Modelling the interest rate risk management with portfolio selection: the case of Crédit Foncier de Monaco

Résumé du document

Since the primary activity of banking is the intermediation between borrowers and lenders, its core business is the transformation of collected deposits into distributed loans. This process generates a net interest margin in the profit and loss statement but engenders financial risks in the balance-sheet. Indeed, the asset-liability mismatches about maturity (short term vs. long term), interest rate (certain rate vs. uncertain rate) and currency, (domestic vs. foreign) respectively provoke liquidity risk, interest rate risk and currency risk. Thus, banks want to maximize their profit and minimize their risk. However, if risk taking is rewarded by an expected risk premium, it also causes instability for the financial institution as well as for the whole financial system.

Extraits

[...] D V D = A A L L ( 2.33 ) r 1 + rL A = V VA V MD A L MDL ( 2.34 ) V V Money markets rates For each category of rate the rate is the sum of a commercial margin (CMt) and a reference rate more or less sensitive to the refinancing rate of money markets (i)37. The sensitivity coefficient (βt) is null for fixed rates, is equal to 1 for variables rates perfectly indexed to refinancing rates and is between 0 and 1 for variables rates imperfectly correlated. [...]

[...] Appendix determines the sensitivity of the net interest margin to the variation of the interest rates; it is equal to of the gap weighted by a factor. 48/ Adaptation We shall adapt the model to the structure and the constraints on the balance sheet at the end of year 2007. Even if we shall focus our analysis on the interest rate risk, we shall also take into account the currency risk and the liquidity risk through interest rates Structure EONIA Eur 1M Eur 3M DD US Lib 1M Lib 3M Lib 6M Other Obligatory Reserves Long-term Loans Short-term Loans Trading Investment Other Assets ASSETS Capital Long-term Deposits Short-term Deposits Trading Debt Other Liabilities LIABILITIES TOTAL Fixed The resources are short-term deposits but also long-term deposits and capital The deposits are mainly fixed-rate or day-to-day The assets are short-term loans ( 92.5 and trading investments ( 7.5 The other assets and other liabilities which are property, plant, intangibles, provisions and miscellaneous are insignificant and there are no trading debts. [...]

[...] To boost the profitability, it is encouraged to play with maturities, currencies and interest rates. But we know since Markowitz that the excess return is a risk premium; the surplus of profit results from financial risk-taking. Thus, the bank, which is adverse to risk, tries to optimize the arbitrage by maximizing its utility and its risk-adjusted performance under commercial and regulatory constraints. Nevertheless, the prudential regulation does not provide a standardized method to manage the interest rate risk of the commercial portfolio. [...]

[...] The gaps analysis is a method which is simple, short-term, intuitive, synthetic and accounting but simplistic because it does not fully capture all the sources of the interest rate risk, and approximate because of imperfect correlation of outstanding rates to market rates and intra-periodic flows and inter-periodic reinvestments Value The economic value is a more complex but synthetic, long term and market method Duration The duration, which takes into consideration the exact date of flows, measures the variation of interest rates on the net present value. The Macaulay duration27 is defined as the payback life, the weighted-average maturity or the investment horizon so that capital gains are offset by reinvestment risk. By linearity, the capital duration is the difference between the asset duration and the liability duration (DL). [...]

[...] Eventually, the gap between rates provokes an interest rate risk (C.f. Appendix 2 - C). For example, at the end of year of the resources were fixed-rate and 70% day-to-day (Eonia or DD USD), whereas the allocation of the assets was respectively and 20% longer maturity (Euribor or Libor USD). The risk manager collects the elements, determines the stable core thanks to historical data, applies a flow law based on assumptions and macro hedges with interest rate swaps to neutralize the position and 47/80 to protect the income. [...]