Freddie Mac 2011 Annual Report Download - page 202

are set at values below those set at the Board level, which is intended to allow us to follow a series of predetermined
actions in the event of a breach of the management limits and helps ensure proper oversight to reduce the possibility of
exceeding the Board limits. We also establish management limits that do not have corresponding Board limits.
Portfolio Market Value Sensitivity and Measurement of Interest-Rate Risk
PMVS and Duration Gap
Our primary interest-rate risk measures are PMVS and duration gap. PMVS is an estimate of the change in the
market value of our net assets and liabilities from an instantaneous 50 basis point shock to interest rates, assuming no
rebalancing actions are undertaken and assuming the mortgage-to-LIBOR basis does not change. (The shock used for
calculating PMVS is not the same as the shock used for calculating duration and convexity, described above under
“Duration Risk and Convexity Risk.”) PMVS is measured in two ways, one measuring the estimated sensitivity of our
portfolio market value to parallel movements in interest rates (PMVS-Level or PMVS-L) and the other to nonparallel
movements (PMVS-YC).
• We calculate our exposure to changes in interest rates using effective duration. Effective duration measures the
percentage change in the price of financial instruments from a 1% change in interest rates. Financial instruments
with positive duration increase in value as interest rates decline. Conversely, financial instruments with negative
duration increase in value as interest rates rise.
• Together, duration and convexity provide a measure of an instrument’s overall price sensitivity to changes in
interest rates. We utilize the aggregate duration and convexity risk of all interest-rate sensitive instruments on a
daily basis to estimate the two PMVS metrics. The duration and convexity measures are used to estimate PMVS
under the following formula:
PMVS = ⫺[Duration] multiplied by [rate shock] plus [0.5 multiplied by Convexity] multiplied by [rate shock]
2
In the equation, [rate shock] represents the interest-rate change expressed in percentage terms. For example, a
50 basis point adverse change will be expressed as 0.5%. The result of this formula is the percentage of sensitivity
to the change in rate, which is expressed as: PMVS = (0.5 Duration) + (0.125 Convexity).
• To estimate PMVS-L, an instantaneous parallel 50 basis point shock is applied to the yield curve, as represented by
the US swap curve, holding all spreads to the swap curve constant. This shock is applied to the duration and
convexity of all interest-rate sensitive financial instruments. The resulting change in market value for the aggregate
portfolio is computed for both the up rate and down rate shock and the change in market value in the more adverse
scenario of the up and down rate shocks is the PMVS. In cases where both the up rate and down rate shock results
in a positive impact, the PMVS is zero. Because this process uses a parallel, or level, shock to interest rates, we
refer to this measure as PMVS-L.
• To estimate sensitivity related to the shape of the yield curve, a yield curve steepening and flattening of 25 basis
points is applied to the duration of all interest-rate sensitive instruments. The resulting change in market value for
the aggregate portfolio is computed for both the steepening and flattening yield curve scenarios. The more adverse
yield curve scenario is then used to determine the PMVS-yield curve. Because this process uses a non-parallel
shock to interest rates, we refer to this measure as PMVS-YC.
• Duration gap measures the difference in price sensitivity to interest rate changes between our assets and liabilities,
and is expressed in months relative to the market value of assets. For example, assets with a six month duration
and liabilities with a five month duration would result in a positive duration gap of one month. A duration gap of
zero implies that the duration of our assets equals the duration of our liabilities. As a result, the change in the
value of assets from an instantaneous move in interest rates, either up or down, would be expected to be
accompanied by an equal and offsetting change in the value of liabilities, thus leaving the fair value of equity
unchanged. A positive duration gap indicates that the duration of our assets exceeds the duration of our liabilities
which, from a net perspective, implies that the fair value of equity will increase in value when interest rates fall
and decrease in value when interest rates rise. A negative duration gap indicates that the duration of our liabilities
exceeds the duration of our assets which, from a net perspective, implies that the fair value of equity will increase
in value when interest rates rise and decrease in value when interest rates fall. Multiplying duration gap (expressed
as a percentage of a year) by the fair value of our assets will provide an indication of the change in the fair value
of our equity to be expected from a 1% change in interest rates.
The 50 basis point shift and 25 basis point change in slope of the LIBOR yield curve used for our PMVS measures
reflect reasonably possible near-term changes that we believe provide a meaningful measure of our interest-rate risk
197 Freddie Mac