Topics covered

 The concept and practice of management

 Types of An Introduction to  Financial Risks: definition

 Basic stat review

(VaR): Basics

 Value at Risk (VaR): Motivation & Definition

Financial Risk Management Nattawut Jenwittayaroje, Ph.D., CFA  Value at Risk (VaR): Three methods of VaR calculation NIDA Business School National Institute of Development Administration  Benefits and extensions of VaR

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Why Practice Risk Management?

 Definition of risk management: the practice of defining the  The Motivation for Risk Management risk level a firm desires, identifying the risk level it currently  Firms practice risk management for several reasons: has, and using derivatives or other financial instruments to  Interest rates, exchange rates and stock prices are more volatile today than in the past. These factors create risks over which most businesses have little adjust the actual risk level to the desired risk level. expertise. Therefore, it makes sense for a business to manage and largely eliminate these risks.

 Significant losses incurred by firms that did not practice risk management

 Improvements in information technology – without enormous developments in computing power, it would not have been possible to do the complex calculations necessary for pricing derivatives and for keeping track of positions taken.

 Favorable regulatory environment – the growth of derivatives (i.e., main tools for managing risks) was fueled by the favorable regulatory environment.

3 4 Risks of Financial Intermediation Risks of Financial Institutions

resulting from intermediation:

 Mismatch in maturities of assets and liabilities.  The risks associated with financial intermediation:

 Interest rate sensitivity difference exposes equity to changes in  Interest rate risk interest rates   Balance sheet via matching maturities of assets and liabilities is problematic for FIs. 

 Inconsistent with asset transformation role   The risk that the cost of rolling over or reborrowing funds (e.g., deposits) will rise above the returns being earned on asset investments  Legal and regulatory risk (e.g., loans)

.

 The risk that the returns on funds to be reinvested (e.g., making loans) will fall below the cost of funds (e.g., deposits)

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Market Risk Credit Risk

 Incurred in trading of assets and liabilities (and derivatives).

 Examples: Barings & decline in ruble.  Risk that promised cash flows are not paid in full.  1995 Barings , forced into insolvency due to losses on its  Firm specific credit risk trading in Japanese stock index futures  Systematic credit risk  1996 Sumitomo Corp. lost $2.6 billion in commodity futures trading

 1997 market volatility in Eastern Europe and Asia  Credit risk is the oldest form of risk in the financial

 1998 losses on Russian bonds and Ruble currency: Big US institutions. have to write off hundreds of millions of dollars in losses on their holdings of Russian government securities

 DJIA dropped 12.5 percent in two-week period July, 2002.

 Heavier focus on trading income over traditional activities increases market exposure.

7 8 Operational Risk Liquidity Risk

 Liquidity risk is the risk that a sudden surge in liability  BIS definition: Risk of losses resulting from inadequate or failed internal processes, people, and systems or from withdrawals may leave a bank in a position of having to external events. liquidate assets in a very short period of time and at low prices.  Operational risk is the risk that existing technology or support systems may malfunction or break down.  May generate runs.

 Power failures, computer problems such as viruses, the failure  Runs may turn liquidity problem into solvency problem. of staff personnel to monitor and record transactions properly,  Risk of systematic bank panics. etc..

 However, operational risk losses do not occur often (but can lead to tremendous losses), so it is difficult to do the analysis.

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Legal and Regulatory Risks Financial Risks

 Market risk is the uncertainty of a firm’s value or cash flow that is  Legal risk is the risk that the legal system will fail to enforce associated with movements in an underlying source of risk (e.g., interest a contract. rates, foreign exchange rates, stock prices, or commodity prices).  E.g., interest rate risk faced by financial intermediary, FX risks faced  For example, suppose a dealer enters into a swap with a by FX dealers, oil price risks faced by oil distributors, and stock price counterparty that, upon incurring a loss, then refuses to pay risk faced by equity fund managers. the dealer, arguing that the dealer misled it or that the  However, because many sources of risk are partially correlated, the counterparty had no legal authority to enter the swap. combined effects of all sources of risk must be considered.  Credit risk is the uncertainty and potential for loss due to a failure to pay on the part of a counterparty. It is the risk that promised cash flows  Regulatory risk is the risk that regulations will change. are not paid in full.

