Considering the challenges faced by treasurers in a constantly changing world, it is important that they are equipped with the right tools to help them make relevant risk management decisions. Almost all modern companies with a reasonable amount of complexity could therefore consider a quantitative approach. Let’s start with this question: when it comes to decision-making, do you narrow frame or broad frame?
To achieve a rational outcome for a complex problem with numerous moving parts using broad framing, a statistical model will be the only feasible solution
Point 1 – Understand the limitation of the human mind1
Imagine that you face the following pair of concurrent decisions. You are required to make both decisions at once. First examine both decisions, then make your choices.
- Decision (i): Choose between:
A. sure gain of USD240
B. 25 per cent chance to gain USD1,000 and 75 per cent chance to gain nothing
- Decision (ii): Choose between:
C. sure loss of USD750
D. 75 per cent chance to lose USD1,000 and 25 per cent chance to lose nothing
Did you choose A and D? The most popular combination of choice is indeed A and D, preferred by 73 per cent of respondents. This is hardly surprising – we know that people tend to be risk averse when facing a sure gain and risk seeking when facing a sure loss. (A notion we discussed in our first article, Three scientific reasons why companies hedge.) However, you were asked to examine both options before making your first choice, and you probably did so. But one thing you surely did not do: you did not compute the possible results of all four combinations (i.e. AC, AD, BC, BD). If you did, you would have noticed:
AD: 25 per cent chance to win USD240 and 75 per cent chance to lose USD760
BC: 25 per cent chance to win USD250 and 75 per cent chance to lose USD750
Therefore, there is at least one option that is a superior choice to AD. But only 3 per cent of respondents chose BC.
Point 2 – Understand this is a necessary mental shortcut
This is a classic example of our tendency towards narrow framing. As opposed to broad framing (ie considering simultaneously all possibilities from a holistic point of view), narrow framing considers simple decisions separately, and as our example shows, this could potentially lead to a suboptimal outcome.
Before we feel demoralised by our irrationality, let’s make it clear that it is very understandable why the human mind needs narrow framing. Imagine 5 simple, binary decisions. A broad framing thinking would require computing 32 different outcomes. If the number of decisions increases to 10, the requirement becomes 1,024 different outcomes! It is simply not practical for the human mind alone to perform broad framing.
One popular analysis our corporate clients are interested in is the ‘efficient frontier’ analysis […] which looks at all hedging scenarios by evaluating all possible hedging combinations for all currencies
Point 3 – Understand the importance of a quantitative and analytical approach
There are two takeaways for treasurers and managers. First, it is important to make decisions from the most holistic point of view possible (ie broad framing) and resist the temptation to make easy decisions independently (ie narrow framing). Risk managers should know this all too well already: it does not make sense to manage risks in silos. This is because risks are subadditive, ie portfolio risk can only be equal to or less than the sum of all individual risks combined.
Second, to achieve a rational outcome for a complex problem with numerous moving parts using broad framing, a statistical model will be the only feasible solution.
For example, one popular analysis our corporate clients are interested in is the ‘efficient frontier’ analysis. The efficient frontier analysis looks at all hedging scenarios by evaluating all possible hedging combinations for all currencies. For example, let’s define each hedging ratio to be anywhere between 0 per cent to 100 per cent, indicating no hedge and full hedge respectively. In each hedging scenario, the risk profile changes and so does the hedging cost. The efficient frontier can be established when we connect all the points with the maximum risk reductions and minimum costs.
Chart 1: An example of the construction of the efficient frontier. A cloud comprises all the random hedge portfolios generated by the risk model. We are only interested in the “frontier” line on which risk cannot be further reduced without some increase in hedging cost. (Source: HSBC GMCS Thought Leadership)
This is a perfect example of broad framing at work. All decisions are made simultaneously and an optimal strategy is found. Note, however, that such analysis can be highly computationally intensive. (Don’t worry, we have worked on a portfolio with more than 70 currency pairs before!)
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.
Next month’s topic
Next month, we will use a simple coin toss experiment to learn about some counter-intuitive facts about random processes and what they could mean about unhedged exposures.
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