Here is an essay on the ‘Measuring Market Risk’ for class 11 and 12. Find paragraphs, long and short essays on ‘Measuring Market Risk’ especially written for school and banking students.

#### 1. Essay on Sensitivity:

Sensitivity captures deviation of market price due to unit movement of a single market parameter. Supply-demand position, interest rate, market liquidity, inflation, exchange rate, stock prices, etc., are the market parameters, which drive market values. For example, change in interest rate would drive the market value of bonds and forward foreign exchange held in a portfolio. If liquidity in the market increases that may result in increased demand that in turn may increase market price.

Sensitivity is measured as change in market value due to unit change in the variable. For example, where market value of a portfolio changes by Rs 100,000 for 1% change in rate of interest, interest rate sensitivity of the portfolio is Rs 100,000. This gives us a measure of risk associated with the portfolio vis-a-vis change in rate of interest.

This measure suffers from the fact that it does not consider impact of other parameters, which may also change simultaneously. Secondly, the measure does not remain constant for all the values of the variable. Say, the interest rate sensitivity of a bond is Rs 100 when the yield on the bond is 5%. If the yield on the bond rises to 8%, its interest rate sensitivity would not remain at Rs 100.

Nevertheless, sensitivity is relied upon as a measure, particularly those that are based on changes in interest rates. Two of them, Basis Point Value (BPV) and Duration that are used quite frequently, are discussed below.

#### 2. Essay on Basis Point Value (BPV):

This is the change in value due to 1 basis point (0.01%) change in market yield. This is used as a measure of risk. The higher the BPV of a bond, higher is the risk associated with the bond. Computation of BPV is quite simple.

For example, a 5 year 6% semi-annual bond @ market yield of 8%, has a price of Rs 92, which rises to Rs 92.10 at a yield of 7.95%. So, for one BP fall in yield, market price changes by Rs 0.02 or gains by Rs 2,000 per Rs 1 crore face values. BPV of the bond is, therefore, Rs 2,000 per crore face values.

This also helps us to quickly calculate profit or loss for a given change of yield. If the yield on a bond with BPV of 2,000 declines by 8 BPs, then that would result in a profit of 8 × 2000 = Rs 16,000 per crore of face value. If one is holding Rs 10,00,000 face value of this bond, he makes a profit of Rs 1,600.

BPV changes with remaining maturity. Suppose the bond described above has 5 years to mature and present BPV is 2000, the BPV will decline with time and on the day of maturity it will be zero.

#### 3. Essay on Duration:

McCauley’s Duration was first proposed by Frederick McCauley in 1938 as a means of describing a bond’s price sensitivity to yield change with a single number. This is equivalent to time, on average, that the holder of the bond must wait to receive the present value of the cash flows. In other words, this represents cash flow ‘Centre of Gravity’.

It implies that if a five-year 6% bond face value of Rs 100 with semi-annual interest has McCauley’s duration say 3.7 years, then total cash flow to be received over the five year period of Rs 130 from the bond would be equivalent to receiving Rs 130 at the end of 3.7 years as a bullet payment.

Duration or Modified duration is McCauley’s duration discounted by 1 period yield to maturity.

The longer the duration of a security, the greater will be the price sensitivity to yield changes and higher would be the risk associated with the bond. Bond price changes can be estimated using modified duration using the following relationship.

Approx % change in price = – modified duration X yield change

#### 4. Essay on Downside Potential:

Risk materializes only when earnings deviate adversely. Downside potential only captures possible losses ignoring profit potential. Downside risk is the most comprehensive measure of risk as it integrates sensitivity and volatility with the adverse effect of uncertainty. This is the measure that is most relied upon by banking and financial service industry as also the regulators.

Value at Risk (VaR):

Management of market risk is concerned with the question – How much can we lose? The answer to it is that there is a possibility that we can lose everything, although it may have a very low probability. VaR attempts to create a more useful answer by altering the question – How much can we expect to lose? Or, what is the loss potential? The answer could be that we can lose a maximum of Rs X (the VaR) over the next week (time horizon) and may expect that with 99% confidence (i.e., it would be so 99 times out of 100).

VaR is defined as the predicted worst-case loss at a specific confidence level over a certain period of time assuming ‘Normal Trading Conditions’.

