Firms Manage Financial Risk

 

Strategies for Risk Management

After identification of the risk, at a high level a firm can pick from below four different risk management strategies. More than one of the below could be used to manage the risk.

• Accept the Risk : 
• The firm could decide to retain or accept the known risk.
• Reasons
• Cost of mitigating the risk is higher than the actual risk impact
• Cost can be of priced into the firms products and passed along to customers.  Here the business risk is accepted.
• Investors / Owners desire exposure to this risk factor
• Eg: When we talk about investors, like owners of a gold mine, desiring exposure to a risk factor such as the market price movements of gold, it means they want their investment returns to be influenced by changes in the price of gold. While it might seem counterintuitive for owners of gold mines to desire exposure to the market price movements of gold since they already have exposure through their business operations, there are several reasons why they might choose to do so. It aligns with their core business interests, provides a natural hedge, reflects their belief in gold as an investment, and allows them to leverage their expertise in the industry.
• Avoid the Risk
• Not to take an action or avoid selling the units of business to avoid risks to their core business units
• Mitigate the Risk
• After accepting risk, may seek ways to strategically mitigate known risks.
• Different techniques are used to handle different types of risk.
• Transfer the Risk
• To the third party the risk is transferred
• Insurance
• Derivatives Contract
• This introduces counterparty risk because the firm is relying on the third party to make good if a risk event arises.

Risk Appetite

Risk Appetite is how much risk the firm is willing to retain. After discussing the above high-level strategies of the risk, here are five steps process to manage the risk.

• Identify the risk appetite
• Map the known risks
• Operationalise the risk
• Operationalizing risk involves taking a theoretical risk identified through risk assessment and turning it into a practical approach for managing that risk within your organization. 
• Implement the plan
• Monitor and adjust continuously 

The risk appetite can be further divided into two sub-parts:

• Risk Willing
• Desire to accept the risk in pursuit of business goals
• Risk Ability
• Based on the factors risk ability can cap risk willingness.
• Less than risk willing
• Controlled by internal risk controls and also regulatory constraints

In layman's terms, assume the car has been driven on a highway:

• Risks Appetite - Highway speed limit for cars
• Risk Willing - Personal preference to drive at a certain speed, but not exceeding the limit
• Risk Ability - Capability of the car to be able to reach a certain speed, less than risk willing

It is important to distinguish between Industry Risk Appetite vs Internal Risk Appetite as both vary, one is based on the current general market sentiments and another is based on the internal firm's control.

There is always potential for errors in the risk estimation process, hence below allowing margin room for errors. For example:

• Max of 200 Crore - After this firm will go bankrupt
• 150 Crore - Internal risk appetite
• 100 Crore - Actual risk accepted

Role of the Board of Directors

• Communication: 
• It is important for senior management and the board of directors to clearly define the company's risk tolerance and communicate it to stakeholders in a quantitative and/or qualitative manner.
• Quantitative:
• VAR: To convey maximum loss for a given confidence level for a given period.
• Notional Principal: Notional principal amount refers to a predetermined dollar value used in various financial contracts, but it's important to understand that it's not actual money that gets exchanged.
• Eg: Imagine a contract between two friends where they agree to split the cost of a movie rental (the notional principal). However, they only exchange the difference between what each owes based on their preferred snacks (the interest payments). The total cost of the movie (notional principal) doesn't physically change hands.
• Stress Testing: Take the possible input to extreme negatives to determine the level of the losses.
• Qualitative
• List of risks that are retained (unhedged), avoided, mitigated (hedged) or transferred.
• External communication, for example, government or media.
• In detailed communication with the employees, the line managers and the risk managers to understand the enterprise-level expectations. Enabling the below:
• Decision making
• Identify trouble spots
• Business planning cycles
• Determine risk appetite between two major stakeholders - Debt holders vs Stakeholders
• Debt holders are less inclined to take risks and instead prioritize receiving principal and interest payments.
• Stakeholders prefer taking calculated risks that are unlikely to generate more profits/equity returns.
• Time Horizon
• Needs to decide either on taking short-term or long-term risks.
• Reputational Risk
• Ensure any risk impacting the brand of the firm
• Entrepreneurial opportunities
• Characterized by the taking of financial risks in the hope of profit, that could also provide a competitive edge if more risk is assumed.
• Limit Based Risk
• Allowing managers to operate with flexibility but given limits that cannot be exceeded, while also clearly communicating the expectations.
• Risk measurement
• It is difficult to reduce risk management to a single value at the firm level.
• VaR, notional limits, and stress testing are useful tools, but the firm should determine the most relevant metric based on their unique business model.
• Measure the risk at the enterprise level and division level.
• Unity of risk appetite
• Different risk types have different appetites.
• Layers of correlated risk
• Taking one risk might lead to other correlated risks.
• The company need to decide which risks to hedge and which to accept or avoid or transfer.
• Note: Notional Limits Vs Notional Principal

• Both notional principal and notional limits deal with theoretical values in finance, but they serve different purposes:  

• Notional Principal: A predetermined dollar value used as a reference point in various financial contracts. It represents the underlying value of an asset or obligation in the contract. Not actual money that gets exchanged.

• Notional Limits:

   Predefined maximum amounts set for specific types of risk exposure. They act as boundaries to control risk within a portfolio or activity. Used to establish a limit on how much risk can be taken for a particular asset class, strategy, or counterparty.
• Here's an analogy to understand the difference: Imagine a baking recipe (the financial contract).
• The notional principal is like the total amount of flour required (the underlying value). You don't necessarily use all the flour at once, but the recipe uses it as a reference for other ingredients.
• The notional limit is like the maximum amount of sugar you should add (the risk boundary). You can use some sugar, but exceeding the limit can ruin the recipe (excessive risk exposure).

