VaR Manipulation Through Put Spreads and P&L Distribution Changes

Summary

The document addresses two points about an example of VaR manipulation: a likely sign error in an inequality and how a put strategy changes reported risk and profit. The answer says the displayed ordering is consistent if the intended condition is that both VaR values are positive and one is smaller than the other; negating them then reverses their order as shown in the figure.

For the strategy, buying a put at a higher strike provides compensation for sufficiently large losses but costs a premium. Selling a put at a lower strike offsets part of that cost while leaving exposure to losses beyond the lower strike. The resulting put spread changes the P&L distribution as well as expected profit, because the premiums are paid or received with certainty and the option payoffs vary with losses. The explanation is qualitative; it gives no numerical example, market assumptions, or general proof about how much VaR or expected profit changes.

Key ideas

• The answer identifies a probable sign error in the stated VaR inequality.
• Buying a put can compensate for losses below its strike, subject to the option payoff.
• Selling a lower-strike put can reduce the purchase premium while retaining deeper-loss exposure.
• Option premiums and payoffs alter both expected profit and the overall P&L distribution.

Tags

# questions on VAR manipulation


# questions on VAR manipulation












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.

## Answer by Richi Wa (score 5)

https://quant.stackexchange.com/a/12755

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.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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