including any products or services, or an invitation, offer, or solicitation to engage in any investment activity. You alone are responsible for determining whether any investment, investment strategy, or related transaction is appropriate for you based on your personal investment objectives, financial circumstances, and risk tolerance. In addition, nothing in this article shall, or is intended to, constitute financial, legal, accounting, or tax advice. We recommend that you seek independent advice if you are in any doubt.
