# Why 10-year versus 2-year spread?

I occasionally see the 10y-2y spread referenced as a recession predictor. See, e.g., https://seekingalpha.com/article/4201787-current-slope-yield-curve-tell-us

Why 10y minus 2y? Specifically, why use 2y as the short rate rather than 1y or 3m?

Perhaps 10y-2y is a better predictor of recessions than other choices but I haven't seen any claim of that. And before I jump in and try to test it, I thought I'd see if there was something obvious that I was missing.

The short answer is that using 2y/10y is not a requirement and many other combinations are commonly used (e.g., 3m/10y, 1y/10y, fed funds/10y). According to a note published by the New York Fed:

With regard to the short-term rate, earlier research suggests that the three-month Treasury rate, when used in conjunction with the ten-year Treasury rate, provides a reasonable combination of accuracy and robustness in predicting U.S. recessions over long periods. Maximum accuracy and predictive power are obtained with the secondary market three-month rate expressed on a bond-equivalent basis, rather than the constant maturity rate, which is interpolated from the daily yield curve for Treasury securities.

The following resources and many references these pages link to should be helpful:

A more recent paper explores using near-term forward yield spread as a leading indicator, which is also worth reading. Table 2 in the paper compares the predictability of various spread metrics.

• I think short term tenor is also a fact of currency. For usd, 3m is good as the curve is quite steep from the very beginning. For eur, 2y is (imho) a better indicator a the yield curve is almost flat in the first year tenors as one can find on ecb.europa.eu/stats/financial_markets_and_interest_rates/… Nov 4 '18 at 22:53

If the business cycle is mature then the central bank (usually) looks to raise the policy rate to keep inflation pressure under wraps. This can necessitate raising policy rates to the point at which the economy slows by so much that it causes recession (defined as two quarters of negative growth). Market expectations about slowing growth and an eventually lower policy rate both work to drive down longer term yields, but the near term prospect of higher (or sticky stable/falling) policy rates means that the two year yield direction can be indeterminate (causing yc inversion), that is, until such time as the central bank cuts policy rates sufficiently in the context of improving expectations about economic recovery (yc normalises).

Why specifically the two year rate? Because this is close to the most sensitive duration with respect to changes in expectations about growth and inflation (which in turn reflects the percieved transmission window of monetary policy in the context of a particular central banks 'inflation flighting credibility'). Why the ten year? My understanding is that the precise term is less important in this case, but using very long rates may introduce other extraneous factors (not related to growth and inflation) such as central bank flows.

• I agree 2y is an important pillar. Please note two more things. 1) On Bloomberg, in the sovereign bond page, 2y10y is explicitely consider as a spread of long vs short. (3m10y is not). 2) LIBOR contributions do not mean banks actually lend money each other: meanwhile 2y bonds are actually traded. Nov 7 '18 at 22:43

In a standard monocurve world, the interest rate curve is increasing with decreasing slope. Something like this. This comes, in very basical environment, as the exponetial cumulative sum of spots rates.

Let me call the 10y-2y difference spread further on.

So why 10y-2y (in general)? This is a $$long-short$$ period difference. During a recessions, central banks lower rates pushing down the i.r. curve. When the spread starts contracting, market expects a coming cut of the i.r. and a future lower curve. For this reason, real world curves (vs academic ones) are decreasing on the long terms: a kind of economic cycle is implied. You may also read the spread under a credit risk point of view: a tight spread means "if an issuer can survive 2y, it is very likely that it will survive also 10y therefore a small extra premium is required". This is very clean in distressed bond issuers: implied yields usually form a reversed term structured (decreasing like an hyperbola).

Why 10y-2y (specific)? When bootstrapping i.r. curves you normally consider EONIA for very short terms, LIBORs and deposits for short terms ($$<1y$$), IRS for medium and long terms. This comes from the fact that is easy to find these instruments quoted on the market. In finance there are a lot of conventions, and this may be such one, but I think it comes from the fact that 10y is a very liquid proxy of long term (like in bond markets), meanwhile 2y is good and liquid proxy for short/medium term. Below 1y terms are too short to catch the credit/economic trends.

• I would comment that LIBOR and EONIA are not comparable and wouldnt be used to build a curve together. First eonia is an ois rate related to the overnight cost a bank has when borrowing from europe fed. Libor is an interbank rate on us deposits. LIBOR and EONIA are not comparable. LIBOR is comparable to the fed fund rate while euribor is comparable to the eonia rate. There are short term and long term libor referenced securities and short term and long term ois references securities. Nov 5 '18 at 19:06
• LIBOR in my answer means XIBOR: the obvious sense is that you use first overnight rates then the XIBORs according to the currency you are considering. By the way, LIBOR is also EUR. There are EURIBOR and EUR-LIBOR. Nov 6 '18 at 20:14