Portfolio Representations: A step-by-step guide to representing value, exposure and risk for fixed income, equity, FX and derivatives

By Jem Tugwell

This book provides a practical and sophisticated insight into each financial asset type, and how the different risks and exposures they involve should be most accurately combined and represented in a portfolio.
The financial issues facing the world since the late 2000s have provided the asset management community with a brutal reminder of the importance of having genuine knowledge of portfolio structures and the risks embedded within them. More so than ever, fund managers need a clear and consistent way of separating value from exposure in their portfolios, allowing a complete 'look-through' to the real risks contained in derivatives and pooled/structured products.
Equally, as fund managers are driven to find risk-adjusted rather than just raw returns, it is imperative that risk measures and the understanding derived from them are applied to the entirety of a portfolio, as opposed to just particular asset classes or sections.
This book, written by hugely experienced investment expert Jem Tugwell, provides a practical and comprehensive solution. Written in plain English and carefully structured to be easy to use, this is the definitive guide to accurately and quickly representing value in financial portfolios of every complexity.
Taking the reader through each asset type in turn, with detailed workings and explanations, it is the most lucid and helpful professional guide yet written on the subject - and something no one working in this area can afford to be without.

• Language: English
• Publisher: Harriman House
• Release date: Jan 16, 2012
• ISBN: 9780857191991

Book preview

Volatility

Publishing details

HARRIMAN HOUSE LTD

3A Penns Road

Petersfield

Hampshire

GU32 2EW

GREAT BRITAIN

Tel: [phone]

Fax: [phone]

Email: [e-mail]

Website: www.harriman-house.com

First published in Great Britain in 2012

Copyright © Jem Tugwell

The right of Jem Tugwell to be identified as the Author has been asserted in accordance with the Copyright, Design and Patents Act 1988.

ISBN: 978-0-85719-199-1

British Library Cataloguing in Publication Data

A CIP catalogue record for this book can be obtained from the British Library.

All rights reserved; no part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise without the prior written permission of the Publisher. This book may not be lent, resold, hired out or otherwise disposed of by way of trade in any form of binding or cover other than that in which it is published, without the prior written consent of the Publisher.

No responsibility for loss occasioned to any person or corporate body acting or refraining to act as a result of reading material in this book can be accepted by the Publisher, by the Author, or by the employer(s) of the Author.

About the Author

Jem Tugwell is a specialist investment management consultant, focusing on institutional investment management strategy and analytics. Jem’s analytical focus involves how to represent different asset classes inside portfolios, the separation of value and exposure, as well as pricing models and risk measurement across all asset classes and their associated derivatives. His commercial expertise is applied in assisting asset management firms to develop and apply these analytical techniques in order to gain a competitive edge, based on clear market differentiation and the ability to deliver superior returns.

Jem’s 20-year track record in the investment management sector includes founding a successful multi-million pound software business, identifying an opportunity for a new generation of buy-side asset management solutions. He is the founding director of Jem Tugwell Associates.

Jem has published articles in the Journal of Asset Management and the Journal of Performance Measurement, amongst others.

Preface

What this book covers

The credit crunch provided the asset management community with a brutal reminder of the importance of having genuine knowledge of portfolio structures and the risks embedded within them. More so than ever, fund managers need a clear and consistent way of separating value from exposure in their portfolios, allowing a complete ‘look-through’ to the real risks contained in derivatives and pooled/structured products.

Simple portfolios no longer exist. And, as fund managers are driven to find risk-adjusted rather than just raw returns, it is imperative that the risk measures and the understanding derived from them are applied to the total portfolio, as opposed to just particular asset classes or sections. This book is intended to provide a practical and sophisticated insight into each asset type and how the different risks and exposures they involve should be combined and represented.

It is not meant to be a detailed work on pricing mathematics; there are numerous good books out there already covering the detail of each pricing model for each asset type. Instead, pricing of each asset type is discussed only in general, using an example model to draw out the relevant risk factors. Uniquely, we will be looking at what the risk factors are for each asset type, how to calculate them and how to combine them in a portfolio view. Risk factors are also known as analytics and the two terms are used interchangeably in this book.

As portfolios cover global markets and multiple asset types, this book covers equity, fixed income, credit, inflation, and currency assets and their derivatives all in one book.

