Hi, In chapter 7, what does the word "coherent" mean when referring to a "coherent risk measure". The notes do not define "coherent" and simply says that the risk measure is said to be "coherent" if it satisfies the 4 conditions. Does it mean that it is easy to understand/ logical? Similarly what is the definition of "coherent" when referring to a "coherent capital allocation method"? Thanks, Amrita
That's just it - coherence means that those 4 conditions hold. As you'll see from the Course Notes, though, coherence isn't necessarily a desirable characteristic.
Hi Was reading this chapter as well and got me thinking on two of the conditions: a) Monotonicity If one portfolio is riskier than the other, shouldn't it be worth more? (higher the risk, higher return required) b) Translational invariance Wouldn't the overall portfolio risk reduce if we add a risk-free portfolio to our existing? Seems to me this condition does not allow for diversification whereas the Sub-additivity condition does.
For the first point on Monotonicity, its the value which is higher and not the worth. So I understood it as - if one portfolio is more riskier than the other identical portfolio, its VALUE (to be paid/investment required) can not be more.
Yes, there's all sorts of criticism on the validity of some of these coherence principles - just search the internet and you'll find all sorts of papers written about it. I rather suspect the maths behind it all is beyond the scope of a possible exam question though, as it's very theoretical and has limited real life application (although I'm sure some mathematicians would argue with me on that point). From an exam point of view, you'll be pleased to know that so far the topic has never been examined.
