Yes, it is a real probability. It is interpreted, like any probability, as the expected frequency: On average, one out of each hundred firms with EDF credit measure of 1% will default within a year.

There is no more trend information in EDF credit measures than there is trend information in stock prices - that is, none. Like the stock price, the EDF credit measure is the best current assessment given the available information. If it were likely that the firm is going to deteriorate in the future, this would already make the current EDF credit measure higher.

This calculation can be done, but what is needed in addition to the two EDF credit measures is the correlation between the asset values of the two firms. We provides these correlations in the Moody's KMV Portfolio Manager™.

The degree of diversification of a debt portfolio can be measured by the ratio of the minimum unexpected loss that can be achieved by diversification to the actual portfolio unexpected loss. In a formula:D=ULmin/ULP where ULP is the portfolio unexpected loss and UL minis the minimum unexpected loss attainable on a comparable portfolio constructed on a given universe.The reason we want to define the diversification measure as the ratio of unexpected losses (rather than the more usual ratio of variances, which is the squared unexpected losses) is that the required capital is roughly proportional to the UL. Thus, if a portfolio has D=50%, it means that it requires approximately twice the capital than would be necessary with a perfectly diversified portfolio. If D=33%, the portfolio takes three times as much capital as would be optimally necessary. The portfolio with the minimum UL can be constructed on various universes. The only criterion is that the portfolio is contained within this universe. We get different diversification measures for different choices of the universe; but that is necessary and desirable. A portfolio of bonds to US companies may have a diversification of D=40% within the US debt market, and diversification of D=20% within the international market. The portfolio manager should be aware of both of these numbers: They show the opportunities attainable by expanding beyond current limits. For each choice of the universe, the portfolio with the minimum UL should be comparable to the actual portfolio. This means specifically that it needs to have the same percentage allocation to different credit quality classes as the actual portfolio. It would be incorrect to compare the portfolio UL to that of a different quality portfolio. The quality classes should be formed as EDF buckets. We define certain meaningful intervals for EDF credit measures, for example, those that correspond to agency ratings, calculate the relative proportions in these categories for the actual portfolio, and construct a portfolio on the given universe that has a minimum UL subject to the requirement that it has the same relative proportions in the EDF categories. In addition, the expected loss within each category of the optimized portfolio should beequal to that of the actual portfolio. Then UL min is calculated from an optimization program subject to these constraints.

Moody's KMV is not confined to a specific theory or framework of model development. We follow all new developments in credit risk management and continuously test new modeling techniques. Moody's KMV, jointly with Moody's Investors Service, has created a special Academic Advisory Board with distinguished members from the academic community to benefit from new developments in the arena of credit risk management.

Our approach to credit risk modeling is based on several basic principles. We believe that default models should be developed, calibrated, and tested on the type of data, firms, and markets on which they will be used. We also believe that models should always be tested out of sample and out of time to assure robust behavior and that models should be powerful but use data that is easily available to the user.

The theory of derivative asset pricing, or options pricing as it is more often referred to, is one of the great achievements of modern finance. It has become an essential tool in the valuation of derivatives. It is indispensable in risk management of derivative books. It allows valuation of corporate liabilities given the value of the firm assets, or valuation of corporate debt given the value of the firm equity.

It deals with the valuation of one asset, or security, called the derivative, relative to the value of another asset or security, the underlying. An asset is called a derivative with respect to another if all of its payouts depend only on the value of the underlying. A simple example is a call option on a common stock. The payout on the call is determined solely by the value of the stock. It is the excess of the stock price over the strikeprice if the call is exercised, or zero if not. Another example is the value of corporate debt. In this case, the underlying is the market value of the firm's assets, that is, the value of its ongoing business. It is obvious that the price of the derivative asset must be related to the price of the underlying one. Since the payout on a call option on a stock depends only on the stock price, the price of the call must be a function of the stock price. But which function? Options pricing provides the answer. The function must be such that the return on the option, which is given by the percentage increment of the function, in excess of therisk-free return must be proportional to the return on the underlying asset in excess of the risk-free return. If this were not the case, the option and the underlying asset could be arbitraged against each other with the use of the risk-free asset to generate a positive gain on a position that necessitates no investment and carries no risk. This should not be possible in an efficient market. This is one of the achievements of the theory of options pricing. That a condition on the increment of the unknown function in relationship to the increment of the underlying asset value, together with the specification of the option payouts provided by its contractual provisions, specifies the function in full. The function can be sought out in either of two equivalent ways. One way is to determine the option value as the solution of a partial differential equation to which the price of any derivative asset mu st conform (this equation was initially derived by Black and Scholes and independently, in more generality, by Merton), subject to boundary conditions given by the form of the payout. The equation was originally solved by Black and Scholes for the European call and put to yield their celebrated formula. The other way to get the option value has the tremendous appeal of bringing out the economic, rather than only mathematical, aspect of the options pricing theory. It is shown that the option is priced as the present value discounted at the risk-free rate of the mathematical expectation of the payouts; provided, however, and this is a deep and subtle point of the theory, that the expectation is calculated not with respect to the actual probability distribution of the payouts, but rather with respect to an alternative probability distribution. This alternative distribution, called the pricing, or risk-neutral, distribution, is the one the payouts would have in a risk-neutral economy. In such an economy, the expected rate of return on all assets is the risk-free rate. The pricing probability distribution is thus obtained as if the underlying asset appreciated on average at the risk-free rate, rather than at its own actual expected rate of return. The reason here is that the relationship of the option price to the price of the underlying does not depend on investors' attitudes toward risk, and therefore must be the same as in a risk-neutral world, and in a risk-neutral world, we know how assets are priced: as the expected present values of their payouts. Besides valuation, the theory yields powerful results for risk measurement and management. The hedging ratios, or deltas, for hedging the risk of derivatives positions can be calculated by differentiation, with respect to the price of the underlying asset, of the option value. These hedge ratios also provide a measure of elasticity, or exposure to the risk of the underlying security. By reducing the delta of a derivative portfolio (they combine linearly), the exposur e to a given risk source is reduced.

They are calculated using the Merton/Black/Scholes theory of derivative asset pricing (option pricing), but not by the Black/Scholes formula. The Black/Scholes formula would be appropriate for a firm whose liabilities consist of a single class of debt paying no interest prior to maturity, and no dividend paying equity. Such firms rarely exist. A realistic financial structure includes interest paying debt of various maturities, convertible issues, dividend-paying preferred and common stock, and so on. The value of equity is still a derivative of the value of assets, but the structure, timing, and preference of the claims on the assets due to the nature of the liabilities is more complex than that assumed by the Black/Scholes formula. The relationship between the value of assets and value of equity, which is used in the MKMV model, must be obtained by applying the option pricing theory to the real firm.

A firm defaults on its debt if the market value of the firm™s assets, that is, its ongoing business, falls below the obligations payable at the time. The option pricing theory permits the determination of the firm™s asset value from the observed equity price and equity volatility, in the context of the balance sheet. Once the asset market value and its volatility are known, it is possible to calculate the probability that the asset value will, within the specified time frame, decline to the point at which default must occur. This probability is the EDF credit measure. The market price is the most objective valuation of the firm. The price volatility reflects the uncertainty about the firm™s value in the future. An EDF credit measure utilizes the market information to make an explicit assessment of the likelihood of default.