# Opposite of Value-at-Risk. Criteria for Optimization

I'm trying to optimize portfolio of undervalued and portfolio of overvalued stocks. I have simulated scenarios of stock returns, and based on them I would like to find optimal weights. One criteria is just to minimize Conditional Value-at-Risk (ES), another - maximize profit (for risky investor). The simple intuition is that risky investor would take overvalued stock because it may continue growing; the defensive one will take undervalued since they are less likely to go lower. (I see that this logic is very very far from perfect, nevertheless, it may have a chance to live). So, there are 2 main questions:

1)Does it make sense to take quantile for 25% highest returns for each stock, and based on this find "likely the most profitable" assets? (Something like an opposite for value at risk).

2)Are there any specific criteria for optimizing porfolio of only undervalued/overvalued stocks? I understand that the question is vague because under/overvalued doesn't imply any specific in behaviour of stock. However, maybe there are some, and I would be glad to hear them. Thank you in advance!

• You could apply the opposite intuition as well. What if your 'risky' investor likes trying to catch falling knives and prefers stocks that have been beaten down? What if the 'defensive' investor likes stocks that 'always go up'? – amdopt Apr 20 at 21:55
• Okay, thank you for the idea! But this doesn't actually answer any of the questions. – Gcube Apr 21 at 9:16
• No, hence it being a comment :) – amdopt Apr 21 at 13:30
• You need to analyze this empirically, with data, not guesswork. FWIW my friend Turan Bali has found that stocks with high "opposite of VaR" during the last month have lower returns going forward than stocks with more modest "opposite of VaR" nber.org/papers/w14804 He defines "opposite of Var" as 1 best return of last 20 days. – Alex C Apr 21 at 16:58