Crash Course in Risk Management
By: Harel Jacobson
Tags: Risk Management, Trading, Quantitative Finance, Derivatives, Volatility

In this post, I’m going to wear the risk manager hat, as it seems like a good opportunity to put my FRM certification to use, and share my knowledge of risk management, trade life cycle, and financial markets.

Everyone who trades in financial markets knows that trading involves risk. Risk is the cost of the chase for returns and yield, and every trader takes some kind of risk when doing so. Obviously, this statement didn’t knock you off your seat, but risk management as a whole is much more than what we, as traders, perceive as risk.

As practitioners (traders, portfolio managers, investors) we mainly focus on “market risk”. Market risk is the risk associated with the market condition (and the underlying asset price dynamic and its derivatives), but as any professional risk manager will tell you, risk management covers a wider array of risks, many of which we rarely think about.

Generally speaking, Risk Management can be broken into three types of risk:

Market Risk Operational Risk Counterparty/Credit Risk

Market Risk

Market risk is probably somewhat intuitive to us. When carrying out positions we are exposed to many risks associated with the underlying assets that we trade (direction, volatility, correlation, etc.). Any practitioner knows the risks he/she is exposed to (directional risk, volatility/skew/ correlation, and basis risk are only a few examples of market risk), so it’s relatively easy to quantify these risks and manage them.

When we run the day-to-day risk of our position we usually use some matrices/methods to quantify our risks (usually the risk of drawdowns, as we happily live with upside risk to our P&L). Option traders like myself will mostly use the option’s greeks (and I must admit that my default set of greeks doesn’t go beyond 2nd order — Gamma/Vanna/Volga), and some kind of spot/vol matrix to test different scenarios of spot/vol shift.

A typical Delta matrix (x-axis = vol level, y-axis = spot level) of a Long 1-month EURUSD 1.20 Call.

On the portfolio level, most practitioners (and risk managers in particular) will use Value-at-Risk (VaR) to assess the downside shock to the P&L of the portfolio (given a pre-defined confidence level).

There are three widely used methods to calculate VaR:

Delta-Normal VaR Historical VaR Monte Carlo Simulation

Delta-Normal VaR

Delta-Normal VaR is, by far, the simplest and easiest way to assess VaR. The idea behind this method is that under the assumption of normal distribution of log-returns, we can assess the potential drawdown given two inputs :

Standard Deviation (Volatility) Confidence Level

Given that we have a good estimation of our portfolio’s volatility (to read more about realized volatility estimation check out my write up) and the confidence level that we choose (most risk models will use a 95% confidence level), we can assess the maximum loss in an adverse scenario. From the calculation standpoint the computation is pretty straightforward:

Credit: Fernando Caio Galdi, L.M Pereira

We take our standard deviation and multiply that by the inverse standard normal distribution. For example: Assuming our volatility is 16% (or 1% in 1-day volatility terms), and our confidence level is 95%, our one-day VaR will be roughly -1.65%.

Obviously, this method fails to capture fat tails and skewed distribution, which is why most practitioners refrain from using it.

Historical VaR

Unlike Delta-Normal VaR, Historical VaR uses actual (historical) distribution to compute the likely drawdown. Obviously, this method is sensitive to the lookback window of returns (same as any volatility measure), but given that we make no assumption regarding the distribution we can capture the true dynamic of the asset/portfolio.

Let’s look at the following example: The only holding in our portfolio is TESLA stock, and we would like to assess the 95% 1-day VaR. We use the 1-year window of returns, as we believe that this window reflects the “true” distribution of returns. Under that assumption, our 95% 1-day VaR is -7.7%. This means that the maximum loss will exceed (given our confidence level) is 7.7%, based on historical returns.

The biggest pitfall of Historical VaR is that our sample might be biased due to the market regime which is being sampled. Extremely calm/volatile periods can skew our VaR assessment.

Monte Carlo Simulation

Monte Carlo Simulation is probably one of the most powerful tools used in quantitative finance, and as such, it is widely used as the VaR method. In short, Monte Carlo simulation is essentially generating a large number of random price paths (given a defined distribution, with a mean and standard deviation). The strength of MC simulation lies in its ability to estimate the risk of non-linear products, and path-dependent products. MC simulation can be used to address the complex relationships between securities.

MC Simulation (1-day, vol = 16% , paths=500 , steps = 1000)

Unlike other VaR methods, MC simulation allows us to calculate multi-period VaR. For example, if we want to calculate 1-week VaR, we can draw path x5 longer than our 1-day VaR to simulate a 5-day price path.

