If a decision rule A always led to better results compared to decision rule B after T decisions, we call rule A T-dominant against B.
Example: Profit of Sales of Superstore
Taking the data of profits and sales for the Canadian retail chain Superstore during the years 2013-2016 we can find the following law:
If Superstore would not have not sold the products for which it granted an discount of over 30% (strategy A), it would have achieved a higher overall profit compared to its actual strategy (strategy B) in each sequence of at least T=155 sales. Strategy A T-dominates strategy B for T=155 sales. This is also an emergent law about the relative consequences of decision heuristics. Taking into account that this law was 25.95 times verified, we can use meta-laws to judge about the quality of the prediction that this pattern will hold. And we find that this prediction belongs to a class of predictions that have been true for at least 90% of the cases.
(We are aware that strategy A is only viable for products Superstore is reselling and which are not stored in a warehouse of Superstore. Therefore this strategy may not be viable for Superstore.)
Example: Choosing credit selection strategies
If we look at realized returns of loans that were arranged via the peer-to-peer lending platform “lending club”, we can see the following:
If an investor chose loans by the simple rule A: “Only take A-rated loans”, his strategy would have been T-dominated by an investor using rule B: “Only take B-rated loans” in every sequence of at least T=17000 loans. This is consistent with the view that higher risk loans must earn an extra return. Using standard risk-adjusted performance measures (RAPM) like Sharpe-ratio or RAROC as a decision criterion, the investor would have chosen strategy A, which until now led to always inferior results, if the investor’s portfolio included at least 17000 loans. This pattern is verified 29.95 times and by using meta-laws we can infer that this pattern will hold for at least 90% of its cases.
In general, the use of RAPM in decision-making often leads to the choice of strategies that are T-dominated. Therefore we are sure that there is “a free lunch everywhere” because of the widespread use of RAPM in decision-making and the resulting distorted market prices.