Market Risk and VaR Measurement at Bank

Posted: December 29, 2010 in Finance

Lehman Down , Merill Lynch acquired, Dubai Crisis ..We have been hearing them so often that I have started anticipating them as the next Hollywood thriller with a tagline ‘Releasing Soon’ and I pray Bollywood don’t release any thriller like SBI crippled or HDFC catastrophe !!

Thanks to BASEL II norms and conservative RBI !!

With Risk being the epicenter of discussion, We would briskly educate ourselves with  type of risk faced by any bank on a global basis on account of the exposure of banks to less regulated environment and thus swaying  to encounter financial and non-financial risk.

Risk can be broadly classified into Credit Risk, Operational Risk and Market Risk with a slight overlap in classification here and there. I hope till now you are able to recall the boredom  packed lecture of your professor at B-School  who used to shout :

Credit Risk is the uncertainty of losing of an investor’s fortune if the borrower defaults on payment”

Operational Risk is uncertainty of losing due to people, system or processes. Self explanatory term like fraud risk, legal risk, environmental risk are part of the operational risk space.”

Market Risk is uncertainty of losing due to change in the key market conditions such as interest rate, stock market index, forex rates etc. “

Having said the definitions, let’s get down to the integrities of our area of love “ Market Risk”.

Market which  can be either Money Markey or Share Market have the same philosophy ‘No Risk, No Gain’ and to play with the market is like playing with the fire, so not to get ourselves burnt we need to equip ourselves with statistical and mathematical coolant.

We have always known Banks to be the organization to push , pull or stabilize liquidity in economy, what about banks’ own liquidity? Hence the liquidity management comes into picture, which is dependent on the inflow and outflow of funds of the bank. The obligation of banking organization to provide for funds whenever withdrawn by customer, providing sums on maturity of schemes like Fixed Deposits, consideration of pre-payment of loan, all this makes the tasks of management of liquidity tough and bears a risk of non able to honour the commitments made by bank. And hence the famous term ‘Liquidity Risk’ needs attention.

Asset-Liability Committee (ALCO) of a bank while considering liquidity risk, keeps an eye on a continuous basis on the money in flow , the match between money borrowed and lent, so as  not to face liquidity crisis at any point of time. Liquidity-Adjusted Value At Risk incorporates exogenous liquidity risk into Value At Risk.(Not to disturb the flow of article we will discuss VaR later). It can be defined at VaR + ELC (Exogenous Liquidity Cost). ELC  refers to liquidity fluctuations driven by factors beyond the bank’s control..Another adjustment is to consider VaR over the period of time needed to liquidate the portfolio. VaR can be calculated over this time period.


Moving further,  We come across a very important parameter that effect the bank’s asset from loan to investment in bonds, i.e, the interest rate. Interest rate is the one which affects earning, value of the asset, value of liabilities and the cash flow. So, managing the Interest Rate Risk becomes a crucial job.

Banks face basically four types of interest rate risks :

Basis Risk : It is faced when the interest rate on asset and liabilities depend on two different bases such as LIBOR and MIBOR.

Yield Curve Risk : Considering the fact that short term interest risk is less than long term interest rate, Bank Borrows on short term and invest in long term, but this relationship can shift quickly and can cause erratic change in revenue and expenses.

Re-pricing Risk: The risk is presented by assets and liabilities that re-price at different times and rates.  For instance, a loan with a variable rate will generate more interest income when rates rise and less interest income when rates fall. If the loan is funded with fixed rated deposits, the bank’s interest margin will fluctuate.

Option Risk : Option of pre-payment of loans and foreclosure of deposits before their stated maturities constitute the Option risk.

There are several methods to calculate the impact of changing interest rate on bank’s portfolio consisting Assets and liabilities.

Assets of a bank consist of the loans dispersed. Stocks, bonds, debentures etc. that the bank owns. Cash in vault and real state possessions are also part of the asset of bank, as all these are kind of receivables income of the bank.

Liabilities of a bank consist of demand deposit, time deposit, saving and current bank account deposits, letters of credit and acceptances etc. as these has to be paid by the bank at respective times.

let’s se e a standard approach of calculating impact of changing interest rate  :-

a) Mark  the portfolio to market. b) stress test this marked to market portfolio. c) Calculate VaR of Portfolio. d) Calculate the multi period cash flow or financial accrual income and expense for N periods forward in a deterministic set of future yield curves. e) Do step ‘d’ with random yield curve movements and measure the probability distribution of cash flows and financial accrual income over time. f) Measuring the mismatch of the interest sensitivity gap of assets and liabilities, by classifying each asset and liability by the timing of interest rate reset or maturity, whichever comes first.

Appreciating the fact that banking industry is a global entity with millions of transactions in foreign currency, this has exposed us to the risk related with foreign exchange risk. This arises due to volatile structure of foreign exchange rate, which may change unfavorably for the bank before receivables are realized or payments are made in foreign currency.

Understanding the different types of market risks faced by banks we need to mitigate it if we are not able to remove it. So we need to measure it. The most common risk measurement technique prevalent in industry is Value at Risk technique.

Value at Risk ( VaR ) is the statistical technique to define a threshold value such that there is certain percentage surety that there will not be loss more than the threshold value in the defined time horizon.

For banking organization the threshold value is calculated on the time frame of 10 days ( also called holding period ) and 99% level of confidence.

There are three main approaches to calculate value at risk :

a)  Analytical VaR or Parametric VaR . b)  Historical Simulation VaR  c) Monte Carlo Simulation VaR

Analytical VaR or Parametric VaR – This method assumes a normal distribution of portfolio returns, which requires estimating the expected return and standard deviation of returns for each asset. This is suitable for simple and linear portfolio.( No complex and non-linear products, like convertible bonds, Default Swap, Options, etc ).

The  formula for the analytical VAR is:

VAR = – (Zα* σ + μ)*S

Zα is the lowest percentile of the distribution

σ is the standard deviation of the distribution (volatility)

μ is the mean of the distribution.

Historical  Simulation VaR – The historical method simply re-organizes actual historical returns, putting them in order from worst to best. It then assumes that history will repeat itself, from a risk perspective.  Depending upon the level of confidence, i.e, if LOC is 99% we take out 1% of total number of data. Let the value we have got is x, then we find the xth value from the top of the list ( worst to best ) , this is the Value at Risk at certain level of confidence for one day.

Understanding the fact that recent data has better relevance to the present market condition and past data has less, we add numerical weights to the worst to best list, giving more weightage to the recent data, and then follow the same process for calculating VaR as in Historical Simulation Methed. This is called Weighted Historical Simulation Method.

Monte Carlo Simulation VaR –  A Monte Carlo simulation refers to any method that randomly generates trials, but by itself does not tell us anything about the underlying methodology.

In a Monte Carlo simulation, a random value is selected for each of the tasks based on the range of estimates. The model is calculated based on this random value. The result of the model is recorded and the process is repeated. When the simulation is complete, we have a large number of results from the model, each based on random input values. These results are used to describe the likelihood, or probability, of reaching various results in the model.

Then the results that we have got is re-arranged from top to bottom in worst to best format and then we select the VaR value as discusses in historical simulation method.


The VaR we have got by different methods is a single day VaR, to convert it to 10 days Holding Period VaR we need to apply the following formula : VaR = VaR(daily) x √(No of days )

As mandated by Basel II, we need Var with a holding period of 10 days and 99% level of confidence, so the formula becomes :  VaR = VaR(daily) x √10 .

The numerical value of VaR that we have achieved by different models can be used for put restriction on traders. They should be not allowed to trade above the VaR limit and can be given full independence within the VaR limit.



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