The nature of premium illusion in finance – Part II
I noted in my last blog that I intend to write a series of blogs that examine premium illusion, describing it as an issue that market risk decision-makers may not realise they even encounter.
Premium illusion is a related topic within the field of financial loss aversion, which has been studied extensively, and which holds that it is basically natural to have a heightened sensitivity to losses versus gains. However, the not unnatural fear of financial loss from the paying of option premiums is quite chronic, but can be found to be unwarranted (illusory).
In this blog I’m going to turn from a market in which I knew (well, in truth I suspected) there would be solid evidence of illusion, to one that I don’t: the Foreign Exchange market.
I’m surprised by what I find with this rather simple analysis. I suspect readers will be too.
Premium illusion defined
In my last blog I did a rather poor job of explaining premium illusion.
Readers should note that the work presented here is predicated on my personal definitions, formed after having worked in markets for financial options for many years. They should also be aware that I have at times been a very heavy user of financial options and a serial payer of option premiums in various dealing settings.
Of definitions, there are plenty of obscure and some better-known financial texts that contain different definitions to my own. What’s important is not necessarily the neatness of the definition, but what readers are able to make of the data analysis presented in this piece.
With those caveats out of the way, I want to try and clear up a key distinction; while premium illusion is related to premium aversion, there are subtle differences in the financial markets’ product context. This is particularly the case where market participants consider the use of option products versus what we might call ‘non-premium’ products:
Premium aversion is the desire or preference to avoid paying premiums, regardless of the assessed value of an option holding in a particular risk setting,
Premium illusion is a mistake of premium value-interpretation and comes in two forms:
the impression that premium expenses are almost certainly irrecoverable, or typically worthless; and
the impression that non-premium instruments are ‘free’ or contain no potential future premium in the form of opportunity, or actual loss.
I should also mention that while option products are somewhat similar to insurance products, there are key differences, which is perhaps a topic for another blog. What readers should note is that typical price-setting frameworks for financial options consists of professional, two-way markets, where premium payers and earners trade freely with each other in increasingly transparent markets for implied volatility (that crucial common determinant of options value).
A crazy way to assess option value?
In keeping with the approach to assessing options value of my first blog, I look at value in a comparative setting between competing products, one containing an up-front premium, and one that does not. Readers will recall that I make no attempt to conduct an assessment of whether premiums paid resulted in positive option pay-offs at expiry.
Why?
Because the terminal pay-off approach can be quite misleading where risk-hedging is concerned. Also, studies of terminal payoffs have been done many times elsewhere, and of course such studies tend to show that options have a chronic tendency to expire worthless (another potentially misleading result and another possible future blog topic); our task here is to demonstrate whether there is a genuine value to holding intertemporal choice!
My approach is very simple. To recap:
Assume you are tasked with hedging a future short exposure to the AUD/USD exchange rate with a 1-Year horizon (i.e., typical of an Australian exporter)
Your mandate requires that you must hedge, but you’re left free to choose between:
entering a 1-Year forward purchase (i.e., hedging fixed)
buying a 1-Year call option to the forward expiry
Here, I exclude the choice of doing nothing for the reason that I am wanting to demonstrate premium illusion between competing financial markets products (doing nothing is certainly a valid strategy, but it does not involve competing products).
Data selection?
While it may be instructive to look at randomly selected data, and this may become a topic for a future blog post, in this study I am simply using ten years of AUD/USD FX data up to February 2022, comprising:
Outright Spot
1-year Forward
1-Year at-the-money forward call premium
There is nothing particularly special, and certainly nothing random about ten years (2,368 observations) of AUD/USD FX data. It is, however, topical for local and some international currency hedgers, and I hope to be able to show some serial features of premium illusion that local readers will be familiar with.
Why only 2,368 points in ten years? A typical market standard of options users is to apply a 262-trading day approach to annualization. However, while we have ten years of historic spot data, we only have nine full years of outcomes.
What are we looking for in the data?
This is the simple bit; we are asking the following question in 2,368 trials of call option outcomes versus outright-long forwards:
How often did subsequent SPOT fall below FORWARD minus CALL premium prior to expiry?
That is, having purchased a CALL option for a premium of X, how often did SPOT AUD/USD market subsequently move to a more favourable level below the outright forward adjusted for the up-front cost (X) of the option.
