Chapter 1. Fundamentals of Risk Management

In 2007, no one would have thought that risk functions could have changed as much as they have in the last eight years. It is a natural temptation to expect that the next decade has to contain less change. However, we believe that the opposite will likely be true.

Harle et al. (2016)

Risk management is a constantly evolving process. Constant evolution is inevitable due to the fact that long-standing risk management practice cannot keep pace with recent development or be a precursor of unfolding crises. Therefore, it is of importance to monitor and adopt the changes brought by structural breaks in a risk management process. Adoption to the changes implies re-defining the components and tools of risk management. Before digging more into the risk management components and tools, let’s discuss the main risk management concepts.

This part of the book presents basic concepts of financial risk management, which I refer throughout the book. This concepts include risk, types of financial risks, risk management, returns, and finally risk management with machine learning.

Risk

Risk is always out there during the course of life but understanding and assessing risk is a bit tougher than knowing it due to its abstract nature. Risk is perceived as something hazardous and it might be expected or unexpected. The expected risk is something that is priced but the unexpected risk that is not accounted for along the way so it might be devastating.

As you can imagine there is no general consensus on the definition of risk. However, from financial standpoint, risk refers to a likely potential loss or the level of uncertainty to which a company can expose. Differently, McNeil et al. (2015) define risk as:

Any event or action that may adversely affect an organization’s ability to achieve its objectives and execute its strategies or, alternatively, the quantifiable likelihood of loss or less-than-expected returns.

These definitions focus on the downside of the risk implying that cost goes hand in hand with risk but it should be noted that there is no necessarily one-to-one relationship among them. For instance, if a risk is expected a cost borne is relatively lower (or even ignorable) than that of unexpected risk.

Return

All financial investments are undertaken to gain profit, which is also called return. More formally, return is the gain made on an investment in a given period of time. Thus, return refers to the upside of the risk. Throughout the book, risk and return will refer to downside and upside risk, respectively.

As you can imagine, there is a trade-off between risk and return, the higher risk assumed, the greater the return realized. As it is a formidable task to come up with a optimum solution, this trade-off is one of the most controversial issues in finance. Markowitz (1952) proposes an intuitive and appealing solution to this long-standing issue.

The way he defines the risk, which was until then ambiguous, is nice and clean and led to change in landscape in financial research. Markowitz (1952) used standard deviation σRi to quantify risk. This clean definition allowed researchers to use mathematics and statistics in finance. The standard deviation can be mathematically defined as (Hull, 2012):

σ=?(R2)-[?(R)]2

where R and E symbols refer to annual return and expectation, respectively. The book uses the symbol E numerous times as expected return represent the return of interest. This is because it is probability we are talking about in defining risk.

When it comes to portfolio variance, covariance comes into the picture and the formula turns out to be:

σp2=wa2σa2+wb2σb2+2wawbCov(ra,rb)

where w denotes weight, σ2 is variance, and Cov is covariance matrix.

Taking square root of the variance obtained above gives us the portfolio standard deviation:

σp=σp2

In other words, return is a weighted average of the possible returns and can be shown as :

?(R)=inwiRi=w1R1+w2R2+wnRn

Let’s explore the risk-return relationship by visualization. To do that I construct an hypothetical portfolio and calculate necessary statistics in Python.

In [1]: import statsmodels.api as sm
        import numpy as np
        import plotly.graph_objs as go
        import matplotlib.pyplot as plt
        import plotly
        import warnings
        warnings.filterwarnings('ignore')

In [2]: n_assets=51
        n_simulation=5002

In [3]: returns=np.random.randn(n_assets, n_simulation)3

In [4]: random = np.random.rand(n_assets)4
        weights=random/sum(random)5
        def exp_port_return(returns):
            rets=np.mean(returns,axis=1)
            cov=np.cov(rets.T, aweights=weights, ddof=0)
            portfolio_returns= np.dot(weights,rets.T)
            portfolio_std_dev=np.sqrt(np.dot(weights,np.dot(cov, weights)))
            return portfolio_returns,portfolio_std_dev6