Risk Mapping

• Risk mapping involves the next logical step of the risk management process.
• All the factors related to risk or that can go bad should be taken into consideration by the risk managers:
• Factors including all the types of risk:
• Market Risk
• Equity Risk
• Interest Rate Risk
• Foreign Exchange Risk
• Commodity Risk
• Credit Risk
• Default Risk
• Downgrade Risk
• Settlement Risk
• Bankruptcy Risk
• Liquidity Risk
• Funding Liquidity Risk
• Market Liquidity Risk
• Operational Risk
• Business Risk
• Strategy Risk
• Legal and Regulatory Risk
• Reputational Risk
• Correlation Risk
• Cross out risk factors
• Granular information should be recorded for each type of risk. 
• It is ideal to conduct a risk assessment for all known risks. If that is not possible, at least the top 10 risks should be thoroughly assessed and all granular information should be provided to the board of directors or senior management. This will enable them to make informed decisions on how to handle the risks, such as accepting, avoiding, mitigating, or transferring them.
• Employees should be informed of all the risks if not then at least the top 10.

Hedging Risk Exposures

• Hedge means to protect, hedging risk means providing financial stability for the organization and mitigating the known risks preventing financial stress.
• Many risks can be hedged, but not all the risks are hedged.
• Some investors would intentionally want the risks unhedged.

Hedging Types

• Static Hedging
• Involves creating an initial hedge position using derivatives (usually options) and then leaving it unchanged throughout the life of the underlying asset.
• May not be as effective in highly volatile markets where the underlying asset price fluctuates significantly.
• Dynamic Hedging
• Involves continuously adjusting the hedge position based on changes in the price of the underlying asset and other relevant factors (volatility, time decay). 
• Incurring frequent adjustments to the hedge can result in additional transaction costs.
• It is important to allocate sufficient time for continuous monitoring and analysis of market conditions, which includes the addition of new data and information to the analysis.
• Here's an analogy to understand the difference:
• Static Hedging: Imagine buying an umbrella before a weather forecast with a 30% chance of rain. You have basic protection but might get caught in unexpected downpours.
• Dynamic Hedging: Think of checking the live weather radar and constantly adjusting your umbrella position (or bringing a raincoat) based on the rain intensity and direction. This offers more tailored protection but requires constant monitoring.

Hedging Tools

Hedging tools are financial instruments used to manage risk by offsetting potential losses in one investment with gains from another.  These tools are particularly valuable when dealing with volatile markets or when you want to protect the value of an existing asset.

Below are two channels for trading various financial instruments:

• Over The Counter (OTC) refers to a direct trade between two parties without involving any intermediaries.
• Direct transaction
• Privacy
• Costomizable
• Involves counterparty risk 
• Can be expensive 
• Not easily liquidate
• Exchange refers a centralized marketplace where investors and other participants can buy and sell various financial instruments such as NSE,  BSE.
• Easily liquidate
• Transparency
• Less transaction costs
• Reduces counterparty risk
• Due to standardization, this may not be flexible and meet the specific security, timing, or location needs of risk managers.

Below are some of the available derivative contracts:

• Forward Contracts
• Forward contracts are customizable OTC products traded between two counterparties in the form of price or physical assets.
• Used to lock in a price for buying or selling an asset at a future date and can be used to hedge against price fluctuations, aiming to profit if the price goes in the desired direction.
• Future Contracts
• Future contracts are standardized exchange products that involve an intermediary unit and eliminate counterparty risk.
• Same as forward contracts but standardized.
• Swap Contracts
• Counterparties exchange swap contracts to trade their economic position. For instance, they can exchange a fixed interest rate with a variable interest rate with the assumption of obtaining benefits from it.
• Swaps can be a valuable tool to hedge against fluctuations in interest rates, currency exchange rates, or commodity prices.
• In layman's terms: Imagine you and a friend are both going on vacation, but you have different preferences for dealing with the weather:
• You: You hate surprises and prefer predictable weather, so you pack for sunshine every day (fixed rate).
• Your Friend: They love adventure and don't mind the occasional rain shower, so they pack for whatever comes (variable rate).
• Let's say halfway through packing, you realize you might miss some exciting rainforests if you're stuck in all sunshine. Your friend, on the other hand, starts to worry about getting caught in a downpour without proper gear.
• This is where a swap contract comes in:
• The Swap: You agree to exchange some of your sunshine days (fixed payments) with your friend's chance of rain showers (variable payments) for a certain period (duration of the swap).
• The Benefit: Now you both get some of what you desire! You still have some sunny days (guaranteed fixed income), but you also have the possibility of experiencing exciting adventures (potential for higher returns with variable payments). Your friend gets some predictability (fixed income from you) while keeping some room for surprises (variable income they keep).
• Key Points in this Analogy:
• Exchange of Cash Flows: The swap is about exchanging streams of payments, just like you exchange sunshine days for rain shower possibilities.
• Customization: The swap agreement can be designed to fit your specific needs, just like you agree on how many sunshine days to exchange.
• Risk Management: The swap helps you manage risk by getting some exposure to what you desire (rainforests for your friend, sunshine for you) while keeping some predictability (fixed income).
• This is a simplified analogy, and swap contracts can be much more complex.
• Options Contracts: Contracts that give you the right, but not the obligation, to buy or sell an asset at a certain price by a certain date. They offer more flexibility than futures contracts and can be used for various hedging strategies depending on your risk tolerance and market expectations.
• Call Option Contract
• In a call option, the buyer has the right to buy shares at a specified strike rate either at or before the maturity date.
• Put Option Contract
• In a put option, the seller has the right to sell shares at a specified strike rate either at or before the maturity date.
• Exotic Option Contracts
• Exotic option contracts are derivatives that differ from standard (vanilla) options like calls and puts by having unique features or payoffs tied to the underlying asset. These features add complexity but can also provide investors with more flexibility and potentially higher returns compared to vanilla options. 
• Swaption Contracts
• Combination of Swaps and Option Contracts, here it has the right to swap but is not obliged to enter into a swap contract at some future date.
• When a swaption contract is initiated, the key terms of the underlying swap are indeed established. These terms would be similar to the terms of a regular swap agreement, but with the crucial difference that the swaption only grants the right, not the obligation, to enter into the swap.

