How to Calculate Earnings at Risk
Posted by Howard Lothrop on Wed, Jun 02, 2010 @ 11:02 AM
A common question that I receive is how do I calculate earnings at risk? Here's a brief and basic example.
Let's assume we have a simple bank that has only one asset, a 10 year U.S. Treasury bond yielding 4%. Further, let's assume that this bank has only deposit funding. The bank's six-month CDs currently cost 1%. The base net interest income equals the 4% yield on the bond less the 1% cost of the deposit, or 3%. This becomes our base net interest income earnings at risk.
Now, let's vary interest rates. If rates go up 100 basis points in an immediate shock, the yield on our 10 year bond will not change. However, after six months, when we go to renew our CD it will now cost 2%. That means that for the first 12 months, we have six months of net interest income at 3% (unchanged from the base) and then six months with a net interest income of 2% (4% bond yield less 2% CD cost). This means that in a rates up 100 basis point scenario, the twelve-month net interest income in the up 100 basis point scenario is now reduced to 2.5%. The 50 basis points of reduction in net interest income is divided by the base and I am of 3%, to yield the earnings at risk of 16.7%.
Similarly, if rates go up 200, 300, and 400 basis points in an immediate shock scenario, our net interest income will decline an additional 50 basis points for each 100 basis points of rate shock increase. This results in an earnings at risk in the up 200 scenario of 33%, 50% in the up 300 scenario, and 66.7% in the rates up to 400 basis point scenario.
The reason that the earnings at risk rate sensitivity is only 50 basis points per 100 basis points of rate change is the initial six-month CD period at 1%. This also represents the main reason why recent regulatory interest rate risk management guidance has suggested performing multi-year earnings at risk tests. As you can clearly see, in year two without the benefit of a six-month starting CD yield, rate shocks of 100, 200, 300, and 400 basis points will reduce our net interest income to 2%, 1%, zero, and then finally a 100 basis point net interest loss.
Of course, actual earnings at risk calculations must include all line items on the balance sheet, as well as interrelationships between and among these items. This makes your earnings at risk a much more complex calculation. However, it is still true that understanding the basics will help you better understand your more complex results as well.
Photo provided by Andres Rueda.
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