In [5]: portfolio_returns,portfolio_std_dev=exp_port_return(returns)7

In [6]: print(portfolio_returns)
        print(portfolio_std_dev)8
        0.031678106722804376
        0.009530493978125805

In [7]: portfolio=np.array([exp_port_return(np.random.randn(5, i)) for i in range(1,101)])9

In [8]: best_fit=sm.OLS(portfolio[:,1],sm.add_constant(portfolio[:,0])).fit().fittedvalues10

In [9]: fig=go.Figure()
        fig.add_trace(go.Scatter(name='Risk-Return Relationship', x=portfolio[:,0], y=portfolio[:,1],
        mode='markers'))
        fig.add_trace(go.Scatter(name='Best Fit Line', x=np.array(portfolio[:,0]), y=best_fit,
        mode='lines'))
        fig.update_layout(xaxis_title = 'Standard Deviation', yaxis_title = 'Mean',width=900
        ,height=470)
        plotly.offline.iplot(fig, filename="images/risk_return.png")
        fig.show()11
1

Number of assets considered

2

Number of simulations conducted

3

Generating random samples from normal distribution used as returns

4

Generating random number to calculate weights

5

Calculating weights

6

Function used to calculate expected portfolio return and portfolio standard deviation

7

Calling the result of the function

8

Printing the result of the expected portfolio return and portfolio standard deviation

9

Rerunning the function 100 times

10

To draw the best fit line, I run linear regression

11

Drawing interactive plot for visualization purposes

SP risk-return
Figure 1-1. Risk-Return Relationship

Figure 1-1 which is generated via the above-given Python code confirms that the risk and return goes in tandem but the magnitude of this correlation varies. However, depending on the characteristic of stock and the market, it is likely to have negative association as well.

Risk Management

Risk management is not about mitigating risk at all costs. Mitigating risk may require sacrificing return and it can be tolerable up to certain level as companies are searching for higher return as much as lowering risk. Thus, to maximize profit while lowering the risk should be delicate and well-defined task.

Financial risk management is a process to deal with the uncertainties resulting from financial markets. It involves assessing the financial risks facing an organization and developing management strategies consistent with internal priorities and policies (Horcher, 2011).

According to this definition, as every organization faces different type of risks, the way that a company deals with it is completely unique. Every company should properly assess and take necessary action against risk. It, however, does not necessarily mean that once a risk is identified, it needs to be mitigated as much as a company can do.

Managing risk is a delicate tasks as it comes with a cost and even though dealing with it requires specific company policies, there exists a general framework for possible risk strategies. These are:

  • Avoid: In this strategy, companies accept all risks and their consequences and prefer to do nothing.

  • Transfer: This strategy involves transferring the risks to a third-party by hedging or some other ways.

  • Mitigate: Companies develop a strategy to mitigate risk partly because its harmful effect might be considered too much to bear and/or supprass the benefit attached to it.

  • Accept risk: If companies embrace the strategy of accepting the risk, they properly identify risks and acknowledge the benefit of them. In other words, when assuming certain risks arising from some activities bring values to shareholder, this strategy can be picked.

Well, it is worth discussing the main financial risks. Generally speaking, market risk, credit risk, liquidity, and operational risk are the most prominent types of financial risks. As I introduce a new Machine Learning based models related to these risks, I would like to confine myself to these types of risks but I want you to let you know that, in some resources, the list is far more encompassing including legal, business, strategic, and reputations risks as well.

Main Financial Risks

Financial companies face various risks in the course of their business life. These risks can be divided into different categories so that source of risk can be identified and assessed. In this part and the book in general introduce only main financial risk types. These main financial risk types are market risk, credit risk, operational risk, and liquidity risk but again this is not an exhaustive list. There are some other financial risks such as regulatory risk, concentration risk and so on. However, we confine our attention to the main financial risk types throughout the book. Let’s take a look at these risk categories.

