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Risk Assessment: Scenario Analysis and Value-at-Risk

The derivatives Greeks are tools derivatives end-users employ to describe and to characterize the various exposures to fluctuations in financial prices inherent in a particular position or portfolio of instruments. Such a portfolio of instruments may include cash instruments, derivatives instruments, borrowing, and lending. In this article, we will introduce two additional techniques for risk assessment and reporting: Value-at-Risk assessment and scenario analysis.

Risk Assessment

Besides the “Greeks” there are other techniques we can use to evaluate, report, and measure risk, namely, value-at-risk assessment and scenario analysis.

Analyzing Risk Assessment

Value at Risk

Financial institutions and corporate Treasuries require a method for reporting their risk that is readily understandable by non-financial executives, regulators and the investment public. They also require that this mechanism be scientifically rigorous. The answer to this problem is Value-at-Risk (VaR) analysis. VaR is a number that expresses the maximum expected loss for a given time horizon and for a given confidence interval as well as for a given position or portfolio of instruments. VaR is applicable under normal market conditions, attributable to changes in the market price of financial instruments.

What does this mean in English? Suppose that we are investment managers with positions in foreign exchange, fixed income and equities. We need an assessment of what we can expect the worst case to be for the position overnight with a 95% degree of confidence. The VaR number gives us this measurement. For example, the portfolio manager might have 100 million dollars under management and an overnight-95% confidence interval VaR of 4 million dollars. This means that 19 times out of 20 his biggest loss should be less than 4 million dollars. Hopefully, he is making money instead of losing money. You can also express VaR as a percentage of assets, in this case 4%.

VaR is also useful when we want to compare the riskiness of different portfolios. Let us now consider two portfolio managers. Each of them starts the year with 100 million dollars under management. Bob makes a return of 30%, handily beating his target of 20%. Jerry makes a return of 20%, coming in on target. Who is the better fund manager? The answer is, as economists always say, “it depends.” To make an accurate judgment, many people believe that we need to compare the risk involved.

Let’s say that Bob’s average overnight-95% VaR was 7 million dollars and Jerry’s average overnight-95% VaR was 2 million dollars. One way of calculating Bob’s return on risk capital is as follows: 30 million dollars/7 million dollars=428.6% Using the same method, Jerry’s return on risk capital is: 20 million dollars/2 million dollars=1000.0% It could be reasonably argued that Jerry is a better fund manager in that he used his risk capital more efficiently. How many people when they invest in mutual funds know anything about the risk that their portfolio managers take in generating a return? Most mutual funds do not report this kind of risk-adjusted number, although some of them could use it to justify or explain their actions.

Calculating Value at Risk

Value-at-Risk is scientifically rigorous in that it utilizes statistical techniques that have evolved in physics and engineering. VaR is questionable in that it makes assumptions in order to use these statistical techniques. Chief among these assumptions is that the return of financial prices is normally distributed with a mean of zero. The return of a financial price may be thought of as the capital gain/loss that one might expect to accrue from holding the financial asset for one day.

Risk assessment software forecasts the volatility of financial instruments and their various correlations. It is this calculation that enables us to calculate the VaR in a simple fashion. Volatility comes into play because if the underlying markets are volatile, investments of a given size are more likely to lose money than they would if markets were less volatile. Volatility here refers to the distribution of the return around the mean. A volatile market is one in which the returns can vary greatly around the mean; a calm market is one in which the returns vary little around the mean.

Correlation is important, too. Modern portfolio theory is familiar to many people who intentionally diversify their investments. If we invest all of our money in a set of financial instruments that move in the same direction and with the same relative speed, that is a riskier portfolio than if we invest in a portfolio of financial instruments that move in different directions at different speeds. If the instruments in the former portfolio all move down, we will lose money on each of these instruments whereas we would expect to make money on some instruments and lose money on the remaining instruments in the latter portfolio. Hopefully, in the case of the latter portfolio, on average we make more money than we lose.

Correlations move with less persistence than volatilities. It is easy to see how complex the management of financial price risk can be with a portfolio containing more than two or three instruments.

Scenario Analysis

In describing VaR there is an emphasis on the fact that VaR is only good for calculating an expected maximum loss under normal market conditions. Because of the generally idiosyncratic nature of financial prices, we must have a way of understanding the implications for our portfolio under abnormal market conditions. Scenario analysis is the tool we use for this purpose. In scenario analysis, the portfolio manager will simulate various hypothetical evolutions of events in order to determine their effect on the value of the portfolio.

Weak Spots in Risk Assessment

Any portfolio manager must understand what the weak spot is in his portfolio. Naturally, this is the first set of scenarios to simulate. By determining the change in value of his portfolio under stressful conditions (called “stress-testing”), the portfolio manager has a better perception of where the risks in his portfolio lie. At that point, he can make trades that reduce this risk to levels with which he is comfortable. At the very least, he has an appreciation of what will happen so that if the worst-case scenario occurs unexpectedly, he can act quicker and more decisively to manage his portfolio. Without this kind of stress-testing, he will be forced to react in a moving market, a situation that can exacerbate his market losses. In a complex derivatives portfolio, stress-testing that reveals excessively risky exposures either to movements in the underlying cash rate or shifts in implied volatility or interest rates (or combinations of these factors) is said to identify “risk holes.”

- Article by Chand Sooran, Point Frederick Capital Management, LLC

Twitter: @csooran