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The book of Financial Risk forecasting by Danielsson gives the following example about VAR manipulation. I have two questions:
1) If $0> VAR_1 > VAR_0$ , why the following figure plots it as $-VAR_1> -VAR_0$. I think $-VAR_1$ should be placed at the left side of $-VAR_0$.
2) I am not clear how does the manipulation strategy marked with yellow work. In other words, why it can lower the expected profit.
First, I am quite sure that this is a typo and it should be $$ 0 < VaR_1 < VaR_0 $$ then $$ -VaR_0 < -VaR_1 $$ and the plot is correct.
Second, the put strategy does not change only the expected profit but the whole distribution of the P&L. If you buy a put with strike $K_1 = -VaR_1$ then you get compensated for losses below $K_1$. But you have to buy this option and pay a premium for it,say $P_1$ - this is a certain loss. To make this hedge cheaper you can sell a put at a lower strike $K_0$ at the price $P_0$. Then you will be compensated for any loss between $K_1$ and $K_0$ and you pay for it $P_1-P_0$. The premium payments change your expected profit but additionally the whole P&L is altered.
