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Thursday 27th August 2015
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updated 1.59pm, Thursday 30th April 2020
Gross redemption yield (GRY) is an inaccurate and inappropriate measure of bond value because it rejects the concept that a longer investment and coupon re-investment term equates to a riskier investment and should therefore attract higher rates of return.
Gross redemption yield (GRY) is an inaccurate and inappropriate measure of bond value because it rejects the concept that a longer investment and coupon re-investment term equates to a riskier investment and should therefore attract higher rates of return.
With any sloping yield curve and/or variable future yields, GRY is only a relative guideline as to return over the full life of a bond. This might be tolerable if bonds were held for their entire life by a single party.
In practice, bonds are rarely, if ever, held by the same investor or investor class from issue date to maturity date, with investor class frequently changing as a bond moves down the curve to maturity.
So if GRY is not the correct approach, what is? The objective should be to maximise the total return over the chosen investment term, taking into account potential interest rate changes during that term. The period total return (PTR) can be defined as the historic actual return achieved, on a bond or portfolio, over a defined period of time. Alternatively, PTR can refer to the calculated actual rate of return expected over a specific future term, for a specific change in a bond's GRY from the current level, over that term. This PTR value is found by deriving the applicable bond price, at the forward settlement date, using the specific forward GRY as the valuation basis, and adjusting this forward price for any bond coupon payments earned/received and accrued interest, during this forward term.
PTR can then be defined as the net change from the bond current market price, inclusive of accrued interest content (the 'dirty' price), to this adjusted forward dirty price, expressed
as a percentage of the current dirty price.
In practice, a table or PTR matrix can be calculated for each individual bond, over a range of forward terms (for example, one week to one year), and a range of potential changes in the bond current GRY (for example, from -50 basis points to +50 basis points). Matrix cells represent the exact individual bond rates of return, for defined future changes from the current bond GRY at specific forward valuation terms from the current date.
Because PTR is a finite rate of return derived from the projected forward GRY/curve and is both forward-yield and forward-term specific, it accords with reality rather than a notional 'hold to maturity' approach. Moreover, because portfolios comprise multiple bond holdings, a PTR matrix of forward terms/yield/average deviations for individual bonds and the combined portfolio satisfies the assessment of this fundamental investment objective.
Consider a one-year bond, with a 2% coupon, payable semi-annually and initially priced at 100, that is, with an initial GRY of 2%. Chart 1 below illustrates five possible pairs of six-month PTR scenarios for five different changes in this bond's yield over its first six months. Scenario 3 reflects the initial GRY assumption, that is, an unchanged, constant re-investment rate assumption over the full one-year term of the bond. The remaining four scenarios illustrate potential different interim and total returns over a range of changes in the bond yield after six months.
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If this bond were bought and held for the full one-year term to maturity, the individual total returns over each of the five scenarios - assuming re-investment of the interim coupon paid - show little variation, ranging between 2.0050% and 2.0151%. So to investors with a one-year time horizon, the five individual scenarios produce broadly similar results over their time horizon of one year.
But the individual scenarios display a wide range of potential first-half returns varying between 0.50% and 1.50% at the end of the first six months, and similarly for second six-month performances.
For investors with time horizons shorter than the remaining one-year life of this bond - for example, six months - the bond interim-period total returns can be of critical importance and bear little resemblance to the GRY at purchase. This PTR/GRY divergence can be greatly magnified for longer dated bonds.
Once you accept that you should regularly optimise PTR, not just GRY at the outset, two questions immediately spring to mind.
A - Are bond prices (particularly of liquid sovereign debt issuance) always 'logical' insofar as they properly reflect the fact that PTR optimisation should be the investment objective of every investor?
B - How can investors evaluate current market prices and future yield-curve scenarios to ensure they are optimising PTR in relation to their curve outlook and investment constraints?