 Regulatory risk means that certain existing or contemplated  Credit risk (or default risk) of loans faced by any lender, and credit transactions can become illegal or regulated. risk of derivatives, i.e., the risk of default faced by any party that may receive obligation payments from another party.

11 12 Basic Stat Review Basic Stat Review (Con’t)

 Want to know the height of Thai population  Want to know the height of Thai population (con’t)

 Sort from the lowest to the highest

 Randomly select 100 people and measure each person’s height

 What is the average height of Thai people? 

 What is the standard deviation of height of Thai people?   How many people have height below 161?  15 people

 What is the percentage of people having height below 161?  How many people have height below 161?  15 from 100 people  15%

 What is the percentage of people having height below 161?

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Basic Stat Review (Con’t) Value at Risk (VaR) Basics

 Want to know the height of Thai population (con’t)  Want to know the risk of my stock portfolio….

 How many people have height above 185?  For example, I now have 100,000 shares of AA stock @$10  What is the percentage of people having height above 185? each.

 So my portfolio is now worth $1,000,000.

 How many people have height between 161 and 185?  What is the percentage of people having height between 161  What is the probability that tomorrow (i.e, one day later) my and 185? portfolio will be worth below $930,000?

 About 5% of people have height below………………?  There is 5% chance that tomorrow (i.e, one day later) my  About 95% of people have height at least………………? portfolio will be worth below $xxxxxx?

15 16 Value at Risk (VaR) Basics (Con’t) Value at Risk (VaR) Basics (Con’t)  Want to know the risk of my stock portfolio…A Better Way  Want to know the risk of my stock portfolio….  Collect data of AA share price over the recent past 100 days;  Collect data of AA share price over the recent past 100 days as follows..

 Compute daily return of AA share price over the recent 100 days..

 Sort the data from the smallest price to the highest price..

(price at 4Jun – price at 3Jun)/price at 3 Jun = (9.57-9.33)/9.33

 What is the probability that tomorrow (i.e, one day later) my portfolio will be worth below $930,000?  Sort the 100 daily returns from the smallest to the highest..  There is 5% chance that tomorrow (i.e, one day later) my portfolio will be worth below $xxxxxx?

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Value at Risk (VaR) Basics (Con’t) Value at Risk (VaR): Motivation

 Want to know the risk of my stock portfolio….  Starting Point: “At close of business each day, tell me  There is 5% chance that tomorrow (i.e, one day later) my what the market risk are across all business and portfolio will be worth ?  $993,000 below $xxxxxx locations”

 In a nutshell, A chairman wants a single amount  Equivalently, there is 5% chance that tomorrow (i.e, one day dollar later) my portfolio will lose more than $7,000 at 4.15pm that tells him JPM’s market risk exposure over the next day – especially if that day turns out to be Value at Risk - VaR a “bad” day.

 If tomorrow turns out to be a bad day, how much will we make loss?

19 20 Value at Risk (VaR) defined Value at Risk (VaR) defined (Con’t)

 A dollar measure of the minimum loss that would be  Equivalently, Value at Risk can be defined as the expected over a given time with a given probability. maximum loss that might be expected from holding a security or portfolio over a given period of time (say, a  Example: single day), given a specified confidence level.

 for at means that the firm VAR of $30,000 one day 5%  VAR of $30,000 for one day at 95% confidence level could expect to lose at least $30,000 over a one day means that the firm could expect to lose no more than period 5% of the time. $30,000 over a one day 95% of the time.

21 22

Calculating VaR (I) Historical method

 Historical method: Uses actual data from a recent historical  Three methods of estimating VAR period to determine the VaR.

(I): Historical Method (or Back Simulation approach)  Specifically, the historical method estimates the distribution of the portfolio’s performance by collecting data on the past (II): Analytical Method (or Variance/Covariance approach) performance of the portfolio and using it to estimate the future probability distribution. (III): Monte Carlo Simulation

23 24 Historical method (Con’t) Historical method: Example

 Collect a sample of actual daily prices (e.g., $US/Baht,  Today (19 Sep 2012), our portfolio consists of 10,000 barrels SET50 index, $US three-month interest rate, oil prices, etc..) of crude oil, and 20,000 shares of IBM stock.

over a given period of time, say 254 days.  On 19 Sep 2012, crude oil is now worth $100 per barrel, and  Revalue the portfolio based on those daily prices every day IBM $203 a share.

for the previous 254 days, and then compute daily portfolio  Therefore, our portfolio is currently worth returns  = (10,000 x $100) + (20,000 x $203)  Construct the histogram of portfolio returns and identify the  = $5,060,000 VaR that isolates the 5th percentiles of the distribution in the left-hand tail (e.g., about 13th lowest value of 254 days), if VAR is derived at the 95% confidence level.  What is the 5% daily VaR of our portfolio??