A bank having 1 day VaR of Rs 10 crore with 99% confidence interval means that there is only one chances in 100 (or 2.5 days per year based on 250 working days in a year) that daily loss will be more than 10 crore under normal trading conditions. This also means that there is 1% chance that the daily loss may exceed Rs 10 crore under normal trading conditions. It does not estimate losses in abnormal situations.

VaR measures the potential loss in market value under normal circumstances of a portfolio using estimated volatility (rate or price move) and correlations (how rates or prices move in relation to each other), for a given horizon (longer the time horizon, more is the VaR) measured with a given confidence interval. In calculating VaR we consider the volatility of prices and correlation of prices with respect to all other assets/liabilities in the portfolio. Normal circumstances refer to the fact that VaR is not a measure when market is under abnormal conditions.

Yield Vs Price Volatility:

Yield volatility is degree of variance in yield. This is largely unaffected by time and duration. It rises as yields fall.

Price volatility is degree of variance in price. This is largely unaffected by yield and substantially affected by time and duration.

Price Volatility = (Yield volatility X BP V X Yield)/Price

There are three main approaches to calculating value-at-risk:

1. The correlation method, also known as the variance/covariance matrix method

2. Historical simulation

3. Monte Carlo simulation.

All three methods are based on three basic parameters – holding period, confidence interval and the historical time horizon over which the asset prices are observed.

Under the correlation method, the change in the value of the position is calculated by combining the sensitivity of each component to price changes in the underlying asset(s), with a variance/covariance matrix of the various components’ volatilities and correlation. It is a deterministic approach.

The historical simulation approach calculates the change in the value of a position using the actual historical movements of the underlying asset(s), but starting from the current value of the asset. It does not need a variance/covariance matrix. The length of the historical period chosen does impact the results because if the period is too short, it may not capture the full variety of events and relationships between the various assets and within each asset class, and if it is too long, may be too stale to predict the future. The advantage of this method is that it does not require the user to make any explicit assumptions about correlations and the dynamics of the risk factors because the simulation follows every historical move.

The Monte Carlo simulation method calculates the change in the value of a portfolio using a sample of randomly generated price scenarios. Here the user has to make certain assumptions about market structures, correlations between risk factors and the volatility of these factors. He is essentially imposing his views and experience as opposed to the naive approach of the historical simulation method.

At the heart of all three methods is the model. The closer the models fit economic reality, the more accurate the estimated VaR numbers and therefore the better they will be at predicting the true VaR of the firm. There is no guarantee that the numbers returned by each VaR method will be anywhere near each other.

Why VaR is Useful?

1. Good tool for all banks, financial institutions, multinationals, and fund managers for protection of customers, shareholders, employees and overall franchise of the business

2. Translates portfolio exposures into potential P and L impact

3. Aggregates and reports multi-product, multi-market exposures into one number

4. Meets external risk management disclosure and expectations

5. A vital component of current best practices in risk measurement

6. Embraced by practitioners, regulators and academics

7. Valuable as a probabilistic measure of potential losses.

Limitation of VaR:

VaR is not worst-case scenario. It does not measure losses under any particular market conditions. VaR by itself- is not sufficient for risk measurement. Measures to get over the limitation include back testing and model calibration and scenario analysis and stress testing.

Role of VaR in Control and Monitoring:

VaR is used as a MIS tool in the trading portfolio in the trading portfolio to ‘slice and dice’ risk by levels/products/geographic/level of organisation, etc. It is also used to set risk limits. In its strategic perspective, VaR is used for decisions as to what business to do and what not to do.

However, VaR as a useful MIS tool has to be ‘back tested’ by comparing each day’s VaR with accruals and necessary re-examination of assumptions needs to be made so as to be close to reality. VaR, therefore, cannot substitute sound management judgment, internal control and other complementary methods. It is used to measure and manage market risks in trading portfolio and investment portfolio.

Estimating Volatility:

VaR uses past data to compute volatility. Different methods are employed to estimate volatility. One is arithmetic moving average from historical time series data. The other is the exponential moving average method. In the exponential moving average method, the volatility estimates rises faster to shocks and declines gradually.

Further, different banks take different number of days of past data to estimate volatility. Volatility also does not capture unexpected events or “event risk”. All these complicate the estimation of volatility. VaR, therefore, should be used in combination with “stress tests” to take care of event risks. Stress test takes into account the worst-case scenario.

#### 5. Essay on Back Testing:

Back testing is a process where model based VaR is compared with the actual performance of the portfolio. This is carried out for evaluating a new model or to assess the accuracy of existing models.

