Primer: What Is The Term Premium?

One of the largest complications associated amongst using charge per unit of measurement expectations equally a modelling technique to decide bond yields is the question: what is the term adventure premium? This article is an introduction to this fairly of import topic.

Note that the term adventure premium is dissimilar than other potential premia inward bond yields, such equally that needed to compensate for default risk. In this discussion, I assume that nosotros are talking most authorities bonds that are gratuitous of default risk, which I volition assert applies to the fundamental authorities bonds of countries similar Canada, the United Kingdom, U.S. (assuming the Tea Party quiets down), in addition to non benighted countries similar those inward the euro area.

As a basic example, at the fourth dimension of writing, the Dec 2014 30-Day Federal Funds futures contract is trading amongst an implied yield of 0.27%. The reward of this contract is the monthly average of the effective fed funds rate. At present, the 20-day moving average of effective fed funds is 0.08%. Two possible interpretations of the Dec 2014 contract value are:

1. The weighted average of marketplace participants’ expectations for the fed funds charge per unit of measurement inward Dec 2014 implies that in that location volition live a charge per unit of measurement hike past times the Fed past times that time.
2. On average, marketplace participants create non await a charge per unit of measurement hike, but in that location is a 0.19% (19 footing points) adventure premium inward the Dec 2014 contract.

If y'all are a marketplace player who has the capacity to teach into in addition to handgrip the seat to maturity, the profitability of the seat is based on the realised futurity value relative to the entry level, in addition to and so y'all could ignore the adventure premium, in addition to teach amongst the kickoff interpretation: create I concur or disagree amongst the raw implied charge per unit of measurement expectation embedded inward the instrument? However, if y'all are discipline to short-term mark-to-market worries, or if y'all receive got to post prices, y'all postulate to accept into describe concern human relationship what kind of adventure premium needs to live embedded inward the price.

I volition at ane time give a elementary illustration based on an alternative the world where the fundamental depository fiscal establishment targets the 1-year null coupon charge per unit of measurement (and meets ane time a year*), in addition to the electrical current null coupon yield is 5%. (To translate the numbers, y'all tin purchase the one-year coupon bond at ane time for $0.9524, in addition to it volition mature in addition to pay y'all $1 inward ane year. The two-year coupon bond costs less, at $0.9053, in addition to pays $1 inward ii years.)

Term	Zero Coupon Rate	Zero Coupon Price	Modified Duration
1 Year	5.00%	$  0.9524	0.952
2 Year	5.10%	$  0.9053	1.903
Memo Item:	1-year rate, 1-year forward		5.20%

For this example, I assume that “everyone” expects that the one-year charge per unit of measurement volition live 5% inward ane year, or at to the lowest degree expectations are symmetric around an unchanged rate. But, I assumed that in that location is a 0.20% adventure premium inward the forrad rate, which pushes the 2-year null charge per unit of measurement 0.10% higher upward the 5% grade that raw expectations would imply. (I receive got supplied these numbers to underline ane point: a gentle upward gradient inward the bond yield bend implies a much steeper gradient inward the term premium. In this case, the premium is double the slope, in addition to it would live an fifty-fifty higher multiple of a par coupon slope.)

In equation form:

Observed bond yield = (Average Expected Short-Term Rates Over Bond’s Lifetime) + (Term Premium).

Why would in that location live this premium? There are ii explanations:

1. A buy-and-hold investor has to necktie upward upper-case missive of the alphabet for ii years rather than one, in addition to and so should demand a yield premium for having to create this. Keynes referred to this equally a “liquidity premium”, which is unfortunately somewhat confusing, equally “liquidity” tin oft live idea to apply to things similar one-the-run versus off-the-run spreads, which are bonds of nearly equivalent time-to-maturity.
2. As the tabular array notes, the 2-year null coupon bond has roughly twice the modified duration (interest charge per unit of measurement sensitivity) than the 1-year bond. We consider inward marketplace information that longer duration instruments volition receive got to a greater extent than render volatility than shorter duration instruments. (Their yields are slightly to a greater extent than volatile - when rates are far from null - but the higher toll sensitivity to yield changes trumps this.) Modern Portfolio Theory argues that in that location should live a render premium for to a greater extent than volatile assets.
3. In a province of affairs similar the introduce (and non the information inward the table), in that location is considerable “one-way” adventure to involvement rates. If the forrad charge per unit of measurement is only higher upward zero, risks are skewed towards higher rates, since rates cannot teach likewise far below zero, but in that location is plenty of room for rates to rise. This creates an option-like asymmetric reward profile, in addition to and in addition to so in that location should live an choice premium embedded inward forrad rates. For this reason, I intend JGB yields are nigh a flooring grade at the fourth dimension of writing, fifty-fifty though I create non await to consider whatever BoJ charge per unit of measurement hikes whatever fourth dimension soon.
4. If y'all believe in that location are supply-and-demand factors determining long-term bond yields, they exhibit upward inward the adventure premium (since expected policy rates should non live affected).

