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Market risk interview questions

Q1 What is the definition of VAR (Value At Risk)?

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. This metric is most commonly used by investment and commercial banks to determine the extent and probabilities of potential losses in their institutional portfolios.

Q2 What are the different VAR calculation and VAR's advantage / disadvantages?

There are three main ways of computing VaR: the historical method, the variance-covariance method, and the Monte Carlo method.

Historical Method:

The historical method looks at one’s prior returns history and orders them from worst losses to greatest gains—following from the premise that past returns experience will inform future outcomes.

Variance-Covariance Method:

Rather than assuming that the past will inform the future, the variance-covariance method, also called the parametric method, instead assumes that gains and losses are normally distributed. This way, potential losses can be framed in terms of standard deviation events from the mean.

The variance-covariance method works best for risk measurement in which the distributions are known and reliably estimated. It is less reliable if the sample size is very small.

Monte Carlo Method:

A third approach to VaR is to conduct a Monte Carlo simulation. This technique uses computational models to simulate projected returns over hundreds or thousands of possible iterations. Then, it takes the chances that a loss will occur—say, 5% of the time—and reveals the impact.

The Monte Carlo method can be used with a wide range of risk measurement problems and relies upon the assumption that the probability distribution for risk factors is known.


Advantages of Value at Risk (VaR):

There are several advantages to using VaR in risk measurement:

  1. It is a single number, expressed as a percentage or in price units, and is easily interpreted and widely used by financial industry professionals.

  2. VaR computations can be compared across different types of assets—shares, bonds, derivatives, currencies, and more—or portfolios.

  3. Thanks to its popularity, VaR is often included and calculated for you in various financial software tools, such as a Bloomberg terminal.

Disadvantages of Value at Risk (VaR)

One problem is that there is no standard protocol for the statistics used to determine asset, portfolio, or firm-wide risk. Statistics pulled arbitrarily from a period of low volatility, for example, may understate the potential for risk events to occur and the magnitude of those events. Risk may be further understated using normal distribution probabilities, which rarely account for extreme or black swan events.

Another disadvantage is that the assessment of potential loss represents the lowest amount of risk in a range of outcomes. For example, a VaR determination of 95% with 20% asset risk represents an expectation of losing at least 20% one of every 20 days on average. In this calculation, a loss of 50% still validates the risk assessment.

The financial crisis of 2008 that exposed these problems as relatively benign VaR calculations understated the potential occurrence of risk events posed by portfolios of subprime mortgages. Risk magnitude was also underestimated, which resulted in extreme leverage ratios within subprime portfolios. As a result, the underestimations of occurrence and risk magnitude left institutions unable to cover billions of dollars in losses as subprime mortgage values collapsed.

Q3 What is the absence of arbitrage opportunity?

The absence of opportunities to earn a risk-free profit with no investment. The essential idea of arbitrage is the purchase of a good in one market and the immediate resale, at a higher price, in another market. If both the purchase and sale prices are known then the resulting profit is risk free. The absence of arbitrage ensures that markets are in equilibrium. 

Q4 How would you interpret the daily, 90% confidence level, value at risk of a portfolio is $100,000?

It could be interpreted as either of the following:

a) 9 out of 10 times, the value of the portfolio will lose less than $100,000.

b) 1 out of 10 times, we would expect the portfolio to lose $100,000 or more.


Q5 From the following given options, determine those that may be classified as ‘ linear ‘ or even ‘ near linear ‘.

i) Swaps

ii) Forwards

iii) Futures

iv) Options

Swaps, forwards and futures can be considered as linear but it is not the case for options.

Q6 What is copula?

Copula “ is a statistical measure that represents a multivariate uniform distribution, which examines the association or dependence between multiple variables. Although the statistical calculation of a copula was invented in 1957, it was not applied to financial markets and finance until the late 1990s.

Q7 What are the challenges in calculating VaR for a mixed portfolio?

Need to measure not only return and volatility of individual assets, but also the correlations between them. When the number and diversity of positions grow, the difficulty and cost of measuring risk grows exponentially.

Q8 What's GVAR? How can you calculate it?

