• The total probabilities of an event occurring or not will always
equal 100 percent. If you have a 10 percent probability that
something may happen, then you have a 90 percent
probability that it won’t.
• The simplest example is the coin toss. You have a 50 percent
probability that the coin will land on either side because only
two options exist.
• When you apply probability theory to the standard deviation,
you end up with something called a normal distribution.
• Probability: chance of an event taking place
Rules relating to probabilities
• If an out come is definitely certain to happen, its probability is
• The probability of an event happening would mostly lie
between 0 and 1
• Sum of probabilities of an event happening must be equal to 1
• Probability can never be a negative number
• Possible outcomes must be mutually exclusive
4. Probability Distribution
• A probability Distribution is a table showing the various
possible outcomes of an event along with their respective
• Normal Probability Distribution is a bell shaped curve, and is
perfectly symmetric around the expected rate of return
which is in the middle
± One standard derivation (ó) 68.3%
± Two standard Derivation (ó) 95.4%
± Three standard deviation (ó) 99.7%
• The third central moment is a measure of the lopsidedness
of the distribution; any symmetric distribution will have a
third central moment, if defined, of zero.
•The normalised third central moment is called the skewness,
• A distribution that is skewed to the left (the tail of the
distribution is longer on the left) will have a negative
• A distribution that is skewed to the right (the tail of the
distribution is longer on the right), will have a positive
• For a calculated skew number (average cubed deviations
divided by the cubed standard deviation),
• For evaluate whether a return is positively skewed (skew >
0), negatively skewed (skew < 0) or symmetric (skew = 0).
•Kurtosis refers to the degree of peak in a distribution.
More peak than normal (leptokurtic) means that a
distribution also has fatter tails and that there are
lesser chances of extreme outcomes compared to a
•It is sometimes referred to as the "volatility
• A statistical measure used to describe the distribution of
observed data around the mean.
• Used generally in the statistical field, kurtosis describes
trends in charts.
• A high kurtosis portrays a chart with fat tails and a low, even
distribution, whereas a low kurtosis portrays a chart with
skinny tails and a distribution concentrated toward the