Freddie Mac 2010 Annual Report Download - page 171

• We calculate our exposure to changes in interest rates using effective duration. Effective duration measures the
percentage change in 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.
• 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.
• Together, duration and convexity provide a measure of an instrument’s overall price sensitivity to changes in interest
rates. Freddie Mac utilizes the aggregate duration and convexity risk of all interest rate sensitive instruments on a
daily basis to estimate the PMVS. The duration and convexity measures provide a convenient method for estimating
the PMVS using the following formula:
PMVS = ⫺[Duration] multiplied by [䉭r] plus [0.5 multiplied by Convexity] multiplied by [䉭r]
2
In the equation, 䉭rrepresents the interest rate change expressed in percent. For example, a 50 basis point 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)
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
sensitivity. Our PMVS measures assume instantaneous shocks. Therefore, these PMVS measures do not consider the effects
on fair value of any rebalancing actions that we would typically expect to take to reduce our risk exposure.
The expected loss in portfolio market value is an estimate of the sensitivity to changes in interest rates of the fair value
of all interest-earning assets, interest-bearing liabilities, and derivatives on a pre-tax basis. When we calculate the expected
loss in portfolio market value and duration gap, we also take into account the cash flows related to certain credit guarantee-
related items, including net buy-ups and expected gains or losses due to net interest from float. In making these calculations,
we do not consider the sensitivity to interest-rate changes of the following assets and liabilities:
•Credit guarantee activities. We do not consider the sensitivity of the fair value of credit guarantee activities to
changes in interest rates except for the guarantee-related items mentioned above (i.e., net buy-ups and float), because
we believe the expected benefits from replacement business provide an adequate hedge against interest-rate changes
over time.
•Other assets with minimal interest-rate sensitivity. We do not include other assets, primarily non-financial
instruments such as fixed assets and REO, because we estimate their impact on PMVS and duration gap to be
minimal.
Limitations of Market Risk Measures
There are inherent limitations in any methodology used to estimate exposure to changes in market interest rates. Our
sensitivity analyses for PMVS and duration gap contemplate only certain movements in interest rates and are performed at a
particular point in time based on the estimated fair value of our existing portfolio. These sensitivity analyses do not consider
other factors that may have a significant effect on our financial instruments, most notably business activities and strategic
actions that management may take in the future to manage interest rate risk. As such, these analyses are not intended to
provide precise forecasts of the effect a change in market interest rates would have on the estimated fair value of our net
assets.
PMVS Results
Table 66 provides duration gap, estimated point-in-time and minimum and maximum PMVS-L and PMVS-YC results,
and an average of the daily values and standard deviation for the years ended December 31, 2010 and 2009. Table 66 also
provides PMVS-L estimates assuming an immediate 100 basis point shift in the LIBOR yield curve. We do not hedge the
168 Freddie Mac