Basis risk refers to the mismatch that occurs between the actual risk and the hedge. It is important to note that the hedge is not always perfect, as in the case of an airline industry that is heavily exposed to volatile jet fuel prices. Unfortunately, there is no exchange-traded product for jet fuel, and due to heavy industry competition, airlines cannot pass on the fuel price risk to customers. As a result, airlines have considered using products linked to crude oil as an alternative. Here it brings in basis risk, due to mismatch.

Hedging Operational and Financial Risks

Hedging operational risks covers a firm's expenses(production) and revenues(sales), which are reflected in the income statement.

Hedging financial risks covers a firm's assets and liabilities, which are reflected in the balance sheet.

Pricing Risk

• Input costs significantly impact a firm's ability to compete.
• Hedging such pricing risk by purchasing a forward or futures contract to buy a specific quantity of the input at a fixed cost, which can be determined in advance.

Foreign Currency Risk

• Hedging foreign currency risk is to control exposure to exchange rate fluctuations that impact both future cash flows and the fair value of assets and liabilities.
• Hedging should consider the cost of hedging, as well as revenue, exchange rate volatilities, and correlations.

Interest Rate Risk

• Hedging interest rate risk is managing the firm's exposure to unfavorable interest rate fluctuations.

Hedging Strategies Challenges

• Misunderstand their risk exposure during the risk mapping process
• Selecting the wrong risks, missing relevant risks, or misestimating risks can result in notional values on derivatives that are either too high or too low. 
• The remains of unhedged during a period when it could create a substantial risk event.
• Market trends are constantly changing
• Affects variables such as commodity prices, foreign exchange rates, and interest rates. These changes impact a company's exposure to risk. 
• To manage risk effectively, the risk management process must be as adaptable as the risk variables themselves. 
• However, the rapid pace of change can make it challenging for some firms to actively monitor and keep up with these variables. 
• Attempting to hedge using a flawed hedging strategy may result in greater losses for a firm than the risks they are trying to mitigate.
• Amplified by poor communication
• Communication of strategy is ineffective and decision makers are not adequately informed about potential consequences.
• Knowledge gaps
• Hedging often requires very specific skills, knowledge, research and time.
• Firms may not have the necessary internal human capital, but they can outsource to trusted third-party risk managers.
• Time horizons
• Relevant time horizons for hedging and ensure the performance evaluations are matched with the time horizons
• Taxation
• Taxation of derivatives is a key issue because of its impact on the firm's cash flow as well as the differing laws between countries.
• Significant effort and cost may required to decipher the complex surrounding derivatives.

Some of these challenges could be overcome by training and education, regular communications about risk, awareness of company goals, articulate the firm's top 10 risks.

Risk Limits

Risk limits are a cornerstone of sound financial risk management. As part of the risk mapping process, it is crucial to understand and potentially control various risk limits. They establish thresholds for various types of risk exposure, helping investors and institutions stay within their risk tolerance.  Here's a breakdown of different types of risk limits, their purposes, and potential limitations:

1. Stop-Loss Limits:

   • Purpose: Set a maximum acceptable loss for a particular position or portfolio. Once the loss reaches the limit, the position is automatically liquidated (sold) to prevent further losses.
   • Weakness: Can lead to unnecessary selling during temporary price fluctuations. Misses out on potential recovery if the price rebounds.

2. Notional Limits:

   • Purpose: Set a maximum total dollar value of exposure to a particular asset class or sector. Helps prevent excessive concentration in any single area.
   • Weakness: Doesn't consider the underlying risk of the assets themselves. A high-risk asset with a low notional value could still pose significant risk.

3. Risk-Specific Limits:

   • Purpose: Set limits for specific types of risk, such as market risk (volatility), credit risk (default), or liquidity risk (difficulty selling an asset). Provides a more nuanced approach to risk management.
   • Weakness: Requires a good understanding of different risk measures and how they interact. Can be complex to implement and monitor, may require hiring someone with very specific skills.

4. Maturity Limits:

   • Purpose: Set limits on the maximum maturity (time to expiry) of an investment. Helps manage interest rate risk and ensures investments align with investment goals.
   • Weakness: May limit access to certain investment opportunities with longer maturities that could offer higher potential returns.

5. Concentration Limits:

   • Purpose: Set limits on the maximum exposure to a single issuer (company), industry, or asset class. Prevents overdependence on any single entity or sector.
   • Weakness: May limit diversification opportunities in smaller markets or asset classes. Outcomes may be correlated even if they are not concentrated.

6. Greek Limits:

   • Purpose: Set limits on exposure to specific risk measures derived from options pricing models (Delta, Gamma, Vega, Theta). Helps manage the risk profile of options positions.
   • Weakness: Greek measures are based on assumptions and can be volatile with market changes. Requires a sophisticated understanding of options pricing.
7. Value at Risk
• Purpose: 
  • Quantitative Measure: VAR provides a single numerical value to represent overall portfolio risk, simplifying communication and risk management processes.
  • Customizable: VAR calculations can be customized to include various risk factors relevant to the portfolio, offering a more tailored approach.
• Weakness: 
• Does not provide a measure of magnitude beyond the threshold. Subject to model risk and input variables can be adjusted to yield desired results.

8. Stress Testing and Scenario Analysis:

   • Purpose: Evaluate how a portfolio would perform under extreme but plausible market conditions (stress testing) or specific hypothetical scenarios. Helps identify potential vulnerabilities and assess risk tolerance.
   • Weakness: Effectiveness depends on the accuracy of chosen scenarios and assumptions. Doesn't guarantee future outcomes.

