A risk analyst at EtaBank wants to estimate the risk exposure in a leveraged position...

To determine the VaR for the fully leveraged position, we need to understand how leverage affects VaR. Leverage magnifies both returns and risks, which means that the VaR for a leveraged position is greater than that of an unleveraged position.

Calculate the leverage ratio:

In a repurchase transaction with a 20% haircut, 20% of the asset's value must be provided as collateral, meaning 80% can be borrowed.

Leverage ratio LLL = 1Haircut\frac{1}{\text{Haircut}}Haircut1​ = 10.2\frac{1}{0.2}0.21​ = 5.

Calculate the leveraged position:

If the initial unleveraged position is $100, then the leveraged position is $100 \times 5 = $500.

Calculate the VaR for the leveraged position:

The unleveraged VaR is $30 on $100.

Therefore, the leveraged VaR will be magnified by the leverage ratio: Leveraged VaR=Unleveraged VaR×Leverage Ratio\text{Leveraged VaR} = \text{Unleveraged VaR} \times \text{Leverage Ratio}Leveraged VaR=Unleveraged VaR×Leverage Ratio = $30 \times 5 = $150.

References

Source: How Finance Works​