Market Risk

This risk arises due to a change in factors in financial market. To be more clear, for instance, an increase in interest rate might badly affect a company, which has short position.

A second example can be given about another source of market risk; exchange rate. International company, whose commodities are priced in US dollars, are highly exposed to a change in US dollars.

As you can imagine, any change in commodity price might pose a thread to a company’s financial sustainability. There are many fundamentals that have direct effect on commodity price, which are market players, transportation cost, gold and so on.

Credit Risk

Credit risk is one of the most pervasive risks. Credit risk emerges when counterparty fails to honor debt. For instance, if a borrower is unable to pay its payment, credit risk is realized. The deterioration of credit quality is also a source of risk through the reduced market value of securities that an organization might own (Horcher,2011).

Liquidity Risk

Liquidity risk has been underemphasized until 2007-2008 financial crisis, which hit the financial market hard. From this point on, researches on liquidity risk have been intensified. Liquidity refers to speed and ease with which an investor executes her transaction. This definition is also known as trading liquidity risk. The other dimension of liquidity risk is funding liquidity risk, which can be defined as the ability to raise cash or availability of credit to finance a company’s operations.

If a company cannot turn its assets into cash within a short period of time, this falls under liquidity risk category and it is quite detrimental to company’s financial management and reputation.

Operational Risk

So, managing risk is beyond being a clear and a foresenable task and exploits a great deal of resources of a company. The questions are now do financial companies a good job for managing risk? Do they allocate necessary resources for this task? Is the importance of risk to a companies sustainability gauged properly?

As the name suggests, operational risk arises when inherent operation(s) in a company or industry poses a threat to day-to-day operations, profitability, or sustainability of that company. Operational risk includes fradulent activities, failuer to adhere regulations or internal procedures, losses due to lack of training etc.

Big Financial Collapse

How important is risk management? This question can be addressed by a book with hundreds of pages but, in fact, the rise of risk management in financial institutions speaks itself. In particular, after the global financial crisis, the risk management is characterized as “colossal failure of risk management” (Buchholtz and Wiggins,2019). In fact, the global financial crisis, emerged in 2007-2008, is just a tip of the iceberg. Numerous failures in risk management pave the way for this breakdown in the financial system. To understand this breakdown, we need to go back to some financial risk management failures. A hedge fund called Long-Term Capital Management (LTCM) presents a vivid instance of a financial collapse.

LCTM forms a team with top-notch academics and practitioners. This led to a fund inflow to the firm and began trading with 1 billion USD. In 1998, LCTM controlled over $100 billion and heavily invested in some emerging markets including Russia. So, Russian debt default deeply affected the LCTM’s portfolio due to fligh to quality 1 and it got a severe blow, which led LCTM to bust (Allen, 2003).

Metallgesellschaft (MG) is another company that is no longer exist due to bad financial risk management. MG was largely operating in gas and oil markets. Due to high exposure to the gas and oil prices, MG needs funds in the aftermath of the large drop in gas and oil prices. Closing the short position results in losses around 1.5 billion USD.

Amaranth Advisors is another hedge fund, which went into banktrupcy due to heavily investing in a single market and misjudging the risks arising from its investments. By 2006, AA attracted roughly $9 billion USD worth of assets under management but lost nearly half of it because of the natural gas futures and options downward move. The default of AA is attributed to low natural gas prices and misleading risk models (Chincarini, 2008).

Long story short, Stulz’s paper titled “Risk management failures: What are they and when do they happen?” (2008) summarizes the main risk management failures resulting in default:

1) Mismeasurement of known risks

2) Failure to take risks into account

3) Failure in communicating the risks to top management

4) Failure in monitoring risks

5) Failure in managing risks

6) Failure to use appropriate risk metrics

Thus, the global financial crisis was not the sole event that led regulators and institutions to redesign its financial risk management. Rather, it is the drop that filled the glass and subsequent to the crisis, both regulators and institutions have adopted lessons learned and improved their process. Eventually, these series of events lead to rise of financial risk management and this book is an attempt to further improvement in risk modeling.

