Derivatives in Risk Management

Derivatives in Risk Management

Introduction

Managing risk is important to a large number of individuals and institutions. The most fundamental aspect of business is a process where we invest, take on risk and in exchange earn a compensatory return. The key to success in this process is to manage your risk return trade-off. Managing risk is a nice concept but the difficulty is often measuring risk. There is a saying “what gets measured gets managed.” To alter this slightly, “What cannot be measured cannot be managed”. Hence risk management always requires some measure of risk. Risk in the most general context refers to how much the price of a security changes for a given change in some factor. In the context of Equities, Beta is a frequently used measure of risk. Beta measures the relative risk of an asset (Whaley 2006).

High Beta stocks or portfolios have more variable returns relative to the overall market than low Beta assets. If a Beta of 1.00 means the asset has the same risk characteristics as the market, then a portfolio with a Beta great than one will be more volatile than the market portfolio and consequently is more risky with higher expected returns. Conversely assets with a Beta less than 1.00 are less risky than average and have lower expected returns. Portfolio managers use Beta to measure their risk-return trade-off. If they are willing to take on more risk (and return), they increase the Beta of their portfolio and if they are looking for lower risk they adjust the Beta of their portfolio accordingly. In a CAPM framework, Beta or market risk is the only relevant risk for portfolios (Schwartz 2007).

For Bonds, the most important source of risk is changes in interest rates. Interest rate changes directly affect bond prices. Modified Duration2 is the most frequently used measure of how bond prices change relative to a change in interest rates. Relatively higher Modified Duration means more price volatility for a given change in interest rates. For both Bonds and Equities, risk can be distilled down to a single risk factor. For Bonds it is Modified Duration and for equities it is Beta. In each case, the risk can be measured and adjusted or managed to suit ones risk tolerance. In each of these cases, financial theory provides a measure of risk. Using these risk measures, holders of either bonds or equities can adjust or manage the risk level of the securities that they hold. What is nice about these asset categories is that they have a single measure of risk. Derivative securities are more challenging (Cuthbertson 2001).

Risk Measures for Derivatives

In the discussion which follows we will define risk as the sensitivity of price to changes in factors that affect an asset's value. More price sensitivity will be interpreted as more risk (Al-Amine 2008).

The basic option pricing model

A simple European Call option can be valued using the Black-Scholes Model3 : European Call Option Value =

Where

N( )· = Cumulative Standard Normal Function

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