The writing style is deliberately straightforward to ensure that the key points are fully understood.

How this book is structured

The first chapter of the book provides an introduction to the representation of assets in a portfolio. This is an essential starting point for readers new to the area, and covers the aspects of a portfolio that are common across all asset types and strategies.

The book is then split into parts by broad asset type. Part 2 covers equities and their derivatives. This is followed by Part 3 on money markets and derivatives. After this we look at fixed income, credit and inflation assets and derivatives. Currency management, a hugely important topic, is dealt with in the subsequent section on covering currency trade types and derivatives. The next section is devoted to fund-of-fund structures. And the final section deals with Cross-Asset-Type Issues.

Each asset-type chapter follows the same structure of:

X.X.1 Introduction

X.X.2 Pricing

X.X.3 Risk factors

X.X.4 Representation

X.X.5 Summary

X.X.6 Glossary

This approach should allow readers to quickly and easily jump to the asset type(s) of particular interest. As there is similarity between some asset types, the chapters reference other places in the book where something has already been covered, in order to avoid repeating large sections.

Throughout the book, examples and worked formulae are provided to bring the theory to life.

Who this book is for

The book is designed to be usable by a wide cross-section of readers. It should be of great use, for instance, to the heads of different business areas within an investment management organisation, who wish to assess the business implications of different portfolio representations. It should also be helpful for fund managers and their assistants interested in the practical and strategic impact of their decision-making; as well as business analysts and programmers.

Such fund managers, for instance, should be able to use the book to explain exactly what they want from programmers or business analysts, who will be able to use it to understand clearly what it is they are being briefed to create.

Its easy-to-read style will hopefully allow beginners to use the book as a learning guide, while the depth and detail of the coverage will enable practitioners to use it as a reference text. Above all, addressing a key challenge for post-credit-crunch portfolio managers, it provides the all-important tools to enable them to distinguish themselves from their competition and to supply a clear, comprehensive audit trail for their decision-making processes.

It is assumed that the reader is familiar with the basic terms and constructs used in the portfolio management industry, i.e. what a portfolio is, that a portfolio is made up of holdings in different assets/securities, that assets have prices and that assets in different currencies need to be converted to a single currency to calculate a total portfolio value.

Jem Tugwell

Chertsey, 2011

CHAPTER 1. Building a Portfolio View

This chapter covers the issue of representing values and risk in a portfolio as they apply to all asset types. Subsequent chapters deal with the detail differences for each specific asset type.

As mentioned in the preface, this is not a book on pricing. With the wide asset coverage of the book, to cover pricing in sufficient detail would be impractical. However, each section provides an outline and examples of pricing to help in understanding the risk factors that need representing in a portfolio. Detailed pricing books, as said, do exist for all asset types discussed; these should be consulted to ensure you use the correct model for accurately pricing the detail of each specific asset.

Our focus is more on the numbers that need calculating and how to represent these numbers, rather than the detail of the mathematics.

1.1 Valuation and Weight

The most basic representation of a portfolio is to calculate the value of each holding and sum these to find the portfolio’s total value.

To calculate this we need to work out the market values of each holding in a single valuation currency. We can do this using the following formula:

Where:

There are two areas that need care here.

The first is that not all assets will have their price quoted in terms of one unit of nominal. For example, with fixed income the convention is for the price to be per 100 nominal. Equities, likewise, are often quoted as a one-hundredth of a currency unit (for example in cents, pence, and so on) or in currency units (dollars, euros, pounds). If we simply multiply the number of shares we hold by a price in cents, we get a value in cents. But as the value of a portfolio is usually large, the convention is to calculate the portfolio value in whole currency units (dollars, euro, pounds, etc.). Therefore we need to divide our price in cents by 100 to get a dollar value. So for assets quoted in units of currency, the price factor will be 1; but for fixed income, equities in cents, etc., the price factor will be 100.

Example

A holding of 100 shares in Vodafone (VOD), worth 16,045p.

The second area that needs care is currency itself. Most market-data vendors provide FX (forex) rates in terms of USD versus another currency. However, FX rates can be either direct or indirect. A direct FX rate is expressed as the number of the units of currency per 1 USD. An indirect FX rate is expressed as the number of USD per 1 unit of currency. Most currencies are quoted directly, but EUR and GBP are both quoted indirectly.

