FIRE 311 F „09
Risk And Return
1
Copyright
David E. Upton
10/25/2009
RISK AND RETURN
Expected Value and Standard Deviation:
None of us has a crystal ball – we don‟t know exactly what will happen in the future.
Every decision we
make is based on uncertainty.
This does not mean, however, that we are completely at a loss about what
might
happen in the future.
We do have some idea, and we know that certain things are more likely to
happen than other things.
When we purchase a stock or a bond, when we decide to undertake a project,
the decision is affected by our expectations of the future.
These future expectations are often hidden in
our subconscious.
But if we leave the treatment of uncertainty to our subconscious, we have poor control
over the decision.
It may be affected by irrelevant factors we are not even aware of, and our decision is
likely to be suboptimal.
In order to make better, more rational decisions, we need to bring the uncertainty
and decision-making as much as possible to the to the conscious level.
While we may never achieve the
total rationality of Mr. Spock (nor in many decisions would we want to), we can and should improve our
decision processes.
Although a full treatment of decision making is well beyond the scope of this course, we can begin by
examining the idea of uncertainty about future outcomes.
To start, quantitative future outcomes can be
described as a random variable.
A random variable is a variable that can assume a number of values, with
the different values, with each value having an associated (usually differing) probability.
This requires that we understand what a “probability” is.
Probability is the
proportion
of times an
outcome is anticipated to occur over a large number of trials.
E.g., if the weatherman says that the chance
of rain is 40% (or 0.4), it means that when similar conditions occur, rain can be expected 40% of the time.
Or, if we say that the probability of getting the ace of spades on a single draw from a fair deck is 1 / 52 =
0.0192308, we mean that if we repeatedly take a single card from a fair deck, the proportion of times we
will get an ace of spades is about once for each 52 tries.
NB:
This does not mean that you will get an ace of spades once in every 52 tries – it means that over
many trials, the
proportion
of times you get the ace of spades will be about 1 / 52.
You may get the ace
of spades three times in a row right away, or not get the ace of spades until your 500
th
try.
It is only over
a large number of trials that the proportion will approach 1 / 52.
A common misperception is that probability works by “compensating” - i.e., if a flipped (fair) coin has
not come up heads in three tries, somehow it is more likely that a head will come up on the next flip.
This
is incorrect, and seems to indicate that the coin has a memory and somehow will remember to balance out
heads and tails.
For example, suppose that you are flipping a fair coin, in which the probability of a head