Buy and Hold Golden Strategies in Financial Markets with Frictions and Depth Constraints

Abstract

This paper deals with coherent risk measures and golden strategies, that is, financial portfolios (or financial strategies) with a negative risk and a non positive price. Golden strategies are important because they enable us to outperform every portfolio in a return/risk approach. In fact, every portfolio of securities is beaten by adding the golden strategy, i.e., the portfolio plus the golden strategy is better than the portfolio alone. Computationally tractable algorithms will be presented, and the general framework will be very realistic. Indeed, the study will incorporate all the classical frictions provoked by the order book of a financial market, and it will be both buy-and-hold and model-free. Numerical experiments involving derivative markets will be analysed.

Keywords:

• Coherent risk
• market depth and frictions
• golden strategy
• computational tractability

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 There are other interesting papers showing the existence of ill-posed problems in portfolio choice. For instance, Jin and Zhou (2008) proved this existence in general continuous time behavioural portfolio selection models under a cumulative prospect theory.

2 Assumption 2.1 is in some sense redundant. For instance, if ρ is sub-additive, homogeneous and decreasing then ρ is continuous. Similarly, instead of ‘mean domination’ one can impose ‘law invariance’, in which case the ‘mean domination’ fulfilment may be proved. Nevertheless, let us present Assumption 2.1 as it is because all the mentioned properties will be used.

3 Expectiles were introduced in Newey and Powell (1987), though one had to wait for several years until expectiles were also interpreted as coherent risk measures.

4 In particular, if one deals with robust risk measures, then the conclusions may become model free.

5 Actually, Balbás, Balbás, and Balbás (2019) introduced the notion of ‘golden option’ as a European option whose price is strictly higher than the risk provoked by the option sale. Later, Balbás, Balbás, and Balbás (2022) introduced this notion of ‘golden strategy’ and showed that the sale of a golden option plus the investment of the golden option price in a riskless asset is a golden strategy.

6 See https://www.meff.es/ing/Home.

7 See https://www.euribor-rates.eu/en/current-euribor-rates/.

8 Many available strikes and maturities are not included because they are not traded in the reported golden strategy.

Additional information

Funding

Partially supported by the Spanish Ministry of Science and Innovation [project number PID2021-125133NB-I00] and University Carlos III of Madrid [project number 2009/00445/003]. The usual caveat applies.