More favourable level? Yes, that’s the level where the hedger can purchase (and swap forward) at a rate more favourable than the prevailing forward. It’s typically referred to as the break-even level, but we have to be careful with that terminology in the context I am using it (since it typically refers to in-the-money break-even).
What are we ignoring?
The framework I’m using here is extremely basic; ignoring elements of potential options value that are particularly hard to assess.
A more robust study, including residual options values, requires a serious data analysis package and ten years of option ‘volatility surface’ data, thus making it a very large computing challenge. This may also become a topic of interest for us in future blogs, where we will be able to more fully demonstrate illusion.
What’s important to note is that the analysis presented below will certainly understate the full extent of premium value, and therefore the illusion in the AUD/USD market for CALL positions. This is for two reasons:
I make no attempt to estimate the extent of residual premium one could recoup by selling back purchased options when favourable spot levels present (wildly underestimating the value of the options strategy).
Likewise, I make no attempt to asses the extent of forward-rate conditions when spot falls to favourable levels, which given the fact that AUD typically trades at a forward discount to USD are likely to be quite advantageous (all-bar 31% of the observations in the data here).
However, notwithstanding the extent to which my basic analysis underestimates the potential value of optionality or intertemporal choice, value is still quite clearly indicated.
How often did a 1-Year CALL present greater value than a forward?
I mentioned in the introduction that even I was surprised by the results of this analysis.
Why?
Because I was unsure what it would show (there’s that randomness), and the results suggest there is a consistent advantage. Consider the following:
To interpret this, think of the results at each end of the spectrum shown here:
41.3% of the time a call option strategy outperformed a forward hedge within 3-months of its purchase date.
75.8% of the time a call option outperformed a forward hedge at some point in its comparable life.
Within 6 months of purchase, at some point, the option product typically outperformed the forward hedge (by quite a robust margin – above 60% of the time).
What the data is not saying?
It’s important to note that the question I asked of the data was how OFTEN did the call strategy beat the forward, not HOW MUCH did it beat it by. That is; I make no attempt to determine the average value gained when the option strategy pays off, since such an analysis would be too cumbersome and require too many forced assumptions to be viable (though I may take a shot at this in the future).
It’s also important to judge potential gains versus the average option premium paid to engage the CALL strategy. This averaged 0.03035 (303.5 USD pips per AUD) over the ten years, which is the average loss relative to the forward when the CALL strategy failed (i.e., 24.2% of the time).
As an early lecturer once made abundantly clear: there is no free lunch with options.
An example
By way of exemplifying the potential value I selected a single random date where there was a positive CALL outcome relative to the forward: 15th February, 2018.
Sticking with our simple hedger-example, we assume that on this day the choice of hedge for a 1-Year exposure is between:
A: An OUTRIGHT FORWARD at 0.79623
B: A CALL Option struck at 0.79623, costing 0.02605
The CALL can only potentially outperform the OUTRIGHT FORWARD if spot falls below 0.77018 (i.e., 0.79623 less 0.02605) at some point is the 12 months prior to expiry of the option.
Which is suggestive of a significant outperformance of the CALL in this single sample.
If we add in a rebate for the sell-back of the remaining CALL option value on three dates (3, 6, and 9 months respectively), the relative outperformance of the CALL can be calculated.
What about PUTS?
At this point it is reasonable to ask: Would PUT options analysis of the same data-set show similar results if we assume the hedge required were to protect against a falling AUD/USD rate.
It turns out that the results for PUTS are not wildly different to CALLS:
In other words, it hasn’t mattered whether we are looking at up-side or down-side hedges, option products appear to have a strong tendency to present favourable hedge outcomes in the historic data.
Is this sufficient to confirm premium Illusion?
The evidence of favourable relative value outlined here is quite strong, perhaps surprising, but is it sufficient to confirm widespread premium illusion?
The answer is no, not in isolation.
In an attempt to confirm the evidence of premium illusion I turned once more to Bank for International Settlements BIS data, which shows (as it did for IR-Swap versus Swaption data) that options use is far outweighed by that of outright spot/forward in product usage:
In other words, FX Spot/Forward product use appears to run at a factor approaching 7-times (6.8x) that of comparable FX-Options products, despite evidence of more balanced value outcomes between the competing products (and this despite the fact that the bulk of FX Options turnover is interdealer driven – approximately 3-1x).
Which suggests there is something fundamental that deters hedgers from deploying option products within hedge programs.
That something is likely to be premium illusion mixed with an overabundance of outright premium aversion.