Group 3
Jeel Sarvaiya
2013018
Standard Deviation:
Case to Consider
If you invest in XYZ
shares (assume that we are listed) you can generate an average year on year
return of 25%. If I see any other stock, I would not be able to generate more
than 20%. Would you invest in XYZ stocks?
If it had been the
good old pre quantitative heavy investing days, I know you would have gladly
invested in XYZ. But now the life is not that easy, Managers understand Risk.
They don't like to invest in shares that go up and down everybody wants a stable
life!
Business Consideration
Average return (or for
that matter any average), never tells the full story. It gives yo the
central value of data, but does not tell you about the spread. It says that you
can generate 25% return, but does not tell you that the return can be -10% to
60%, so that the average would be 25% (But one might have to exit at -10%).
So we need to measure
spread (which is akin to risk!)
Measuring Spread (Risk) using Range
The
simplest measure is Range [Min, Max]. It gives a fair idea of spread.
But it again gives only half of the story. The Minimum and Maximum might be skewed. It would be
the same for data sets that are uniform, but have an extreme min and max and
same for skewed data around min and max.
Excel
gives simple functions to calculate Range. Min and Max.
Measuring Spread Using Standard Deviation
Just like Range gave
us the simple measure of spread by telling the Min and Max values of data,
we have another measure called standard deviation (or an equivalent measure
called variance) to measure spread. Standard Deviation essentially
· Measures the
spread (Differences of individual data points) from the mean
·Squares the
differences (So that positives and negatives all become positive)
Takes the average
of these squared differences
Excel makes life
easier. Just use the function, StdevP or VarP and show it the data. It does all
the number crunching on its own!
Reasons why Standard Deviation is very Popular
Standard deviation has
its own advantages over any other measure of spread.
It measures the
deviation from the mean, which is a very important statistic (Shows the central
tendency)
·It squares and
makes the negative numbers Positive
The square of
small numbers is smaller (Contraction effect) and large numbers larger
(Expanding effect). So it makes you ignore small deviations and see the larger
one clearly!
The square is a
nice function!
Standard Deviation and Finance
Perhaps standard
deviation is the most important concepts as far as finance is concerned.
Finance and banking is all about measuring and managing risk and standard
deviation measures risk (Volatility). Standard deviation is used by all
portfolio managers to measure and track risk. One of the most important ratios
in portfolio management, Sharpe Ratio (for which William Sharpe got a Nobel
Prize) uses Standard Deviation to measure risk adjusted return (and hence
incentivizes portfolio managers to generate return by taking minimum risk).