Information Asymmetry in Financial Risk Management

Though it is theoretically intuitive, the assumption of completely rational decision maker is too perfect to be real. This idea, therefore, attacked by behavioral economists, who believes that psychology plays a key role in decision making process.

Making decisions is like speaking prose—people do it all the time, knowingly or unknowingly. It is hardly surprising, then, that the topic of decision making is shared by many disciplines, from mathematics and statistics, through economics and political science, to sociology and psychology.

Kahneman and Tversky (1984:341)

Information asymmetry and financial risk management goes hand in hand as cost of financing and firm valuation are deeply affected by the information asymmetry. That is, uncertainty in valuation of a firm’s assets might raise the borrowing cost posing a thread to a firm’s sustainability (See DeMarzo and Darrell (1995) and Froot, Scharfstein, and Stein (1993)).

Thus, roots of the failures described above lie deeper in a way that perfect hypothetical world in which rational decision maker lives is unable to explain them. At this point, human instincts and imperfect world come into play and a mixture of disciplines provide more plausible justifications. Adverse Selection and Moral Hazard are two prominents categories accounting for the market failures.

Adverse Selection

It is a type of asymmetric information in which one party tries to exploit its informational advantage. Adverse selection arises when seller are better informed than buyers. This phemomenon is perfectly coined by Akerlof (1970) as “The Markets for Lemons”. Within this framework, lemons refer to low-quality.

Consider a market with lemon and high-quality cars and buyers know that it is likely to buy a lemon, which lowers then equilibrium price. However, seller is better informaed if the car is lemon or high-quality. So, in this situation, benefit from exchange might disappear and no transaction takes place.

Due to the complexity and opaqueness, mortgage market in the pre-crisis era is vivid example of adverse selection. More elaborately, borrowers knew more about their willingness and ability to pay than lenders. Financial risk was created through the securitizations of the loans, i.e., mortgage backed securities. From this point on, the originators of the mortgage loans knew more about the risks than the people they were selling them to investors in the mortgage backed securities.

Let’s try to model adverse selection using Python. It is readily observable in insurance industry and therefore I would like to focus on this industry to model adverse selection.

Suppose that the consumer utility function is:

U(x)=eγx

where x is income and γ is a parameter, which takes on values between 0 and 1.

Note

Utility function is a tool used to represent consumer preferences for goods and service and it is concave for risk-averse indivudials.

The ultimate aim of this example is to decide whether or not to buy an insurance based on consumer utility.

For the sake of practice, I assume that the income is $2 USD and cost of the accident is $1.5 USD.

Now it is time to calculate the probability of loss, π, which is exogenously given and it is uniformly distributed.

As a last step, in order to find equilibrium, I have to define supply and demand for insurance coverage. The following code block indicates how we can model the adverse selection.

In [10]: import matplotlib.pyplot as plt
         import numpy as np
         plt.style.use('seaborn')

In [11]: def utility(x):# risk-averse utility function
             return(np.exp(x**gamma))1

In [12]: pi=np.random.uniform(0,1,20)
         pi=np.sort(pi)2

In [13]: print('The highest three probability of losses are {}'.format(pi[-3:]))3
         The highest three probability of losses are [0.84613078 0.8762047
          0.88033329]

In [14]: y=2
         c=1.5
         gamma=0.4

In [15]: Q=5
         def supply(Q):
             return(np.mean(pi[-Q:])*c)4

In [16]: D=0.01
         def demand(D):
             return(np.sum(utility(y-D)>pi*utility(y-c)+(1-pi)*utility(y)))5

In [17]: plt.figure()
         plt.plot([demand(i) for i in np.arange(0,1.9,0.02)],np.arange(0,1.9,0.02),'r',
label='insurance demand')
         plt.plot(1+np.arange(20),[supply(j) for j in 1+np.arange(20)],'g',
         label='insurance supply')
         plt.ylabel("Average Cost")
         plt.xlabel("Number of People")
         plt.legend()
         plt.savefig('images/adverse_selection.png')
         plt.show()
1

Writing a function for risk-averse utility function

2

Generating random samples from uniform distribution

3

Pick the last three items

4

Writing a function for supply of insurance contracts

5

Writing a function for demand of insurance contracts

Figure 1-2 exhibits the insurance supply and demand curve. Surprisingly, both curve are downward sloping implying that as more people demand contract and more people is added on the contract, the risk lowers that affects the price of the insurance contract.

