Movers Appendix

Appendix 5A

 

BIS Risk-Based Capital Requirements

 

In March 1987 the Bank of England and the Federal Reserve issued a document concerning the risk based capital requirements for swaps, derivatives and other off-balance sheet transactions. In the 1988 Capital Adequacy Accord the BIS and the supervisory authorities of the G-10 defined a framework for determining capital adequacy for both on and off balance sheet items.

 

The risk adjusted exposures for the on balance sheet items are the sum of the principal times a risk weight for each asset. The risk weights by type of assets are as follows: standard risk 100% for commercial loans; moderate risk 50% for residential mortgages, municipal revenue bonds;  low risk 20% for cash in collection, short-term claims on US depository institutions, general obligation municipal bonds; no risk 0% for cash, deposits with Fed, short-term Treasury securities. Off-balance sheet items are converted into balance sheet equivalents. First the notional amounts are converted into credit risk equivalent values. Then the credit risk equivalent is weighted by a factor of 0-50% based on counterparty credit quality. The counterparty credit weights are: 0% for sovereigns, 10% for local governments and state owned entities, 20% for OECD banks and 50% for corporations.

 

The BIS calculates the loan equivalent amounts for swap contracts:

 

              Current Exposure = max (mark-to-market value, 0)

              Interest Rate Swap Exposure = .005 x notional principal

              Currency Swap Exposure = .005 x notional principal

              Loan Equivalent Amount = Current Exposure + Potential Exposure

 

To calculate the reserve requirements the BIS considers two types of capital. Tier One Capital is shareholder’s equity exclusive of goodwill; Tier Two Capital is subordinated debt, loan requirements and other long-term capital. The capital reserve ratios require that Tier One Capital divided by Risk Adjusted Exposure be greater than .04 and that Tier Two Capital divided by Risk Adjusted Exposure be greater than .08.

 

In addition to derivatives foreign exchange risk was also a concern. The BIS recommended two approaches to establish capital requirements for foreign exchange. One, the shorthand method attempts to use some correlations between currencies to obtain a net open position. The other is the simulation method. This more complex technique (see part B below) utilizes actual historical exchange rates to value foreign exchange positions by calculating simulated gains and losses. A five year period for exchange rate observed data was recommended by the BIS with 1,300 observations. A 95% confidence level equivalent to 2 standard deviations is consistent with the BIS guidelines.

 

The Basel Committee has been building on the foundation built by the current Accord; the new Basel Two standards are in various stages of implementation. The Committee proposes replacing the existing approach by a system that would use external credit assessments for determining risk weights of exposures to banks, securities firms and corporates. There was also a new risk weighting scheme to address asset securitization.

 

 

 

Appendix 5B

 

Measurement of Risk Exposure

 

At the Federal Reserve Bank of New York we developed a number of computer models to assess the risk of swaps for the BIS capital adequacy guidelines. For the measurement of interest rate swap exposure  static models were implemented which assumed a fixed book of swaps put on at different swap rates to measure the effect on exposure of various replacement rates. Exposure was defined as the present value of the rate differential for the remaining maturity of the swap where the replacement rate plus an add factor is less than the original rate in the case of a fixed rate receiver or greater than the original rate in the case of a fixed rate payer. For currency swap exposure the static models assumed a fixed book of swaps put on at different spot rates and measured the effect on exposure of various replacement spot rates.

 

We also ran a dynamic series of Monte Carlo simulations to measure swap exposure. This is a technique that combines historical observed statistical parameters with computer generated random numbers to perform a multitude of virtual experiments. These models are used with replacement rates based on a stochastic process and run to generate large numbers of interest or spot rate scenarios. Frequency distributions are then constructed of exposures for swap or spot rate intervals for each year during the life of the swap. The Monte Carlo simulation method was also used to measure the risk of foreign currency holdings.

 

Appendix 5C

 

The Fat Tails Problem

 

Much work has been done on the assumption that changes in securities prices, foreign exchange rates and investment returns are normally distributed. But in fact these distributions have fatter tails and higher peaks than does the normal distribution. This phenomenon, referred to as leptokurtosis, implies that the probability of substantial losses due to extreme movements in the markets would be quite large.

 

There are two alternative hypotheses to account for the observed leptokurtosis of returns on financial assets. One views the distribution of returns as a finite variance mixture of normal distributions for which the mean is constant but the variance changes over time. The other hypothesis is that returns are distributed according to some non-normal member of the family of stable Paretian distributions. The normal distribution is one member of this class and the only member for which the variance exists. The most famous alternative member of this class is the Cauchy distribution with infinite variance. These are specified as follows.

 

Normal density function where µ = mean and   σ = standard deviation:

 

f(x) =       1      e^{-(x-µ)^2/2σ^2}

            σ√2π

 

 

Cauchy density function with parameter ϴ:

 

g( x) = 1/(π (1+(x-ϴ)²)