The short answer to question A is 'no', even in highly liquid sovereign debt markets. Because of the fixation with GRY, prices do drift away from their 'correct' levels, which optimise PTR. Some bonds will become 'cheap' relative to the rest of the market whereas others will become 'expensive'. Crucially, these anomalies for individual bonds tend to correct themselves over time, with new anomalies emerging, thereby creating ongoing opportunities for enhanced portfolio returns.
The answer to question 'B' is 'not easily' - if it were easy, the anomalies would be short-lived. PTRs for any investment term will, of course, be determined not only by today's market prices but by the shape and level of the yield curve at the end of the term. Accordingly, investors need to employ quantitative calculations using simulated forward-curve levels and their resultant bond parameters to ensure more informed scenario analysis and improved investment policy decision making.
All analytics should accommodate user-specific requirements and existing investment policy
constraints.
Therefore, in addition to standard and non-standard bond parameters, investors should focus on quantitative PTR analytics, which overcome the shortcomings of GRY as a measure. The attraction of PTR analysis is that all calculations and analytics rely solely on market price, coupons, dates, and more, and do not depend on trend, momentum or time series criteria, which are inherently subjective. Analytics should facilitate multiple-scenario analysis and permit detailed re-valuations and analysis of current portfolio holdings including open switches.
The process then becomes one of optimising PTR, either for a specific forward term/yield change or scenario analysis over a chosen range or ranges. PTR optimisation should permit the user to set as fixed, or change in absolute or in percentage terms, any user-defined weighted parameter (for example, any benchmark constraint), either inclusive or exclusive of adjustments for any changes in net capital investment. Ideally, the analytics processes should also assist in the efficient implementation of one-off structural changes to the bond portfolio - for example, the timely and accurate execution of revisions to a house view or investment policy/strategy.
Significant relative portfolio out-performance can be added to indexed portfolios by adopting a regular routine of even modest PTR optimisation, through consideration and risk-neutral 'housekeeping' switches without risky deviations from the benchmark or other constraints.
In summary, GRY remains the most frequently cited of all the individual bond parameters, partly due to convention and ease of calculation. However, within a bond's life cycle, and to its many, often temporary owners, the shorter term specific PTRs are more important measures, as their cumulative total is the measure applied in fund manager portfolio performance evaluations.
With any sloping yield curve and/or variable future yields, GRY is only a relative guideline as to return over the full life of a bond. This might be tolerable if bonds were held for their entire life by a single party.
In practice, bonds are rarely, if ever, held by the same investor or investor class from issue date to maturity date, with investor class frequently changing as a bond moves down the curve to maturity.
So if GRY is not the correct approach, what is? The objective should be to maximise the total return over the chosen investment term, taking into account potential interest rate changes during that term. The period total return (PTR) can be defined as the historic actual return achieved, on a bond or portfolio, over a defined period of time. Alternatively, PTR can refer to the calculated actual rate of return expected over a specific future term, for a specific change in a bond's GRY from the current level, over that term. This PTR value is found by deriving the applicable bond price, at the forward settlement date, using the specific forward GRY as the valuation basis, and adjusting this forward price for any bond coupon payments earned/received and accrued interest, during this forward term.
PTR can then be defined as the net change from the bond current market price, inclusive of accrued interest content (the 'dirty' price), to this adjusted forward dirty price, expressed
as a percentage of the current dirty price.
In practice, a table or PTR matrix can be calculated for each individual bond, over a range of forward terms (for example, one week to one year), and a range of potential changes in the bond current GRY (for example, from -50 basis points to +50 basis points). Matrix cells represent the exact individual bond rates of return, for defined future changes from the current bond GRY at specific forward valuation terms from the current date.
Because PTR is a finite rate of return derived from the projected forward GRY/curve and is both forward-yield and forward-term specific, it accords with reality rather than a notional 'hold to maturity' approach. Moreover, because portfolios comprise multiple bond holdings, a PTR matrix of forward terms/yield/average deviations for individual bonds and the combined portfolio satisfies the assessment of this fundamental investment objective.
