Histogram Accumulator Frequency of Returns and Buckets

Risksvr™ can produces a wide variety of reports that vary both in type and kind.

Histogram or Bucket Reports are used widely in Financial Risk Analysis as they are a very simple and yet easy to understand.

Histograms combined with quantiles provide a powerful and intuitive predictive capabilities to grasp a position's risk-reward potential as it evolves over time.

Technically, Histogram Accumulator reports, which are also known as Bucket Reports,  display the frequency of your portfolio's return distribution.

In common parlance the Histogram Accumulator report displays the number of times your portfolio's performance has fallen within a given performance range (bucket).

Buckets in a Nutshell

The term bucket illustrates perfectly the process at stake:

Imagine 10 buckets that have been placed side by side. Let's assume we assign each bucket a given performance range.
Since we have 10 buckets, we will take the highest and lowest values we believe our portfolio can take and divide this range into 10 smaller ranges. We then assign each buckets a range.

Now, at the end of each sampling frequency, which is usually daily, we look at the performance of our portfolio.

Every time our portfolio falls within a bucket range, we fill the bucket.

At the end of a selected investment horizon the histogram accumulator or bucket report reveals the cumulative distribution of returns.
We can then read he number of times a returns has fallen within a bucket range, . directly the probabilities or chances of reaching a chosen performance, of falling above or below a threshold by reading the relative quantity in each bucket.

Setting the Histogram Accumulator Buckets

The production of good Histogram Reports can actually be tricky as you need to know how your position or portfolio will behave in advance.

If the position  you are analyzing has a narrow distribution or your buckets are not scaled properly , you returns might all stack up  into the same bucket On the other hand if you have too many bins, you will end up with a monotonous result that will be inconclusive.

This is where custom histogram / buckets come into play. Instead of following complex numerical procedures that work in most cases, the custom histogram bucket allows you to fix the number and size / range of each bucket.

In the Histogram Accumulator, we prime every Histogram Accumulator with a number of pre-runs [1]. 
This means that we find the minimum and maximum range of our portfolio and then divide the intervals into the number of buckets used to bin our returns. We also create two additional buckets to catch values that fall below the minimum and above the maximum return range.
If a return then comes along and falls outside of the minimum maximum  interval we save it [2].

At the end of the Simulation run, we have the N buckets, and a few returns that fell into either the left (Lowest returns or Losses) on right (Highest Returns) tail.

If you are running advanced reports, all returns are saved.

The histogram accumulator usually assumes returns in a given bin are uniformly distributed.