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Historical method (Con’t) Historical method (Con’t)

 For example, our  Sort from the lowest daily return to the highest daily returns. portfolio consists of 10,000 barrels of  Then locate the 13th observation (as a fifth percentile). That value crude oil, and 20,000 is the value below which 5% of the data lie. shares of IBM stock.

 Suppose such 13th observation is about 10%.

 For portfolio of $5.06 million, VaR at 5% is approximately a loss of 10% or $5,060,000(0.10) = -$506,000. Sort from the lowest to the highest returns  The portfolio would be expected to lose at least $506,000 in one day about 5 percent of the time (which is about once a month).

-252 -253 -254 27 28 Historical method – Advantages and Disadvantages Historical method – More examples

 Advantages:  Example1: A Thai bank has a long position in Japanese Yen of  Simplicity 30,000,000 and US dollar of 700,000. The current rates are  Does not require normal distribution of returns (which is a critical yen30/1Baht, and 35Baht/1USD. What is 1-day VAR at 5%? assumption for Analytical Method)

 Does not need correlations or standard deviations of individual asset returns.  Example2: A Thai investor currently holds 5,000 shares of PTT,  Disadvantage: 40,000 shares of BBL, and 10,000 shares of ADVAN. The  254 observations is not very many from statistical standpoint. current PTT share price is 280 baht, BBL 160 baht, and  However, increasing number of observations by going back ADVAN 300 baht. What is 1-day VAR at 1%? further in time is not desirable. That is, the greater the sample, the older are some of the data and the less reliable they become.

 It also is limited by the results of the chosen time period, which might not be representative of the future.

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Basic Stat Review revisited Basic Stat Review revisited (Con’t) Normal Distribution (x) vs  Histogram Standard Normal Distribution (z)  The height of 100 randomly selected Chula students  Normal distribution.

 The height of all people in Thailand (i.e., population)

x ሺݔ െ ߤሻ ݖൌ +3 +2 +1 0 -1 -2 -3 ߪ 31 32 Basic Stat Review revisited (Con’t) Basic Stat Review revisited (Con’t)

 Standard normal distribution  1) What proportion of Thai people have height of less than 155?  Table Z scores  z = (155-165)/3.5 = -2.86  P(z < -2.86) = 0.0021

 2) What proportion of Thai people have height between 163 and 170?  Assume the Thai people height is normally distributed with mean of 165 and standard deviation of 3.5. (where mean and SD are  z = (163-165)/3.5 = -0.57 and z = (170-165)/3.5 = +1.43 estimated from the sample 100 people).  P(-0.57 < z < +1.43) = 0.6393

 3) About 1% of Thai people have height of less than…???..cm  1) What proportion of Thai people have height of less than 155?  P(z < Z) = 0.01  z = -2.33  -2.33 = (x-165)/3.5  2) What proportion of Thai people have height between 160 and  x = 156.85 170?  4) About 5% of Thai people have height of less than…???..cm  3) About 1% of Thai people have height of less than…???..cm.  P(z < Z) = 0.05  z = -1.65  -1.65 = (x-165)/3.5  4) About 5% of Thai people have height of less than…???..cm.  x = 159.23

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VaR: Calculation idea of VaR VaR: Calculation idea of VaR (Con’t) For discrete probability:

 Idea behind VAR is to determine the probability distribution VAR at 5% is $3 million loss (e.g., normal distribution) of the underlying source of risk  there is a 5% probability (e.g., gold price, stock prices, oil price) and isolate the worst that over the given time period, the portfolio will lose given percentage (e.g., 1%, 5%) of outcomes. at least $3million

 Using 5% as the critical percentage, VAR will determine the For continuous distribution. 5 percent of outcomes that are the worst. The performance In a normal distribution, a 5% VAR at the 5 % mark is the VAR. occurs 1.65 standard deviations (z=1.65) from the expected value (i.e., mean). A 1% VAR occurs 2.33 standard deviations (z=2.33) from the mean.

