The maths involved in bond investing

It is worth considering the maths involved in bond investing, in light of concerns, with yields so low and with the possibility that the 35 year bond bull market may be over, or indeed reversing, that there’ll be a bond market rout.



Stuart Dear
Head of Fixed Income

Outlook and strategy

After the fireworks of 2016, 2017 has, to date, been more like an aromatic candle in terms of market moves. In part, a lack of action is because we await ‘new news’. The economic data and sentiment indicators – in most parts of the world – continue to suggest a renewed expansion phase for the global economy. The strength and durability thereof, and the policy responses, are key unknowns. The broad outlines of Trump’s fiscal plans are known, the details, timing and impact are not. With this being the status quo since late in 2016, markets have broadly continued to reflect these positive themes – equities, credit and emerging markets continuing to perform – without much fanfare.

As fixed income investors, the pause provides an opportunity to reflect on our asset class. As a starting point, it is worth considering the maths involved in bond investing, in light of concerns, with yields so low and with the possibility that the 35 year bond bull market may be over, or indeed reversing, that there’ll be a bond market rout. Embedded in this fear is an asymmetric perception that losing money on a fixed income investment is worse than losing money on an equity investment – with some justification given that fixed income should play a more defensive rather than return seeking role in a broader portfolio – and that the quantum of losses could be similar.

The starting point for bond returns is always the current yield. This is because it represents the return on a bond if held to maturity, under the highly certain assumption for investment grade bonds that the issuer will meet their obligations (ie not default). For a buy-and-hold investor, and assuming a positive starting yield, ‘losses’ are only the temporary effect of capital price depreciation (as yields rise) outstripping coupon income gains over short periods, in the same way that ‘gains’ are only the pull-forward of future returns. A buy-and-hold investor will earn the return on the bond represented by the yield at which it was purchased, so clearly fears about losses are misplaced for such an investor.

Over shorter periods than the term to maturity, returns on bonds are dictated by the interaction of 1) income gains and 2) capital price variability driven by yield moves and the price sensitivity to yield moves (approximated by a bond’s duration). The lower the starting yield, the larger the yield move and the faster it occurs, and the longer the bond’s duration, then the greater is the ratio of capital price changes to income gains. Where the move in yield is upwards, and especially for longer duration bonds, short term losses are likely. In the current context, where starting yields are low, and fixed income benchmark durations (as an approximation for an investor’s average portfolio duration) are longer, losses are more likely. 

The quantum of likely losses over short periods is perhaps the greatest source of concern and confusion for non-practitioners. The maths is actually pretty straightforward - it depends on how much yields move, how much duration you have, and how much the income offset is (determined by the starting yield and the length of time under consideration).  As an example, the current Bloomberg Ausbond Composite index has about 5 years of duration and a yield of 2.5%. A 1% rise in yields will see a capital repricing of -5% (extrapolated in a more or less linear fashion for different yield moves), offset by income gains of 2.5% over a year. The most pessimistic bond forecasters currently suggest yields could rise by 1.5% over the coming year, which if it were to occur would deliver a total return loss on the benchmark of 5% - not good, especially for a defensive asset, but not terrible either in the context of possible losses on other assets.

A few final observations on the maths around bond returns and yield rises.  Firstly, buy and hold investors with short investment horizons will actually be happy that yields rise. This is because the rise in yields allows them to reinvest at a better rate when their existing investment matures, meaning that total returns over longer periods will actually increase. Secondly, because a longer term bond is effectively a series of back-to-back short term bonds with different starting dates, we are able to observe current market expectations for future bond yields of differing maturities. This is useful because the way bond maths works, if current yields move to market expectations of bond yields in, say, 1 year’s time, then over that timeframe an investor should be indifferent between holding cash and bonds (ie bonds will return the same as cash). 

Moving to our current outlook and portfolio positioning, our view remains that duration is expensive, though clearly less so than in the middle of last year when yields were 1% lower. The cyclical picture has improved, both globally, driven in large part by Chinese fiscal stimulus and the associated lift in commodity prices, and in the US, on expectations of Trump’s delivery of both large fiscal spending and an overhaul of the tax system. Together, the valuation and cyclical elements suggest that government bonds remain vulnerable, although we are growing a little more cautious that much of the recent good cyclical news is ‘in the price’. Market expectations, reflected in forward-starting bond yields, are that the Fed lifts the Funds Rate by a further 1.5% over the next few years. With other markets lagging in their pricing for policy tightening, US bonds are at least starting to offer better relative value versus those of other key regions, notably Europe.

Through the December quarter our expectation of higher yields was reflected in three main ways – our relative to benchmark short duration position, our yield curve steepening exposure and our inflation-linked exposure. While broadly holding our short duration position - we went a little longer at the start of Feb and a little shorter at month end – we’ve moderated our yield curve steepening exposure in Australia and our long inflation position in the US. This leaves the portfolio retaining the majority of its positioning for higher yields, and reasonably well diversified in this positioning. Our short duration remains spread across the US, with the strongest cyclical pulse, Germany, where valuations are worst, and Australia, where cyclical prospects are improving and we’re beginning to position for an eventual reversal of the RBA easing cycle.

Credit continues to enjoy the benefit of a stronger cyclical environment, but the narrowing of spreads has taken corporate bond valuations back into expensive territory. Having pared our exposures considerably in the June quarter of last year, we have been running a small, high quality, domestic-only absolute exposure, which represented only a very modest overweight exposure versus benchmark. However we used further spread tightening in February to further trim our Australian credit exposure back to benchmark, and will likely reduce further should spreads continue to narrow. We’ve also slightly reduced our exposure to semi-government bonds, at tight spread levels to government bonds.

Cash remains reasonably elevated, and combined with our interest rate and credit positioning, leaves us defensively positioned and focused on protecting capital as markets adjust to developments.

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Stuart Dear
Head of Fixed Income


Fixed Income
Stuart Dear
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