Hedging Trade-Off

• Advantages
• Cost reduction
• Lowering the cost of capital, whether through debt or equity, can lead to economic growth.
• Debt: When a company is seen as less risky, lenders are more likely to offer them loans with lower interest rates. This makes borrowing cheaper, freeing up more capital for investment and growth.
• Equity: Reduced risk also makes a company's stock more attractive to investors. This can lead to a lower cost of equity, meaning the company can raise capital by issuing new shares at a lower price dilution to existing shareholders.
• Increase in debt capacity by reducing the volatility of its earnings/cash flows.
• Imagine a company's earnings as a bumpy rollercoaster ride. Lenders are hesitant to lend money on such a risky journey. The company smooths out the ride by using hedging as safety rails, making it a more predictable and reliable borrower. This entices lenders to offer more favourable loan terms, allowing the company to take on more debt for growth.
• Borrowing arrangements for firms with less volatile earnings/cash flows usually contain fewer conditions and restrictions imposed by the lenders.
• Possible cash flow impact could be tax reduction
• Hedging strategies can generate tax-deductible losses that can be used to offset taxable income. This can be particularly relevant for companies that hedge against certain risks.
• Imagine a company uses futures contracts to hedge against a potential decline in oil prices (if they're a heavy oil consumer). If oil prices do fall, the company might experience a loss on the futures contract. This loss can be deducted from their taxable income, potentially lowering their overall tax burden.
• Beyond risk transfer, there is also the potential for a cash flow advantage.
• Positive cash flow, though only when hedging is done through options
• Imagine with the effort to hedge commodity prices and end up with a large profit position in future contracts.
• Signal to stabilize income
• Stability in a firm's income operations signals strength to its stakeholders.
• Reputational message could impact lenders, customers, suppliers, employees and as well reflected in the firm's stock price.
• Communicate the risk appetite to the firm's board of directors.
• Makes business easier
• Firms can make better decisions for the future if they demonstrate stability.
• As risks are controlled.
• Lock in strong margins
• Hedging can serve as a crutch to meet short-term performance goals. However, it can also help lock in solid performance when it arises organically.
• Cheaper than purchasing insurance policy.
• Disadvantages
• The assumption of no transaction cost or taxes is highly unrealistic in real world.
• In addition to systematic risk, which affects all market participants, unsystematic or idiosyncratic risk pertains to the inherent uncertainty or potential loss associated with an individual investment or a small group of assets. However, diversification efforts may lead to transaction costs.
• Unplanned cost involved to hedge
• Cost involved to hedge, like talent and expertise, software, transaction cost, legal and compliance, market data, training and education, and some more.
• Hidden cost involved, when management can get distracted, and lose focus on the core business activities of the firm.
• Hedging as a "zero-sum game" might not be entirely accurate. In a zero-sum game, one participant's gain is exactly balanced by another participant's loss. Hedging is a risk management strategy used to offset potential losses in one investment with potential gains from another.
• Extremely complex and not as accurate as equity or bond pricing, reflect all of its relevant risk factors.
• The goal is to achieve a more predictable outcome, rather than a win-lose scenario.
• Hence hedging with derivatives may not be a zero-sum game of transferring risk between periods or between participants.

Credits and References

https://blog.deltafx.com/en/what-does-hedging-mean/

https://gemini.google.com/

https://chat.openai.com/

SchweserNotes and BionicTurtle Notes

#Chapter2

An Introduction To Financial Risk Management

 

Introduction

The term risk refers to the uncertainty surrounding outcomes, here the outcome could be positive/upside side or negative/downside. However, an investor is generally more concerned about the negative impact as it would lead to losses. 

A natural trade-off between risk and return is observed, high risk has the potential for high returns and lower risk also has return potential. On the other hand, risk is not always related to the size of potential loss, for instance, predictable losses can be accounted for using risk management techniques. Risk-taking means to accept known risks to pursue incremental gains.

As risk is about the variability of losses and not about the size of the loss, it can be measured using standard deviation.

Risk Management Process

• Risk Management includes the set of activities aimed to eliminate or reduce expected or unexpected losses and determine if the perceived reward justifies the expected risk. 
• In other words risk is unexpected volatility in asset prices or earnings.
• Natural trade-off between risk and returns is observed, higher risk there leads to the potential of higher returns.
• Risk is not necessarily related to the size of the potential loss.
• The risk management process is a formal series of actions designed to determine if the perceived reward justifies the expected risks.

Steps involved in the Risk Management Process:

• Identify Risk
• Through brainstorming sessions
• Key business leaders and relevant teams
• Industry level experts - eg., regulatory standards, industry surveys, expert opinions, third-party tools, external sources
• Scenario analysis
• Used for identifying risks.
• Quantitative analysis
• Actual loss data to discern the magnitudes and frequency of various losses. 
• Measure and Manage Risks
• Distinguish between Expected or Unexpected Risk
• Address the Relationships among Risks
• Develop a risk mitigation strategy
• Avoid Risk
• Avoiding risk refers to a strategy in risk management where an organization takes deliberate actions to completely eliminate exposure to certain risks.
• Avoiding risk entirely is often not feasible or desirable for organizations, as it may prevent them from seizing opportunities.
• Retain Risk
• Depending on the expected rewards based on the probability, frequency and impact
• Mitigate Risk
• Reduce the magnitude or frequency of exposure to the given risk factor
• Transfer Risk
• Using third party derivatives or structured products
• Purchase of insurance
• Monitor the risk mitigation strategy and adjust as required

Loss Categories

• Expected Loss
• Simply the average loss that we would expect from the given exposure over a period of time.
• Probability of Default
• Built Pricing of Product
• EL = Probability * Exposure * LGD (Loss Given Default)
• Unexpected Loss
• Is the amount of loss that actually exceeds the expected amount.
• Separate capital base to meet this loss.

Classification of Risk on the basis of knowledge of Risk

• Known
• Known
• Easy to identify to manage
• Probability and Impact are known
• Eg: Losing customer to the competition
• Unknown
• Also called as Knightian uncertainty
• The firm is aware of this risk
• Probability and Impact is unknown
• Eg: Law suite impact
• Unknown 
• Known
• Aware of the risk but negligent in treating risk
• Unknown
• Also known as tail risk events
• No knowledge about the existence of the risk
• Eg: Covid before 2019

Zero Sum Game

• Risk management is also known as a zero-sum game, in this some "winning" parties will gain at the expense of some "losing" parties. If enough parties suffer devastating losses due to an excessive assumption of risk, it could lead to widespread economic cries.

