# ECONOMIC VALUE (EV)

The economic value of the banking balance sheet is the mark-to-market value of assets minus the mark-to-market values of liabilities. As such, it discounts at market rates all cash flows from assets and liabilities. Economic value is mentioned under Pillar 2 of the Basel 2 Accord which deals with ALM issues. Since amortizing flows are summarized by liquidity gaps, economic value is identical to the present value for all liquidity gaps plus all interest flows.

Nil and book values have drawbacks. The net interest income is a popular target of interest rate risk management because it is a simple measure of current profitability that shows up directly in the accounting reports. But, because it is periodical, it characterizes only particular periods, ignoring any income beyond the horizon. Book values are not risk-adjusted, whether mark-to-market values are to the extent that any spread from a risky loan, for example, appears as a mark-to-market value higher than face value, provided that we use as discount rates the risk-free rates. Moreover, embedded options, common in retail banking, do not appear in book values, but would be valued in "economic values."

The economic value is, in fact, a mark-to-model value because loans are not tradable^{[1]}. The calculation of an EV does not imply any assumption about liquidity of loans. It is an "economic" value calculation, based on the DCF model, not the price at which assets could trade. The EV has other distinctive features. It differs from the "fair values" of assets by the value of credit risk of borrowers, because it uses risk-free rates^{[2]}, without differentiating them according to the risk of individual borrowers. The credit risk of borrowers is in the spread over risk-free rate that they pay to the bank.

EV and market value of equity are not at all identical. EV can be negative, whereas equity value is always positive. In addition, equity is not a fixed income liability. Since equity investors take on all risks of the bank, the required rate of return should be above the cost of debt. Therefore, it does not make sense to consider the equity investor as a "pure net lender," who would be long with bank's loans and short with bank's liabilities. The market value of equity is the discounted value of the flows that compensate equity, with a risk-adjusted rate equal to the required return on equity, given the risk of equity measured by the (3 of the bank's stock. Moreover, the EV can be negative, when stock prices cannot, since it is a difference.

Several discount rates can be considered. Fair value should use risk-adjusted market rates inclusive of credit spreads applying to the credit grade of borrowers. The cost of financing of the bank also makes sense because any spread of assets above this cost of financing would show up as an excess spread. The cost of financing of the bank is the weighted average of all sources of funds, equity and debts, or weighted average cost of capital (Wacc) of the bank.

In fact, we will show that the risk-free rate and the DCF are relevant for highlighting major properties of EV.

Economic value, or EV, is a target variable for ALM because it can be shown that it measures the present value of all net interest incomes over all future periods. When focusing on short-term horizon, say up to 2 years, ALM's natural target is the N11 and the gap model remains appropriate, except for options. When focusing over the long-term, the EV becomes appropriate and it becomes necessary to derive risk measures for this new target variable.

In this section, we look at different "views" on the EV. The present value of the stream of future flows *Ft* is:

The market rates are the risk-free zero-coupon rates *r* derived from yield curves. The formula provides a value of any asset that generates contractual flows. The EV is the net value of a portfolio long in assets and short in liabilities. It can be positive or negative. The change in EV depends entirely upon the sensitivities of these two portfolios. The next chapter, Chapter 27, discusses the behavior of EV when market rates change.

- [1] Mark-to-model differs from mark-to-market in that the latter would use all market parameters that should be embedded in market prices, in order to replicate those prices. Mark-to-model can be seen as a partial mark-to-market.
- [2] The subsequent paragraph discusses the choice of a proper discount rate.