Risk Mgt and the use of derivatives Part 1

Risk reduction refers to recognizing and reducing, eliminating, or avoiding risk in general As part of the risk management process, management must identify which risks can be managed and the proper management tools to use (if available). If the necessary information or tools to manage the risk are not available, the manager should avoid the risk. Risk governance is the name given to the overall process of developing and putting a risk management system into use.

Types of risk Market risk Credit risk Liquidity risk Operational risk Settlement risk Model risk Sovereign risk Regulatory risk Tax, accounting and legal/contract risk Any risk associated with external capital markets, including transactions, is considered financial risk. Other risks are considered nonfinancial.

Analytical Value at Risk (VAR) VAR is used as an estimate of the minimum expected loss (alternatively, the maximum loss)over a set time period at a desired level of significance (alternatively, at a desired level of confidence). For example, a 5% VAR of sh1,000 over the next week means that, given the standard deviation and distribution of returns for the asset, management can say there is a 5% probability that the asset will lose a minimum of (at least) sh1,000 over the coming week. Stated differently, management is 95% confident the loss will be no greater than sh1,000.

Example

When estimating VAR for a portfolio, the correlations of the returns on the individual assets must be considered. That is, the overall VAR is not just the simple sum of the individual VARs.

VAR considers only the downside, or lower tail, of the distribution of returns. Unlike the typical z-score you have worked with in generating confidence intervals, the level of significance for VAR is the probability in the lower tail only (i.e., a 5% VAR means there is 5% in the lower tail).

Recall that the confidence interval generated by adding and subtracting 1.96 standard deviations leaves the highest and lowest 2.5% of values in each of the tails of the distribution (95% of the values fall between the tails). When you estimate a 5% VAR, on the other hand, you want the entire 5% in the lower tail. So, for a 95% VAR you will use a z-value of 1.65.

Analytical VaR Method Analytical VAR requires the assumption of a normal distribution. This is because the method utilizes the expected return and standard deviation of returns. Also referred to as variance-covariance method For example, in calculating a daily VAR, we calculate the standard deviation of daily returns in the past and assume it will be applicable to the future. Then, using the asset’s expected 1-day return and standard deviation, we estimate the 1-day VAR at the desired level of significance.

Example The expected annual return for a sh 100m portfolio is 6%, and the historical standard deviation of annual returns is 12%. Calculate daily VAR at 5% significance.

=[6-1.65(12)](sh100m) =-sh 13,800,000 The interpretation of this VAR is that there is a 5% probability that the minimum annual loss is sh13,800,000. Alternatively, we could say we are 95% confident the annual loss will not exceed sh13,800,000.

If you are given the standard deviation of annual returns and need to calculate a daily VAR, the daily standard deviation can be estimated as the annual standard deviation divided by the square root of the number of reporting periods in a year

Do! A portfolio contains two assets, A and B. The expected returns are 9% and 13%, respectively, and their standard deviations are 18% and 21%, respectively. The correlation between the returns on A and B is estimated at 0.50. Calculate the 5% (analytical) VAR of a sh100,000 portfolio invested 75% in A and 25% in B. List two advantages and disadvantages of analytical VAR.

Answer VAR=sh100,000[0.10-1.65*(0.1675)]=sh-17,637

The analytical method Advantages: It is easy to calculate and easily understood. It allows modeling the correlations of risks. It can be applied to different time periods according to industry custom. Disadvantages: The need to assume a normal distribution. The difficulty in estimating the correlations of very large portfolios. No indication of the size of potential losses in the tail.

The Historical VAR Method The historical method for estimating VAR is sometimes referred to as the historical simulation method. The easiest way to calculate the 5% daily VAR using the historical method is to accumulate a number of past daily returns, rank the returns from highest to lowest, and identify the lowest 5% of returns. The highest of these lowest 5% of returns is the 1-day, 5% VAR.

Example You have accumulated 100 daily returns for your sh100m portfolio. After ranking the returns from highest to lowest, you identify the lowest five returns: –0.0019, –0.0025, –0.0034, –0.0096, –0.0101 Calculate daily VAR at 5% significance using the historical method.

Answer Since these are the lowest five returns, they represent the 5% lower tail of the “distribution” of 100 historical returns. The fifth lowest return (–0.0019) is the 5% daily VAR. We would say there is a 5% chance of a daily loss exceeding 0.19%, or sh190,000.

Advantages of the historical method Easy to calculate and easily understood. No need to assume a returns distribution. Can be applied to different time periods according to industry custom. The primary disadvantage is the assumption that the pattern of historical returns will repeat in the future (i.e., is indicative of future returns). This becomes particularly troublesome the more the manager trades. Also many securities (e.g., options, bonds) change characteristics with the passage of time.

The Monte Carlo VAR Method The Monte Carlo method refers to computer software that generates hundreds, thousands, or even millions of possible outcomes from the distributions of inputs specified by the user. The several thousand weighted average portfolio returns will naturally form a distribution, which will approximate the normal distribution. Using the portfolio expected return and the standard deviation, which are part of the Monte Carlo output, VAR is calculated in the same way as with the analytical method.

Example A Monte Carlo output specifies the expected 1-week portfolio return and standard deviation of the sh100m portfolio as 0.00188 and 0.0125, respectively. Calculate the 1-week VAR at 5% significance.

References CFA Level 3 Curriculum 2017 CFA Level 3 Schweser notes 2017 Introduction to Investment Analysis and Portfolio Management by Reilly and Brown