Subportfolios

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Contents

Introduction

In addition to performing attribution on standard portfolios of securities, FIA can also model subportfolio holdings in a natural and elegant way.

Subportfolio modeling is an important capability that allows great flexibility in how you monitor your exposures and returns. While you do not have to use subportfolios to generate useful results, you may find them extremely useful in a range of situations.

Definition

A subportfolio is defined as a portfolio that is held, in part or entirely, by another different portfolio. Subportfolios can be used to model the following situations:

All these cases can be modeled quickly and easily using FIA’s subportfolio capabilities.

How to set up a subportfolio

Suppose you have two portfolio files, STF1.CSV and STF2.CSV, containing weights and returns of a group of securities for portfolios STF1 and STF2, at two dates. Each fund only holds two bonds, so the files might look as follows:

01/01/2009 STF1 SECURITY1 10 -0.04
01/01/2009 STF1 SECURITY2 10 0.04
31/01/2009 STF1 SECURITY1 10 -0.02
31/01/2009 STF1 SECURITY2 10 0.04

Portfolio STF1


01/01/2009 STF2 SECURITY3 8 -0.10
01/01/2009 STF2 SECURITY3 8 0.06
31/01/2009 STF2 SECURITY4 8 -0.01
31/01/2009 STF2 SECURITY4 8 0.08

Portfolio STF2


SUBPORTFOLIOS DIAGRAM 1.jpg

Diagram 1: Two separate portfolios


Next, suppose you want to roll STF2 into STF1. To do this, simply add the contents of the STF2 file into the STF1 file as follows:

01/01/2009 STF1 SECURITY1 10 -0.04
01/01/2009 STF1 SECURITY2 10 0.04
31/01/2009 STF1 SECURITY1 10 -0.02
31/01/2009 STF1 SECURITY2 10 0.04
01/01/2009 STF2 SECURITY3 8 -0.10
01/01/2009 STF2 SECURITY3 8 0.06
31/01/2009 STF2 SECURITY4 8 -0.01
31/01/2009 STF2 SECURITY4 8 0.08

STF1 and STF2 combined


SUBPORTFOLIOS DIAGRAM 2.jpg

Diagram 2: A root portfolio and a subportfolio. STF1 is the root portfolio, and STF2 is the subportfolio.

This isn’t quite the full story, however. If you try to run file ‘STF1.TXT’ through FIA, the program will display an error message of the form

Errors found in imported data:
0022: On date 31/01/2009, 2 root nodes were found, but there should be  
only 1. They were: [STF1 STF2]

The reason for this message is that each portfolio passed to FIA must have be in the form of a tree structure with one – and only one- root portfolio. All other portfolios must be set up as subportfolios of that root portfolio. Since we have not told the system that STF2 is a subportfolio of STF1, the system thinks that you are trying to run attribution on two separate portfolios at the same time, and flags an error.

The way to set up STF2 as a subportfolio of STF1 is to treat STF2 as a security in its own right, and to record a holding of one unit of STF2 at each date. This is the reason for the ‘1.0’ shown on the line linking STF1 and STF2 in Diagram 2. For each date on which the subportfolio is active, add an extra line into the portfolio file, showing the holding and its amount:


01/01/2009 STF1 SECURITY1 10 -0.04
01/01/2009 STF1 SECURITY2 10 0.04
31/01/2009 STF1 SECURITY1 10 -0.02
31/01/2009 STF1 SECURITY2 10 0.04
01/01/2009 STF2 SECURITY3 8 -0.10
01/01/2009 STF2 SECURITY3 8 0.06
31/01/2009 STF2 SECURITY4 8 -0.01
31/01/2009 STF2 SECURITY4 8 0.08
01/01/2009 STF1 STF2 1
31/01/2009 STF1 STF2 1

STF1 and STF2 combined with subportfolio holdings added


The extra holdings are shown in bold on the last two lines. Note that:

More about subportfolios

Number of subportfolios

There are no limits on how many subportfolios can be held in a portfolio.

Degree of subportfolio nesting

There are no limits on how deeply portfolios can be nested, or on the complexity of the portfolio structure. For instance, if you have four portfolios STF1, STF2, STF3, STF4, STF5, they might be arranged as follows:

31/01/2009 STF1 STF2 1
31/01/2009 STF1 STF3 1
31/01/2009 STF1 STF4 1
31/01/2009 STF1 STF5 1


SUBPORTFOLIOS DIAGRAM 3.jpg

Diagram 3: Portfolios nested one level deep


Here, STF1 holds one unit each of STF2, STF3, STF4 and STF5. Alternatively, the portfolio might be formed as follows:

31/01/2009 STF1 STF2 1
31/01/2009 STF1 STF3 1
31/01/2009 STF3 STF4 1
31/01/2009 STF3 STF5 1

SUBPORTFOLIOS DIAGRAM 4.jpg

Diagram 4: Portfolios nested two levels deep

Here STF1 holds one unit of STF2 and STF3, while STF3 holds in turn one unit of STF4 and STF5.

Fractional holdings

FIA allows fractional holdings of portfolios. For instance, if STF1 actually held 50% of STF2, this would be represented as follows:

01/01/2009 STF1 STF2 0.5
31/01/2009 STF1 STF2 0.5


SUBPORTFOLIOS DIAGRAM 5.jpg

Diagram 5: Fraction portfolio nesting

When fractional holdings are used, the contribution to performance from a subportfolio is adjusted by the fractional holding of that subportfolio.