Challenges in the Risk Management Process

• Fail to consistently prevent market disruption or financial fraud
• Use of derivatives as complex trading strategies of many entities
• Inaccurate information would not allow the policies to be effective

Measuring Risk

Quantitative Risk Measures

• Value at Risk(VaR)
• Calculates an estimated loss amount given a certain probability of occurrence assuming normal market returns. 
• Under known circumstances the maximum loss. 
• There are different approaches for calculating VaR.
• ES (Shortfall)
• EC (Economic Capital)
• Is the amount of liquid capital necessary to cover unexpected losses.
• Expected tail risk event.
• RAROC (Risk Adjusted Return On Capital)
• One valuable metric to consider risk exposures across business units, related to economic capital.
• RAROC = after-tax risk-adjusted expected return / economic capital
• Application of this formula
• This formula is essentially a reward per unit of risk.
• Used in calculating the value of the cost of equity.
• Business comparison, when different levels of economic capital exist for each segment.
• Investment analysis, evaluate potential new product offerings.
• Pricing strategy, the current pricing strategy provides sufficient return relative to the estimated risk taken.
• Risk management, highlight areas where risk is not being properly covered with expected rewards.

Qualitative Risk Assessment

Using historical data alone calculates the risk, but history may not repeat itself. Such scenarios use hypothetical forecasts based on a risk manager's assumptions, though such a model can be error-prone and involve risk but a useful exercise to fully understand a firm's risk.

Scenario Analysis

• Compare the best-case scenario to the worst-case scenario, by shocking variables to the extreme known values.
• Considers potential future risk factors and associated alternative outcomes.
• To understand the assumed full magnitude of potential losses even if the probability of the loss is very small.

Stress Testing

• The primary objective of stress testing is to evaluate the resilience of a system or portfolio to extreme, adverse events or scenarios.
• A crucial evaluation method to ensure a firm's sustainability. 
• It assesses extreme scenarios that may occur rarely but can have a significant impact on losses. 
• On the other hand, probabilistic risk metrics, such as VaR, ES, or Standard Deviation, are suitable when the frequency of losses is high, and the severity of losses is low.

Sensitivity Analysis

• Sensitivity analysis is used to understand how changes in specific input variables or assumptions affect the output or outcome of a model, system, or decision.
• It focuses on assessing the sensitivity of results to changes in individual factors.

Managing Risk - Enterprise Risk Management

• ERM is a process of risk management centrally and highly integrative deployed at the enterprise level.
• One challenge with the ERM approach is a tendency to reduce risk management to a single value (e.g., either VaR or economic capital), but in dynamic risk management this attempt is too simplistic.
• Risk managers learned from the financial crisis of 2007-2009 that risk is multi-dimensional and requires consideration from different perspectives or angles.
• ERM framework requires both statistical analysis and informed judgement on the part of risk managers and plays an equally important role in assessing and managing risks.

Expected and Unexpected Loss

• Expected Loss
• Measure of the probability is known - Expected Loss
• Formula:
• EL = EAD * PD * LGD
• Here,
• EL = Expected Loss
• EAD = Dollar Exposure At Default
• PD = Probability of Default
• LGD = Loss Given Default - The expected severity of the loss if the risk event does occur
• When EL can be modelled with confidence, it can be treated as a predictable expense or a variable cost
• Unexpected Loss
• Measure of the probability is unknown - Unexpected Loss
• Unfavourable events happen together, and the correlation risk drives potential losses to unexpected levels.

Risk and Reward

• Higher the risk then higher the expected profit.
• There is a trade-off between risk and reward, as it becomes much more complex to analyze assets that are thinly traded or not publicly traded.
• Illiquid assets as well is very complex to analyze.
• In complex systems extreme unexpected losses may occur.
• Drivers of the potential list of loss drivers could be exhaustive.
• Potential for conflicts of interest: Those in the position to be most aware of the presence, probability and potential impact of various risk factors are sometimes the ones who try to profit from its presence.
• Risk recognition by frontline employees and division managers.
• A robust risk management system with daily oversight.
• Periodic independent audits to ensure that steps 1 and 2 are functioning properly.
• Danger arises when the frequency of tail events increases because the pace of structural uncertainty accelerates such as behavioural shifts, industry trends, government interventions and new innovations.

Types of Risk

Market Risk

Market risk refers to the potential for losses in investments due to movements in market factors. The key to mitigating these risks is to understand the relationship between positions. 

