FINM1001 Lecture Notes - Lecture 15: Covariance, Random Variable, Normal Distribution
FINM1001 Week 5 Lecture A
● Diversification:
○ Want diversity because if you have everything in the same basket if something
happens they all crack
● What is a random variable?
○ Random variable can take on a number of various values
○ Return on a share -> there can be multiple (4-5) outcomes e.g. a boom, average
and a not so good year -> return outcomes for each thus return of a share over a
year
○ Can plot the uncertain by probability and distribution
○ Normal distribution characterised by 4 “moments”
■ Mean: average/expected value
■ Variance: how close they are to the mean thus the higher the variance the
less certain we are. Large variance = not much certainty with the outcome
thus measure of risk or uncertainty but more useful to talk about standard
deviation and is expressed as a percentage
■ Skewness: If the bell shape is right shaped or left shaped
■ Kutosis:
○ Normal distribution can be explained by the expected value, the mean and the
variance. Thus assume share returns follow normal distributions but in reality
they are skewed to the right due to the value of a share can go up to infinity but
never below 0 thus right
● How do we calculate the expected value of a random variable?
○ Insert formula
○ Check the probability like the one in the example on page 6 column b if they don’t
add to give 100% then there is a problem
○ Insert formula for standard deviation/variance which gives you the risk of a
random variable. Measuring the outcomes relative to the expected value
● What attitude do investors have towards risk?
○ Risk averse = less risk
○ Make 2 assumptions about investor preferences
■ Investors are greedy thus prefer more wealth to less
■ Investors are risk averse
○ Utility = happiness
○ More wealth we accrue the more happy we are thus eventually having more
wealth wont increase the happiness by much
○ Thus having more wealth will increase the happiness at a decreasing rate thus
risk averse
○ For risk averse will avoid the impact of losing $100 worth of happiness is far
more than winning $100.
○ Risk investor has to be paid to take on risk
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
Want diversity because if you have everything in the same basket if something happens they all crack. Random variable can take on a number of various values. Return on a share -> there can be multiple (4-5) outcomes e. g. a boom, average and a not so good year -> return outcomes for each thus return of a share over a year. Can plot the uncertain by probability and distribution. Variance: how close they are to the mean thus the higher the variance the less certain we are. Large variance = not much certainty with the outcome thus measure of risk or uncertainty but more useful to talk about standard deviation and is expressed as a percentage. Skewness: if the bell shape is right shaped or left shaped. Normal distribution can be explained by the expected value, the mean and the variance.
