# What is risk: A review of basic concepts for beginners

Editor’s note: A very warm welcome to Danish, the newest member of our risk practice who is going to document his journey of getting up to speed with risk management on these pages. Follow Danish’s journey as new risk resource as he navigates basic terminology, builds his first models, and takes his first computational finance exam.

# What is risk management?

You have decided to take the first step in your quest to understanding the risk management framework of Banks and their regulations, Basel II and Basel III. This involves understanding the basic concepts underlying most of risk management, concepts that you will come across time and again as you make your way through the immense store of knowledge available out there on this subject. Among other things these include:

1. Risk Preferences
2. Diversification
3. Arbitrage
4. Market Efficiency
5. Market Completeness
6. Asymmetric Information
7. Time consistency
8. Moral Hazard
9. Nash Equilibrium
10. Bayes Rule

## Risk Preferences

We first consider the interaction of economic agents with the economic situations they face. It is necessary to understand the psychology of the participants before reaching any conclusion about their behavior. What are the varying attitudes among participants engaged in risky activities?

Suppose you are playing a game in which you are presented with two options;

1. Receive a guaranteed amount of \$200 or
2. Consider this gamble: A fair coin is flipped with equal chances of heads or tails showing up. If it turns up with heads you win \$400, if the result is tails, you get nothing.

What would you choose? If you say both options are fine and equal then you are being indifferent to risk. That is the first attitude; of being risk neutral.

Your friend ignores the gamble and instead opts for the first option which guarantees \$200. His choice indicates that he is risk averse. In order to partake of the second option the risk premium he would need from that option needs to exceed the guaranteed option. In this case the expected return from the second option (0.5*400+0.5*0 =200) matches the guaranteed payoff of the first option. This means the risk premium for the uncertain option is zero and therefore, preferring less risk to more, he will opt for the first option.

Another friend says “If I was offered \$250 instead of \$200 in the first option I would go for the certain option, but as it stands I would like to try my luck with the second option”. This shows that he is risk loving, preferring the riskier and potentially higher rewarding option to the certain one, in a situation where expected returns from both options are the same. Next time you want to go on a roller coaster ride with someone, be sure to invite this risk preferring friend.

Why know all this? An important assumption in finance theory is that individuals are risk averse requiring greater risk premium to compensate for undertaking greater risk.

## Diversification

We’ve all heard of the saying: “Don’t put all your eggs in one basket”. This provides a fairly accurate picture of diversification in finance – invest in multiple opportunities to reduce your overall risk. For risk adverse individuals this is an important concept.

Consider the following instance. You have some spare money which you want to invest to fund your college education. What would be more beneficial for you; buying stocks of just one company or buying stock from 20 different companies bellowing to varying industry or sector categories? Choosing stocks whose returns are not strictly positively correlation ensures that as the number of stocks in your portfolio increases, the risk of any individual stock reduces. In other words diversifying your investment opportunities helps to reduce the risk of your portfolio. Note however that this reduces only specific risk, i.e. risk that is specific to a particular investment.

Now ask yourself this question, “Why do seemingly diversified portfolios (benchmarks such as the S&P 500 index) still incur losses of such magnitude as was the case with the Financial Crisis of 2008?”

The answer lies with non-diversifiable or systematic risk. There are a number of reasons why risk may be non-diversifiable. One reason is that all markets may be impacted by a single event, be it a man-made event such as a liquidity crisis or a natural disaster such as a tsunami. These events tend to break down historical correlations and cause markets to react in a similar way across sectors and industries, thus reducing any previous advantages of diversification that holding a varied securities portfolio entailed.

But there are other sources of systemic risk. Due to purchasing power, mobility etc, an investor may only have access to a particular market and therefore to the instruments in that given market. If the market is constrained as to the number of securities (including range across sector or industry) and investment opportunities, the investor will have limited choices for diversification.

Other reasons include the cost of administering and rebalancing a portfolio and the cost of researching new industries and sectors to invest in versus the benefit of reusing information. These act as disincentives for diversification.

## Arbitrage

Defined simply, arbitrage is profit without risk and investment, i.e, a free lunch on the back of an ignorant market. Most of financial theory is based on the assumption that arbitrage is not possible in an efficient market. Empirically speaking, instances of exploiting arbitrage opportunities have existed in the past and will continue to come up in the future as savvy investors take advantage of pricing disparities. However these advantages are usually short lived and of questionable magnitude as market forces quickly act to remove any existing discrepancies. Arbitrage-free assumption is crucial for Arbitrage Pricing Theory as well as the influential Black Scholes Framework which covers valuation of derivatives.

## Market Efficiency

The basic idea is that markets are efficient. After all why would anyone trust the market with their hard earned money if it was not? Efficiency is displayed in markets prices of securities confiscating or assimilating all appropriately defined information immediately and fully. This is achieved through competition among investors and the resultant exchanges of information between them.