Despite being the most flexible and robust, it is the slowest to compute, as it requires us to simulate thousands of paths to calculate the VaR. As our portfolio grows, the calculation time grows exponentially, so one needs a well-written algorithm to efficiently calculate VaR using MC simulation.

Operational Risk

Operational Risk is often being overlooked by practitioners, as it’s the unsexy side of risk management, which deals with technical aspects of trading (execution, post-trade lifecycle, and settlement).

Most traders/ portfolio managers don’t like to deal with OpRisk because they believe that alpha is being created prior to the execution of the trade (research, analysis, model/algo development, etc..), and I do tend to agree with that, but understanding OpRisk and the potential risks that can arise from the moment we trade until the trade is actually settled can make a huge difference between profit and loss.

We can breakdown OpRisk into three potential risk pillars:

Trade Execution Post-Trade (trade lifecycle) Backoffice and cashflow

Trade Execution

A lot can go wrong when we execute our trade(s). Our trade execution is the link between our research/model and actually running the risk of it. Anything from faulty execution to price slippage can occur the moment we execute our trade. Let’s take the following examples to explain execution risk and the importance of proper execution risk management:

Fat Finger is probably the most common trading error most traders encounter. I reckon that any trader had at least one (or two) incidents of trading error (could be anything from trading the wrong side to trading the wrong asset or price). We could say that Fat Finger error is part of the trading game, but it is, in fact, an operational risk (which tends to be costly and adds up to our overall costs).

One of the most famous cases of execution error is the case of Knight Capital. Back in 2012 Knight Capital was one of the leading market-making firms in the US equity market (with a market share of about 17% on the NYSE/NASDAQ). On Aug 1, 2012, the firm’s trading algorithm suffered a severe malfunction (after a failed midweek software update, I kid you not). This “small” error caused a whopping $440 million loss for Knight Capital (and eventually forced them to be acquired by Getco). I guess somewhere in the world there is an IT technician still banging his/her head against the wall saying “Always debug your code before running in production!”

Knight Capital emphasizes the sheer loss that can occur due to faulty execution, which is why many firms and traders put a lot of effort in placing fail-safe to minimize execution errors.

Post-Trade (Trade Life Cycle)

The moment we execute our trade, we initiate a chain of events that ensures our trade is accepted by our counterparty and settled correctly. This chain of events is called the “Trade Life Cycle”. A Post-Trade process is a well-oiled machine that ensures trades are sent, margined, confirmed, cleared, and settled correctly, and that trades don’t get lost along the way (from the moment we place our order until the moment the trade is settled). The Trade Life-Cycle has seven stages from the moment we execute our trade until it’s settled:

Order execution — The client’s order is received by the front office sales desk of the broker/dealer. The order is fed (either via e-platform by the client, or by the sales trader) to the firm’s risk/middle office systems. Risk Management —Once fed into the risk management system, the order is being assessed for margin and available equity in the account to withstand the risk level. After all, checks are done and cleared the trade is sent to the exchange. Matching at the exchange — After the trade is sent to the exchange it’s placed in the exchange order book, waiting for a match on the other side. Once a matching order is available, the client’s order is matched against that. Trade made — A new trade is born, now the exciting stage of post-trade begins with the exchange sending both parties’ brokerage firms a confirmation of the trade (so they could inform their clients). Trade confirmation — Now that the trade is done, both parties need to confirm the trade’s details in order for the process to continue. Without a matching of the details from both sides the trade will not be able to be processed to clearing at the clearinghouse. Usually, trade needs to be confirmed until T+1 (1-day ) from the moment it’s matched. Clearing — Once the trade is confirmed by both parties it needs to be cleared by the clearinghouse. The purpose of the clearinghouse is to make sure both parties meet their obligations. Trades are usually referred to as T+1, T+2 or T+3, where the ‘T’ referred to the transaction date (the date on which the trade was executed). On the settlement date, the sell-side must have transferred their security and the buy-side must have transferred the money for their purchase. Settlement — At the end of the trade life cycle process the day of settlement arrives. The settlement process is done within the clearinghouse, where the cash and securities are transferred between the parties’ accounts. At the end of the trade date, the clearinghouse will provide reports on settled trades to the exchanges and custodians.

