Risk Indicator Roundup
A matter of tasteBy Rafael Ballestas  May 15, 2019  Category: Philosophy
What is the best risk indicator? Bottom line: there is no "best", only different approaches to the same thing. Ultimately, it’s up to you. Here we will show the pros and cons of each risk indicator so you can make an informed decision.
VaR
Recall that Value at Risk (VaR
) measures the
worstcase scenario in an uncertain return by telling us the endpoint
beyond which our losses will likely not go, up to a certain degree of
confidence, in a definite period of time. Thus a daily 1% VaR
of $10
million means the probability that you will lose more than $10 million
is 1%, which is the same as saying that you are 99% confident that the
losses will not exceed $10 million.
Pros:

Gives a good idea of how much to save in order to avoid bankruptcy in most (95%) cases.

Is a wellestablished standard, used by most banks and a requirement per international banking regulations.
Cons:

Says nothing about what might happen beyond the threshold.

Is a single number, therefore, its expressiveness is rather narrow. It says nothing about what happens elsewhere with the distribution of returns.
tVaR
While the VaR
gives a worstcase scenario with a certain confidence,
what if that confidence is broken, i.e., the VaR
is breached? What can
we expect? That’s precisely the tail value at risk tries to answer. By
using the expected value of a conditional
probability, it gives us,
in a single number, what would be expected if a worstcase scenario
occurs.
There is no better way than this plot by
Nematrian to summarize both
VaR
and tVaR
.
Figure 1. (t)VaR illustration
Pros:

Prepares you for the worst of the worst.

Single number, easy to compare or monitor over time.
Cons:

Not easy to compute (involves an integral).

Results can be overly pessimistic, thus impeding you from seeing the other side of the coin.
ALE
This is a relatively new one. Remember we discussed Return on Control
(ROC
) to decide whether investing in a given defense is worth the
hassle?
Figure 2. Return on control
The change in loss was obtained from two simulated scenarios: one with the control and another without it. Both were obtained by "averaging out", i.e. finding the expected value of a simulated distribution for the loss.
The Annualized Loss Expectancy (ALE
) is related to such a computation
in that it is also obtained from a couple of expected, estimated values.
These estimated values are the expected number of ocurrences of an event
in a year (the Annualized Rate of Occurrence, ARO
), and the expected
loss for a single ocurrence (Single Loss Expectancy, SLE
). Thus, total
= reps x single. Too many acronyms for too little content:
Figure 3. You don’t want to ask Chandler about his Annual Net Usage Statistics!
Experts can estimate the ARO. Suppose it is known that a data breach
will most likely occur at least once in 10 years. The ARO
for such an
event is 1/10 = 0.1 events per year. The SLE
is to be estimated by
your own experts. How much would such a breach cost you? Say, $100
million. Then the loss expected in every one of those years is 0.1x100 =
$10 million. However, this rate will be fixed for each of the next ten
years. It is static and unlikely to be true since risks and threats
change daily.
Pros:

Simple computation.

Single number, thus easy to compare.
Cons:

You’re stuck with the one year period.

Not very "realistic".
LEC
The loss exceedance curve is a decidedly different one, and one of our favorites at that. We have already discussed it at length in our introduction to quantitative risk, our general Monte Carlo simulation article, and gave an example of implementing in Quantitative Python. In a nutshell, it’s a graph that tells you the probability of losing a given amount or more of money, for any amount in a range. It’s like having all possible valuesatrisk for all confidence levels. We believe the graph speaks for itself.
Figure 4. Loss Exceedance Curve from Hubbard et al.
Pros:

All the information you could want about losses in a single plot.

Since it’s a visual tool it’s helpful when you’re considering a range of risks you’re willing to take, especially when it’s combined with residual risk and risk tolerance curves.
Cons:

Harder to compare since it’s not a single number.

Harder to obtain, since it involves simulations.
Overall, single number risk indicators (ALE
, VaR
and tVaR
) are
good for making quick comparisons and monitoring them over time. In
contrast, the LEC
might allow you to make a more finegrained decision
regarding how much risk you are willing to take vs. how much you would
have to lose in many different scenarios, all in a single chart.
For ease of use, we’d say ALE
is the winner. However, we wouldn’t
expect its predictions to be the most accurate of the lot. Also, its
time period (one year) might be too much for the fastpaced market we
currently live in. If you have to choose one singlenumber indicator, we
would recommend using VaR
, wich international banking regulations
(Basel II) use,
since the tVaR
might be a tad too extreme.
In the end, it’s your choice. Or there might not be any choice to make at all. Who says you cannot use them all at once? If done well, they should not be contradictory, but complimentary. Find out all you can about your investment, use all the tools at hand, and then make the best decision possible in terms of risk vs gain.