• Equity Price Risk
• Refers to the volatility of stock prices.
• Two parts
• General market risk, which is the sensitivity of the price of a stock to change in broad market indices. Cannot be diversified away.
• Specific risk, which is the sensitivity of the price of a stock due to company-specific factors eg rising cost of inputs, strategic weakness. Could be mitigated by holding assets with less-than-perfect correlations.
• Interest Rate Risk
• Interest rate risk refers to the potential for a financial institution or investor to experience losses due to fluctuations in interest rates.
• Uncertainty flowing from changes in interest rate levels.
• Interest Price Goes Down Bond Value Goes Up
• Change in the shape of the yield curve
• The yield curve is a graphical representation of the relationship between the yields (interest rates) and the maturity dates of bonds of similar credit quality but different maturity dates. 
• It shows the yield (return) investors can expect for bonds with different maturities (how long until they mature).
• Normally, the yield curve slows upwards, indicating that longer-term bonds have higher yields than shorter ones. 
• This is because investors typically demand higher yields for locking in their money for longer periods due to the increased uncertainty and risk associated with longer-term investments and reflects the concept of the time value of money and the inherent risk of lending for longer periods
• Changes in the shape of the yield curve can occur for various reasons and can have different implications:
• Steeper curve: Good for banks, bad for long-term bondholders (potential price decrease). 
• Steepening Yield Curve: Imagine you're comparing two roads. One road is a gentle slope upwards, and the other is a steeper incline. The steepening yield curve is like the steeper road. If you're willing to take the longer journey (investing for the long term), you'll see a bigger payoff (higher interest rates). It's like choosing the steeper road because you know the view at the top will be worth it. 
• Flatter curve: Not ideal for banks, but okay for long-term bondholders (stable prices). 
• Flattening Yield Curve: Picture a hill that's gradually leveling out as you walk along it. At the start, it's steep, but as you keep going, it gets flatter and flatter. That's what happens with a flattening yield curve. It means that whether you're walking a short distance or a long one (investing for the short or long term), the effort and payoff are becoming more similar. It's like walking along that hill and noticing that the difficulty doesn't change much whether you go a short distance or a long one.
• Inverted curve: Risky for banks, potentially good for long-term bondholders (opportunity to buy high-yielding bonds).
• Inverted Yield Curve: Think of a situation where you lend something to a friend, but instead of getting back more later (like with interest), you actually get back less. That's what happens with an inverted yield curve. It means that if you lend your money for a short time, you get more back (higher interest rates) than if you lend it for a long time. It's like your friend saying, "I'll give you back less if you lend me your stuff for a longer time." It's unusual and often signals that something unusual or worrying might be happening with the economy.
• Positions that are partially or completely unhedged
• **Unhedged Positions**: When an investment or a portfolio is unhedged, it means that there is no protection against adverse movements in interest rates. For example, if you invest in long-term bonds without any measures in place to mitigate the impact of potential interest rate changes, your investment is considered unhedged.
• **Partially Hedged Positions**: Partial hedging means that some, but not all, of the risks associated with an investment are mitigated. In the context of interest rate risk, this might involve hedging against changes in short-term interest rates but not long-term rates, or vice versa. Alternatively, it could involve hedging only a portion of the portfolio rather than the entire position.
• Here's how interest rate risk arises from having positions that are either completely or partially unhedged:
• **Exposure to Interest Rate Movements**: Unhedged or partially hedged positions leave investors vulnerable to adverse movements in interest rates. If interest rates rise, the value of fixed-income investments such as bonds typically decreases, leading to losses for investors holding unhedged positions. Conversely, if interest rates fall, unhedged investors may miss out on potential gains.
• **Duration Mismatch**: Duration is a measure of the sensitivity of a bond's price to changes in interest rates. Unhedged positions may have a duration mismatch, meaning that the duration of the investment does not align with the investor's time horizon or interest rate outlook. For example, holding long-term bonds in an unhedged position when expecting interest rates to rise can lead to significant losses due to the higher sensitivity of long-term bonds to interest rate changes.
• **Cash Flow Risks**: Unhedged positions can also expose investors to cash flow risks. For instance, if an investor has liabilities or obligations that are sensitive to changes in interest rates (such as variable-rate debt), holding unhedged positions that are adversely affected by interest rate movements can lead to financial difficulties.
• To manage interest rate risk effectively, investors often employ hedging strategies such as using interest rate swaps, options, or futures contracts to offset the impact of interest rate changes on their portfolios. By hedging their positions, investors can reduce their exposure to interest rate risk and potentially minimize losses or take advantage of opportunities in changing interest rate environments.
• Basis risk
• Basis risk refers to the potential pitfall you encounter when trying to hedge (protect) yourself from a price movement in one asset using another asset. It arises because the two assets, although related, might not move in perfect lockstep. 
• Imagine you're using an umbrella (hedge) to protect yourself from the rain (price movement of the asset you care about), but there's a chance the umbrella might not fully cover you (basis risk).  
• Hedging: Imagine you own a house (asset) and you're worried about the price going down. You buy insurance (hedge) to protect yourself in case the value drops. 
• Basis: The insurance policy (hedge) might not perfectly match the value of your house (asset). There might be a difference in coverage (basis). 
• Basis Risk: This difference in coverage between your asset and the hedge is basis risk. In a financial context, it's the risk that your hedge won't completely offset the losses in your main investment.
• Forex Risk
• Monetary losses that arise from either fully or partially unhedged foreign currency positions.
• Occurs from imperfect correlation in currency price movement and international interest rates.
• Commodity Risk
• Price volatility/fluctuations of commodities e.g., precious metal, base metals, agricultural products, energy.
• These prices can be influenced by various factors like weather, geopolitics, and supply and demand imbalances.
• Volatility due to specific commodities are concentrated in the hands of relatively few market participants.
• Sudden price jumps from one level to another.
• Lack of Trading Liquidity: This means that it can be difficult to quickly buy or sell a particular commodity at a fair price. Unlike stocks or bonds that trade on exchanges with many buyers and sellers, some commodities might have a limited number of participants or complex purchasing processes.
• Trading Liquidity: Liquidity refers to the ease with which an asset can be bought or sold in the market without significantly affecting its price. In financial markets, assets such as stocks and bonds often have high liquidity because they are actively traded, meaning many buyers and sellers are willing to transact at any given time. 
• Commodity Markets: In contrast, commodity markets can sometimes lack trading liquidity, especially for certain types of commodities or in specific geographic regions. This lack of liquidity can be due to factors such as limited trading volumes, fewer market participants, or logistical challenges associated with physical delivery or storage of the commodity. 
• Impact on Price Volatility: When a market lacks liquidity, even relatively small trades can have a significant impact on prices. In commodity markets with low liquidity, a large buyer or seller entering or exiting the market can cause prices to move sharply in response to the imbalance between supply and demand. This phenomenon is often referred to as "slippage."

Credit Risk

Credit risk refers to a loss suffered by a party where the counterparty fails to meet its contractual obligations. Increasing risk of default by the counterparty throughout the contract.

• Default Risk
• Potential non-payment of interest and/or principal on a loan by the borrower.
• Probability of Default is a fundamental concept in risk management, providing a quantitative measure of credit risk that enables financial institutions to assess, monitor, and mitigate the potential for default within their lending and investment activities.
• Downgrade Risk
• Decreased creditworthiness of a counterparty.
• Creditor would charge higher lending rate to compensate for the increased risk.
• Downgrade risk could lead to default risk.
• Settlement Risk
• Using derivatives transactions between two counterparties.
• At the settlement rate, one is in net gain (winning) and the other is in net loss (losing) position. The position which is losing my refuse to pay and fulfil obligation. Also known as counterparty risk or herstatt risk.
• Bankruptcy Risk
• Stops Operating
• Real Value < Loan Amount

Example:

• Net gain of $1000 at settlement date.
• Counterparty experienced financial difficulty
• Recovery rate/value, estimated payment while handling above risk - Only able to pay $800 or 80%
• Loss given default (LGD) - $200 loss or 20%
• If the recovery value is 0% or LGD is 100%, complete default and the possibility of a bankruptcy scenario.