Credit : Quora

Backoffice and cashflow

The backoffice, although missing the aura of the trading unit (the front office), is the backbone of the trading business. The Backoffice is in charge of making sure trades are settled correctly, accurate cashflows, and securities inventories within the trading accounts. As millions of trades are executed (and settled) on a daily basis in the financial markets, it’s crucial that the trade processing will be verified and monitored closely.

Credit (Counterparty) Risk

The aftermath of the subprime crisis emphasized the importance of credit risk management. We rarely think that our biggest risk in the market is credit, but back in 2008, this risk almost singlehanded brought the entire financial market to a halt.

It’s important to first understand what credit risk is. Credit risk is defined as the risk that one of the parties involved in a trade will default on its contractual obligation.

Let’s imagine that we are a client of Morgan Sachs, and we want to buy a 1.20 3-month call option on EUR/USD. After a month the spot trades at 1.25, and we want to sell the option back, so we shop to get a good bid on the option. JP Lynch shows us a good bid, so we sell the option. At first glance, it seems like we booked the profit, and the option is closed, but in fact, we are at substantial credit risk. If Morgan Sachs defaults prior to the option’s expiration (assuming the option is ITM) we are exposed, as we are short the option facing JP Lynch (which will be exercised), but our long exposure is not going to be fulfilled. This example is only one of many scenarios that emphasize how important it is to assess credit/counterparty risk. Back in 2008, in the aftermath of Lehman Brothers’ collapse, credit risk threatened to take down the financial markets as Lehman was a significant counterpart in many trades across different products and asset classes. Furthermore, as banks found that their peers could go under, they were unwilling to lend each other (and trade with each other given the great credit risk).

Credit risk remedies — XVA

In an attempt to tackle the credit risk banks developed a framework to account for counterparty risk, as well as funding risk. The two valuation adjustments are CVA (Credit Valuation Adjustment) and FVA (Funding Valuation adjustment). In short, when pricing an instrument, the trading desk will adjust the price according to the risk of its counterpart to reflect the default probability and funding cost.

Credit Valuation Adjustment (CVA)

CVA is the difference between the risk-free portfolio value and the mark-to-market given the default probability of the counterparty. When the trading desk prices the CVA it takes into account the counterparty credit spread (if the counterparty has issued bonds, or CDS traded), or asses the default probability is given market risk factors that could affect the counterparty’s solvency. The mathematical expression of CVA can be written the following way:

credit: Wikipedia

Where :

T is the trade maturity,

Bt is the future value of a risk-free bond,

LGD is the loss given default,

PD(s,t) is the default probability between times s and t

Funding Valuation Adjustment (FVA)

Derivatives funding is probably the most underrated issue in finance. When practitioners trade in-and-out of products such as swaps, options, and swaptions they don’t put much effort into understanding the mechanism of funding the transactions (rightfully, as they shouldn’t), But the mechanism itself is the bedrock of financial markets. Up until 2008 GFC, the day-to-day funding was a given, with many derivatives traded as non-collateralized derivatives (meaning that the parties didn’t post daily collateral against the mark-to-market), and collateralized derivatives were discounted at the LIBOR rate. Both issues were found to be extremely risky for banks in the aftermath of Lehman Brothers’ collapse. As banks were unwilling to lend each other and trade with each other without assurances in case of a default, the spread between the LIBOR and OIS (Overnight Index Swap), aka LOIS spread, spiked to 350bp.

Credit : Bloomberg

That spread reflected the fear banks had lending each other without substantial risk premium. While the entire subject of margin and collateral agreements is far too deep for this post, it’s important to understand the risks that involve funding leveraged products, as the entire market microstructure is driven, at the end of the day, by the funding cost of the trading business.

To remedy the funding risk of the derivatives business banks use FVA (Funding Valuation Adjustment), which accounts for the cost of uncollateralized derivatives. In short, FVA can be thought as the difference between the hedging cost difference between uncollateralized trade and the collateralized hedge in the interdealer market.

In practice, banks have dedicated XVA (CVA/FVA) desks with the sole purpose of hedging the trading business credit/funding risk. These desks are in charge of making sure the trading floor’s credit/funding risk is being mitigated using different types of products such as CDS/CDX, basis spreads, and different types of options (or swaptions).

In this risk management crash course, I tried bringing the essence of risk management 101, and while the topic is far deeper than what I wrote, I believe it highlights the different aspects of trading risk that most of us (trading practitioners) rarely think about (unless you are a hedge fund manager or a risk-geek like myself).

Hopefully, this blog post gave you some food for thought.

Twitter: Harel Jacobson