Execution Costs – Mysterious or manageable?
One of the less well understood areas of finance is the impact of transaction costs on standard risk-reward models. While market makers with deep experience know that transaction size impacts costs, this is often not communicated to end market users in a transparent or quantitative manner.
In this first of a series of pieces, I use the efficient-market hypothesis to examine a number of hedging approaches and their impact on deal outcomes. I will show that averaging can be relatively efficient regardless of transaction size, but also that averaging’s benefits are positively correlated to deal size.
Crucially I use historic data to demonstrate that all-in cost probabilities can be quantified.
The Black-Scholes option pricing model transformed modern finance. Whereas prior to 1973 option prices could only be guesstimated, Black-Scholes presented a ground-breaking framework that birthed standardised pricing.
Coupled with the advent of the personal computer, Black-Scholes changed the manner and speed with which markets calculated risk. While arguments as to the limits of the model abound, elements of the original framework can be readily applied to advance our thinking in other domains.
In this piece I draw on the hotly contested efficient market hypothesis, which posits that market movements are essentially unpredictable, and might be thought of as a 50:50 hypothesis. I have often thought of it as simply that “markets are just as likely to go up, as they are to go down.”
As we shall see, while the hypothesis doesn’t perfectly hold, we can leverage it to assess the efficacy of different dealing execution strategies probabilistically. In this piece I use it to demonstrate that a carefully formulated execution strategy can minimise execution costs.
A market example
Let’s start by defining a simple scenario with key assumptions, of which I have chosen four:
As a hedger we are concerned about adverse market movements in the standard 3-year Australian dollar interest rate swap (IRS) market.
We are worried about adverse movements over the coming 3 months.
We have only two choices of how to execute our hedge:
a. At-Close Risk Cover - a single transaction executed at the end of three months, or
b. Progressive Risk Cover - transacting equal portions daily, accumulating in the outright exposure at the end of three months (i.e., approximately 1/60th hedged per day without exception).
All dealings are conducted at closing rates without execution costs.
I purposely chose the divergent forms of execution since they sit at extreme ends of the hedging spectrum. This is to highlight the importance of hedging strategy and the impact that deal size has on transaction costs.
For the sake of scenario framing, the following chart displays 3-year close-on-close swap yields from February 1991 until May 2023, which has been used in this analysis.
What becomes immediately obvious is that there has been a serial decline in yields (a generally rallying bond market) since 1991. We should remind ourselves that while historic outcomes don’t predict the future, the historic hedging outcomes show serial bias, and this has tended to favour swap payers.
Payers were favoured under At-Close Risk Cover ...
Under At-Close Risk Cover, the hedger is exposed to open market risk through the 3-month period, from initiation to close, with final cover being achieved only at the end-of-period closing price.
If the efficient market hypothesis held, we should expect a broadly 50:50 dispersion of favourable versus adverse outcomes, between payers and receivers.
However, as predicted, the long-term decline in 3-year yields within the dataset skews the outcome in favour of paying hedgers under the At-Close Risk Cover since 1991:
Payers, 53.46%
Receivers, 46.3%
Sum of favourable outcomes, 99.80%
Notice here that I have calculated the sum of favourable outcomes, which seems unnecessary. While this may seem superfluous the sum can be used to illustrate an important point and it gives us our results at base-100 which assists make our key point.
Notice, also, that in the case of At-Close-Cover the results do not precisely sum to 100%. This is because of 8,355 observations; a zero return was found on 17 occasions. On those dates neither payers or receivers obtained an advantage.
…. and Payers were likewise favoured under Progressive Risk Cover.
Under a Progressive Risk Cover model, it is assumed that it is possible to hedge the 3-month/3-year IRS risk at the mid-market daily close in equal daily proportions. This results in an ‘achieved transaction rate’ that is equal to the arithmetic mean of closing rates for sixty trading sessions.
The range of achieved rate outcomes (average rate minus initial rate) should still adhere to the efficient market hypothesis, that is: approximately 50:50 outcome split between payers and receivers.
Again, while our analysis uncovers a favourable bias for payers, it remains fairly close:
Payers 53.96%
Receivers 46.04%
Sum of favourable outcomes, 100.00%
And in this case the sum of favourable outcomes sums neatly to 100%.
What happens when we incorporate execution costs?
The two execution scenarios I have described here rely on the ability of hedgers to transact with perfect efficiency. That is: we’ve assumed hedging can be conducted at market-mid, which is obviously unrealistic.
So, what do we find in more realistic settings?
When transaction costs are included in our analysis, we find three things:
Favourable hedging outcomes are inversely related to transaction size under all execution approaches.
Progressive Risk Cover is more efficient than At-Close Risk Cover regardless of size,
The costs related to At-Close Risk Cover are positively correlated with increased transaction size, both nominally and relative to Progressive Risk Cover.
These findings will be unsurprising to market makers and those with deep markets experience. In fact, those who understand the nature of such costs will be right to ask, so what?
While we have proven the seemingly obvious, the point is:
The magnitude of transaction costs and their impact in large transactions, often fail to be quantitively defined for end users.
And yet there are few reasons for this lack of transparency.
While our experience in this domain would allow us to make reasonable transaction cost estimates, we have conducted soundings with market peers to arrive at indicative spreads.
The following graph collates these estimates of transaction costs and plots the impact they play on efficiency relative (based on 100 being perfectly efficient) to transaction size.
What does this show?
The difference in percentage-favourable results is quite stark.
· The blue line plots the percentage-favourable outcomes under Progressive Risk Cover,
· The red line plots the percentage under At-Close Risk Cover.
What we find is that under all deal size scenarios Progressive Risk Cover outperforms At-Close Risk Cover in terms of transaction costs. And as we noted, deal efficiencies decline as deal size grows for both approaches but maintains near-100 efficiency for Progressive.
Motive Asymmetry?
The field of behavioural finance is strewn with examples of the skewed perspectives found between those who seek to avoid risk and those who actively seek risk for profit. What should be clear is that regardless of motive, transaction costs can alter the standard efficiency paradigm no matter whether you are risk seeking or risk avoiding.
What should also be clear is that how you execute matters, and that the extent of that impact is magnified as deal size grows.
This makes specialist approaches to large or highly complex transactions a must, since a carefully formulated execution strategy can minimise both market risk and execution costs.
What next?
My next blog will focus on the risks associated with different execution approaches, again using progressive versus at-close scenarios and historic data quantitatively. This we will tie in with our work on premium illusion to demonstrate that there really is no such thing as a ‘free lunch’ when it comes to managing risk.
For those who would like to discuss the scenario, its outcomes, and/or the frameworks we use to quantify hedge-efficient approaches, please reach out at: info@martialis.com.au.