Quantification of Risk in Finance 

While risk may initially seem like an abstract concept, the ability to quantify and  compare the risk which comes with acquisitions and investments is one of the concepts which falls at the heart of modern finance. This allows financial institutions to make decisions regarding investments by providing a metric to compare an investment’s return with the risk it is associated with. Overall, it allows investors to manage the risk to their securities/portfolio. From pension funds to day traders, the ability to quantify risk shapes investment decisions all over the world. 

Types of Risk 

Risk can be divided into various categories, the largest of which are systematic and unsystematic risk. 

Systematic Risk, also known as market risk, is an in-diversifiable and unpredictable type of risk which affects an entire market or sector, rather than a single company or security. While it can somewhat be mitigated through diversification across sectors and markets, it is impossible to significantly reduce as it inevitably affects the majority of securities an investor is able to hold in their portfolio. An example of systematic risk would be things such as a severe recession or unexpectedly high levels of inflation 

Unsystematic risk is a type of risk which only affects a small group of securities. Because of this, it can be reduced far more than systematic risk through methods such as portfolio diversification. As unsystematic risk is far more case specific than its aforementioned counterpart, it is often divided into various types.  

Credit Risk is the probability of financial loss resulting in a borrower defaulting (failing to repay) on a loan. A major example of credit risk is the 2008 financial crisis, particularly when Lehman Brothers was forced to file for bankruptcy following hundreds thousands of people defaulting on mortgages. 

Operational Risk is the risk associated with the potential loss which results from inadequate internal procedures and poor execution of a company’s day to day business activities. For example, in 2012 Knight Capital Group experienced a trading loss of $460 million as a new trading software placed billions of dollars worth of unintended stock orders due to a coding glitch, a prime example what can happen when operational risk is not properly considered and adequate precautions are not put into place. 

Liquidity Risk is the risk that a company may not be able to obtain the necessary liquidity(cash) in a short term period at a reasonable price and therefore in consequence may not be able to meet its financial obligations. A recent example of liquidity risk was during COVID when even typically stable assets such as government bonds became hard to sell, meaning bond holders were unable to liquidate their assets. 

Tools for risk representation and management 

The main aim for an investor or fund is to minimize the risk associated with an investment/portfolio while maximizing the returns the portfolio can produce. Some tools that firms can use to do so are:  

Standard Deviation 

A mathematical concept that measures the amount by which individual data points differ from the mean movement of the market, i.e. determines the range of asset price from its average price. More variation from the mean price causes a higher standard deviation 

The formula below is used to calculate the standard deviation: 

  

This equation calculates the variance for each data point by subtracting the mean from the value of the data point, squaring said variance, then adding all these values and dividing them by the number of data points in the set. This gives you the variance of the data set from its mean value. 

This value is used as a measurement of market volatility and can be used to predict with high levels of certainty the range in which a security’s price will fall. This is possible because (in a normal distribution) individual values will fall within one standard deviation of the mean 68% of the time, and with two standard deviations of the mean 95% of the time. An example of this in practice would be if the closing price for a security is $100 and it has a standard deviation of $5, the next closing price has a 95% chance of being between $90 and $110. This allows investors to predict returns even if securities/the market go down over time and allows worst case scenarios to be predicted, as well as best case scenarios.  

Overall, the greater the standard deviation of a security, the more volatile it is, meaning it has the capability of producing both greater loss and greater return; in other words, the more an investment’s  price varies from its own mean, the riskier the investment. 

Value at Risk (VaR) 

VaR is a calculation of the maximum possible loss which a portfolio can experience over a set period of time. It is represented by using the amount of potential loss, the probability of said loss actually occurring, and the time frame in which the loss would occur (i.e. the maximum potential loss a portfolio could experience within a set of predefined parameters.) For example, a firm might calculate that a security has a 5% 3 month VaR of 2%, meaning that there is a 5% chance of the asset losing 2% of its value over 3 months. This method allows firms to project future loses and ensure they have enough capital available to survive and cover said loses if they were to occur, and if not, allows them to identify which high-risk assets need to be reduced/removed from the portfolio.  

To calculate the VaR, firms can choose one of three methods: 

Historical Calculation – looks at a security’s prior returns and uses it to assume future profits and losses 

Variance-Covariance Calculation – assumes a normal distribution of returns (gains and losses), therefore allowing the losses to be calculated using the standard deviation from the mean. It is best for large and well understood distributions; it begins to lose accuracy when the number of data points available reduces. 

Monte Carlo Simulation – uses computational modeling to represent projected returns over thousands of possible iterations. Following this, it assumes a loss will occur an arbitrary percentage of the time (e.g. 5% of the time) and indicates what the impact would be (relies on the idea that the distribution probability of the risk factors is known). 

Beta  

A security’s Beta is a measurement of how closely an asset on the market follows the overall movement of the market. A high beta would represent high levels of volatility relative to the market, meaning a change of 2% in the market might cause a 10% change in the value of the security. On the other hand, a beta of less than one would indicate the opposite, and a negative beta suggests an inverse relationship between the movement of the market and that of the value of the security. 

