기간 프리미엄 (Term premium) 개요

수익률 곡선과 장단기 스프레드 이야기를 하다보면 종종 기간 프리미엄 이야기가 나온다. 사실 기간프리미엄은 시장에서는 그다지 유의미한 재료가 아니긴 하다. 애시당초 이론적인 개념이라 통일한 산출 방식이 없고,  상품 가격을 도출하는데 쓰이지도 않으며, 현물 장단기 스프레드랑 비슷하게 움직여서 굳이 기간 프리미엄을 들여다볼 유인도 적다. 그렇지만 미래 금리 경로나 장기물 가격을 디테일하게 생각하다 보면 피할 수 없는 주제이기도 하다. 

기본적으로는 현물 장기금리 - 기대 단기금리 예상경로로 도출한다.
이하는 기간 프리미엄 설명과 동인에 대한 짜깁기 글이다. 자주 인용되는 기간 프리미엄 모델로는 Kim-Wright(Fred)와 ACM이 있다.

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◆기간 프리미엄(term premium)이란 만기가 긴 채권에 추가로 요구되는 금리 수준을 의미한다. 채권을 장기간 보유하는 데에 따른 위험을 반영한 보상 격이다.

장기 채권은 단기 채권보다 만기까지 통화정책이나 인플레이션, 상환 위험 등의 불확실성에 더 많이 노출되기 때문에, 투자자들은 장기 채권에 더 높은 이자를 요구한다.

일반적으로 장기 국채의 명목금리를 구성하는 요소는 ▲인플레이션 기대치 ▲실질 단기금리 ▲기간 프리미엄 등이 있다. (*주: 모형에 따라 다르다)

시장 일각에서는 최근 미국 장기 국채 금리가 상승한 원인으로 기간 프리미엄의 상승을 지목했다.

미국 국채의 수요는 감소했지만, 재정적자 확대로 중장기채 공급이 많아지는 등 미 국채 수급의 장기 불확실성이 확대된 것이 기간 프리미엄 상승 배경 중 하나로 꼽힌다.

중립 금리 상향 논쟁이 벌어지며 인플레이션 경로에 대한 우려가 높아진 점도 기간 프리미엄 상승을 자극한다.

로리 로건 댈러스 연방준비은행(연은) 총재는 지난 9일 "기간 프리미엄 상승으로 장기 금리가 높은 수준을 유지하면 기준금리 인상 필요성이 줄어들 것"이라고 언급하기도 했다.

기간 프리미엄을 추산하는 공식은 정해져 있지 않아 기관마다 편차가 있다.

뉴욕 연은이 ACM(Adrian, Crump, Moench) 모형 등으로 추산한 미국 10년물 국채의 기간 프리미엄은 올해 8월 기준 0.158%다. (금융시장부 윤은별 기자)

출처 : 연합인포맥스(https://news.einfomax.co.kr)

