Ties in Conservative Payoff Decisions and Secondary Risk Measures

Summary

The document considers how to choose between decisions when both maximize the minimum payoff under a conservative decision rule. Its main point is that “minimum” depends on the scenarios or range of outcomes included: in continuous settings, worse outcomes may always be possible, so the worst case is not an absolute or universally fixed quantity.

For comparing portfolios, the response suggests applying a second risk or performance measure when the first measure gives a tie. It gives an illustrative example: if two robust portfolios have the same 10% quantile of weekly returns, an investor could prefer the one with the higher median return. This is a tie-breaking approach, not a claim that one secondary measure is always best. The choice of scenarios, quantile, and follow-up measure depends on the investor’s objectives and assumptions; the brief exchange offers no empirical comparison or formal selection rule.

Key ideas

• A conservative choice depends on how the worst-case outcome is defined.
• In continuous settings, there may be no absolute lower bound on possible losses.
• When two portfolios tie on one risk measure, a second measure can guide selection.
• A higher median return can break a tie in the lower quantile of returns.

Tags

# conservative approach payoff table


# conservative approach payoff table












With the conservative approach, we choose the decision which maximises minimum payoff. I was wondering which decision is chosen if 2 decisions have equal minimum payoff (which is the maximum)?

Thanks

## Answer by Marie. P. (score 0)

https://quant.stackexchange.com/a/14681

Problematic is already the use of the words "conservative" and "minimum". There is no absolute minimum, worst case (in continuous models, i.e. reality), as things can always get worse than they have ever been before and than anybody anticipated. Depending on where one defines the minimum, there can always be an even more conservative investor in the market.

Given your tags, let me say that in quantitative areas like portfolio management, if we compare two strategies, e.g. portfolios, for which one risk measure gives equal minimum payoff, then we may apply another risk measure and choose the portfolio which scores better in this risk measure. For example, if a conservative investor considers the robust portfolios with maximized 10%-quantile of weekly returns, and two portfolios are equally good in this measure, he may turn to the one that offers better median returns.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.