Implied Inefficiency in Betting Markets
How to measure the net impact of market price disparities
The margin of inefficiency (MOI) in a betting market equals the width of the range of underlying true probabilities for any given market price. It is calculated as the range of probabilities for which a trader would not be incentivized to trade at the current price, supposing the true probability were known. So, for example, if the current price is $0.50 with a MOI of 5% (written 0.50 +/- 0.05), then a trader who knows the true probability of the event is between 50.1-55% would not have incentive to purchase at the current price. Conversely, a trader who knows that the true probability is between 45-49.9% would not have incentive to sell (go short) at the current price of $0.50. The concept of MOI was introduced an explained in further detail in a previous post.
As discussed previously, several factors can contribute to the margin of inefficiency, including commissions, fees, transaction costs, minimum tick size, short-term interest rates, opportunity costs, regulations, legal restrictions, taxes, and other frictions involved with funding accounts and trading. Some of these factors, such as commission and fee structure, minimum tick size, and short-term interest rates, are well-defined and their impact on MOI can be computed precisely. Others, such as regulatory factors and opportunity cost, are less quantifiable and, therefore, must be estimated.
In this article, we analyze the margin of inefficiency in further detail by decomposing it into endogenous and exogenous inefficiency factors. Endogenous factors of inefficiency are determined by internal market attributes, such as commissions, fees, minimum tick size, and volume restrictions. Exogenous factors are determined by external forces, such as short-term interest rates, opportunity costs, and regulations. The contribution to margin of inefficiency from endogenous factors is called endogenous MOI (eMOI) and the contribution from exogenous factors is called exogenous MOI (xMOI)
MOI = eMOI + xMOI
The premise of this decomposition is that endogenous factors are determined by factors within the control of the market operator, while exogenous factors are determined by macroeconomic and other factors external and out of the control of the market. So, in theory, endogenous MOI is the amount of inefficiency that is specific to a market and can be attributed to the market operator itself. Exogenous MOI applies more or less equally to all markets and represents the bare minimum amount of inefficiency that can be expected in any given market, simply due to uncontrollable economic and other forces. A market operator can drive endogenous MOI down as close to 0 as possible, but can never escape exogenous MOI.
Computing Endogenous MOI
While the contribution of some endogenous factors to market inefficiency, such as restrictions on volume or participation, is hard to quantify, the key drivers, including commissions, fees, and the minimum tick size, make for straightforward analysis. Our calculation of eMOI, therefore, only considers these quantifiable factors.
First, the minimum tick size puts a lower bound on market inefficiency, as it is the smallest resolution to which the market can resolve event probabilities. A market with a minimum tick size of $0.01, such as Kalshi or PredictIt, for example, cannot resolve the difference between, for example, 49% and 50%. If the last traded price is $0.49 and the true probability is known to be 50%, then the fair value of the contract is known to be $0.50. But the minimum tick size implies that the next highest available price above the currently reflected price of $0.49 must be $0.50, which squeezes any value out of bringing the price into closer alignment with the true probability. In a market with a minimum tick size of $0.001, on the other hand, trading could continue all the way up until $0.499, at which point the minimum tick size would once again eliminate any further incentive to trading. Note that the minimum tick size is most impactful on extreme ends of the probability spectrum. For example, the difference between $0.01 and $0.02 is 100% in relative terms, and this difference cannot be resolved in a market with a $0.01 tick size.
Second, commissions and fees reduce the apparent edge of otherwise profitable trades, and can make a profitable trades unprofitable in terms of expected value. For example, a contract trading at $0.50 on Betfair for which the true probability is 50.5% has an expected profit of $0.005 in the absence of commissions. After commissions, which Betfair assesses as 2% net profits per market, the expected value of this contract is $0.00. When accounting for commissions, a trader with the opportunity to purchase a contract at $0.50 that he believes to be worth any value up to $0.505 would not have incentive to trade.
For the sake of simplicity, we take the above two factors as the basis for the endogenous margin of inefficiency (eMOI) for any market.Â
eMOI = maximum( tick size, commission )
Because other, less quantifiable factors do contribute to eMOI, our calculation based on the above is necessarily a lower bound on eMOI. However, these factors account for the bulk of eMOI in the vast majority of cases. The endogenous MOI defines the range of true underlying probability values with which a market price is consistent only accounting for endogenous market factors. External factors such as interest rates, opportunity costs, and regulations are not considered in eMOI.