Straight line presents the insurance supply and average cost of the contract and the line, showing step-wise downward slope, denotes the demand for insurance contracts. As we start analysis with the risky customers as you can add more and more people to the contract the level of riskiness diminishes in parallel with the average cost.

adv selection
Figure 1-2. Adverse Selection

Moral Hazard

Market failures also result from asymmetric information. In moral hazard situation, one party of the contract assumes more risk than the other party. Formally, moral hazard may be defined as a situation in which more informed party takes advantages of the private information at his disposal to the detriment of others.

For a better understanding of moral hazard, a simple example can be given from the credit market: Suppose that entity A demands credit for use in financing the project, which is considered as feasible to finance. Moral hazard arises if entity A utilizes the loan for the payment of credit debt to bank C, without prior notice to the lender bank. While allocating credit, the moral hazard situation that banks may encounter arises as a result of asymmetric information, decreases banks’ lending appetites and appears as one of the reasons why banks put so much labor on credit allocation process.

Some argue that rescue operation undertaken by FED for LCTM can be considered as moral hazard in a way that FED enters into contracts on bad faith.

Conclusion

This chapter presents the main concepts of financial risk management with a view to make sure that we are all on the same page. This refresher helps us a lot throughout this book because we take advantage of these terms and concepts.

In addition to that, an approach attacks the rationality of the finance agent takes place in the last part of the first chapter so that we have more encompassing tools at our disposal to account for the sources of financial risk.

In the next chapter, we will discuss the time series approach, which is one of the main pillars of the financial data analysis in the sense that most of the financial data has a time dimension requiring special caution and technique to deal with.

Further Resources

Papers and articles cited in this chapter:

  • Akerlof, George A. “The market for “lemons”: Quality uncertainty and the market mechanism.” In Uncertainty in economics, pp. 235-251. Academic Press, 1978.

  • Buchholtz, Alec, and Rosalind Z. Wiggins. “Lessons Learned: Thomas C. Baxter, Jr., Esq.” Journal of Financial Crises 1, no. 1 (2019): 202-204.

  • Chincarini, Ludwig. “A case study on risk management: lessons from the collapse of amaranth advisors llc.” Journal of Applied Finance 18, no. 1 (2008): 152-74.

  • DeMarzo, Peter M., and Darrell Duffie. “Corporate incentives for hedging and hedge accounting.” The review of financial studies 8, no. 3 (1995): 743-771.

  • Froot, Kenneth A., David S. Scharfstein, and Jeremy C. Stein. “Risk management: Coordinating corporate investment and financing policies.” the Journal of Finance 48, no. 5 (1993): 1629-1658.

  • Stulz, René M. “Risk management failures: What are they and when do they happen?.” Journal of Applied Corporate Finance 20, no. 4 (2008): 39-48.

Books cited in this chapter:

  • Horcher, Karen A. Essentials of financial risk management. Vol. 32. John Wiley & Sons, 2011.

  • Hull, John. Risk management and financial institutions,+ Web Site. Vol. 733. John Wiley & Sons, 2012.

  • Kahneman, D., and A. Tversky. “Choices, Values, and Frames. American Psychological Association.” (1984): 341-350.

  • Harle, P., Havas, A., & Samandari, H. (2016). The future of bank risk management. McKinsey Global Institute.

  • McNeil, Alexander J., Rüdiger Frey, & Paul Embrechts. Quantitative risk management: concepts, techniques and tools-revised edition. Princeton university press, 2015.

1 Flight to quality term refers to an herd behavior by which investors stay away from risky assets such as stocks and takes long position in safer assets such as government-issued bond.

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