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FacebookFacebook logoTwitterTwitter logoRedditReddit logoLinkedInLinkedIn logoWhatsAppWhatsApp logoThe investment of any nature financial or physical assets comes with reward and risk. In order to prosper a company or an individual has to take risk. Generally, investors are risk averse. The risk can be estimated and managed in certain way such that the expected future earnings can be obtained while reducing potential future distress. The key to any investments is pursuing calculated risk path and achieving balance between risk and expected return.

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The question presented in this assignment also highlights one of the important tools in the risk assessment called Value at Risk. Value at Risk (VaR) is simple but more powerful tool to understand the impact of risk on the portfolio over the period of time. The second part of the assignment explains the stress and back testing covering up some of VaR’s shortcomings.

(1) Question:

Explain and critically evaluate the model building approach to Value at Risk (VaR). To what extent may the weaknesses of this approach be addressed by stress testing and back testing?

A variety of approaches to this essay may be adopted. For example, a case-study or quantitative based essay are equally appropriate.

Answer:

The investors are risk average. They want to minimise the risk and achieve expected profit out of their investment. The risk can be calculated and managed so that financial benefits can be maximised out of the investments. Value at Risk ( VaR) is one of simple and powerful tool to provide a single number summary of the total risk in a portfolios. The tools are being widely used by senior management corporate treasures and fund managers of a financial institution as well as monetary regulators. The VaR declaration is mandatory for the banks as per the Basel Accord ( Hull, 2011).

VaR tells the investors, managers or regulators in a summary statement, how bad things might get. VaR enable companies or investors to consistently produce risk measures and risk management across all financial investments (Durham MBA). The VaR enable an analyst to make a statement that he/she is X percent certain that there will not be a loss of more than V dollars in the next N days (Hull, 2011).

Here the V is the VaR of the portfolio and it is function of Time (N) and confidence level (X).

The key advantage of the VaR statement is, it shows the aggregate risks faced by a financial institution or investor. This simple statement allows senior management to assess the situation and understand how bad things can get (Whitfield, n.d.).

There are two approaches in computing VaR namely a) Historical Simulation approach 2) Model-Building approach (Durham MBA)

## Model-Building approach

It is a main alternative approach to historical simulation approach. It is also known as variance-covariance approach (Hull, 2011).

An important component in the calculation of VaR is the daily volatility of the asset. Usually the volatility of an asset is in volatility per year. While calculation of VaR using model-building approach, time is expressed in days and volatility of an asset is expressed in volatility per day (Hull, 2011). Therefore, volatility quoted annually can be converted in daily by

Ïƒday = Ïƒyear/ âˆš 252.

Where,

Ïƒday = Daily Volatility

Ïƒyear = Annual Volatility

252 = Assumption about 252 trading day in year. ( Source Hull, 2011).

## Single Asset case

The single asset case is the simple situation of calculating VaR using model-building approach, where the portfolio of asset contains a single stock. For example, we can consider portfolio of $10M in shares of ABC Inc. The other assumption are N =10 and X=99. We want to estimate loss level over 10 days with 99% confidence level. We can assume that the volatility of ABC Inc. is 2% per day with 32% per year (Hull, 2011).

Standard deviation of daily changes = Ïƒ = 2% of $10 million

= $200,000

We say that value change in portfolio over a one-day period is $200,00 with mean Zero and we can assume that the change is normally distributed. Using cumulative normal distribution table, N(-2.33) = 0.01. We can say that there is 1% chances that a normally distributed variable will decrease in value by more than 2.33 standard deviation (Hull, 2011).

It is safely assumed that the expected change in a market variable over the period can be considered to be zero for calculation VaR.

Therefore the one-day VaR is = 2.33 x $200,000 = $466,000

We can calculated 10 day VaR at 99% confidence level as

= $466,000 x âˆš 10 = $1,473,621

Therefore, we can say that with 99% confidence, we will not lose more than $1,473,621 off the value of portfolio in next 10 days (Hull, 2011).

## Two Asset Case

The risk reduction can be achieved through diversification of the portfolios. There are two types of risk associated with investment namely systematic and unsystematic. Unsystematic risk is company or industry specific risk. It can be reduced using appropriate diversification.

For understanding two Asset case, we can consider price example with one more company. Let’s consider we have $5million positions in XYX Inc and the daily volatility is 1%. (Hull, 2011).

Change in value of portfolio in one day = 5,000,000 X 0.01 = $50,000

And 1-day 99% VaR is = $50,000 x 2.33 = $116,500

10-day 99 % VaR is = $116,500 x âˆš 10 = $368,405.