35 36 (II) Analytical Method Analytical Method (Con’t)

 Example: suppose that a portfolio manager holds 20  For a weekly 5% VAR, convert the daily figures to weekly figures. million baht of PTT stock.  = 0.0476% x 5 = 0.238%  Volatility = 0.945% x = 2.113%.  PTT stock has an expected return (i.e., mean) of 0.0476% per day and volatility (i.e., SD) of 0.945% per day.  With a normal distribution, we have a weekly 5% VAR = 0.238 - 1.65(2.113) = -3.248%  What is daily 5% VaR for our portfolio???  So the weekly 5% VAR is 20,000,000(-3.248%) = -649,690 baht.

 In other words, the portfolio would be expected to lose at least  With a normal distribution, we have a daily 5% VAR = 0.0476 - 1.65(0.945) = -1.51% 649,690 baht in one week 5 percent of the time or one out of twenty weeks  So a daily 5% VAR is 20,000,000(-1.51%) = 302,300 baht.

 In other words, the portfolio would be expected to lose more than 302,300 baht in one day 5 percent of the time or one out of twenty days.

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Analytical Method (Con’t) Analytical Method (Con’t)

 1) What about monthly VAR at 5% ? 1) 0.0476%*22 – 1.65*0.945%*sqrt(22)  2) What about yearly VAR at 5% ? 2) 0.0476%*252 – 1.65*0.945%*sqrt(252) 3) 0.0476% – 2.33*0.945%

 3) What about daily VAR at 1% ? 4) 0.0476%*5 – 2.33*0.945%*sqrt(5)

 4) What about weekly VAR at 1% ? 5) 0.0476%*22 – 2.33*0.945%*sqrt(22)

 5) What about monthly VAR at 1% ? 6) 0.0476%*252 – 2.33*0.945%*sqrt(252)

 6) What about yearly VAR at 1% ?

39 40 Analytical Method: Two Assets Analytical Method: Two Assets Expected Return and SD of each asset

Consider the following two risky assets. There is a 1/3 chance of each state of the Note that stocks have a higher expected return economy and there are two assets than bonds and higher risk. Let us turn now to available - a stock fund and a bond fund. the risk and return a portfolio that is 50% invested in bonds and 50% invested in stocks.

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Analytical Method: Two Assets Analytical Method: Two Assets Variance of a Portfolio – 50% in each  Analytical method: Uses knowledge of the parameters (expected return and standard deviation) of the probability distribution and assumes a normal distribution.  VAR calculations require use of formulas for expected return and standard deviation of a portfolio: The method requires the input values (i.e., mean, SD, covariance) and any necessary pricing models along with an assumption of a normal distribution. The variance of the rate of return on the two risky assets portfolio is  where

 E(R1), E(R2) = expected returns of assets 1 and 2

 1, 2 = standard deviations of assets 1 and 2   = correlation between assets 1 and 2

 w1, w2 = % of one’s wealth invested in asset 1 or 2 where BS is the correlation coefficient between the returns on the stock and bond funds. 43 44 Analytical Method: n assets Analytical Method: Example of a two-asset portfolio Formula of Standard Deviation  Example: suppose that a portfolio manager holds two of a portfolio with n assets. distinct classes of stocks.

 $20 million of S&P 500 with expected return of 12% per year and (annualized) volatility of 15% and

 $12 million of Nikkei 300 with expected return of 10.5% per year and (annualized) volatility of 18%.

 Correlation between the Nikkei 300 and the S&P 500 is 0.55.

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Analytical Method: Example of a two-asset portfolio (Con’t) Analytical Method: Example of a two-asset portfolio (Con’t)

 Using the above formulas, the overall portfolio expected return is  For a weekly VAR, convert the yearly figures to weekly 0.1144 and volatility is 0.1425. figures.

 Expected return = 0.1144/52 = 0.0022 or 0.22% per week.

 Volatility = 0.1425/ = 0.0198 or 1.98% per week.

