# What is an optimised portfolio?

We can approach almost every portfolio construction issue by designing a portfolio of XTBs around any given set of needs. Everyone’s needs are different, so everyone desires a different portfolio. We call them ‘custom portfolios’. The point of this article is to explore how we construct custom portfolios. This allows you to do it yourself, or at least understand what we are doing when we do it for you.

## Introduction to portfolio construction

In the example below, we assume that an investor wants a portfolio of equally weighted XTBs. We often relax this assumption when solving for particular needs, but for discussion purposes we include this assumption. Throughout this article, we ignore the trivial ‘portfolio’ of 100% of the investment in any given XTB.

If we only have 2 XTBs to choose from, XTB A and XTB B, there is only one possible portfolio that would meet this set of criteria: 50% in XTB A, 50% in XTB B.

If we had 3 XTBs for choose between, we would have four portfolios that meet the equal weighting assumption:

#### Table 1: Portfolio options available for 3 XTBs

PORTFOLIO | XTB “A” | XTB “B” | XTB “C” |

ONE | 50% | 50% | 0% |

TWO | 50% | 0% | 50% |

THREE | 0% | 50% | 50% |

FOUR | 33% | 33% | 33% |

With 4 XTBs we have a choice of 11 possible portfolios and it starts to grow pretty quickly – so let’s add some more restrictions.

Say for diversification purposes we want exactly 3 XTBs in each portfolio and have 4 possible XTBs to choose from, that gives us 4 possible portfolios again.

#### Table 2: Portfolio options available for 4 XTBs with 3 being included in each portfolio

PORTFOLIO | XTB “A” | XTB “B” | XTB “C” | XTB “D” |

ONE | 33% | 33% | 33% | 0% |

TWO | 33% | 33% | 0% | 33% |

THREE | 33% | 0% | 33% | 33% |

FOUR | 0% | 33% | 33% | 33% |

It’s sometimes easier to visualise what is happening.

The chart 1 shows the construction of these portfolios graphically. The **Teal Dots** represent the Maturity and Yield to Maturity (YTM) of four different XTBs. The **Black Crosses** represent the 4 portfolios above. The red arrows show the effect of averaging of three of the XTBs into one of the possible portfolios (the cross is roughly ‘in the middle’ of the three dots). All the other crosses are ‘in the middle’ of different combinations of three teal dots.

#### Chart 1: Construction of XTB portfolios

The portfolio we have highlighted above has an average maturity date of 10-May-2020 and an average YTM of 3.441%. The table below shows the data used to plot the chart above. This data may not represent the currently available YTMs on any XTB:

#### Table 3: Data used to plot Chart 1

INSTRUMENT | MATURITY DATE | YTM |

XTB A | 28 OCT 20 | 3.600% |

XTB B | 13 MAY 20 | 2.750% |

XTB C | 19 MAY 22 | 3.252% |

XTB D | 19 NOV 19 | 3.974% |

PORTFOLIO ONE | 10 MAR 21 | 3.201% |

PORTFOLIO TWO | 10 MAY 20 | 3.441% |

PORTFOLIO THREE | 10 JAN 21 | 3.609% |

PORTFOLIO FOUR | 15 NOV 20 | 3.325% |

Let’s now look at a portfolio based on a universe of 5 possible XTBs, still including 3 in each portfolio – that gives 10 possible portfolios as per chart 2. Note that the diversity of outcomes for portfolios is always less than that of individual XTBs.

#### Chart 2: A portfolio based on a universe of 5 possible XTBs

## How many different portfolios are there?

There are currently 49 XTBs on issue. If we limit ourselves to buying 5 XTBs per portfolio *and in equal weights* as we have done above, then there are 1,533,939 possible portfolios. If we include a 6th XTB there are 10,737,573 possible portfolios; relax the restriction on equal weightings and there is essentially an infinite number of portfolios.

No one should sift through this volume of portfolios to choose one that suits their needs, so we have built tools to do the work. Our tool allows us to plug in the specific restrictions or criteria the investor determines and then sets to work choosing a portfolio that best delivers the required outcome.

The process for constructing a portfolio is:

- Define the universe of possible XTBs for the portfolios
- Determine the properties of each possible portfolio
- Select a criteria to ‘optimise’
- Select the particular portfolio which best satisfies all of the above criteria.

We discuss this further below.

### Define the universe of available XTBs

As the number of XTBs grows, the number of portfolios grows rapidly. To narrow the number of portfolios, we consider whether we can add other restrictions to refine the potential constituents. For example, an investor may also want a portfolio that provides:

- ‘Coupons that only pay in January and July’. To meet this requirement we simply remove XTBs that do not satisfy these criteria from the potential universe prior to constructing portfolios.
- ‘At least one cash flow in each quarter’. Again, we refine the universe of XTBs to include only those that satisfy the rule.

The result is a set of XTBs that satisfy these particular rules and allow us to design a portfolio that, therefore, also satisfies any such rules.

### Determine the properties of each portfolio

This process is identical to what we have done earlier in the article. We simple calculate the average properties of each possible portfolio within the universe of portfolios.

### Select a criteria to ‘optimise’ on and selecting a single portfolio

To select the final portfolio we need something other than a rule. We need a single criteria to optimise on or around. For example, highest YTM or shortest maturity – or even “highest YTM divided by Year’s to Maturity”.

We calculate this measure for each portfolio in the available set produced by our tools, and from this identify the largest/smallest one to meet our goal.

As you can imagine, this can be cumbersome when looking at millions of portfolio options. Fortunately, a well-designed tool can do the grunt work and provide the selection for us. All we do is provide the particular rule to the tool, and it does the selection process.

The end result is a portfolio which satisfies all of the investor’s rules and provides the best outcome possible given those rules.

## Pre-defined Portfolios

To simplify this process for you, we have already developed a set of portfolios to meet the most commonly requested requirements from clients:

- High Yield (8 XTBs)
- Concentrated High Yield (5 XTBs)
- Maturity Ladder (5 XTBs)
- Cash Plus (3 Floating-Rate XTBs)

In setting up these portfolios, we followed the process above, using rules that we think made sense for general investors.

## What if I want something else?

Do you have a client whose needs don’t fit those of the ‘general’ investor? They have their own set of specific requirements – such as needing coupons only in June and August, or they require a certain amount of income in each year. If so, we can construct a customised portfolio for you using our tools and market experience – contact us