Financial Risk Management: A Simple Introduction

Financial Risk Management: A Simple Introduction

By K.H. Erickson

Copyright © 2014 K.H. Erickson

All rights reserved.

No part of this publication may be reproduced, stored in or introduced into a retrieval system, or transmitted in any form or by any means, including electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the author.

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Microeconomics

Table of Contents

1 Introduction

2 Financial Risk Exposure

2.1 Debt and Leverage

2.2 Duration

2.3 Modified Duration and Risk Sensitivity

2.4 Convexity

2.5 Effective Duration and Effective Convexity

3 Value at Risk

3.1 Value at Risk Defined

3.2 Variance-Covariance Method

3.3 Historical Simulation

3.4 Monte Carlo Simulation

3.5 Comparison of VaR Methods

3.6 Square Root of Time Rule

4 Exponentially Weighted Moving Average

4.1 Time-Varying Volatility Analysis

4.2 Backtesting

5 Orange County 1994 Bankruptcy Case

5.1 Background to Orange County Failure

5.2 Balance Sheet and Risk at Bankruptcy

6 Risk Management for Orange County

6.1 Value at Risk for Orange County

6.2 EWMA for Orange County

7 Hedging Strategies for Orange County

7.1 Hedging Interest Rate Risk

7.2 Financial Derivative Instruments

Bibliography

1 Introduction

Individuals, businesses, corporations, and governments are always searching for profitable investment opportunities which can offer an increased return. But the potential for a greater return will typically go hand in hand with greater risk, and there’s a danger than an investment strategy can backfire and end up costing more than it creates. Risk can come in many forms and while much risk can be avoided with well researched investments, or eliminated with a diversified portfolio, a degree of unavoidable market risk will always remain and therefore effective financial risk management is a central part of any investment strategy.

One of the most significant elements of market risk is interest rate risk, as changing yield rates can reduce the value of an asset or portfolio, and interest rate risk is a focus of this book. The field of financial risk management is explored in depth using theory, formulas, calculations, and examples, and then applied to the case study of the 1994 Orange County, California bankruptcy to examine whether the financial failure could have been avoided. Basic prior knowledge of derivatives and econometrics is assumed and used in the analysis.

Financial risk management involves first determining the risk exposure of an investment or portfolio, and this is explored using leverage, duration, modified duration, convexity, effective duration and effective convexity. Value at risk (VaR) is the next focus, and the three main variance-covariance, historical simulation, and Monte Carlo methods are explained and compared, along with the related square root of time rule. Detailed steps to calculate the variance-covariance, historical simulation, and Monte Carlo value at risk in Excel are provided. An exponentially weighted moving average (EWMA) is then introduced to predict factor change, interest rate or return volatility, and simple steps to calculate the EWMA and backtest the data for reliability in Excel are presented.

An extended empirical case study for Orange County’s bankruptcy in 1994 takes up the remainder of the book. First the history of how the situation came to pass is explained, with Orange County’s balance sheet, leverage, duration, effective duration, and modified duration examined to determine the extent of the county’s risk exposure, and assess whether the bankruptcy was inevitable or if alternatives were available. This discussion is then built upon with detailed value at risk and EWMA analysis as the potential for risk management is debated. The final section looks into theoretical hedging strategies for Orange County, examining a range of financial derivatives and how they may be used to hedge interest rate risk.

2 Financial Risk Exposure

2.1 Debt and Leverage

The level of debt held, known as the leverage, is a key factor affecting the risk exposure of an investor. Greater debt levels increase risk exposure as debt involves interest payments to the creditors who issued it, which must be paid before other commitments can be funded, and if interest rates change then greater repayments may be owed by an investor. This type of risk is known as interest rate risk, and an investor may be able to avoid it on a fixed repayment plan for small amounts of debt, but for large amounts of debt such as with mortgages the repayment costs will depend on the level of interest rates.

An investor’s balance sheet can be examined to calculate their leverage, and leverage is the ratio of all liabilities to non-debt liabilities (i.e. shareholders’ equity). It can be found by dividing the total value of all liabilities by the total value of all non-debt liabilities:

Leverage = Total liabilities / Non-debt liabilities

Leverage = Total liabilities / Shareholders’ equity

If an investor has no debt at all then debt liability value will be zero, and non-debt liability value = total liability value. This simplifies the equation to that below:

An investor without debt

Leverage = Total liabilities / Non-debt liabilities

Leverage = Total liabilities / Total liabilities

Leverage = 1

The case of an investor without debt or interest rate risk, with a leverage level of 1, is used as a basis to evaluate situations where an investor does have debt and risk exposure to interest rate risk. The higher the leverage factor moves above 1 the greater the risk factor an investor will face.

For example, an investor’s total liabilities may come to £100 million,