How do realized returns change
objectives for this section are:
i. To examine the
scatter plot of returns over time,
ii. To test the null hypothesis that returns are
iii. To examine the behavior of volatility over time.
We start with looking at i. for American Express (AXP).
Select Depicted Weights (the default below the
button Plot Return Histogram) and enter a 1 under AXP leaving all other
stock weight fields blank (see above). Then first click on the Plot Portfolio
Returns buttons. This plots the realized (in this case monthly) returns
over time. We are interested in whether they appear to be randomly changing
over time plus whether they exhibit any systematic characteristic such as
clusters of more volatile (widely dispersed) over sub periods of time. A
scatter plot of returns lets you become familiar with the data visually
which is an important first step.
For example, if returns exhibit non random behavior over time then this
is inconsistent with weak form of market efficiency. The indication of the
extent to which it is serially correlated is provided by the Autocorrelation
statistic. For the case of AXP this is low (0.030).
Similarly, if volatility of returns tend to cluster into high and low regimes
over time this is also inconsistent with the weak form of market efficiency.
For risk management purposes we are interested in the behavior of extreme
negative returns which this module lets you analyze.
Our immediate goal, however, is to test whether observed returns come from
the stationary and symmetrical Normal Distribution.