Consider a one-year bond, with a 2% coupon, payable semi-annually and initially priced at 100, that is, with an initial GRY of 2%. Chart 1 below illustrates five possible pairs of six-month PTR scenarios for five different changes in this bond's yield over its first six months. Scenario 3 reflects the initial GRY assumption, that is, an unchanged, constant re-investment rate assumption over the full one-year term of the bond. The remaining four scenarios illustrate potential different interim and total returns over a range of changes in the bond yield after six months.
If this bond were bought and held for the full one-year term to maturity, the individual total returns over each of the five scenarios - assuming re-investment of the interim coupon paid - show little variation, ranging between 2.0050% and 2.0151%. So to investors with a one-year time horizon, the five individual scenarios produce broadly similar results over their time horizon of one year.
But the individual scenarios display a wide range of potential first-half returns varying between 0.50% and 1.50% at the end of the first six months, and similarly for second six-month performances.
For investors with time horizons shorter than the remaining one-year life of this bond - for example, six months - the bond interim-period total returns can be of critical importance and bear little resemblance to the GRY at purchase. This PTR/GRY divergence can be greatly magnified for longer dated bonds.
Logical thinking
Once you accept that you should regularly optimise PTR, not just GRY at the outset, two questions immediately spring to mind.
A - Are bond prices (particularly of liquid sovereign debt issuance) always 'logical' insofar as they properly reflect the fact that PTR optimisation should be the investment objective of every investor?
B - How can investors evaluate current market prices and future yield-curve scenarios to ensure they are optimising PTR in relation to their curve outlook and investment constraints?
The short answer to question A is 'no', even in highly liquid sovereign debt markets. Because of the fixation with GRY, prices do drift away from their 'correct' levels, which optimise PTR. Some bonds will become 'cheap' relative to the rest of the market whereas others will become 'expensive'. Crucially, these anomalies for individual bonds tend to correct themselves over time, with new anomalies emerging, thereby creating ongoing opportunities for enhanced portfolio returns.
The answer to question 'B' is 'not easily' - if it were easy, the anomalies would be short-lived. PTRs for any investment term will, of course, be determined not only by today's market prices but by the shape and level of the yield curve at the end of the term. Accordingly, investors need to employ quantitative calculations using simulated forward-curve levels and their resultant bond parameters to ensure more informed scenario analysis and improved investment policy decision making.
All analytics should accommodate user-specific requirements and existing investment policy
constraints.
Therefore, in addition to standard and non-standard bond parameters, investors should focus on quantitative PTR analytics, which overcome the shortcomings of GRY as a measure. The attraction of PTR analysis is that all calculations and analytics rely solely on market price, coupons, dates, and more, and do not depend on trend, momentum or time series criteria, which are inherently subjective. Analytics should facilitate multiple-scenario analysis and permit detailed re-valuations and analysis of current portfolio holdings including open switches.
The process then becomes one of optimising PTR, either for a specific forward term/yield change or scenario analysis over a chosen range or ranges. PTR optimisation should permit the user to set as fixed, or change in absolute or in percentage terms, any user-defined weighted parameter (for example, any benchmark constraint), either inclusive or exclusive of adjustments for any changes in net capital investment. Ideally, the analytics processes should also assist in the efficient implementation of one-off structural changes to the bond portfolio - for example, the timely and accurate execution of revisions to a house view or investment policy/strategy.
Significant relative portfolio out-performance can be added to indexed portfolios by adopting a regular routine of even modest PTR optimisation, through consideration and risk-neutral 'housekeeping' switches without risky deviations from the benchmark or other constraints.
In summary, GRY remains the most frequently cited of all the individual bond parameters, partly due to convention and ease of calculation. However, within a bond's life cycle, and to its many, often temporary owners, the shorter term specific PTRs are more important measures, as their cumulative total is the measure applied in fund manager portfolio performance evaluations.
Ciaran Deeney is a principal with Enhanced Bond Analytics
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