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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 estimate the market risk inherent in portfolios of securities. If excess returns above the risk-free rate are sought, which many investors do, risk must be taken. If the market is largely efficient then there are very few free lunches, and excess returns will only be broadly available when some additional risk is borne. The kind of risk that should carry a risk premium, i.e. risks on which the market requires a higher payout in return for intentionally bearing the risk, is market risk. Market risk is the risk of unexpected variability in the price of securities. Other risks are sometimes discussed in relation to investing, including liquidity risk, interest rate risk, operational risk, credit risk, legal risk, brand risk, etc. Risk is something of a buzzword and some of these ‘risks’ do not really describe a single, coherent, consistent concept. Others are capable of being redefined as an element of market risk, e.g. credit default risks cause prices to change, and should be described as part of a complete market risk framework. We need to know if the return being sought is sufficient for the level of risk required to achieve it. A better risk model will give us a better estimate of the risk, and our actions will be more efficient. T Risk as variance The central measure in risk control is variance (or sometimes standard deviation, volatility , which is the square root of variance). The core supporting concept is the covariance matrix. The covariance matrix is a table that includes the relative variance of every security with respect to every other one. Popularised by Harry Markowitz in the 1950’s, his insight into its use was so important that it earned him the Nobel Prize. (Note: Some people propose the use of semi-variance, which only measures negative deviations. Underpinning such measures is the belief that we should only be interested in ‘downside’ measures of risk. This is in itself a naïve interest. When a fund manager delivers significant underperformance, all investors are unhappy. When the fund manager delivers outperformance beyond their stated aim or risk limits, everyone should equally be unhappy. It means the process was not really under control, and the manager was only lucky that the performance was up rather than down. Risk measures are principally about how much the value of some securities can vary, and placing limits on that variance. Whether performance 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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2 T or down is a function of how good their predictions of return were, and the risk system should not be partial to positive or negative deviations.) If we have an accurate covariance matrix, we can compute most (but not quite all) of the important risk statistics.
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