 With a normal distribution, we have a weekly VAR = 0.0022 - 1.65(0.0198) = -0.0305 or -3.05% per week.  With a normal distribution, we have a yearly VAR =  So the weekly VAR is $32,000,000(-0.0305) = -$976,000. 0.1144 - 1.65(0.1425) = -0.12073  In other words, the portfolio would be expected to lose at  So a yearly VAR is $32,000,000(-0.12073) = -$3,863,200. least $976,000 in one week 5 percent of the time or one out of  In other words, the portfolio would be expected to lose no more twenty weeks than $3,863,200 in one year 95 percent of the time or nineteen out of twenty years

47 48 Analytical Method: Example of a two-asset portfolio (Con’t) Analytical Method: calculation of parameters in practice

 What about monthly VAR with 99% confidence level?

0.1144/22 – 2.33*0.1425/sqrt(22)

 What about daily VAR with 99% confidence level?

0.1144/252 – 2.33*0.1425/sqrt(252)

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Analytical Method – VaR for Fixed Income Analytical Method – VaR for Fixed Income Securities Securities

 For example, a bank wants to know its market risk in terms  Suppose that a bank has a $1 million market value position in of 1-day VAR. 7-year zero-coupon bonds with a market value of $1,000,000.  Today’s yield on these bonds is 7.243% per year. And we define  1-day VAR = dollar market value of position × price sensitivity × potential adverse changes in yield “bad” yield changes such that there is only 5% chance of the yield change being exceeded in either direction.  where price sensitivity = (-Modified Duration)  Assuming normality, 90% of the time yield changes will be within  If we assume that yield changes are normally distributed, we 1.65 standard deviations of the mean. can construct confidence intervals around the expected value.  If the yield change has a standard deviation is 10 basis points (and  Assuming normality, 90% of the time the yield changes will be within 1.65 standard deviations of the mean. mean is zero), this corresponds to 16.5 basis points.

51 52 Analytical Method – VaR for Fixed Income Analytical Method – VaR for Equity Portfolios Securities  VaR for equity portfolios  Assume that the modified duration of the bond is 6.527. (Since bond is zero-coupon, D = 7 years, MD = D/(1+R) = 7/(1+0.07243) = 6.527,  For equities, if the portfolio is well diversified then where Modified duration = Maculay duration/(1+R)

 1-day VAR VaR = dollar value of position × stock market return volatility

= (Market value of position)  (-MD)  (Potential adverse change in where the market return volatility is taken as 1.65 M at 5%

yield) where M the volatility of the returns of the (e.g., = ($1,000,000)  (-6.527)  (0.00165) S&P500, SET index) = ($1,000,000)  -1.077% = -$10,770  Suppose the bank holds a 1 million baht trading position in 100 stocks β  To calculate the potential loss for more than one day: listed on SET. Empirically, the 100-stock portfolio has a of 1.1. What is 1-day VaR and 5-day VaR?  (VARN) = 1-day VAR × N  VaRP = β .VaRM since P = β . M  Example:  5-day VaR = 5 x 1-day VaR  For a five-day period, VAR5 = -$10,770 × 5 = -$24,082

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Analytical Method – VaR for Equity Portfolios (III) Monte Carlo Simulation Method

 VaR for equity portfolios  Monte Carlo Simulation method

 Inputs on the expected returns, standard deviations, and correlations  Suppose the bank holds a 1 million baht trading position in 100 stocks listed on SET. Empirically, the 100-stock portfolio has a β of 1.1. What is for each security are required. 1-day VaR at 5% and 5-day VaR at 5%?  Make sure that the portfolio’s returns properly account for the correlations among the securities in the portfolio (i.e., one set of  Suppose that M is empirically estimated to be 1.58% per day. returns can be generated but the other set of returns must reflect any correlation between the two sets of returns.  VaRP = 1.1 x VaRM since P = 1.1 x M  To obtain the VAR, Monte Carlo simulation generates random  P = 1.1 x 1.58% = 1.738% outcomes based on an assumed probability distribution.  1-day VaR at 5% = 1.65 x 1.738% x 1,000,000 baht = 28,677 baht  Benefits: flexible  allow the user to assume any known probability  5-day VaR at 5% = 5 x 1-day VaR at 5% = 5 x 28,677 = 64,123 baht distribution and can handle relatively complex portfolios.

 Disadvantages: computer-intensive.