Risk managers consider the below while credit risk identification process.

• Instruments diversified both geographically and by industry?
• Interest charged on the instrument is in proportion to the risk taken?
• Correlation between instruments and risk factors been properly considered?
• Firm or industry-specific financial ratio indicating cause for concern?
• Exposed to a large number of small loans or a small number of large loans leading to concentration risk?
• PD of various instruments owned?
• Probabilities of default correlated in any way?

Liquidity Risk

• Risk of sustaining significant losses due to inability to take or exit position at a price.
• Trading Liquidity Risk
• Losses flowing from a temporary inability to find a needed counterparty.
• Ability to turn assets into cash at any reasonable price.
• Bid-ask spread, can be thought of as the loss that would be sustained by a trader who sells an asset and then immediately buys it bank. The higher the spread the lower the market liquidity and vice versa.
• Funding Liquidity Risk
• Refers to the risk that an institution will not be able to, raise the cash necessary to make debt payments
• Unable to pay down - cash obligations to counterparties or fund capital withdrawals.
• Fulfill cash, margin and collateral requirements of counterparties.
• Meet capital withdrawals resulting in a loss.
• Asset Liability Mismatch
• Redemption risk
• Some investment funds, particularly those that invest in less liquid assets like real estate or private equity, might not hold enough cash readily available to meet all redemption requests immediately. If a large number of investors redeem their shares at once, the fund manager might be forced to:
  • Sell other assets, potentially at a loss if they need to sell quickly.
  • Suspend redemptions temporarily, restricting investors' access to their money.
• Margin/haircut funding risk
• Imagine you want to buy a house (investment) but don't have enough cash upfront. The bank (broker) requires a down payment (margin) and might also consider the value of your car (collateral) as additional security. However, they might not value your car at its full market price (haircut). This all affects how much you can borrow (leverage). If you experience a financial setback and need to sell your car quickly to raise cash (funding liquidity), you might face difficulties due to a less liquid market, potentially leading to financial problems.
• Rollover risk
• Risk that investors may not be able to roll over short-term debt to finance the purchase of an asset.

Operational Risk

• Potential losses flowing from inadequate or failed internal processes, human error or external events.
• Technology risk - inadequate computer system
• Natural disaster
• Cyber security risks
• Fraud
• Accidental mistakes
• Very challenging to quantify

Legal and Regulatory Risk

• Legal Risk
• Potential litigation to create uncertainty for a firm.
• One party suing another party..
• Regulatory Risk
• Uncertainty surrounding actions by government entities.
• Legal and regulatory risks are highly integrated with both operational and reputational risks.

Business Risk 

• Variability in inputs that influence revenues
• customer demand trends
• product pricing policies
• Cost structures
• cost of production inputs
• supplier negotiations
• Diverse business elements
• new product innovations
• shipping delays
• production cost overrun

Strategic Risk

• Long-term decision-making about fundamental business strategy. Eg: after spending millions of dollars in developing a new product but then that failed in the marketplace.
• Regulatory landscape could change and materially alter the profitability of a project.

Reputation Risk

• Reduce brand value, will suffer loss in public perception or consumer acceptance.
• Loss of confidence in the firm's financial soundness.
• Perception of a lack of fair dealing with stakeholders.
• Experiencing a loss in another risk category could lead to reputation risk.
• Social media amplify reputation risk which may or may not be accurate.
• Could start with loss of profits but then could lead to bankruptcy.

Risk Factor Interactions

• Correlated risks
• Significant danger in risk management occurs when independent risk factors are correlated. 
• For example default risk leading to credit risk, business risk and reputation risk.
• Most dangerous with unexpected losses.
• Risk managers could consider historical correlations between identified risk factors and forecast the nature of these relationships to measure the risk planning process.
• Challenge of understanding risk aggregation which can be applied to measure all risks at the enterprise level.
• Using notional could cancel out cancel out each other, although risk is involved.
• Market participants have resorted to using option Greeks to model uncertainty, but these values cannot be aggregated with other positions at the enterprise level.
• Drawback of VaR
• Can alter the computed value by adjusting the number of days or confidence level.
• It measures the largest loss at a specified cutoff point but not the magnitude of tail risk.
• Expected shortfall
• Statistical measure designed to estimate the magnitude of aggregate tail risk losses.

Credits and References

https://www.javatpoint.com/financial-risk-management

https://www.investopedia.com/

SchweserNotes 2023

BionicTurtle Notes 2023

Chapter 1

Time Value of Money in Financial Management

Introduction

The time value of money (TVM) is a fundamental concept in finance that states that a certain amount of money is worth more today than the same amount in the future. This is because the money has the potential to earn interest or increase in value over time. As a result, having the money now is more advantageous than receiving the same amount at a later date.

Interest Rate

The interest rate is the amount charged on top of the principal by a lender to a borrower for the loaned amount. Interest rate and discount rate are almost used interchangeably.

Interest Rate Interpretation

• Discount Rate
• Required Rate of Returns
• Opportunity Cost

Components of Interest Rate

• Real Risk-Free Rate
• Real - When there is no inflation
• Risk-Free - When there is no risk
• Risk Types
• Default Risk - Risk of not recovering of money on time
• Reinvestment Risk - Possibility that an investor will be unable to reinvest cash flows received from an investment, such as coupon payments or interest, at a rate comparable to their current rate of return.
• Inflation Premium
• Inflation reduces the purchasing power of a unit of currency. Hence this needs to be compensated to investor for expected inflation.
• The inflation premium is the additional return that investors demand to compensate for the expected erosion of purchasing power due to inflation.
• Default Risk Premium
• Probability of not recovery money either on due date or not at all
• Liquidity Premium
• Liquidity premium is the additional compensation used to encourage investments in assets that cannot be easily or quickly converted into cash at fair market value. For example, a long-term bond will carry a higher interest rate than a short-term bond because it is relatively illiquid.
• Maturity Premium
• The maturity risk premium is the additional compensation investors demand for holding long-term bonds instead of short-term bonds. As bonds have longer maturities, investors take on additional interest rate risk and inflation risk. To compensate, long-term bonds must offer higher yields than short-term bonds.