The Global VAR is an econometric model used to analyze the relationships between multiple time series variables from various countries or regions on a global scale. It is commonly employed in macroeconomic and financial research to study the interdependence and spillover effects between different economies.

The Global VAR model is an extension of the standard VAR model, which is widely used for time series analysis. In a Global VAR model, variables from multiple countries or regions are incorporated into a single system, allowing for the examination of cross-country interactions and responses to shocks or changes in economic variables.

The process of calculating the Global VAR model involves the following steps:

  1. Data Collection: Gather time series data for the selected variables of interest from different countries or regions.

  2. Data Preprocessing: Ensure that the time series data are stationary or transform them to make them stationary (e.g., by taking first differences).

  3. Model Specification: Decide on the number of lags (time periods) to include in the model and the appropriate variables to be included in the system.

  4. Estimation: Estimate the parameters of the Global VAR model using techniques like ordinary least squares (OLS) or Bayesian methods.

  5. Impulse Response Analysis: Analyze the responses of each variable to shocks in other variables or to exogenous factors.

  6. Granger Causality Test: Perform causality tests to determine if there are significant causal relationships between the variables.

  7. Forecasting and Policy Analysis: Use the estimated Global VAR model for forecasting future values of the variables and conducting policy analysis under different scenarios.

It's worth noting that the Global VAR model can be complex and computationally intensive, especially when dealing with a large number of countries or variables. Advanced econometric software packages are typically used to estimate and analyze Global VAR models effectively.

Q9 What do you know about extreme value theory?

Extreme Value Theory (EVT) is a branch of statistics that deals with the modeling and analysis of extreme events or rare occurrences. These events are characterized by being far from the central tendency of a dataset and are of interest because they can have significant impacts in various fields, such as finance, engineering, environmental sciences, and insurance.

The key focus of extreme value theory is on the tail of the distribution of a dataset, as it aims to estimate the probabilities of extreme events happening beyond the range of observed data. EVT is particularly relevant when traditional statistical methods are insufficient due to the scarcity of extreme observations.

There are three main types of extreme value distributions that EVT deals with:

  1. Gumbel Distribution (Type I): The Gumbel distribution is often used for modeling the maximum or minimum values of a dataset. It is also known as the "double exponential distribution" and is widely used for modeling the upper tails of distributions.

  2. Fréchet Distribution (Type II): The Fréchet distribution is suitable for modeling the right tail of a dataset. It is used when the tail is heavier than that of the Gumbel distribution.

  3. Weibull Distribution (Type III): The Weibull distribution can be used to model both the right and left tails of a dataset. It is a versatile distribution that can take on various shapes.


The practical application of extreme value theory involves identifying an appropriate extreme value distribution for a dataset and estimating its parameters using statistical techniques. One of the fundamental results in EVT is the Generalized Extreme Value (GEV) distribution, which encompasses the three main types mentioned above.

EVT finds applications in diverse fields, including:

  1. Finance: EVT is used to model extreme market events (e.g., stock market crashes) and estimate Value at Risk (VaR) for risk management purposes.

  2. Environmental Sciences: EVT is used to assess and predict extreme weather events, such as hurricanes, floods, and heatwaves.

  3. Engineering: EVT is applied to study the occurrence of rare and extreme failures in engineering structures, like bridges and dams.

  4. Insurance: EVT is used to estimate the tail risk for insurance companies, helping them to set appropriate premiums and reserves for extreme events.


Overall, extreme value theory plays a crucial role in understanding and quantifying extreme events, which are often of paramount importance in decision-making and risk management in various domains.

Q10 What is Expected Shortfall? How is it calculated? Why is it considered better than VaR? What are the disadvantages?

Expected Shortfall (ES), also known as Conditional Value at Risk (CVaR), is a risk measure used in finance and risk management to quantify the potential losses of an investment or portfolio beyond a specified Value at Risk (VaR) level. While VaR provides an estimate of the maximum loss at a given confidence level, Expected Shortfall goes further by measuring the average loss that would occur in the tail of the distribution, specifically for the worst outcomes.

Calculation of Expected Shortfall:

  1. Compute the VaR at a desired confidence level (e.g., 95% or 99%). VaR represents the threshold below which the losses are quantified.