Comparison To The Equity Risk Premium

There is a rattling large literature around the equity adventure premium. This working newspaper past times Pablo Fernández discusses three concepts of the equity adventure premium:

1. Required adventure premium. This matches the concepts discussed above: what premium create y'all postulate to add together to the expected render to describe concern human relationship for the higher returns volatility. It assumes y'all receive got a model for spitting out a premium based on volatility, which I, at least, create non have.
2. Historical adventure premium. The historical outperformance of the property over a base of operations property (for bonds, this would live Treasury Bills).
3. Expected adventure premium. What premium is priced into the marketplace right now?

The historical adventure premium is straightforward to calculate. It volition live to a greater extent than interesting inward a century or so, when nosotros receive got plenty modern bond marketplace information to live useful. Before the 1970’s, investors operated inward a Gold Standard mindset, in addition to and so their bond pricing rules are non useful for fiat currencies. We at ane time receive got inflation stability, they operated amongst an supposition of toll grade stability. And until in that location was widespread role of digital computers inward the 1980’s, forwards were non examined, in addition to bond marketplace analysis was done inward a primitive fashion. This caused all mode of relative value opportunities that were afterward crushed out of the market.

From the information laid nosotros receive got available, the historical adventure premium has been massive. This is non surprising, equally nosotros receive got been inward a generational bull marketplace inward bonds. This muddies discussions of what should live expected, equally I volition speak over farther below.

Turning to the expected term premium, nosotros consider that it is unmeasurable. We create non receive got access to actual investor expectations for futurity brusque rates. We tin endeavour the following:

• Use a survey stair out of expected rates. This begs the question: create investors truly believe the economists who provide the survey measure? Another severe work amongst using surveys is that they are updated sporadically, whereas observed yields motility inward reply to each slice of news. This technique may live workable for a low-frequency (e.g., monthly) model, although some attention is needed to align the information timing.
• An investor could plug inward their ain expectations. However, this is only a restatement of what the investor already thinks, in addition to and so it provides no novel information.
• A model for the term premium could live created. This is a little increment manufacture inward academic in addition to fundamental depository fiscal establishment enquiry (affine term construction modelling). I volition encompass this discipline inward afterward articles.

Unfortunately, nosotros cannot calibrate off of historical data. We are at the cease of mega bull marketplace inward bonds, in addition to historic realised term premia receive got been “unreasonably” large. (For example, if nosotros applied the historical term premium for 10-year bond yields to the electrical current yield curve, the implied average “expected” rates would likely live negative.) There are ii primary plausible explanations**: investors in addition to economists receive got been systematically wrong inward their charge per unit of measurement forecasts for ii decades; or else term premia were likewise high. Since the kickoff possibility is rather impolite, I tend to write that historical term premiums were likewise high, but the term premium should live to a greater extent than sensible going forward.

Since the reward on fiscal instruments is based on observed forrad rates, in addition to that I experience that term premia should live little for a diversity of reasons, I intend the best modelling strategy is to assume that expected term premia are little in addition to stable.  I volition encompass this betoken inward to a greater extent than depth when I speak over affine term construction models, where nosotros consider that the modelled term premia are non little in addition to stable.

* The Swiss fundamental depository fiscal establishment targets a 3-month rate, in addition to thus unremarkably sets the target every three months. H5N1 fundamental depository fiscal establishment cannot target a policy involvement charge per unit of measurement which has a maturity longer than its side past times side regular policy meeting.

**Another explanation is that the economic scheme has been hitting amongst a laid of random shocks that all coincidentally led to lower yields. Yeah, right.

(c) Brian Romanchuk 2013