Back testing for evaluating a new model requires comparison with actual performance on a continuous basis for a given period.

Assessment of accuracy of an existing model needs back test on a regular basis. Banks should generally back test risk models on a monthly or quarterly basis to verify accuracy. In these tests, they should observe whether trading results fall within pre-specified confidence bands as predicted by the VaR models.

If the models perform poorly, they should probe further to find the cause (e.g., check integrity of position and market data, model parameters, methodology). The BIS outlines back testing best practices in its January 1996 publication “Supervisory framework for the use of back testing” in conjunction with the internal models approach to market risk capital requirements.

#### 6. Essay on Stress Testing:

Market value of a portfolio varies due to movement of market parameters such as interest rate, market liquidity, inflation, exchange rate, stock prices, etc. Movement in market parameters, on a day-to-day basis causes the change in the market value of the portfolio. This represents the normal risk that is associated with normal day-to-day movements. There remains the risk of large non-normal movement in market parameters that signifies abnormal market conditions. Risks arising due to such movements fall beyond the day-to-day risk monitoring but that could potentially occur.

Stress testing essentially seeks to determine possible changes in the market value of a portfolio that could arise due to non-normal movement in one or more market parameters. The process involves identifying market parameters to stress the quantum of stress and determine the time frame. Once these are determined, it is applied on the portfolio to assess the impact on it.

Market value of a portfolio varies with Stress Testing Techniques. Stress testing covers many different techniques.

The four discussed here are listed here:

a. Simple Sensitivity Test

b. Scenario Analysis

c. Maximum Loss

d. Extreme Value Theory.

a. Simple Sensitivity Test:

A simple sensitivity test isolates the short-term impact on a portfolio’s value of a series of predefined moves in a particular market risk factor. For example, if the risk factor is exchange rate, the shocks may be exchange rate changes of +/-2%, 4%, 6% and 10%.

b. Scenario Analysis:

A scenario analysis specifies the shocks that might plausibly affect a number of market risk factors simultaneously if an extreme, but possible, event occurs. It seeks to assess the potential consequences for a firm of an extreme, but possible, state of the world. A scenario analysis can be based on an historical event or a hypothetical event.

Historical scenarios employ shocks that occurred in specific historical episodes. Hypothetical scenarios use a structure of shocks thought to be plausible in some foreseeable, but unlikely circumstances for which there is no exact parallel in recent history. Scenario analysis is currently the leading stress testing technique.

c. Maximum Loss:

A maximum loss approach assesses the risks of a portfolio by identifying the most potentially damaging combination of moves of market risk factors. Risk managers who use such ‘maximum loss’ approaches find the output of such exercises to be instructive but they tend not to rely on the results of such exercises in the setting of exposure limits in any systematic manner, an implicit recognition of the arbitrary character of the combination of shocks captured by such a measure.

d. Extreme Value Theory:

Extreme value theory is a means to better capture the risk of loss in extreme but possible circumstances. EVT is the statistical theory on the behaviour of the ‘tails’ (i.e., the very high and low potential values) of probability distributions. Because it focuses only on the tail of a probability distribution, the method can be more flexible. For example, it can accommodate skewed and fat-tailed distributions.

A problem with the extreme value approach is adapting it to a situation where many risk factors drive the underlying return distribution. Moreover, the usually unstated assumption that extreme events are not correlated through time is questionable. Despite these drawbacks, EVT is notable for being the only stress test technique that attempts to attach a probability to stress test results.

What Makes a Good Stress Test?

A good stress test should:

i. Be relevant to the current position

ii. Consider changes in all relevant market rates

iii. Examine potential regime shifts (whether the current risk parameters will hold or breakdown)

iv. Consider market illiquidity

v. Consider the interplay of market and credit risk

It should help the management to be forward looking in managing disasters mooted by market factors.

How should risk managers use stress test?

Stress tests produce information summarising the bank’s exposure to extreme, but possible, circumstances. The role of risk managers in the bank should be assembling and summarising information to enable senior management to understand the strategic relationship between the firm’s risk-taking (such as the extent and character of financial leverage employed) and risk appetite. Typically the results of a small number of stress scenarios should be computed on a regular basis and monitored over time.

Some of the specific ways stress tests are used to influence decision-making are to:

i. Manage funding risk

ii. Provide a check on modeling assumptions