  2. Identify all the losses that exceed the VaR value.

  3. Calculate the average of these extreme losses. This average is the Expected Shortfall.

Reasons why Expected Shortfall is considered better than VaR:

  1. Tail Sensitivity: VaR only considers the magnitude of potential losses beyond a certain threshold, while Expected Shortfall also considers the severity of those losses. It provides more information about the tail risk, making it sensitive to extreme events.

  2. Coherence: Expected Shortfall satisfies the property of coherence, which means it is a sub-additive risk measure. In simpler terms, the ES of a portfolio is always less than or equal to the sum of ES values of its individual components. This property ensures consistency and allows for better risk aggregation across different assets or portfolios.

  3. Risk Management: Expected Shortfall provides a more conservative estimate of potential losses during extreme market conditions. It is particularly useful for risk management as it better captures the tail risks that VaR may overlook.


Disadvantages of Expected Shortfall:

  1. Additional Complexity: Calculating Expected Shortfall requires additional computational effort compared to VaR, especially when using historical simulation or Monte Carlo methods.

  2. Data Requirements: Accurate estimation of Expected Shortfall relies on having sufficient historical data, particularly extreme losses. In markets with limited historical data or infrequent extreme events, the estimation can be less reliable.

  3. Sensitivity to Tail Behavior: Expected Shortfall is sensitive to the tail behavior of the underlying distribution. Small changes in extreme observations can lead to significant variations in the calculated ES.

  4. Non-Convexity: The optimization process involving Expected Shortfall may lead to non-convex problems, making it harder to find unique solutions.


Despite these drawbacks, Expected Shortfall remains a valuable tool for risk managers, especially in contexts where capturing extreme tail risk and ensuring risk coherence are critical for decision-making and risk assessment. It is essential to choose the appropriate risk measure based on the specific characteristics of the investment or portfolio and the underlying market conditions.

Q11 What is incremental default risk?

Incremental default risk refers to the additional risk of default that arises when adding a new exposure or credit exposure to a portfolio. In other words, it measures the impact on the portfolio's overall risk if a new credit instrument or counterparty is introduced.

In the context of credit risk management, when a financial institution extends credit to a borrower or enters into a new financial contract with a counterparty, it introduces a potential default risk into its portfolio. The incremental default risk helps assess the change in the portfolio's credit risk due to this new exposure.

The concept of incremental default risk is important for several reasons:

  1. Risk Assessment: Financial institutions need to evaluate the creditworthiness of new borrowers or counterparties before extending credit or entering into transactions. By assessing the incremental default risk, they can determine if the new exposure aligns with their risk appetite and risk management strategies.

  2. Capital Allocation: Regulatory frameworks, such as Basel Accords, require financial institutions to set aside a certain amount of capital to cover potential credit losses. Accurate measurement of incremental default risk helps in appropriate capital allocation for the new exposure.

  3. Portfolio Diversification: Understanding the incremental default risk can help financial institutions maintain a well-diversified portfolio. Adding exposures that have low correlation with existing portfolio components may lead to better risk-adjusted returns.

  4. Stress Testing: In stress testing scenarios, where extreme market conditions are simulated, financial institutions can analyze the impact of potential default events on the overall portfolio by considering incremental default risk.


To calculate incremental default risk, financial institutions typically employ various credit risk models, such as credit rating models, credit default models, or stress testing approaches. These models use historical data, credit ratings, financial ratios, and other relevant factors to estimate the probability of default and potential loss given default for the new exposure.

It's important to note that the incremental default risk is just one aspect of credit risk management. Financial institutions also consider other factors, such as exposure size, credit rating, recovery rate, and overall portfolio diversification, to make informed decisions regarding credit extensions and risk mitigation strategies.

Q12 What are the uses of the yield curve?

The yield curve is a graphical representation of the interest rates of bonds or fixed-income securities with varying maturities. It shows the relationship between the interest rate (or yield) and the time to maturity for a set of bonds issued by the same entity but with different maturity dates. The yield curve is an essential tool in finance and economics, and it serves various uses:

  1. Interest Rate Analysis: The yield curve provides insights into the prevailing interest rate environment. By observing the slope and shape of the curve, analysts can assess whether interest rates are rising, falling, or remaining stable. Changes in the yield curve can signal shifts in monetary policy, inflation expectations, and economic conditions.

