FRM Notes 2011 Unit IIA Basic Concepts in Measuring Risk

# FRM Notes 2011 Unit IIA Basic Concepts in Measuring Risk -...

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Version: January 3, 2011 FIN 7400: Financial Risk Management Unit IIA Notes Page 1 of 36 D. M. Chance, LSU II. TOOLS AND APPLICATIONS OF MARKET RISK MANAGEMENT A. Basic Concepts in Measuring Risk In order to manage risk, we have to be able to measure it. We start with some basic measures of risk. Of course, the first is variance or standard deviation. We also sometimes use the term volatility , which nearly always means standard deviation (not variance). We assume you already know what volatility is. Now let us move on to more specific measures of risk, the first of which is Value-at-Risk (VAR). The Concept of Value-at-Risk (VAR) VAR is defined as the minimum loss that will be incurred x % of the time over a given holding period. Some people define it as a maximum loss that will be incurred 1 - x% of the time. It is easy to be careless with the definition of VAR. Let us consider an example. Suppose our VAR for a one-day holding period at 5% is \$1 million. This means that, defining VAR, as a minimum, we would say that On 5% of the days, we will lose at least \$1 million. Defining VAR as a maximum, we might say On 95% of the days, we will lose no more than \$1 million. Note, however, that technically the second sentence implies that we lose money 100% of the days, or in other words, on every day. On 95% of those days, we lose less than \$1 million. On 5% of those days we lose at least \$1 million. This is not what we intend to say. On some of the days, usually at least one-half, we make money. Also the use of VAR as a maximum can give the impression to naive executives that the VAR figure is the most we can lose. In fact the VAR figure is expected to be exceeded 5% of the time. My personal preference is for VAR to be stated as a minimum. Here’s an interesting note on how VAR can be misinterpreted. On May 5, 2004 The Wall Street Journal (p. A1) gave the following statement about Goldman Sachs. Goldman’s last quarterly results indicated that the average sum it could lose on any given day grew to \$71 million, up from just \$28 million in the fourth quarter of 2000.

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Version: January 3, 2011 FIN 7400: Financial Risk Management Unit IIA Notes Page 2 of 36 D. M. Chance, LSU Goldman’s quarterly report shows a VAR for the three months ending February 2004 of \$71 million on p. 59. On p. 58, Goldman correctly defines VAR as follows: Value-at-Risk (VaR) is the potential loss in value of Goldman Sachs’ trading positions due to adverse market movements over a defined time horizon with a specified confidence level. For the VaR numbers reported below, a one-day time horizon and 95% confidence level were used. This means that there is a 1 in 20 chance that daily trading net revenues will fall below the expected daily trading revenues by an amount at least as large as the reported level. Thus, shortfalls from expected trading net revenues on a single trading day greater than the reported VaR would be expected to occur, on average, about once a month. Shortfalls on a single day can exceed reported VaR by significant amounts.
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FRM Notes 2011 Unit IIA Basic Concepts in Measuring Risk -...

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