Financial Risk and Distribution Analysis PDF

Stuvia - Koop en Verkoop de Beste Samenvattingen Chapter 3: Distribution of financial terms We are going to look at one particular type of risk: price risk We are not going to look at the other two:  Default risk = the risk that someone is not able to pay  Liquidity risk = the risk that yo...

Stuvia - Koop en Verkoop de Beste Samenvattingen Chapter 3: Distribution of financial terms We are going to look at one particular type of risk: price risk We are not going to look at the other two:  Default risk = the risk that someone is not able to pay  Liquidity risk = the risk that you don’t find a counterpart if you want to sell your assets Normal distribution For assessing the risk of an investment, one should consider the whole distribution and not only the variance. It is useful to first introduce higher moments of distribution. We already know the mean (first moment) and the variance (second moment). The third moment is the (sample) skewness. S KEWNESS The skewness provides information about a distribution’s symmetry. Skewness of 0 = symmetric distribution Negative skewness = left-skewed or skewed to the left. The tail on the left side of the distribution is longer than the right side and the majority of the probability mass is located to the right of the mean. Positive skewness = right-skewed or skewed to the right. Realization to the right tend to be larger. If a return distribution is left-skewed, the investment provides frequent small gains and few extreme losses. A right-skewed return distribution provides frequent small losses and few large gains. Investors will be more attracted by positively skewed return distributions, because they provide large gains (although they occur rarely). Left-skewed distributions are bad for investors because the rare extreme losses may jeopardize the investor’s wealth. Gedownload door: hannahducatteeuw | [email protected] Wil jij7€76 per Dit document is auteursrechtelijk beschermd, het verspreiden van dit document is strafbaar. maand verdienen?  Stuvia - Koop en Verkoop de Beste Samenvattingen K URTOSIS The fourth moment is the kurtosis. A normal distribution has a kurtosis of 0. Positive kurtosis = leptokurtic Negative kurtosis = platykurtic A higher kurtosis means more of the variance is the result of infrequent extreme deviations, as opposed to frequent modestly sized deviations. As a result, the leptokurtic distribution has a higher peak around the mean compared to the normal distribution, i.e. the probability density is concentrated around the mean and at the tails. The distribution is therefore said to have fat tails. Leptokurtic return distributions are DANGEROUS, because the fat (negative) tails make extreme losses occur more frequently. Neglecting them may lead to a dangerous underestimation of (tail) risk. We have too many extreme changes, too many changes that are close to zero and but a few moderate changes… The extreme changes are very important for risk management, because these changes can determine whether you go bankrupt or not. If you work on a normal distribution (the red one) you might underestimate these risks because, when in fact, the blue one is the true distribution then the risk is much higher and that is a problem. With the red line you underestimate the risk of an extreme event. (links en rechts onderaan, die verschillen) See p.36 book for example Stylized fact 1: The distribution of high-frequency financial market returns is leptokurtic Stylized fact 2: The kurtosis of financial returns declines with temporal aggregation. Stylized fact 3: Almost symmetric return distributions. The skewness of financial returns does not systematically differ from zero. Stylized fact 4: the volatility of financial time series clusters. “Large changes tend to be followed by large changes, of either sign, and small changes tend to be followed by small changes.” Gedownload door: hannahducatteeuw | [email protected] Wil jij8€76 per Dit document is auteursrechtelijk beschermd, het verspreiden van dit document is strafbaar. maand verdienen?