It helps to know (and be assured with certainty) that if some data set follows the normal distribution pattern, its mean will enable us to know what returns to expect , and its standard deviation will enable us to know that around of the values will be within standard deviation, within standard . Stock market returns are often assumed to follow a normal distribution. However, in reality, return distributions tend to have fat tails, and therefore have kurtosis greater than three. Such returns have typically had moves greater than three standard deviations beyond the mean more often than expected under the assumption . Lognormal, as we discusse is extremely useful when analyzing stock prices. As long as the growth factor used is assumed to be normally distributed (as we assume with rate of return ), then the lognormal distribution makes sense. Normal distribution cannot be used to model stock prices because it has a . Professors Fama and French gave this response: “Distributions of daily and monthly stock returns are rather symmetric about their means, but the tails are fatter (i.e., there are more outliers) than would be expected with normal distributions.

How to calculate Expected Return. The Normal Distribution. Investor Preferences under Uncertainty. Appendix A: Some Useful Probability Rules.

Associated SP 5percentage move, Actual SP 5occurrences ( vs ( expected from normal distribution ). This video describes how to calculate mean and standard deviation using the TI- BA II Plus financial. Before we proceed to formally test our return data for normality, we can . One may define several kinds of returns, of which the two most common are arithmetic and geometric returns. In Section we explain the difference between the two types. It is common to assume that single-period geometric returns follow a normal distribution. Why returns have a normal distribution.

There is a special distribution within the class of stable distributions called the normal distribution. It is the only one that has a finite variance. If I have a normal distributon, Expected return of: , vol of and a one year holding period I can easily look at a table and find out what is the probability of having a return of or less for example. How can I do the same for a longer holding perio say I have a ten year holding period and I want to see . Bootstrap distributions of continuously compounded returns approach normal distributions for longer return horizons. If continuously compounded returns approach a normal distribution (i.e., the returns are symmetric on both sides of the mean), we would expect the natural log of the same variable would . Joint distributions capture how asset classes behave together rather than individually.

However, we find that in many cases correlations under extreme conditions are quite different than under normal conditions. In other words, the expected linear correlations . As the certainty of the return increases (i.e. the less potential difference between the actual and expected result), the smaller the amount of uncertainty or risk. In a normal distribution.

Let us then assume that they have the same mean price change, say 0. Thanks to the three sigma rule, we can then infer that in the first case of the time the rate of return will be between 0. In order to help clear some of the confusion, this article examines some interesting facts about the properties of expected geometric return in portfolio analysis. Differing time horizons. If returns are assumed to follow a log- normal distribution and are serially independent, the exact relationship between the expected annual . Although expected return is the best estimate available of future returns, the actual return is not likely to equal the expected return.

For this reason, investors and managers would like to have an idea of how precise their estimate might be. To help quantify the precision of their estimates, you use two concepts: variance and . It is customary to assume in VAR calculations that the expected return over period considered is (because in practice calculations are done over very short periods). It is also customary to assume normal distribution of returns.

Because the 1st percentile of the standard normal distribution is -2. By assuming that the distribution of compound return can be approximated by a normal distribution for finite N, risk policies were found which maximize: a) the probability that a given compound return rate or level of N- period terminal wealth .