## SECURITIZATION ECONOMICS: THE RETURN ON EQUITY

Category: Risk Management in Banking

In our example, the influence on the equity return results from both the lower level of equity and the reduced cost of funding through securitization. The gain value is either a present value or an improvement of yearly margins averaged over the life of the transaction. The capital saving is a preset forfeit percentage, used as an input, in the example. When considering the global economic picture, this same percentage of assets would result from modelling economic capital and would be an output of a portfolio model. In both cases, analysing the economics of the transaction aims at finding whether the securitization improves the risk-return profile of the banks portfolio. Enhancing the risk-return profile means getting closer to the efficient frontier or increasing the RaRoC or Sharpe ratio of the banks portfolio. This would imply calculating RaRoCs both pre-and post-diversification and comparing them.

The Gain/Loss of the Sale of Assets for Banks Shareholders

The value of assets is the discounted value of cash flows calculated at a rate equal to the required return to investors. The average required return by the outside investors, who buy the securities issued from securitization, is 10.081%. For the lenders and shareholders who fund the bank, the average asset return is 10.20%. But the existing shareholders would like to have 25% instead of the 19.80% resulting from the insufficient return on assets of 10.20%. In order to obtain 25%, the return on assets of the bank should be higher and

reach 10.304%.

The present value of the securitized assets for outside investors is the discounted value of future flows at 10.08%. The value of the same assets for those who fund the balance sheet results from discounting the same cash flows at 10.20%, either with the current effective ROE of 19.80%, or 10.30% with a required ROE of 25%. In both cases, the average cost of funds for the bank is higher than the cost of funding through securitization. Therefore, the price of existing assets, at the 10.08% discount rate required by outside investors, will be higher that the price calculated with either 10.20% or 10.304%. The difference is a capital gain for the existing shareholders of the bank.

Since the details of projected cash flows generated by assets are unknown, an accurate calculation of their present value is not feasible. In practice, a securitization model generates the entire cash flows, with all interest received from assets, prepayments, defaults and recoveries, and interest from the pool of assets. For this example, we collapse the entire process into a small number of very simple shortcuts, bypassing the technicalities of structure models. The easiest way to get a valuation is through the duration formula. We know that the discounted value of future flows generated by the assets at 10.20% is exactly 1000 because they yield 10.20%. With another discount rate, the present value differs from this face value. An approximation of this new value derives from the duration formula, since:

This means that the sale of the assets to the securitization structure generates a capital gain of 0.833% over an amount of 1000, or 8.33 in value.

The Additional Annualized Return from Securitization

It is possible to convert the gain from securitization into an additional annualized margin obtained over the life of the transaction. A simple proxy for this yearly margin is equal to the instantaneous capital gain averaged over the life of the transactions (ignoring the time value of money). The gain is 0.84% x 1000 = 8.4 in value.

This implies that after securitization, the assets provide the 10.20% plus the yearly return of 0.0833% applicable only to the fraction, 1000, securitized. Once securitization is done, the size of the balance sheet drops to 9000. These 9000 assets still provide 10.20%. There is an additional return due to the capital gain. Since this annualized capital gain is 0.0833% of 1000, it is (0.0833%/1000) x 9000 in percentage of remaining assets, or 0.00926% applicable to 9000. Accordingly the asset all-in yield increases from 10.200% up to 10.20926% post-securitization. This increased yield also implies a higher return on capital, reviewed next.