55 56 A Comparison of Analytical vs Historical A Comparison of Analytical vs Historical (con’t)  Suppose we have a portfolio of 1,000 troy ounce of 99.5% gold. VaR – 5% Analytical Historical  VaR 1% is (always)  The current price (as of 20 Sep 2013) of gold is 1,349.25. So our 1 year 29,136 25,312 higher than VaR 5%. gold position is now $1,349,250. 3 years 26,830 25,607  For 1% VaR,  A sample of daily prices of gold for the past five years is 5 years 29,637 27,873 Historical method provided. gives higher VaR numbers than VaR – 1% Analytical Historical Analytical method 1 year 40,590 44,805  Compute VaR using Analytical vs Historical methods… see does. Excel sheet attached.. 3 years 37,966 44,686 5 years 42,090 51,693

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A Comparison of Analytical vs Historical: Two A Comparison of Analytical vs Historical: Two assets assets(Con’t)

 As of today (i.e., 20 Sep 2013), we have a portfolio consisting of the following assets; Analytical Historical  A group of stocks, which have a beta of 1, using DJIA as a market VaR – 5% 36,084 36,683 portfolio. The current market value (as of the end of 20 Sep 2013) is $1,500,000. VaR – 1% 51,265 58,410

 1,000 ounces of gold, in which its current value (as of 20 Sep 2013) $1,349,250 (=1,000x1,349.25).

 A sample of daily prices of DJIA index and gold for the past three years is  Again, VaR 1% is (always) higher than VaR 5%. provided.  For 1% VaR, Historical method gives higher VaR numbers than Analytical method does.  Compute VaR using Analytical vs Historical methods… see Excel sheet attached..

59 60 A Comparison of the Two Methods A Comparison of the Two Methods

Key considerations: Key considerations: (con’t)

 VaR is a number that is quite sensitive to how it is calculated.  Always follow up the calculation with an ex post evaluation,  Wide ranges such as this are therefore common. called “back testing”.  Even more variation if our data is collected over different time  For example, if we settle on a VaR of 540,000, this figure should be periods, or over different frequency (weekly or monthly instead of daily). exceeded NO more than 5% of the time.

 A wide range of VaR numbers does not mean VaR is useless or  Over a long period of time, the risk manager can determine whether unreliable. such VaR figure is a reasonable reflection of the true risk. That is, if

 Instead, knowing the potential range of VaR is itself very useful. the $540,000 VaR is exceeded far more or less than 5% of the time, the figure was not a good estimate, and the methodology used to compute VaR should be re-evaluated.

61 62

Benefits of VaR Extensions of VaR  Benefits of VaR  Stress testing

 Widely used by nearly every major (derivatives) dealer and an increasing  Stress testing involves estimating how the portfolio would have performed number of end users. under some of the most extreme market moves.

 Facilitates communication with senior management. A VaR number  In other words, a stress test determines how badly the portfolio will perform conveys a lot of useful information that the CEO can easily grasp. under some of the worst and most unusual circumstances.

 Acceptable in banking regulation. Most banking regulators use VaR as a  To test the impact of an extreme movement, let’s presume that in a given measure of the risk of a bank. day markets perform terribly.

 Used to allocate capital within firms.  Consider the portfolio of $20 million in the S&P500 and $12 million in the Nikkei300.  Banks engaged in significant trading activities commonly use VaR as a measure to allocate capital, that is, they set aside a certain amount of  Let us presume that in a given day both markets perform terribly, for capital to protect against losses. example, with S&P500 losing 6% (roughly 6 SD) and Nikkei300 losing 5% (also roughly 6 SD).  Used in performance evaluation.  Then a total loss for the portfolio will be 5.625% or $1.8 million.  The modern approach to performance evaluation is to adjust the return performance for a measure of the risk taken in achieving that performance.  If the performance is tolerable under such extremely unlikely situations, VaR is often used as a measure of risk in this context. then the portfolio risk is assumed to be acceptable.

63 64 Extensions of VaR

 Stress testing can be considered as a way of taking into account extreme events that do occur form time to time but that virtually impossible according to the probability distribution typically assumed for market variables.

 A 5-standard-deviation daily move in a market variable is one such extreme event.

 Under the assumption of a normal distribution, it happens about once every 7,000 years! But, in practice, it is not uncommon to see a 5-standard-deviation daily move once or twice every 10 years.

 Stress testing can be quite valuable as a supplement to VaR.

 Therefore, one major advantage of the stress testing is that it could cover situations commonly absent from the historical data.

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