SEMINAR 2 – MN3002 Financial Market Efficiency and Behavioural Finance

1. Simulate 778 observations of a Gaussian White Noise process using the excel function NORMINV (RAND(), mean, std dev). Alternatively, use NORMINV (RANDARRAY(), mean, std dev). Assume zero-mean and unit standard deviation. Next, plot the generated time series process.

2. Use the Gaussian White Noise in point 1 to simulate a random walk process and plot it with the other time series simulated in point 1. Assume zero as a starting value for the random process. What can you observe?

3. Go to Canvas and download monthly prices for the S&P 500 equity index (Ticker: ^GSPC) from January 1950 to August 2016. Do the following:

a. Estimate the following regression:

pricet = Φpricet-1 + εt

Are S&P 500 index prices well described by a random walk process?

b. Compute continuously compounded (cc) returns and estimate the same regression (as in point a) using cc returns rather than prices. Comment on the results.

4. Using the Excel function AVERAGE(), compute both the 50-month and 150-month moving averages (MA). Plot the index prices together with the two computed moving averages in a line graph. Just by looking at the graph, do you think you could have beaten the market by using any of the technical trading rules covered in the lecture assuming an investment of £1000 at the start of December 2012?

a. What return would a buy-and-hold strategy (passive strategy) have generated?

b. What return would a technical rule (active strategy) which buys (sells) when the price is greater (lower) than the 50-month MA have generated?

You can use the Excel function “IF” to implement the trading rules. Also, include trading costs assuming a flat fee per trade of 0.4% applied on the final amount at the end of the period. Assume continuously compounded (cc) returns.

5. Based on a run test performed during the same period December 2012 to August 2016, do you find evidence of momentum or reversal (mean reversion) in price changes?

6. During the same time period as in the previous point, calculate the correlation between each month’s return and the prior month (autocorrelation function at lag 1). Is the autocorrelation coefficient significant at the 5% significance level?