There are three types of market efficiency. Weak form efficiency is when prices assimilate all historical information. This implies that tomorrow’s price may be forecasted by using the entire spectrum of historical prices or alternatively just today’s price (which already includes the information of all past prices). Mathematically, predicting tomorrow’s price is a Markov Process where an event is predicted using its present state (today’s price) alone.

Semi strong form efficient markets are markets where the current price reflects all publically available information. Strong form efficient markets are markets where prices reflect all information; even those known only to insiders. Most economists rule out strong form markets to be realistic preferring to use the weaker versions in forecasting future prices.

## Market completeness

A complete market is a market where the price of any new security may be valued using the prices of those already existing in the market, such as a derivative product that can be dynamically replicated via cash and the underlying asset. Replicated means any desired profile can be achieved through available securities without friction. Although real world markets are far from complete, the conceptual beauty of a complete market is that it can give individuals total freedom to design portfolios with desired payoffs in varying economic states, subject to only their purchasing power limitations.

Note that in reality the innovation we see in financial markets is a response to the lack of market completeness as financial investors devise ways to work in a world where expectations regarding payoffs and returns exceed the range of securities available to play with.

## Asymmetric Information

Economic transactions involve different people with different sets of information. Statements like “the members of the stock exchange run the market, the market does not run them” illustrate the general sentiment that those with access to privileged information exploit opportunities created by such knowledge. On the other hand it is also expected that those uninformed, know that they are uninformed and anticipate their asymmetric information handicap by acting in a manner that reflects how they foresee those better informed will behave. It is this asymmetry that causes market inconsistencies and irrationality to impact the collective behavior of the market. A good example is a bank run. In a name crisis for instance people anticipate that those with access to insider information will withdraw their money and in response will begin withdrawing their own funds. This often times irrational behavior quickly goes out of control leading to the failure or bankruptcy of many banks.

## Time consistency: Renegotiation proof and Adverse Selection

An important part of financial products is that the contract terms, caveats or conditions within them will be upheld by both parties to a deal over the period of the contract. The assumption is one of time consistency- that the contract will be renegotiation proof and will not allow for adverse selection.

When contract terms are weak, any party may exploit the terms to their advantage and to the detriment of the other parties to the deal. A borrower for example may default on a payment and then rather than be considered a defaulter, the lender may be forced because of weak contract terms to restructure the deal whenever this happens to enable the borrower to be considered active. Such a leeway could provide an incentive to borrowers to continue to be irresponsible about their commitments to lenders. The lenders in turn would have to suffer a higher cost of restructure and renegotiating the deal.

In the insurance industry weak screening processes and badly conceived contracts may lead to adverse selection. For example, if there is no effective screening process for smokers then smokers may be provided standard (non-smoker) rates despite the increased risk. The resulting higher incidence of deaths among the insured population will be greater than the mortality assumption and related cost factored in the insurance premiums exposing the insurance company to greater mortality risk than expected.

## Moral Hazard

I vaguely remember a crime story in which the husband killed his wife by maliciously tampering with the iron and she died due to the electrocution. In the end, when police were able to extract the truth from him, he said he had committed this heinous act to receive the insurance money on her wife’s life. Talk about stacking the odds.

This is an example of moral hazard but note that it is an extreme one. In most cases these events may not even be illegal. A moral hazard occurs when the interest of the principal for example an employer, bank or an insurance company does not match with that of the agent for example an employee, investor or policyholder and causes conflicts, such as an agent making the principal cover a false claim on insurance due to ineffective underwriting processes. Therefore in setting up contracts, the principal has to account for the possibility of agents gaming the system and include terms and conditions to prevent or reduce these occurrences from happening.

## Nash Equilibrium

Nash Equilibrium occurs when two players or more in the game, knowing each other’s possible moves, enter into a situation which is optimal for each and there is no motivation for them to change positions. It is the collective resolution of individual actions. The motivation or belief is that players acting in collective interest produce better results as compared to the outcome if players acted alone. An example is an oligopoly where a few dominant firms rule the market. Real world instances include oil and gold companies. For instance, OPEC oversees decisions in the oil sector, routinely making decisions like production quota allocations to each member country instead of letting them compete in the open market. OPEC countries therefore can control supply and hence oil prices often to the monetary advantage of each member.

## Bayes Rule

Bayes rule is composed of three components; prior beliefs that a person already may have regarding a certain random event before the arrival of new data or information, the likelihood of various outcomes based on observation and posterior perceptions which are a result of the combination of prior beliefs, existing data and observed outcomes about a random event. The rule indicates how a rational person would react to new information- reassessing previously held expectations based on revised circumstances and conditions.

Please see Greenbaum and Thakor’s “Contemporary Financial Intermediation” for a more in depth treatment of the above topics