Now the combine portfolio with $10 Million Shares of ABC Inc and $5 Million positions in XYZ Inc. will have standard deviation of

Ïƒ X+y = âˆš (sq(Ïƒ X) + sq(Ïƒ y) + 2 Ï Ïƒ X X Ïƒ y ) ( source. Hull, 2011).

Where Ï correlation coefficient on return on two asset & we assume it is 0.3.

Ïƒ X ( ABC Inc. ) = 200,000 and Ïƒ X ( XYZ Inc. ) = 50,000

Therefore, the standard deviation of total portfolio over one-day period is

Ïƒ X+y = âˆš (sq(200,000) + sq(50,000)+ 2X0.3X 200,000 X 50,000

Ïƒ X+ y = 220,227

Hence, the 1-day VaR at 99% of total portfolio is = $ 220,227 X 2.33 = $ 513,129

Hence, the 10-days VaR at 99% of total portfolio is = $ 220,227 x âˆš 10 = $ 1,622,657.

We can conclude as

10-days 99% VaR of ABC Inc. only is $1,473,621

10-days 99% VaR of XYZ Inc. only is $ 368,405

10-days 99% VaR of a portfolio combining ABC Inc. and XYZ Inc. is $ 1,622,657

The difference in addition of two individual versus combine value represents the benefit of Diversification. In this case, it is £219,369 (Hull, 2011).

## Stress Testing

There are several shortcomings in VaR calculation. The main critic is that the tool underestimates the potential losses and the actual loss could be much higher (Whitfield, n.d.).

Therefore, financial institutions also carry out other techniques called stress testing along with VaR calculation. The stress testing involves study how a portfolio would have performed in case of extreme market conditions. The extreme condition can be a scenario provided by senior management or from historical situation (Whitfield, n.d.).

For example, stress testing can be conducted by setting the percentage change in all market variables equal to those on 19th October, 1987, when S&P 500 moved by 22.3 standard deviation. Similarly, many such historical events can be found out by analysing historical data and depending upon risk assessment levels, those scenarios can be applied to portfolio to estimate how it behaves under extreme conditions (Hull, 2011).

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Depending upon type of portfolio, suitable events from the historical data can be found out and better understanding of portfolio can be derived by applying stress test. For example Dot.com bubble busts scenario, Oil price extreme scenario, change in interest, higher commodity price scenarios and natural calamities. All these scenario’s percentage changes in all market variable can be found by analysing historical events and then simulating scenario effect on portfolios (Hull, 2011).

Stress testing enables the financial institutions to consider the extreme events that can occur from time to time but the chances of such events are very less. After credit-crisis of 2007, the regulators are insisting of stressed VaR test from all financial institutions considering all market variables present during one of the stress period like year 2008(Hull, 2011).

## Back testing

Back testing is an important reality check on the portfolio. Whatever method used for calculating VaR but the back testing remains important. It analyze the past performance of the portfolio and its calculated VaR. It consists of testing how good the VaR estimates were correct in past. For example, if we calculated a one-day 99 % VaR, back testing would analyze how often the loss in a day exceeded the one-day 99% calculated VaR corresponding to that day. If the exceeded loss is in the range of 1% of that day, it can be reasonably considered that the methodology is working and correctly predicting the loss. However, the loss are above 7% of the day and for many days, there is doubt about methodology and someone has to analysis the methodology & to fix it (Hull, 2011).

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FacebookFacebook logoTwitterTwitter logoRedditReddit logoLinkedInLinkedIn logoWhatsAppWhatsApp logo## FAQs

### What is the model building approach? ›

This involves **assuming a model for the joint distribution of changes in market variables and using historical data to estimate the model parameters**. The model-building approach is ideally suited to a portfolio consisting of long and short positions in stocks, bonds, commodities, and other products.

### What is value at risk in finance? ›

Value-at-risk is **a statistical measure of the riskiness of financial entities or portfolios of assets**. It is defined as the maximum dollar amount expected to be lost over a given time horizon, at a pre-defined confidence level.

### What is the significance of the value at risk method? ›

Value at risk (VaR) is a financial metric that you can use to estimate the maximum risk of an investment over a specific period. In other words, the value at risk formula **helps you to measure the total amount of potential losses that could happen in an investment portfolio, as well as the probability of that loss**.

### Is value at risk a quantitative approach? ›

VaR was developed as a systematic way to segregate extreme events, which are studied qualitatively over long-term history and broad market events, from everyday price movements, which are **studied quantitatively using short-term data in specific markets**.

### What are the primary differences between the historical and model-building approach to estimating VAR? ›

The key assumption in historical simulation is that the set of possible future outcomes is fully represented by what occurred in a definite historical time frame/window. On the other side, **model-building approach involves assumptions about the joint probability distributions of the returns on the market variables**.

