APT_Risk_Model_Theory___Background - T APT Risk Model...

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APT Risk Model Theory - Background 1 T T Market Risk There is a need to es ti mate the mar ket risk in her ent in±port±fo± lios±of±se±cu±ri±ties.± If ex cess re turns above the risk-free rate are sought, which many in ves tors do, risk must be taken. If the mar ket is largely ef fi cient then there are very few free lunches, and ex cess re turns will only be broadly avail able when some ad di tional risk is borne. The kind of risk that should carry a risk pre mium, i.e. risks on which the mar ket re quires a higher pay out in re turn for in ten tion ally bear ing the risk, is mar ket risk. Mar ket risk is the risk of un ex pected vari abil ity in the price of se cu ri ties. Other risks are some times dis cussed in re la tion to in±vest± ing,±in±clud± ing±li±quid± ity±risk,±in±ter±est±rate±risk, op er a tional risk, credit risk, le gal risk, brand risk, etc. Risk is some thing of a buzz word and some of these ‘risks’ do not re ally de scribe a sin gle, co her ent, con±sis±tent±con±cept.±Oth±ers±are±ca±pa±ble±of±be± ing re de fined as an el e ment of mar ket risk, e.g. credit de fault risks cause prices to change, and should be de scribed as part of a com plete mar ket risk frame±work. We need to know if the re turn be ing sought is suf fi cient for the level of risk re quired to achieve it. A better risk model will give us a better es ti mate of the risk, and our ac tions will be more ef fi cient. T Risk as vari ance The cen tral mea sure in risk con trol is vari ance (or some±times±stan±dard±de±vi±a±tion,± vol±a±til± ity , which is the square root of vari ance). The core sup port ing con cept is the covariance ma trix. The covariance ma trix is a ta ble that in cludes the rel a tive vari ance of ev ery se cu rity with re spect to ev ery other one. Popu lar ised by Harry Markowitz in the 1950’s, his in sight into its use was so im por tant that it earned him the No bel Prize. (Note: Some peo ple pro pose the use of semi-vari ance, which only mea sures neg a tive de±vi±a±tions.±Un±der±pin±ning±such±mea±sures±is±the be lief that we should only be in ter ested in ‘down side’ mea sures of risk. This is in it self a naïve in±ter±est.± When±a±fund±man±ager±de± liv±ers±sig±nif± i±cant underperformance, all in ves tors are un happy. When the fund man ager de liv ers outperformance be yond their stated aim or risk lim its, ev ery one should equally be un happy. It means the pro cess was not re ally un der con trol, and the man ager was only lucky that the per for mance was up rather than down. Risk mea sures are prin ci pally about how much the value of some se cu ri ties can vary, and plac ing lim its on that vari ance. Whether per for mance is up This discussion focuses on why estimating market risk is important, what kind of variables can be used to capture market risk, the problems with variance - the main risk measure, how the problems are resolved by using factor models, and why some kinds of factor model are more suitable than others.
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This note was uploaded on 04/09/2010 for the course NBA 5450 taught by Professor Richardmarin during the Fall '09 term at Cornell University (Engineering School).

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APT_Risk_Model_Theory___Background - T APT Risk Model...

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