$1.$What is the intuitive meaning of efficient frontier? Explain in plain words.

$2.$ What is meant by risk aggregation and risk decomposition? Which requires an in$-$depth understanding of individual risks? Which requires a detailed knowledge of the correlation between risks?

$3.$ Explain in plain words the meaning of delta hedging.

$4.$ Explain the difference between hedging, speculation, and arbitrage.

$5.$ Suppose the true loss is heavy$-$tailed, while we calculate Value$-$at$-$Risk $($VaR$)$ by assuming it is normally distributed. Is the true VaR underestimated or overestimated? Why?

$6.$ In general, does VaR satisfy risk diversification? If we assume that P&L$$s follow normal distributions with mean zero, does VaR satisfy risk diversification? Why?

$7.$ What is the difference between conditional Value$-$at$-$Risk $($CVaR$)$ and Value$-$at$-$Risk? What is the theoretical advantage of CVaR over VaR?