Cube Return: How is it Calculated?June 16, 2014 - 15:44
CUBE Research offers a number of different measures of return that you can use to compare one product with another. Our Cube Return score is the one we think provides the most useful insight when comparing one product with another.
A reliable and representative calculation of the average return that a product has offered in the past, or is expected to offer in the future is an important part of any product evaluation process. There are a number of different ways to calculate the average return which all have some merit. There are also some ways that this calculation can be done that can lead to very misleading results. We can use the simple example below to illustrate the way that we calculate the expected return:
Example: Suppose for a moment that you are offered a product that costs £1, and that historically it has delivered one of two outcomes:
- 50% of the time the product matures in one year returning £1.10
- the other 50% of the time the product matures at par (£1) after six years
What then is the average return of this product? The simplistic answer is to calculate the probability-weighted annual return from each occasion and conclude that the average return is 5%, but this would exaggerate the return that investors had received in the past.
Do the Right Maths
Calculating the average return for structured products is not as simple as it might seem, and it is very easy to fall into a trap of doing a calculation that seems right, but is in fact very wrong. Calculating possible returns is made more complicated when there is a probability that the product will mature at different times.
Calculating Cube Return
The Cube Return is the probability-weighted average payoff discounted by the probability weighted average term of the product. We calculate this for both forward-looking stress tests and also the backtest.
The first part of this calculation is to multiply each possible payoff by the chance that it will happen according to the historic or simulated data.We calculate the average of these outcomes to gives us the weighted average payoff.
The second part of the calculation is to ascertain the average term of the product. This is also done using historic or simulated data to determine the probabilities of a product maturing on a specific date multiplied by the time (measured in years) to that date.
Finally, we calculate the Cube Return by discounting the average payoff by the average term. For the mathematicians among you it looks like this: ((Σ pt Pt/100)^ 1/Σpt Tt)-1, where p is a probability, P is a payout, and T is the term of ‘t’th instance of the product.
Applying this process to the example at the top we can break down the calculation into its constituent parts:
a. 50% of the time an investor receives £1.10 (50%*£1.10=55p)
b. the other 50% of the time they receive 0% (50%*£1=50p)
The payoff of these two outcomes is 55p +50p = £1.05. So the probability weighted payoff is 5%, (£1.05 divided by £1).
a. 50% of the time the product matures in one year (50%*1yr = 0.5yrs)
b. the remaining 50% of the time the product runs for six years (50%*6yrs = 3yrs)
The total maturity of these two outcomes is 0.5yrs + 3yrs = 3.5yrs. So the probability weighted maturity is 3.5yrs.
So on average the investor has received a pay-off of 5% over an average term of 3.5 years.
This means that the average return is 1.4% per annum (1.05%^(1/3.5)). The average return is not 5%.
David has been involved in equity derivatives, equity structuring and the structured product market for over 25 years. Before setting up CUBE in 2013 David worked at J.P. Morgan, Barclays and RBS. David has worked with and for retail product providers, discretionary managers and institutional investors.