Example
Excluding subportfolios, STF1 has a market value of $1mm, and a return of 1%, over a given month.
STF2 has a market value of $0.5mm, and a return of 2% over the same month.
STF1 has a 0.5 holding in STF2.
Then the overall return of STF1 over the month is given by 
($1mm * 1%) + (0.5 * $0.5mm * 2%) / ($1mm + 0.5 * $0.5mm) = 1.2%

Accumulating fractional holdings

Fractional holdings are accumulative. For instance, suppose STF1 holds 0.5 units of STF2, while STF2 holds 0.2 units of STF3. Then for STF1, the contributions to return by fund STF3 will be multiplied by 0.5*0.2 = 0.1.

Holdings can vary by date, just as for securities. For instance, if the holdings of STF2 dropped from 100% to 30% over the month, the holdings lines would look as follows:

01/01/2009 STF1 STF2 1
31/01/2009 STF1 STF2 0.3

In this case, the contribution to return made by STF2 will drop on 31/1/2009 due to its lower holding.

Changing fund topology

The topology of the fund can change over time.

For instance, suppose a fund is reorganized during January 2009. Previously, STF1 held 100% of STF2, and STF2 held 50% of STF3. For administrative purposes, we want to move the 50% holding of STF3 from STF2 to STF1. This is modeled as follows:


01/01/2009 STF1 STF2 1
01/01/2009 STF2 STF3 0.5
31/01/2009 STF1 STF2 1
31/01/2009 STF1 STF3 0.5

Synthetic instruments

Suppose we have defined an interest rate swap as a portfolio containing a $1 holding of a bond, and a -$1 holding of an FRN. Rather than modeling the return of the swap as a set of holdings in both securities, FIA allows you to set up the swap as an independent portfolio in its own right, so that other portfolios can hold units of this synthetic security.

On each date, the swap would be represented as the following two lines:

01/01/2009 IRSWAP 2015 BOND 1
01/01/2009 IRSWAP 2015 FRN -1

Then a $1mm holding of this swap in portfolio STF1 is represented as follows:

01/01/2009 STF1 IRSWAP 1000000

Carve-outs

Suppose that you want to monitor a particular trade, such as a barbell, in your main portfolio. A barbell position replicates the duration of a bullet bond by replacing it with two other securities, one with a long and one with a short maturity, so that the duration of the two securities is the same as the original bond, but the convexity is higher.

For accounting purposes, you may wish to keep the holdings of these securities separate from other holdings in the same security. Assuming the barbell is made up of $1mm of ‘LONG BOND’ and $1mm of ‘SHORT BOND’, set up a subportfolio called BARBELL:

01/01/2009 BARBELL LONG BOND 100000
01/01/2009 BARBELL SHORT BOND 100000

Then buy 1 unit of subportfolio BARBELL in your main portfolio:

01/01/2009 MAIN PORTFOLIO BARBELL 1

The return of BARBELL will be shown in a separate report (see below) and the returns of the subportfolio will be shown as if it were a separate security in the main portfolio’s report.

Returns of a subportfolio

Usually, the returns field of a subportfolio can be left empty. However, there are some cases in which you may want to provide a specific return.

In a previous section we showed how an interest rate swap may be modeled. Very probably, your back office has an official return for this security that should be used in the attribution report.

In this case, the official returns (in local and base currency terms) for the swap can be included in the last cells of the swap holdings line:

01/01/2009 STF1 IRSWAP 1000000 0.142 0.142

It may well be that the official return differs to some degree from the return calculated by FIA. Whatever the reason, the official return will be used for all further attribution calculations, ensuring that the overall return of the portfolio is identical that that of the back office report. Since an official return is supplied for this synthetic security, a residual will also be calculated, and this can be monitored over time to flag any pricing problems (see Chapter 11, Residuals).

Reporting

Reporting is covered in more detail in Chapter 10. However, the main points relating to subportfolios are as follows:

Suppose we have two portfolios STF1 and STF2. STF2 is a sub-portfolio of STF1. Then the following reports will be generated for both STF1 and STF2:

Although STF2 is a subportfolio of STF1, its risk reports will be calculated as if it were a stand-alone portfolio.

The summary risk report for STF1, and risk report by date and risk for STF1, will include the return contributions from STF2.

The risk report for STF1 by date and security will show the return generated by each security that was held in STF1. In addition, the report will show the return generated by STF2 as if STF2 were a security in its own right. This includes return generated by any subportfolios of STF2, if they exist. Remember that the return contribution made by a sub-portfolio will almost certainly be different to its actual return.

In general, risk reports are generated automatically for all sub-portfolios, but you are free to ignore and delete reports that are not of interest.

Constraints on portfolio modeling

The following rules are enforced by the system:

31/01/2009 STF1 BOND1 1000
31/01/2009 STF2 1000
Disallowed: there are two root portfolios STF1, STF2
31/01/2009 STF1 STF2 1
31/01/2009 STF2 BOND2 1000
31/01/2009 STF3 BOND3 -
Disallowed: there are two root portfolios STF1, STF3. 
STF3 is an orphan portfolio as it is not connected to any other portfolio
31/01/2009 STF1 STF2 1
31/01/2009 STF2 STF3 1
31/01/2009 STF3 STF1 1
Disallowed: STF1 owns part of STF2, which owns part of STF3, which owns part of STF1

An attempt to run attribution on a portfolio with any of these issues will generate an error report, containing a clear description of where and why the problem occurred.

At present, there is no facility to link different portfolio files together at runtime, but we may introduce this option in future.

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