Sharpe Ratio 

A Sharpe Ratio is a measurement used to represent the performance of an investor in relation to the risk taken by said investor. It is calculated by subtracting the risk free rate of return from the projected return of a portfolio and dividing this figure by the standard deviation of said portfolio. For example, if an investment manager operated in an area with a risk-free rate of 5% and their portfolio generated a return of 20%, if the standard deviation of the portfolio is 8%, the Sharpe ratio would be 1.875 ((20-5)/8). 

This example would be considered an adequate Sharpe Ratio. Typically, a ratio of 2 or above is considered very good, while 1 and above is adequate.  

The advantage this method has compared to other methods is that is allows risk and reward to be compared directly and objectively with each other, rather than only considering the risk associated with an investment and not the return it produces as the methods above do. 

Overall, the Sharpe ratio allows an investor’s return to be directly compared with the risk they take on to achieve said return. 

Behavioral Risk 

Behavioral risk differs somewhat from the risk types discussed above. It covers a more intangible side of risk which is dictated by the actions of an investor themselves. It encompasses things like making irrational decisions due to sentimental or cultural factors and the different ways people process cognitive inputs which could eventually lead to differing (and potentially sub-optimal) returns on an investment. 

While it is very difficult to minimize, the best way to reduce the risk of sub conscious bias and behaviour affecting the return of a portfolio are to ensure there are no conflicts of interest between a portfolio manager and the securities they manage. This ensures decisions are taken unanimously and as a collective, rather than being dictated by a singular individual who may have strong personal beliefs or attitudes that could skew returns. 

Strategies for Risk Minimization 

• Diversification 

One of the most common risk minimization strategies, diversification involves holding a wide variety of investments and securities, reducing both systematic and unsystematic risk. It does this as it limits the risk to the portfolio from one singular asset and allows losses experienced in one investment to be made up for/covered by other assets in the same portfolio. This approach is most commonly used when trying to have a constant, long-term yield, rather than high levels of portfolio growth in a short space of time.  

Typically, investors will look to diversify a portfolio both through industry (e.g. defense vs tech), and through a variety of asset classes, the most important of which are: 

• Stocks (also known as shares) 

Stocks can be divided into value and growth stocks, which have slightly different purposes in a portfolio. Growth stocks are expected to show high levels of growth due to projected revenues (i.e. cashflows) which are higher than the industry average, while a value stock is a stock which currently appears to be trading at a discount (or in other words is undervalued) on the market, and is therefore expected to be worth more in the future 

• Bonds 

Bonds can vary in length and yield, going from 1 year to 30 in duration and all having different interest rates, further allowing an investor to diversify.  

• ETFs 

Some examples of ETFs would be S&P 500 or FTSE 100 ETFs. These can be very useful to investors as they themselves are already very diversified, often holding 100 different securities or more within them. 

Non-correlating Assets 

Similar to Diversification, including assets such as Real Estate and Commodities in a portfolio can reduce the systematic risk said portfolio is subjected to as so-called ‘non-correlating’ assets tend to react differently to movement in the market, often showing an inverse relationship, providing a form of safety net for a portfolio in the case of recession or a very bearish market. 

Hedging 

In simple terms, hedging is the process of betting against yourself in an investment by using futures and options to offset any potential losses. It involves trading in two securities which are likely to move in opposite directions; this means that while it may reduce the risk to a portfolio, it is also likely to reduce the overall returns the portfolio would receive.  

There are 2 main Hedging Strategies: 

Volatility Index Indicators 

A volatility Index functions in a similar way to an ETF. This means that when the volatility of calls and puts on the S&P 500 increases, the value of the chosen Volatility Index also increases. (N.B. a volatility index is not an ETF in and of itself, but there are ETFs on the market which represent volatility indexes.) This allows investors to hedge their portfolio as if market volatility increases and their returns are put at risk or even begin to reduce, the volatility index will rise in value, reducing the net loss the portfolio experiences.  An example of a Volatility index can be seen below. 

Modern Portfolio Theory 

Modern Portfolio Theory (MPT) is a process which makes use of the idea of diversification; it creates groupings of assets designed to reduce volatility. MPT makes use of statistical calculations in order to obtain an efficient frontier (a set of portfolios which offer the greatest possible return for the risk that they are associated with) and find the desired return for X amount of risk. This then allows the correlation between assets, their volatility and expected return to be examined and an optimal portfolio to be created which maximizes return and minimizes risk. An example of what an ‘optimal portfolio’ might look like can be seen below. 

  

Hard Stop Orders 

Hard-Stop orders allow portfolio managers to have a built-in fail safe in their investments. They allow securities to be sold automatically if their price falls below a certain value.  For example, if the price of a share were to fall by more than one standard deviation, then a portfolio manager may have installed a hard-stop order which would automatically sell the shares to minimize the loss experienced by the portfolio. 

Risk can never be entirely eliminated, but it can be managed through some of the methods mentioned above. These practices are essential in finance as they allow investors to maximize their returns while minimizing the risk they experience and ensure that a fund or investor’s portfolio is never overexposed to certain types of risk.