Question

​You are working at a bank, and after analyzing the $295 million portfolio of debt securities, you have determined a portfolio duration of 3.65, and an average Yield to Maturity of 5.65%. If you believe interest rates will be increasing by 0.75%, what is your expected change in portfolio value? If on the other hand, the prevailing wisdom is that rates will drop by 0.25%, what is the expect change in portfolio value? VERY briefly, what is wrong with this type of analysis? Additionally, what would be wrong with regulators coming in and asking you to repeat this analysis for an increase in interest rates of 2.5%?

Answer 1

Portfolio Value	$          295,000,000
Portfolio Duration =	3.65
YTM =	5.65%
Modified Duration= Portfolio Duration /(1+YTM)
So Modified Duration=3.65/(1+0.0565)=3.45.
As we know for every % change in Interest rate
there will be Modified Duration*same % change in price in the opposite direction.
	A
Interest rate change	% Change in Porfoilio Price=-Modified Duration *% nterest change	Amount of Porfolio Price change =$295M*A
Increase by 0.75%	-2.59%	$           (7,633,125)
Drop by 0.25%	0.86%	$             2,544,375
The issue with such analysis is that in case od sharp increase or decrease
in interest rate, the process will overestimate or underestimate the
corresponding change in price.
Therefore the analysis can throw some projections which may give
wrong forecasts and may create confusions.
Market regulators may have objections in such cases as the projections
can be quite misleading.

Suppose the analysis is performed for interest rate increase of 2.5% , that will cause
a price drop of 9.125% in portfolio . The duration considers a linear relationship between
interest rate change and price change in reverse direction. This generally does not happen
that shaply in huge interest rate changes. Therefore the regulator may have problem
with the price change projection that may confuse the financial market.