  2. Economic Indicator: The yield curve is often considered a leading economic indicator. An upward-sloping or steep yield curve typically indicates an expansionary economic environment, while a downward-sloping or inverted yield curve may signal an impending economic slowdown or recession.

  3. Forecasting Interest Rates: Investors and financial institutions use the yield curve to forecast future interest rates. For example, the shape of the curve can indicate market expectations of future rate changes, helping investors make decisions regarding bond investments, loans, and other interest-sensitive financial instruments.

  4. Valuation of Bonds: The yield curve is used to price and value bonds. By comparing the yield of a specific bond to the corresponding yield on the yield curve, analysts can assess whether the bond is trading at a premium (yield lower than the curve) or a discount (yield higher than the curve).

  5. Risk Assessment: The yield curve helps in assessing the credit risk and overall health of the economy. A flat or inverted yield curve might imply a higher perceived risk of default, while a steep yield curve could indicate a stronger economic outlook.

  6. Monetary Policy Decisions: Central banks often monitor the yield curve as part of their monetary policy analysis. An inverted yield curve (short-term rates higher than long-term rates) may prompt central banks to adjust their interest rates to influence economic growth and inflation.

  7. Asset Allocation Strategies: Investors use the yield curve to determine their asset allocation strategies based on the risk and return expectations of different maturities. For example, in a steep yield curve environment, investors may prefer longer-term bonds for potentially higher yields.

  8. Yield Curve Spreads: Analyzing the spreads between different segments of the yield curve (e.g., 2-year and 10-year spread) can provide valuable information about market sentiment and expectations for economic growth and inflation.


Overall, the yield curve is a versatile tool that offers valuable insights into the current and future state of the economy and the financial markets. Investors, policymakers, central banks, and analysts use the yield curve in a wide range of applications to make informed decisions and assess risk and return dynamics in the financial world.

Q13 What's the riskiest part of the yield curve?

The riskiest part of the yield curve is typically the segment associated with the longest maturities, often referred to as the "long end" of the yield curve. This refers to the yields on bonds or fixed-income securities with longer time to maturity, such as 10-year, 20-year, or 30-year bonds.

There are a few reasons why the long end of the yield curve is considered riskier:

  1. Interest Rate Risk: Bonds with longer maturities are more sensitive to changes in interest rates. When interest rates rise, the prices of existing bonds with longer maturities tend to fall more significantly than those with shorter maturities. This sensitivity is known as interest rate risk, and it increases as the time to maturity lengthens.

  2. Inflation Risk: Longer-term bonds are exposed to higher inflation risk because inflation erodes the purchasing power of future interest payments and principal repayment. If inflation rises faster than expected, the real return of long-term bonds could be negatively affected.

  3. Market Volatility: The long end of the yield curve can experience higher volatility compared to shorter maturities. Market sentiment, economic conditions, and geopolitical factors can cause significant fluctuations in long-term yields.

  4. Liquidity Risk: Long-term bonds may have lower liquidity, making it harder to find buyers or sellers at desirable prices, especially during periods of market stress.

  5. Reinvestment Risk: For bond investors who rely on periodic interest payments, the long end of the yield curve poses reinvestment risk. When interest rates decline, the interest income from maturing bonds may be reinvested at lower rates, reducing overall returns.

  6. Economic Uncertainty: Long-term bonds are more exposed to uncertainty and changes in economic conditions over extended periods. Economic conditions can shift significantly over time, affecting the performance of long-term investments.


Despite these risks, the long end of the yield curve also offers the potential for higher yields and returns compared to shorter maturities. Investors who can tolerate the additional risks may be attracted to longer-term bonds as part of a diversified investment strategy.

It's essential to note that risk perception can vary among investors, and individual risk preferences play a crucial role in determining suitable investment choices along the yield curve. For some investors, the long end may be perceived as riskier, while others may view it as an opportunity for potentially higher returns in their investment portfolios. As with any investment decision, it's crucial for investors to consider their financial goals, risk tolerance, and investment time horizon when selecting investments along the yield curve.

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