Financial Institutions - Chapter 15: Market Risk

What is market risk?

The risk of losses in on and off-balance-sheet positions arising from movements in market prices.

What are the two types of market risk?

1. Systematic risk

2. Unsystematic risk

What is systematic risk?

The risk that impacts the entire market, not just one company. It can be measured with beta.

What is unsystematic risk?

Risk specific to one company or a small group of companies. For example, a company and it’s suppliers or customers. This type of risk can be reduced or eliminated through diversification unlike systematic risk.

Briefly explain the two categories OFSI uses to separate the banks assets and liabilities

1. Trading book: Financial instruments the bank buys to sell soon or to make money from quick price changes. Instruments are heavily subjected to market risk

2. Banking book: Mainly loans and deposits that are usually held until maturity, not subjective to much market risk.

What assets and liabilities are held in the banking book?

• Assets: Cash, loans, premises and equipment and other illiquid assets

• Liabilities: Deposits, capital and other illiquid borrowed funds

What assets and liabilities are held in the trading book?

• Assets: Bonds (long), commodities (long), FX (long), equities (long) mortgage backed securities (long), derivatives (long)

• Liabilities: Bonds (short), commodities (short), FX (short), equities (short) and derivatives (short)

Define value at risk (VaR)

Value at risk measures the worst expected loss over a given horizon, under normal market conditions at a given confidence level.

What does it mean when a bank says that the daily VaR of its trading portfolio is $35 million at the 99% confidence level?

There is a 99% chance that over the next day the maximum loss on this portfolio is $35 million under normal market conditions.

Why is VaR an important industry benchmark for risk?

It measures an important aspect of risk, specifically, how bad thinks can get with a certain probability. It summarizes downside risk in one value.

How is VaR used?

• Information reporting: Communicating the risk of a certain portfolio or multiple portfolios

• Controlling risk: Can be used to set position limits for traders. For example, traders can make trade any trades they want as long as their VaR doesn’t go above a set limit

• Managing risk: Used to allocate capital and adjusting returns for risk

Who uses VaR as a benchmark risk measure?

• Financial Institutions

• Regulators

• Non financial corporations

Briefly explain the two parameters of VaR

1. Confidence level: Regulators require banks to report their VaR computed at a 99% confidence level.

2. Horizon: In general, the horizon matches the average period for major portfolio rebalancing.

When is the square root rule applicable for converting VaR

If returns are independent and identically distributed under normal distribution. There must be no correlation between returns and they all must come from the same distribution.

What are the three methods of measuring VaR

1. Parametric method

2. Historical simulation method

3. Monte carlo method

Briefly explain how the parametric method is used to measure VaR

This method assumes a normal distribution. In this case, the VaR calculation uses the market value of the portfolio, the mean and standard deviation based on historical data and the lower standard normal deviate that corresponds to the confidence level.

What is alpha for a 95% and 99% confidence level

• 95% = -1.65

• 99% = -2.33

How do you determine the VaR of a portfolio

In order to aggregate the VaRs from individual exposures we must compute the correlation matrix. The VaR of the portfolio will be less than the sum of individual VaRs if there are diversification benefits.

What are the advantages of the parametric method

• Easy to implement as it only uses the mean and standard deviation

• Computationally fast

What are some drawbacks to the parametric method

• Assumption of normality

• Assumption that variables are independent (not correlated)

Briefly explain the historical simulation method of measuring VAR

This method looks at historical data over the last 250 days and applies current weights to a time-series of historical returns

What are some advantages of the historical simulation method?

• Simple to implement

• Unlike the parametric method, it can’t account for fat tails (when the actual distribution has fatter tails than the normal distribution)

• Don’t have to calculate the correlations or standard deviations of returns since they are implicit in the data being used

What are disadvantages of the historical simulation method?

• Assumes a sufficient history of price changes

• Only one sample path is used

• It becomes difficult to use for large portfolios

• There may not be enough extreme events for estimatation

Briefly explain the Monte Carlo simulation method of measuring VAR

In this method, you will have to make assumptions about the random way financial variables change overtime and simulate fictitious price paths for all variables of interest. The portfolio is marked-to-market and each of these realizations are used to compile a distribution of returns.

What are the advantages of the Monte Carlo simulation method

• It’s the most sophisticated method and commonly used by the large banks

• Works for any distribution and non-linear securities

• Generates the entire distribution, not just one quantile

What are the drawbacks of the Monte Carlo simulation method

• Requires computer time and a good understanding of stochastic processes

• Must be robust as it’s subject to model risk

Is VaR a measure or estimate?

An estimate, based on a certain confidence level. It depends on the method used and underlying assumptions, therefore, the value is uncertain.

How did regulators address the uncertainty of VaR estimates

They introduced the requirement for back testing and stress testing

What is back testing?

A statistical framework that consists of verifying that actual losses are in line with projected losses. Involves comparing the VaR forecasts with their associated portfolio returns.

What happens if an institutions fails back testing?

if a model fails more than the expected number of times, then the regulator will require a higher capital level. There will be a penalty that will take into account the back testing results

What is stress testing?

Assuming extreme scenarios to identify potential areas of vulnerability, that goes beyond the normal losses measured by VaR. For example, what will be the value of my portfolio if the stock market crashes by x percent.

What are the limitations of the VaR measure?

• It doesn’t provide a measure of absolute loss.

• It doesn’t describe the losses in the left tail.

• It assumes that the portfolio remains the same over the horizon

• There’s no economic theory behind how VaR parameters are chosen

• It’s measured with some error

• It’s not sub-additive (the risk measure can overstate the risk of the combined portfolio)

• Black swan - events that are very hard to predict, and if they occur consequences are severe.

Regulators introduced another measure of market risk, what is it?

Expected short fall. This accounts for the average of losses once you surpass the VaR. The expected loss conditional for the left side of the data.