For example, the following table shows different currencies and their market convention FX quotes. The fourth column shows each currency in direct terms. Therefore if the market convention is to quote directly, the market convention FX rate and FX rate in direct terms will be the same. If the market convention is to quote indirectly, the market convention FX rate and FX rate in direct terms will be different: direct FX rate = 1/indirect FX rate.

Throughout the book we use the abbreviation Ccy for currency:

Valuing a portfolio in non-USD terms

If we want to value an entire portfolio in, say, EUR, we need to convert all of the data vendor-supplied rates (in terms of USD) into rates per 1 EUR. To do this we first need the direct EUR FX rate to the USD. This is 1/market convention indirect value, i.e. 1/1.2897 = 0.7754. We can then calculate the direct FX rate to EUR by dividing the EUR/USD direct rate we have just calculated by the appropriate USD/Ccy direct rate. So for the currencies above, we find:

We can then use these rates directly to value each holding in EUR using the previous formula. This is shown in the following table:

This gives the portfolio a value (in EUR) of 70,100,686.

Measuring portfolio exposure

Having thus established the value of each holding in the portfolio (as well as how to value the whole portfolio in different currencies) we can begin looking at exposure. Probably the oldest measure of portfolio exposure is to look at the percentage, or weight, of a holding in the total portfolio. This is simply:

Using holding 5 as an example, its weight is its value in EUR divided by the total portfolio value in EUR, i.e. 92,124/70,100,686 = 0.13%

And for our portfolio:

This is very much a one-dimensional view of the portfolio exposure, but it does allow us to see the relative scale of the holdings, and, implicitly, the risk in the portfolio to be quantified.

The weight of each holding in the portfolio is also used when scaling other risk factors (see the next section). The weights are also used to define compliance constraints on a portfolio. For example, if the portfolio has a compliance rule that says that the portfolio must be 50% invested in EUR, the portfolio owner has a simple way of controlling the foreign currency exposure the fund manager can take on the portfolio, and the fund manager can see immediately if this is being fulfilled (in this case the portfolio would currently be in breach; it only has 48.83% in EUR).

The other advantage of using portfolio weights is that they allow simple comparison with other funds and benchmarks that have different total market values, since it is a contrast of proportions (percentages) rather than specific figures.

1.2 Scaling Risk Factors

We can use the weight of a holding in a portfolio to scale risk factors and therefore measure the importance of any risk factor at the total portfolio and sub-total level.

For example, say Holding A has an exposure to a risk factor of 5 and Holding B has an exposure to the same risk factor but at a value of 6. What is the portfolio’s overall exposure to the risk factor?

To answer the question, we first need the weights of each holding in the portfolio. In this example, let’s say Holding A has a weight of 40% and Holding B has a weight of 60%. Next we multiply Holding A’s risk factor value (5) by Holding A’s weight in the portfolio (40% in this example) and multiply Holding B’s risk factor value (6) by Holding B’s weight in the portfolio (60% in this example). We then add the results together to get a total figure for what the risk factor of these holdings is to the portfolio. This is shown in the following table:

The total portfolio has an exposure to the risk factor of 5.6. Holding A contributes 2 and Holding B contributes 3.6.

When we multiply a holding’s risk factor by its weight in the portfolio in this way, the answer we get is each holding’s risk factor ‘contribution’: i.e. the amount of exposure to the risk factor a holding contributes to the total portfolio’s exposure.

In general:

As we will discuss in Chapter 7 (Cross Asset-Type Issues), there are two implicit assumptions in the previous formula that need careful consideration.

We add the contributions to form a total for the portfolio of 5.6. In doing this we are implicitly assuming that all of the holdings are perfectly correlated with respect of the risk factor. If Holding A is a petrochemical company and Holding B is a transportation company, can we really expect the value of both companies to be affected by a change in risk by exactly the same amount? For example, if the risk factor being measured is exposure to oil prices, the petrochemical company’s earnings would increase and have a positive share price affect but the transportation company’s costs would increase, having a negative share price affect. Clearly the two companies’ share prices are not perfectly correlated with respect to oil prices.

