Article Detail

Price of Risk – Recent Evidence from Large Financials

Journal 32: Applied Finance

Manmohan Singh, Karim Youssef

Probability of default (PD) measures have been widely used in estimating potential losses of, and contagion among, large financial institutions. In a period of financial stress however, the existing methods to compute PDs and generate loss estimates have generated results that vary significantly. This paper discusses three issues that should be taken into account in using PD-based methodologies for loss or contagion analyses: (i) the use of “risk-neutral probabilities” versus “real-world probabilities;” (ii) the divergence between movements in credit and equity markets during periods of financial stress; and (iii) the assumption of stochastic versus fixed recovery for the assets of financial institutions. All three elements have non-trivial implications for providing an accurate estimate of default probabilities and associated losses as inputs for setting policies related to large banks in distress.

Measures for the probability of default (PD) of financial institutions have been widely used in estimating potential losses of, and contagion among, large financial institutions.2 However, different methodologies used to arrive at such estimates have not necessarily produced uniform results. During the recent financial crisis, two types of PDs (based on CDS spreads and Moody’s KMV, respectively) have differed markedly for large banks, and the resulting loss estimates have also varied significantly. In order to properly identify policies with respect to large banks in distress, a closer review of the key differences arising from the various methods to extract PDs is necessary. Indeed, the difficulties in harmonizing the results of the methodologies discussed need to be spelled out, as they could potentially have an impact on authorities’ reactions and subsequent policy advice.

These differences start with the underlying market signals used to calculate the PDs. Credit default swap (CDS) spreads providing signals from debt and/or credit markets – given an assumed level of recovery – have been used to arrive at a PD measure. By design, it is risk neutral because it does not take into account investors’ varying degrees of risk aversion. Risk neutrality allows us to bypass the need to calibrate a real world measure of investors’ utility by assuming that all investors are risk neutral. That is to say, risk neutral methods assign greater probabilities to worse outcomes. PDs derived via the risk neutrality assumption are widely accepted when pricing credit instruments, or assessing the impact of default risk on a portfolio of assets with similarly priced components.

The Moody’s KMV methodology, which accounts for investors’ risk aversion by extracting signals from equity markets to arrive at a “real world” measure of risk have also been used to extract PDs. In contrast to risk neutral PDs, which use only market prices as inputs, risk measures based on the real world approach also use balance sheet inputs. It is generally accepted that real world measures provide for a better approximation of investors’ risk aversion and are as such better suited to carrying out scenario analysis to calculate potential future losses caused by defaults [Hull (2009)]. Nevertheless, the nature of the inputs used for real world measures also provide for the potential of missing important market signals (especially during distress).

The resulting implication is that losses computed from risk neutral PDs may need to be adjusted downward to arrive at the real world probabilities, while during periods of market stress, the assumptions underlying some of the models yielding real world PDs may become tenuous. The difficulties associated with the transformation of risk neutral PDs to real world PDs are discussed below, along with issues that need to be considered and explored further. In particular, in adjusting the risk neutral probabilities with a conversion factor (the price of risk), we explore the importance of: (i) deviation between credit and equity prices during periods of financial market stress and (ii) the role of the assumption of stochastic versus fixed recovery for financial institution assets.


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