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The term premium is the extra return required to hold to maturity a long-maturity bond versus rolling over short-maturity debt (e.g., three-month T-bills). Term premia are on average positive and rising with maturity: investors typically require extra yield to hold long-maturity bonds relative to shortmaturity bonds. While the average slope of the yield curve pins down average term premia, term premia at a point in time cannot be directly observed. I make no effort to estimate them. There is a cottage industry of models attempting to pin them down, and all estimates have wide standard errors and are sensitive to specification. My focus is identifying the forces that drive time-variation in term premia.
Mechanically, the determinants of term premia are all factors that influence a bond’s yield, other than the current interest rate and expected future interest rates. In practice, two key factors tend to drive term premia: 1) changes in perceived riskiness, and 2) changes in demand and supply
1)Perceived Riskiness
On the risk side, term premia are higher when bonds are truly riskier and when investors’ tolerance for risk is lower – i.e., when investors are more risk-averse.
The most important risk factor for (fixedrate) government bonds is inflation. Yields incorporate inflation expectations over the life of the bond, but unexpected increases in inflation erode a bond’s real return. Inflation risk is likely the main driver behind the fact term premia are on average positive: the possibility of unexpected inflation makes holding long-maturity bonds riskier than rolling over short-maturity debt.
By the same logic, variation in inflation risk should be a key driver of time-variation in term premia. When uncertainty about future inflation is high, say during the 1970s and into the 1980s, a period where inflation rates averaged in the double digits and inflation volatility was extremely elevated, investors require a larger expected return to holding long-maturity bonds relative to their shorter-maturity counterparts. Wright (2012) and Bauer et al (2013) verify this intuition empirically. Using a large international panel data set, both papers find a strong link between estimates of term premia and measures of inflation uncertainty.
In addition to inflation uncertainty, risk aversion – the compensation investors require for bearing risk – also varies materially over time. Theoretical and empirical research supports the view risk aversion varies countercyclically, being higher during recessions than expansions (e.g., see Cochrane (2011)). Indeed, Bauer et al find evidence of a pronounced countercyclical pattern in term premia across international bond markets: term premia estimates on long-maturity bonds are meaningfully higher in recessions than expansions.
2)Demand and Supply
Variations in net demand can arise from exogenous macroeconomic and geopolitical events, or from the explicit monetary policy actions of central banks.13 Their relative safety, liquidity, and ability to meet regulatory capital and liability-hedging needs make government bonds appealing to investors. These features are especially attractive during times of financial market stress (e.g., “flight-to-quality” and “flight-to-liquidity” episodes), during which safe-haven demand for government bonds tends to suppress their term premia. Secular trends in net demand, such as increases in the holdings of government bonds by foreign central banks, also influence term premia. Monetary policy may affect term premia as well. Indeed, quantitative easing and all its variants – “yield curve control,” “operation twist,” etc. – feature the purchases of longer-maturity bonds (among other securities) by central banks, reducing their net supply, with the explicit objective of suppressing their term premia.
The key drivers of term premia can be expressed succinctly:

How important is time-variation in term premia in explaining the dynamics of bond yields? During the Treasury market “conundrum” of 2004-2006, the Federal Reserve raised interest rates from 1.5 to 5.25 percent, yet long-maturity yields were virtually unchanged. This anomalous behavior is generally attributed to a fall in term premia. What drove the decline? Likely a combination of factors. Inflation uncertainty was quite Term Premium ~ Inflation Uncertainty (+), Risk Aversion (+), Net Demand (–) 12 What Drives Bond Yields? | July 2021 low, both due to improved inflation-fighting credibility of the Fed and more secular forces (this period – “the great moderation” – featured exceptionally low macroeconomic volatility). Low risk aversion was another likely factor, as the economy enjoyed a prolonged expansion. 14 See Backus and Wright (2003) for a more complete discussion. 15 Using realized values versus forecasts can make a big difference. See this blog post by Ben Bernanke. Lastly, the “global saving glut,” which led to heightened demand for Treasuries by foreign central banks and sovereign wealth funds, fueled an increase in demand for safe and liquid US government debt.14

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https://www.federalreserve.gov/data/three-factor-nominal-term-structure-model.htm

Three-Factor Nominal Term Structure Model

https://fred.stlouisfed.org/series/THREEFYTP10

Term Premium on a 10 Year Zero Coupon Bond

->Fred에서 나오는 명목채 텀프리미엄 항목 내용이다. 모형으로 3요인 명목기간구조를 사용하는데, 일반적인 텀프리미엄에서 컨벡시티 프리미엄을 따로 빼서 도출하고 있지만 사실 빼든 안빼든 큰 차이는 없다고.
How are term premiums defined?

Here, term premiums are defined as departures from the expectations hypothesis. Thus, the term premium in yields is defined as yield minus the expected average short rate (over the life of the bond), and the term premium in forward rates is defined as forward rate minus the expected short rate (for the same horizon as the forward rate contract).
This way of defining term premium embeds the so-called convexity premium in the term premium. In other words, our definition of term premium can be written as “term premium = pure term premium + convexity premium”. The “pure term premium” reflects compensation for interest rate risk. The convexity premium arises from the nonlinearity in the relationship between bond prices and yields; if the expected path of short rates was flat and the pure term premium was zero, the yield curve should have a slightly negative slope because the convexity premium contributions are negative. An alternative definition of term premium used in the literature3 corresponds to what we refer to as the “pure term premium” here, i.e., a measure that excludes the convexity premium. Because the magnitudes of convexity premiums tend to be fairly small, the difference between the two term premium definitions is often negligible; this is especially the case when looking at the changes in term premiums. However, when comparing the levels of term premiums, it may be worthwhile to keep in mind that our “term premium” is mechanically slightly lower than the “pure term premium” because of the negative convexity premium