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We have some bad news for you. Look again at Exhibit 2.4. In the case of equity portfolios, we note that a fully diversi ed portfolio can be achieved with a limited number of equities. The number of assets needed to create a fully diversi ed portfolio of loans or other credit assets is much larger. It is certainly bigger than 100 assets and it may be larger than 1,000 assets. But we have some good news for you as well. The diversi cation effect for portfolios of loans or other credit assets will be larger than the diversi cation effect for portfolios of equities. Remember that the bedrock risk the risk that cannot be diversi ed away is average covariance. As before, I nd it easier to think about correlations than covariances, so, since both of them are telling me about the same thing, I switch and talk about correlation. The typical correlation of equity returns is 20% 70%. However, the typical correlation of defaults is much smaller 5% to 15%. So the risk that cannot be diversi ed away will be smaller. The bad news is that it is going to take many more assets in the portfolio to achieve a fully diversi ed portfolio. The good news is once you have a fully diversi ed portfolio, you re going to get a much larger diversi cation effect.

P(A = a, B = b)

[Schwarz 1978] G Schwarz Estimating the Dimension of a Model Annals of Statistics 6:461 464 Institute of Mathematical Statistics, Hayward, CA, USA 1978 [Shachter et al 1990] RD Shachter, TS Levitt, LN Kanal, and JF Lemmer, eds Uncertainty in Artificial Intelligence 4 North-Holland, Amsterdam, Netherlands 1990 [Shafer 1976] G Shafer A Mathematical Theory of Evidence Princeton University Press, Princeton, NJ, USA 1976 [Shafer and Pearl 1990] G Shafer and J Pearl Readings in Uncertain Reasoning Morgan Kaufmann, San Mateo, CA, USA 1990 [Shafer and Shenoy 1988] G Shafer and PP Shenoy Local Computations in Hypertrees (Working Paper 201) School of Business, University of Kansas, Lawrence, KS, USA 1988 [Shakhnarovich et al 2006] G Shakhnarovich, R Darrell, and P Indyk Nearest-Neighbor Methods in Learning and Vision: Theory and Practice MIT Press, Cambridge, MA, USA 2006 [Shannon 1948] CE Shannon The Mathematical Theory of Communication.

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The Bell System Technical Journal 27:379 423 Bell Laboratories, Murray Hill, NJ, USA 1948 [Shawe-Taylor and Cristianini 2004] J Shawe-Taylor and N Cristianini Kernel Methods for Pattern Analysis Cambridge University Press, Cambridge, United Kingdom 2004 [Shenoy 1991b] PP Shenoy Conditional Independence in Valuation-based Systems (Working Paper 236) School of Business, University of Kansas, Lawrence, KS, USA 1991 [Shenoy 1992a] PP Shenoy Valuation-based Systems: A Framework for Managing Uncertainty in Expert Systems In: [Zadeh and Kacprzyk 1992], 83 104 [Shenoy 1992b] PP Shenoy Conditional Independence in Uncertainty Theories Proc 8th Conf on Uncertainty in Artificial Intelligence (UAI 92, Stanford, CA, USA), 284 291 Morgan Kaufmann, San Mateo, CA, USA 1992 [Shenoy 1993] PP Shenoy Valuation Networks and Conditional Independence Proc 9th Conf on Uncertainty in AI (UAI 93, Washington, DC, USA), 191 199 Morgan Kaufmann, San Mateo, CA, USA 1993 [Singh and Valtorta 1993] M.

another lm. So, if my agent has gathered a table of my likes and dislikes, it can offer it to a brokering agent which might hold the preference tables for a large population of viewers. Comparing my likes and dislikes with the other viewers preferences, it is possible to identify lms which likeminded viewers have seen and liked, but which I have not seen. The broker agent can then send this information to my personalised agent saying, I think you ll like this . If I decide to view it, I will afterwards be asked to review it and this will lead to a modi cation of my preference table. That is, to an adaptive element has entered into my agent s selection strategy. (But not to my goal, which remains, Locate enjoyable lm .)

In the create pricer function we use the Hull White Monte-Carlo model factory to create the Hull White pricer. Note that the model arguments dictionary is set so that the number of simulation equals 5000 and the seed for the variate generator equals 1234.

Singh and M Valtorta An Algorithm for the Construction of Bayesian Network Structures from Data Proc 9th Conf on Uncertainty in Artificial Intelligence (UAI 93, Washington, DC, USA), 259 265 Morgan Kaufmann, San Mateo, CA, USA 1993 [Smith et al 1993] JE Smith, S Holtzman, and JE Matheson Structuring Conditional Relationships in Influence Diagrams Operations Research 41(2):280 297 INFORMS, Linthicum, MD, USA 1993.

In this book, you ll find several notification icons Note, Caution, Tip, and Cross-Reference that point out important information. Here s what the four types of icons look like:

P. Taylor, Alan Mathison Turing (1912 1954), Australian Mathematics Trust, May 14, 2002.

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