### How to Calculate Economic Value of Equity: Part 1

Building upon the last post concerning how to calculate earnings at risk, we now extend our "how to calculate" series to EVE, or the economic value of equity. The first part of this post will focus on calculating base EVE, before we shock interest rates. An added bonus is that this exercise will enable you to see the interrelation between earnings at risk and the economic value of equity.

As you might recall, earnings at risk is the simple difference between the yields earned and yields paid given shifts in interest rates. Specifically, earnings at risk generally looks at this relationship for a given 12 month period. Recent regulatory guidance on interest rate risk management has observed that a multi-year view of earnings at risk is preferable. Keep in mind that even with a multi-year horizon, earnings at risk still represents the simple difference between the yields, converted into dollars.

Economic value of equity extends this concept in two ways. First, building upon the multi-year horizon mentioned above, the economic value of equity is calculated over an extremely long time horizon, sufficient to allow all assets and all liabilities to have fully repriced. Second, rather than comparing simple dollar differences in yields, economic value of equity converts these yields to a present value equivalent, giving effect to the time value of money.

Here's a quick example. Assume your bank had only one asset, $10 million of a 10 year treasury bond yielding 4%. Similarly, assume that the liability side of the balance sheet consisted of $5 million in transaction accounts, $4 million in two year CDs at a cost of 2%, and $1 million in equity. Simple earnings at risk analysis would show that the bank has no short-term interest rate risk for the first two years. Over those first two years, the bank will earn $400,000 in interest income, while spending $80,000 on CD expense, resulting in $320,000 in net interest income.

To convert this information to an earnings at risk perspective, we must first start by fair valuing the balance sheet components. Assuming that the 10 year treasury bond is at market, total assets remain at book value of $10 million. Similarly, assuming that the current CD rate is also at market, this CD liability also remains at $4 million, its book value.

Now, here's where it gets interesting. The $5 million in transaction accounts costs the bank nothing in terms of interest expense. Yet, as we have just seen, market yields on assets are 4%. Since we have "free money" that we can invest at 4%, the present value of these transaction accounts is less than their book value. And since we know that our total assets retain a book value of $10 million, if the market value (present value) of our transaction accounts is less than their book value, our base EVE must be greater than the $1 million in book equity. In our simple example, we will reduce the transaction account liability by the present value of the gross benefit received ($5 million times 4% per year equal $400,000, which reduces to approximately $363,000 on a present value basis). This results in a base economic value of equity of $1,363,000, the total of the book equity plus the economic benefit of our transaction accounts.

What's the lesson here? Bulking up on transaction accounts helps build your interest rate margin while limiting interest rate risk. Our next post will look at the impact of varying interest rates.

Phot provided by CogDogBlog.