Calculation of eMOI for well-known markets
Betfair contracts are priced in decimal odds with increments of 0.02, which for implied probabilities in the range of 50% (decimal odds 2.0) implies a minimum tick size of about $0.005. The 2% commission also implies a factor of $0.005 and the endogenous MOI equals the maximum of minimum tick size and commission factor, which equals 0.5% for Betfair. Smarkets similarly quotes prices in decimal odds and charges a commission of 2%, giving an endogenous MOI of 0.05%. Kalshi does not charge commissions presently, so its endogenous MOI equals its minimum tick size of 1%. PredictIt has a 10% commission on winning trades plus a 5% withdrawal fee on all funds, for an endogenous MOI of 7.25%. Polymarket charges no commissions and has a $0.001 tick size for an endogenous MOI of 0.1%, the lowest among these markets.
From these calculations, we compute each market’s range of implied probabilities as the market price +/- the endogenous MOI:
Market Consensus Forecast
In a previous post, I defined the market consensus forecast as the range of probabilities that is consistent (i.e., overlaps) with the ranges of each market. Note that there are no probability values that fall within each of the above ranges. However, the above ranges do not account for all factors that contribute to price discrepancies between markets. In particular, we have not accounted for short-term interest rates, opportunity costs, and other frictions that might prevent traders from arbitraging away price differences in markets.
Our decomposition of MOI above shows that MOI = eMOI + xMOI, and so far we have only accounted for eMOI in each market. Except for specific exogenous factors, such as short-term interest rates (which are currently 4.8% annually), the main factors contributing to xMOI are hard to quantify, and many are even hard to identify. In the previous post, margin of inefficiency was calculated by estimating the xMOI component and reporting the total MOI. Here we take a different approach by calculating the smallest possible xMOI that can bring the markets to a concensus. This concept is called implied margin of inefficiency.
Implied Margin of Inefficiency
We define the implied margin of inefficiency (iMOI) as the smallest additional factor by which each market’s MOI must be increased in order to arrive at a consensus forecast. For the above markets, the implied inefficiency is 0.9%, which when added to the above MOIs yields a market consensus of 47.3% for Harris and a range of 52.4-52.9% for Trump.
As a metric, the implied margin of inefficiency indicates how much exogenous inefficiency is necessary to rationalize any observed discrepancies in market prices. A value of 0% means that all price discrepancies can be explained by built-in endogenous factors. Because a market cannot expect to overcome distortions caused by its own built-in design or structural flaws, endogenous MOI is essentially the lowest inefficiency any market can hope to achieve given its current structure, and an implied margin of inefficiency of 0% is the best any group of markets can achieve. In general, iMOI is lower than the true xMOI at any given time, and so iMOI provides an estimate of the theoretically best (i.e., lowest) margin of inefficiency achievable (if every market were to drive its eMOI down to 0).
Interpreting implied margin of inefficiency
The iMOI is most informative when a group of markets cannot achieve a consensus based on eMOI alone. When markets are in consensus based on eMOI alone, the implied MOI will be 0%. However, this does not imply that there are no exogenous factors to inefficiency. It only means that those exogenous factors are not relevant for explaining any current price discrepancies among the markets. Internal market characteristics are sufficient.
When the eMOI is not enough to achieve consensus, as in the above Presidential market calculation, the iMOI estimates the amount of exogenous inefficiency that is contributing to the price differences. A well-functioning class of markets will generally have iMOI > 0, and that iMOI will be informative for explaining why any differences exist.
For the calculations above, the implied MOI of 0.9% is a sensible value, of which about 0.33% can be accounted for by time-value considerations — the short-term interest rate of 4.8% equals about 0.33% per month, and there is a month between now and the election. The remaining 0.57% can easily be explained as an opportunity cost and risk premium that market participants are requiring in order to lock up capital that could potentially be used for more profitable trades and for the inherent risks of trading, such as adverse selection, information asymmetry, and errors in estimating underlying probabilities.