In this worksheet I will discuss moving averages and conditional expectations on price. 

A moving average is a simple arithmetic mean ( expected value) that drops the last observation

when new price observation is coming in.  

For example a five period moving average is given by 

When a new price observation is observed the five period moving average becomes: 

We can further illustrate a moving average as follows: 

The basic idea is to filter out noise and visualize the signal ie trend. 

However remember that a moving average on price indirectly only deals with one of the component

of a trend and that is expected return. It does not say anything about the volatility of returns.  

Now the slope of the moving average is equal to the rate of change of an investors  

price expectations. We can now do some empirical investigation and test if a moving  

average trading strategy can increase an investors returns. 

The trading strategy is as follows: 

- If the slope of the one year moving average is positive then we take a long position. 

- if the slope of the one year moving average in negative we take a short position. 

We starting by loading monthly data for 14 global stock indices for the period 1997 to 2009 as follows 

restart;

(1)

(2)

We can plot a sample of the return distributions as follows: 

We can plot an sample of the stock indices with their corresponding one year moving averages as follows: 

This means that the slope of the moving averages at any point in time are given by: 

(3)

We now note that if the slope of the moving average is positive then we get +1*return and  

if the slope of the moving average is negative we get -1*return 

(4)

We can plot our absolute returns as follows: 

We can plot the equity curves as follows: