How accurate is accurate enough?
Let's begin with a simple task – estimating the total number of words printed in a 200-page book, accurately.
You only have one minute for the task. You probably would have no choice but to adopt some "sampling strategy" which looks like this: Choose a page at random and count all the words on that page, and multiply by page count. This should give you a good ballpark number. Let's say this estimate is around 85 per cent accurate.
To improve beyond 85 per cent accuracy, more time is needed. Take another minute. To spend it wisely, you look for the "lowest hanging fruit" which can give you the best accuracy boost. Potentially, you could consider scanning the whole book to look for and subtract blank spaces in terms of page count from the total. This revised estimate is likely to be much more accurate and possibly get you to within 5 per cent inaccuracy.
Intuitively, we have just built a model for our "word-counting" problem which bears the following formula. "Estimated total word count" (A) = "average word count per page" (B) multiplied by "adjusted page count." (C) The more time we spend on the task, the better we can refine our estimates for the two parameters (B and C) in our model, and the closer we can get to being fully accurate.
The Pareto principle
In the above example, we see that the first two minutes spent were arguably the most worthwhile as they covered 95 per cent of the task at hand. Obtaining the final 5 per cent in terms of accuracy is not only costly, but may well not be necessary, depending on the context of the problem.
Graphically, the time-versus-accuracy tradeoff looks something like this chart below. An "efficient" manager may decide to terminate his word counting effort at the 2-minute mark and move onto other tasks.
Chart 1: The manager decides that spending further time to refine what is already a 95 per cent accurate estimate is not worth it.
This efficient manager has unconsciously but intuitively applied the "Pareto principle" (also known as the "80-20" rule) to his great benefit.
How can we apply the Pareto principle to currency risk management?
There is one striking difference between the word-counting example above and real-life currency risk management. The word-counting manager cannot have possibly spent negative time on the task. However, a risk manager can spend a negative cost. i.e. receive a benefit, from hedging.
This is possible because the forward point of a currency pair can be positive or negative depending on the direction of the interest rate differential between the two currencies. For example, based on the current rates environment, selling EUR forward against USD, or swapping your USD debt into EUR debt, can derive some cost benefit.
In the risk management world, the Pareto point, or the "sweet spot" can be different for different companies in the context of their financial risk appetite and budget
A negative hedging cost is very often efficient, making sense for portfolios because it will reduce risk and overall costs of hedging at the same time.
What do we mean by "efficient"?
Here, we introduce the concept of "Pareto efficiency", a concept tangentially related to the Pareto principle. It represents a state where it is impossible to improve one variable without harming another. If it is possible to improve both variables at the same time, or improve one variable whilst keeping the other unchanged, we are not yet in an efficient state, and should continue acting until we reach this point.
Imagine you are the word-counting manager again. You noticed a subordinate spent his two minutes counting more pages to arrive at his estimate. You then tell him that it is wiser to spend one minute on one page and another minute scanning the whole book adjusting for the total page count.
You have just helped him improve his accuracy without prolonging his total time spent. He was in a state of inefficiency.
Similarly, in a currency portfolio, it is often possible to reduce risk without increasing the overall cost. This is achieved by hedging multiple currencies in a fashion such that the forward premia received equal any forward premia paid, whilst minimising portfolio risk. This is illustrated by "Arrow 2" in the chart below.
Chart 2: "No real trade-off until the efficient frontier is reached." The overall hedging cost remains at net zero but USD 100m of risk has been hedged away. (Arrow 2)
Harnessing the power of Pareto principle and Pareto efficiency
Once you are at a point of Pareto efficiency, which is to say you have already exhausted all possibilities to improve both costs and risks, you are at the "frontier", the boundary containing all possible results in terms of risks that may arise from the underlying portfolio and various hedging overlays. (That's why the line of Pareto efficiency is often called the "efficient frontier").
From this point onward, any risk reduced will have to come at a cost. (Correspondingly, any cost benefit will come at the expense of higher risk).
We can now return to the Pareto principle, and apply it to this efficient frontier. As risk is reduced (moving from right to left along the efficient frontier), marginal costs rise. (Notice the curve caving upwards). Where to stop along this curve is subjective, and will depend on the risk appetite of the individual company.
Whilst the manager in our first example decided to stop at the 2-minute mark to achieve 95 per cent accuracy. Others may have preferred spending 10 minutes to achieve 99 per cent accuracy. Both would be Pareto efficient, but represent a different weighting of costs and benefits.
In the risk management world, the Pareto point, or the "sweet spot" can be different for different companies in the context of their financial risk appetite and budget. (See "Arrow 4" of Chart 2)
Key takeaway for CFOs and treasurers
Machine learning and optimisation may sound complicated and technical. But the intuition needs not be. In fact, the principles are more important because they represent the why's rather than the what's. Technology should be seen as an enabler to help companies more fully and consistently apply their favourite principles.
In this article, we have explored the intuition of optimality and efficiency using the concept of Pareto principles. They can be applied in the following two steps.
- First, look for all untapped opportunities which can improve both cost and risk, thereby attaining a "Pareto efficiency."
- Second, once you are already Pareto efficient, look for the optimal tradeoff along the efficient frontier, subject to appetite for cost and risk. (One could use the concept of equilibrium to search for his own optimal point, i.e. equilibrium is the point at which marginal benefit equals marginal cost).
Both can be obtained and graphically visualised by a quantitative technique called the "efficient frontier" analysis.
Please see our third "Rethinking Treasury" article – "The importance of quantitative approaches in risk management in three points" which is a related article explaining how an analytical approach such as the efficient frontier analysis can help broad framing and understanding the underlying cost and risk tradeoff of the portfolio better.
HSBC's Thought Leadership has dedicated expertise to help companies optimise their portfolio risks via analytical models such as value-at-risk and efficient frontier analysis.
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