While “walking on the moon”, as the popular rock band, The Police, reminded us in 1979, is a strange experience, describing the relationship, between asset allocation and bond maturity, is also a strange topic for many investors. One of the reasons that this is the case is that to describe the three dimensional relationship between asset allocation and bond maturity is somewhat intensive from a computational point of view. By “crunching the numbers”, we effectively open up the description of the landscape, or the three dimensional representation of the relationship between bond maturity and asset allocation so as to improve the effectiveness of location for our investors.

In this note we estimate bond returns by using data from the Australian interest rate swap curve, which is the effective mid-point, between government and corporate debt yield, although that relationship varies over time. Data was derived from Bloomberg for each point on the Australian interest rate swap curve and the ASX for the period from January 2001 to July 2013, as this was the largest data set available for all the various maturities. We generate price data for each swap point and then estimate annual return for each point on the swap curve, for around 2900 observations, for all six points on the swap curve - so nearly 18,000 calculations. ASX All Ordinaries Accumulation Index data was used to estimate Australian equity return, which excludes franking credits. After we do all these calculations, we then take average annual risk and annual return observations from the annual data for the each of the five portfolio allocations, which as follows:

- 0% equities – 100% bonds:
- 25 % equities - 75% bonds:
- 50% equities – 50% bonds:
- 75% equities – 25 % bonds:
- 100% equities – 0 % bonds:

In other words, each annual risk and annual return observation requires 18,000 calculations, and then we vary the allocation to equities five times for each of the above allocations, so almost 100,000 calculations are used, assuming a two asset allocation model, where the alternatives are only bonds, as represented by the swap data as described above, or equities, as presented by the ASX All Ordinaries Index, with no account made of franking credits.

More specifically, we describe the following three dimensional “surfaces”:

- the “return surface”, which describes the three dimensional relationship between bond maturity and asset allocation, in terms of annual portfolio return,
- the “risk surface”, which describes the three dimensional relationship between bond maturity and asset allocation, in terms of annual portfolio risk, and
- the “return/risk surface”, which describes the three dimensional relationship between bond maturity and asset allocation in terms of annual portfolio return divided by annual risk,.

**1. Return surface**

Return is only one aspect of the investment landscape, and the thing that stands out from this analysis is the way the longer 30 year bond flattens out the return result for all asset allocations, as Figure 1 and Table 1 show. Some comments on each asset allocation are as follows:

- 0% equities – 100% bonds: notice how return really falls for the shorter bonds, yet holds up for longer bonds.
- 25 % equities - 75% bonds: notice how return starts to decline for the shorter bonds, where, for example, portfolio return drops roughly 60 bps, from 100% equities to 75% equities, for the 3 year part of the curve,
- 50% equities – 50% bonds: notice how return falls much less for this allocation, when duration is longer,
- 75% equities – 25 % bonds: here again, notice how the longer maturities generate better return,
- 100% equities – 0 % bonds: notice how this allocation generates the highest return.

Table 1 provides all the return data, as commented on above, where some of the interesting points in the table, in terms of return tenor and asset allocation, are highlighted in Table 1,

*Table 1*

Also, bear in mind these return estimates are extremely conservative as a spread above swap of 100 bps is used for all points on the swap curve, not the larger spread above swap that is typically associated with corporate bonds which can trade many hundreds of basis points over swap. If the extra return, which is typically associated with corporate bonds was introduced with higher spreads for longer bonds, then the arguments for bonds would be much more potent.

Notice how the return surface is upward sloping, from the short maturities, as indicated by the lighter tones. Darker tones are lower returns, and it looks very much like the longer the maturity, the higher the return for all allocations.

*Figure 1*

**2. Risk surface**

Risk is the essential aspect of investing that many portfolios do not adequately account for in terms of asset allocation. Here, we can see that risk dramatically falls way for every reduction in equities and increase in bonds, except for the longer bond maturities. So, while the longer bonds offer the highest and most stable return, risk does start to pick up for the longer bonds, especially for the longer maturities after more than 50% of bonds are allocated to the portfolio.

These results are shown in Table 2 below, where some of the interesting allocations and points on the swap curve are indicated,

*Table 2*

Notice the kick in annual risk, when the allocation to bonds is high and the longer bonds are used, as shown in Figure 2 below, however the portfolio annual risk attributes are quite controlled out to around the 50% allocation to fixed income, and after that allocation, annual risk tends to increase.

*Figure 2*

**3. Return/Risk surface**

When we divide annual return by annual risk, we can express a surface that describes annual return divided by annual risk, as shown in Table 3 and Figure 3 below. Notice how the surface peaks in the 5-7 year area, which is much longer than the traditional bond portfolio. Also, note that the return to risk attributes of long bonds hold up well, until one allocates more than 50% to bonds. In other words, if you have a small allocation to bonds, below 50%, then the idea is that you can increase return without much additional risk by using longer bonds. Extra interest rate risk really helps to dampen overall portfolio risk, while improving return. As the allocation to bonds grows, then the need for longer bonds then diminishes, yet the optimal position is still in the 5-7 year maturity range.

*Table 3*

Annual return divided by annual risk peaks in the medium term maturities, yet remains adequate out to the 50% allocation; where return is still greater than risk. Hence, the idea is that where one has large allocations to fixed income one should concentrate on 5-7 year maturities, where one has low allocations to fixed income, one should have longer maturities, out to 30 years.

*Figure 3*

Also, notice that the 100% equity portfolio has a poor ratio of annual return divided by annual risk, and one can almost triple the ratio, of annual return to annual risk, by switching from 100% equities to 50% bonds, using the thirty year maturity, with a fall in return of under 10 basis points. In other words, a significant reduction in risk occurs, from roughly 19%, to roughly 6%, for a marginal reduction in return, from 9.35% to 9.23%.

**Conclusion**

Describing the return and risk characteristics of different portfolio allocations for different bond maturities, requires a lot of computational power. After “crunching the numbers”, we can describe the relationships in three dimensional format, so that we describe a “surface”, or what can be thought of as a landscape. In this way, by jumping the computational hurdle for our investors, we de-mystify the relationship between bond maturity and asset allocation, so that investors might target the fixed income within their investment portfolio allocation much more effectively. What was once strange, therefore what was like “walking on the moon”, is made much clearer as a result of the enclosed analysis

In terms of return, we find that long bonds stabilize return very well across all allocations, while the opposite is the case with short bonds. In contrast, long bonds can increase portfolio risk, if the allocation to bonds is over 50%, while short bonds flatten risk substantially across all allocations. While bonds dramatically cut overall portfolio risk in general, they can boost overall portfolio risk, when high portfolio allocation is combined with longer maturity. When return and risk are combined, we see that the best place to be is longer than the typical Australian allocation, in the 5-7 year area, although the risk dampening aspects of fixed income are evident in longer maturities for allocations that are up to around 50%.

In other words, if you have a small allocation to bonds, then we argue that one should use longer bonds, yet if the allocation is larger, then the need for longer bonds moderates. Failing to have any bonds in the portfolio, in terms of this analysis, remains irrational, as the marginal fall in return that occurs from allocating to bonds, will control risk substantially, as the enclosed analysis is very conservative with regard to return estimates for corporate bonds.