In a multi-currency fund, summing the weights of holdings so as to form a portfolio weight implicitly says that all currencies are, again, perfectly correlated, i.e all currencies appreciate and depreciate by the same amount at the same time. This is clearly not true. When we then use this weight to scale a risk factor, we compound the problem. Will Holding B’s US transportation company’s share price really change by exactly the same amount due to a change in a risk factor as Holding A’s UK petrochemical company and at the same time?

These assumptions are discussed further in the section Correlation and Volatility (7.2).

Where the risk factor is expressed in currency units (e.g. dividend per share), it is more normal to calculate the holding’s contribution to the risk factor and the total portfolio exposure in currency units. We can do this by multiplying the holding’s risk factor exposure by the nominal as opposed to the weight. This gives us an exposure to the risk factor in the currency of the holding. To be able to sum these to calculate a portfolio total we must convert them to the valuation currency in the same way as calculating a total portfolio value.

Price-based risk factors are useful when seeing the amount in money terms that is at risk in a portfolio. Weight-based contributions (i.e. the method of evaluating a holding’s risk factor explained previously) are useful when comparing the risk across differently sized portfolios and comparisons relative to a benchmark (see 1.4).

1.3 Multiple Risks from a Single Holding

As will be seen from the chapters specific to different asset types, all assets have multiple risk factors.

These could be, for example, sensitivity to interest rates, default, inflation and so on. Each of these sensitivities will have a risk factor that will need to be represented in the portfolio, although different fund managers will place different emphasis on the importance of the risk factors in their portfolios. E.g. an equity fund manger will be much less concerned about interest-rate risk than a fixed-income manager.

With all asset types, the risk factors that can be measured, and therefore need to be expressed in a portfolio, are the factors that move the price of the asset. Most asset types have more than one variable (e.g. the current level of inflation, the current perception of default risk, etc.) that affects the value (price) of the asset and therefore each input variable to the pricing equation will result in a risk factor. The relative importance of each risk factor may also vary with different asset types.

The banking industry has always been very innovative and is good at finding ways around problems. So if the portfolio is constrained to hold USD-denominated assets, but the fund manger wants to buy some EUR-denominated assets, they are prohibited from doing so in the fund. However, if, for example, the fund is allowed to hold structured products, there are many banks that could construct a simple structured product that would allow them to accomplish something similar. The structured product could be made up of a EUR-denominated equity and a EUR/USD FX trade. This product would be denominated in USD and could now be held by the portfolio. This structured product could be left to be a single line in the portfolio unless one looks through the structure to the actual risks it contains. Looking through an asset to its component risks is a fundamental theme of the book and the different risks contained in each asset type are explained in the section for that asset type.

In this way, many asset types are composites of other asset types – for instance, composite holdings in the case of a fund-of-funds, multiple derivatives in the case of an index CDS, and multiple legs in the case of swaps. The representation of a single holding cannot be assumed to be one line in a portfolio representation; and all of the components cannot be assumed to be the same currency. These issues are explored in detail in the appropriate section for each asset type.

The traditional view that a holding has one type of risk and exposure to one market is no longer valid.

1.4 Relative to the Benchmark Differences

Many portfolios are run against a benchmark. The benchmark allows the portfolio owner, the fund manager’s client, to measure the fund’s return relative to another portfolio. The client can also control the markets the portfolio is invested in and the size of the holdings, by imposing constraints on the portfolio in terms relative to a benchmark. (E.g. no more than 5% more than the benchmark of x in petrochemical stocks or no investment outside of the benchmark holdings.)

The benchmark is also used to compare returns, or in other words performance.

Usually there will be a constraint on the fund manager to exceed the benchmark return. E.g. benchmark return + 50bp [¹] . The 50bp of return effectively both provides a target for outperformance and sets the amount of risk the fund should take to achieve the excess return. The excess return (50bp) has to come from the fund manager doing something different compared to the benchmark. The larger the relative outperformance target is, the more risk relative to the benchmark the fund manger will have to take.

The fund manager may be measured by a relative benchmark return. However, clients tend only to like relative returns when there is a positive return. Proudly saying that, although the client has lost 50% of their money, the benchmark lost 55%, rarely proves effective consolation.

Using weights and contributions, as described in 1.2, to compare a portfolio to a benchmark is simple. It is just a question of: portfolio value minus benchmark value.

Here’s how it works.

If we add a benchmark to our portfolio we have:

We can then simply calculate portfolio value minus benchmark value to find our relative weight and