Cashflow

Cash flow refers to the net balance of cash moving into and out at a specific point in time. Below are few common terms for series of cashflows:

• Annuity - is a finite set of level sequential cash flow
• Ordinary Annuity - first cash flow that occurs one period from now (indexed at t=1)
• Annuity Due - first cash flow occurs immediately (indexed at t=0)
• Perpetuity - perpetual annuity or a set of level never ending sequential cash flows, with the first cash flow occuring one period from now.
• r - rate of interest per period
• FVn - future value of the investment N periods from today
• PV - present value of initial investment
• m - frequency of compounding

Future Value

Future value (FV) is the value of a current asset at a future date based on an assumed growth rate. Investors and financial planners use it to estimate how much an investment today will be worth in the future. External factors such as inflation can adversely affect an asset's future value.

• Single Cashflow
• Time value associated with a single cashflow or lump sum investment
• Formula:
• FVn = PV((1+r)^n)
• Example:
• r = 0.05
• n = 2
• Original investment = $100
• Interest for the first year = ($100 * 0.05) = $5
• Interest for the second year = ($100 * 0.05) = $5
• Interest for second year based on interest earned in the first year = ($5 * 0.05) = $.25
• Total sum in 2 years = $100 + $5 + $5 + $.25 = $110.25
• The interest earned on the interest is known as compounding.
• n and r must be in same unit if N is in months then r should not be in years, it should also be in months. Else we need to transform the r to make to months.
• Non Annual Compounding
• Here the time value of money is calculated on the investments paying interest in different frequencies of compounding.
• Formula:
• FVn = PV(( 1 + r/m)^mn)
• Continous Compounding
• So far compounding period illustrates discreate compounding, now if the number of compounding periods per year becomes infinite, the the interes is said to compound continously.
• Formula
• FVn = PV*(e^rn)
• Series of Equal Cashflow
• Equal cash flows can grow significantly over time due to compound interest. The longer the investment period and the higher the interest rate, the greater the future value will be.
• Formula:
• Future Value (FV) of annuity due = PMT x [(1 + r)^n - 1] / r
• Example:
• Scenario: Imagine you decide to save $100 every month for the next 5 years (60 months) into an investment account that offers a yearly interest rate of 8% (compounded annually). This represents an equal cash flow of $100 each month.
• Goal: We want to calculate the future value of this series of equal cash flows at the end of 5 years.
• Solution: There's a specific formula for future value of an annuity due (a series of equal cash flows at the beginning of each period) which is ideal for this scenario. However, for equal monthly deposits, we can slightly adjust the formula to account for monthly compounding. Here's the breakdown:
• Number of compounding periods (n): In this case, with monthly deposits for 5 years, we have monthly compounding. So, n = total months = 5 years * 12 months/year = 60 months.
• Interest rate per period (i): Since the interest rate is yearly (8%), we need to convert it to a monthly rate for compounding. So, i = annual rate / number of compounding periods per year = 8% / 12 = 0.667% per month (converted into a decimal).
• Cash flow per period (PMT): This is the amount deposited each month, which is $100.
• Formula:
• Future Value (FV) of annuity due = PMT x [(1 + i)^n - 1] / i
• Plugging in the values:
• FV = $100 x [(1 + 0.00667)^60 - 1] / 0.00667
• Calculation:
• Using a calculator, you'll find the FV to be approximately $8,103.77.
• Interpretation:
• By consistently depositing $100 every month for 5 years at an 8% annual interest rate (compounded monthly), your investment will reach a future value of approximately $8,103.77 at the end of the 5 years.
• This example demonstrates how equal cash flows can grow significantly over time due to compound interest. Remember, the longer the investment period and the higher the interest rate, the greater the future value will be.
• Series of Unequal Cashflow
• Calculating the future value of unequal cash flows requires a slightly different approach compared to equal cash flows.
• Example:
• Scenario: You receive three unequal payments from an investment:
• • Year 1: $500
  • Year 3: $1,000
  • Year 5: $2,000
  • The interest rate is 10% annually compounded annually.
  • Goal: Find the future value of all these cash flows at the end of year 5.
  • Solution:
  • For unequal cash flows, we can't use the formula for annuities. Instead, we need to consider each cash flow individually and find its future value at the end of year 5.
  • Future Value of Each Cash Flow:
  • Year 1: FV of $500 at year 5 = $500 x (1 + 0.1)^4 = $500 x 1.4641 = $732.05
  • Year 3: FV of $1,000 at year 5 = $1,000 x (1 + 0.1)^2 = $1,000 x 1.21 = $1,210.00
  • Year 5: The $2,000 is received at year 5 itself, so its future value is simply $2,000.
  • Total Future Value: Now, add the future values of each individual cash flow to find the total future value at year 5.
  • Total FV = $732.05 + $1,210.00 + $2,000 = $3,942.05
  • Interpretation:
  • In this scenario, the total future value of the unequal cash flows at the end of year 5, considering the 10% annual interest, is $3,942.05.

Present Value

Lets look into formulas alone here as its similar to FV.

• Single Cashflow
• Formula: PV = FVn((1+r)^-n)
• Non Annual Compounding
• Formula: PV = FVn((1+r/m)^-mn)
• Series of Equal Cashflow
• Formula: PV = A[ (1 - 1/(1+r)^n) / r]
• Series of Unequal Cashflow
• Similar to FV but only the formula changes using the above.
• Present value of Perpetuity
• Formula: A/r

Credits and References

https://www.canarahsbclife.com/content/dam/choice/blog-inner/images/what-is-the-time-value-of-money.jpg

https://gemini.google.com/

https://www.investopedia.com