### What is group modeling? ›

Group model building (GMB) is **a participatory approach that is widely used to build the capacity of practitioners to think in a systems way**. However, it is a resource-intensive approach that requires high-level buy-in and the investment of time.

### What is Value at Risk in simple words? ›

Value at risk (VaR) is **a statistic that quantifies the extent of possible financial losses within a firm, portfolio, or position over a specific time frame**.

### How do you find the value of risk? ›

How Do You Calculate Value at Risk? There are three ways to calculate VAR: **the historical method, the variance-covariance method, and the Monte Carlo method**. The historical method examines data from prior observations, with the assumption that future results will be similar.

### How do you calculate Value at Risk example? ›

Value at Risk (VAR) can also be stated as a percentage of the portfolio i.e. a specific percentage of the portfolio is the VAR of the portfolio. For example, **if its 5% VAR of 2% over the next 1 day and the portfolio value is $10,000, then it is equivalent to 5% VAR of $200 (2% of $10,000) over the next 1 day**.

### Which is the most widely used methodology to calculate VaR? ›

**Parametric method**

The most common way of calculating VaR is the parametric method, also known as variance covariance method. This method assumes that the return of the portfolio is normally distributed and can be completely described by expected return and standard deviations.

### What are the features of Value at Risk? ›

In Lay man terms Value at Risk **measures largest loss likely (in future) to be suffered on a portfolio position over a holding period with a given probability (confidence level)**. VAR is a measure of market risk, and is equal to one standard deviation of the distribution of possible returns on a portfolio of positions.

### What are the methodologies used for VaR calculation? ›

- Philippe Jorion's.
- Orange County Case: 3.2 Methods to measure VAR. ...
- (1) Delta-Normal Method. The delta-normal method assumes that all asset returns are normally distributed. ...
- (2) Historical-Simulation Method. ...
- (3) Monte Carlo Method. ...
- Comparison of Methods.

### How accurate is Value at Risk? ›

**75 percent of the full sample results**. For the out-of-sample period, the average bank VaR was about the same as for the full sample, while the average of mean violations was somewhat lower. The average violation rate also was very close to . 01.

### What is the greatest difficulty in determining Value at Risk? ›

**False sense of security**

Many people think of VAR as "the most I can lose", especially when it is calculated with the confidence parameter set to 99%. Even when you understand the true meaning of VAR on a conscious level, subconsciously the 99% confidence may lull you into a false sense of security.

### What is a key drawback of VaR? ›

The limitation of VaR is that **it is not responsive to large losses beyond the threshold**. Two different loan portfolios could have the same VaR, but have entirely different expected levels of loss. VaR calculations conceal the tail shape of distributions that do not conform to the normal distribution.

### What are the advantages of Value at Risk? ›

Pros of value at risk

One of the main advantages of the VaR metric is that **it is easy to understand and use in analysis**. This is why it is often used by investors or firms to look at their potential losses. The metric can also be used by traders to control their market exposure.

### What is confidence level in VaR? ›

The confidence level is **expressed as a percentage, and it indicates how often the VaR falls within the confidence interval**. If a risk manager has a 95% confidence level, it indicates he can be 95% certain that the VaR will fall within the confidence interval.

### What is the historical method of calculating VaR what are its advantages? ›

One advantage of historical VaR is that **it is extremely simple to calculate**. Another advantage is that it is easy to explain to non-risk professionals. The historical approach is non-parametric. We have not made any assumptions about the distribution of historical returns.

### How do you calculate value at risk in a normal distribution? ›

In the standard normal distribution, the 95% cut-off is –1.64 (the 99% cut-off is –2.33). But remember, the standard normal distribution has a standard deviation of 1. To obtain the VaR for our stock, we **multiply the cut-off by the standard deviation of the stock return, (sigma)**.

### What is value at risk margin? ›

Value at Risk (VAR) refers to **the potential loss that might occur while dealing with securities for a given timeframe**. VAR margin is required to cover up for the losses arising due to uncertain risk conditions. VAR margins are covered for a single day for Liquid securities and three days for illiquid securities.

### Who invented Value at Risk? ›

Invented by **JPMorgan** in the 1980s, VaR, or Value at Risk, is a way of measuring the amount of money a bank can expect to lose on its portfolio of tradable assets (eg, stocks and bonds) if markets plummet. VaR is calculated for a specified period of time and for a specified level of confidence.

### What is VaR and how is it calculated? ›

The VaR calculation is a probability-based estimate of the minimum loss in dollar terms expected over a period. This data is used by investors to strategically make investment decisions.

### What does VaR represent? ›

acronym. VAR is an abbreviation for Value at Risk, a financial term that is used to measure the risk of loss on a portfolio of investments. An example of VaR is a 5% potential to lose $1 million dollars in a day without trading.

### Why do banks use VaR? ›

Value at Risk (VaR) a statistical tool to measure and quantify financial risk within a firm or portfolio over a specific time frame. This metric is often used by Banks **to determine the extent and probability of occurrence of a potential loss on the advances**.

### Is VaR minimum or maximum loss? ›

VaR is often misinterpreted as "maximum loss". It is in fact the minimum loss that one should expect in a few instances. Maximum loss expected for the portfolio over the time period can often be much greater and much more difficult (if not impossible) to estimate.

### What are the advantages and disadvantages of VAR? ›

**The Pros**

- Better Decision Making.
- Excitement During Games.
- Maintaining Player Discipline.
- Avoiding Controversial Decisions.
- Improving the Game.
- Time Wastage.
- Lack of Transparency.
- It Can Still Get Decisions Wrong.

### What are the uses of VAR? ›

VAR is used only for "**clear and obvious errors" or "serious missed incidents" in four match-changing situations: goals; penalty decisions; direct red-card incidents; and mistaken identity**.

### What are the problems with VAR? ›

The main argument against the use of VAR is that **it disrupts the way in which football is played**. This momentary pause in action has been the subject of hefty debate amongst football fans nation-wide. The game's flow and momentum are what drives football and set it apart from the stop-start nature of other sports.

### What are the steps in model building? ›

**The model building process**

- Define the purpose of your model, the problem you are trying to solve, or the story you are trying to tell. ...
- Determine the model boundary. ...
- Map the model. ...
- Build the model. ...
- Test the model. ...
- Create an interface. ...
- Share the model.

### What is model building in quantitative techniques? ›

Model building in Quantitative techniques

In industry and engineering, **it is common practice for a team of people to work together in building a model, with the individual team members bringing different areas of expertise to the project**.

### What is model building in data analytics? ›

The model building process involves setting up ways of collecting data, understanding and paying attention to what is important in the data to answer the questions you are asking, finding a statistical, mathematical or a simulation model to gain understanding and make predictions.

### What is model building in biology? ›

It involves the use of computer simulations of biological systems, including cellular subsystems (such as the networks of metabolites and enzymes which comprise metabolism, signal transduction pathways and gene regulatory networks), to both analyze and visualize the complex connections of these cellular processes.

### What is the purpose of model building? ›

Architects use the model building because it **brings their ideas to life**! It is a form of three-dimensional sketching. It helps them see how light can illuminate certain rooms and spaces. They can analyze the spatial relationships of every form or element of the design.

### What is the significance of building a model? ›

Modeling **gives graphical representation of system to be built**. Modeling contributes to a successful software organization. Modeling is a proven and well accepted engineering technique.

### How do you build a model building? ›

Architecture Model Making Tutorial (Using a Real Project) - YouTube

### Which data is used in model building? ›

**Training Data** is the correct answer to this question.

### Why is modeling important in management? ›

Tools and models provide a framework to structure this information, to distinguish between relevant and irrelevant information, to realign information so that new interdependencies and connections become visible, and they provide formats to present information and conclusions. Thus, they facilitate thinking.

### What are models explain with example? ›

The definition of a model is **a specific design of a product or a person who displays clothes, poses for an artist**. An example of a model is a hatch back version of a car. An example of a model is a woman who wears a designer's clothes to show them to potential buyers at a fashion show.

### What is outcome of model building phase? ›

Phase 4: Model Building –

**Team develops datasets for testing, training, and production purposes**. Team also considers whether its existing tools will suffice for running the models or if they need more robust environment for executing models.

### What is the purpose of model planning phase? ›

The purpose of the Planning Phase is to plan all project processes and activities required to ensure project success and to create a comprehensive set of plans, known as the PMP, to manage the project from this phase until project termination.

### What is meant by model system? ›

A model system is **scientists' jargon for a particular species of animal that has been developed over many years to be experimentally powerful to answer particular questions**.

### Is modelling helpful in understanding a biological concept What are its advantages? ›

Models play a key role in scientific explanations and understanding. They are representations that **can describe or simplify complex phenomena, be used to make predictions about future events, facilitate the communication of ideas** (Svoboda & Passmore, 2013. (2013). The strategies of modeling in biology education.

### Why are models useful in biological research? ›

Biologists use models in nearly every facet of scientific inquiry, research, and communication. Models are **helpful tools for representing ideas and explanations** and are used widely by scientists to help describe, understand, and predict processes occurring in the natural world.