Risk Measurement

## Risk Measurement

Interest rate risks are measured by its sensitivity to interest rate movements. Interest rate sensitivity is basically the changes in the value of the financial instruments when interest rate changes. The most common and widely used is present value of one basis point (PVBP01). As a standard, PV01 is done by shifting the interest rate curve used for valuation by one basis point.

For illustration, PVBP01 of an FRA will be done by shifting the forward rate, instead of the curve. Equation 2-1a or 2-1b can be used to calculate PVBP01. The following calculator uses Equation 2-1b for the purpose.

CALCULATOR: PVBP01
###### Notional Principal

Principal amount of the borrowing/lending. It is referred to as notional principal because the amount is not delivered.

###### Value Date

Valuation date of the FRA. It should be a date on or prior to expiry date.

###### Expiry Date

Expiry date of the FRA. Settlement and expiry dates are assumed to be the same.

###### Maturity Date

Theoretical maturity date of the borrowing/lending via FRA.

###### FRA Rate (%)

The contracted FRA rate.

###### Forward Rate (%)

The current rate for the FRA period. Often this has to be calculated. For our illustration, it has been calculated as 2.8309 for value date June 17, 2020.

###### Stub Rate (%)

The applicable rate for the period from Value Date to Expiry Date

###### Convention

The day count convention to be used for all the rates

###### Settlement Amount

The value of the FRA as at value date. If value date is the expiry date, it is the settlement amount of the FRA

###### Settlement Amount After Shift

The value of the FRA as at value date after shiting the forward rate by 0.01%.

###### PV01

It is 'Settlement Amount After Shift' less 'Settlement Amount'. It the the present value of one basis point shift in forward rate

When the forward rate is raised by 0.01% the FRA value changes by MYR245.90. Recall that the FRA Equation 2-1a and 2-1b is from the perspective of a borrower, resulting in a better valuation for the borrower for any upward shift in interest rate curve, hence the positive number. On the other hand, the counterparty of the transaction i.e. the forward lender will have negative sensitivity of -MYR245.90.

Repeating the same calculation with an assumed decrease in forward rate by 0.01% will yield a sensitivity of -MYR245.91. While the difference is only MYR0.01, a tiny amount for consideration, its implication is significant - a non linear relationship between forward rate and FRA value which is referred to as convexity. Convexity is more pronounced for longer term products with a fixed rate exposure such as bonds, interest rate swaps and cross currency swap. These are the topics which will be covered in subsequent chapters.

Readers are encourage to input different value for any of the fields to see its impact on PV01, which can be seen clearly with large value for 'Notional Principal' more clearly

Calculation of PV01 was done on an FRA that will expire in three months which is relatively close to current date. If the expiry date is further away from the current date, the PV01 will be smaller due to the lower value of the discount factor.

### Example 2-2

Let's consider a 9 x 12 FRA in Table 2-1 quoted at 3.03%/2.93% and assume Bank B dealt at 3.03%, agreeing to borrow at that rate. The fair no arbitrage forward rate can be calculated using the this calculator by changing the settlement and maturity date. Rates and other information in Table 2-2 are used in the calculation. The fair no arbitrage rate for the FRA is calculated to be 2.9108%. Take note of the value for 'Rate to Settle Date (%)'and 'FRA Rate (%)'. They are equivalent to 'Stub Rate (%)' and 'Forward Rate (%)' in the above calculator, respectively. Copy the value and transfer to the above calculator and click 'Calculate'.

As expected, the PV01 of a 9 x 12 FRA is MYR241.49 and is lower than the PV01 of a 3 x 6 FRA of MYR245.90. The observation on the relationship between FRA’s PV01 and its expiry date will be compared against the PV01 of a similar product i.e. 3-month KLIBOR futures.