You are a Junior Stock Analyst for F&H Investment Plc, with responsibility for tracking FTSE 100 stocks on the London Stock Exchange. One of your core duties is to determine the right price and return of stocks, which in turn, informs traders on buying or selling decisions of the stocks in their portfolio.
The asset returns/pricing model used is the capital asset pricing model (CAPM), which proposes the market (systematic) risk as the single determinant of stock value.
The CAPM is estimated using the following empirical model
R_(i,t)-r_(f )= α_i+ β_i (R_(m,t)- r_f) (1)
where, i= 1,…, N and t=1,…,T
R_it = return on asset i at time t (your selected stock, e.g., Barclays)
r_f = return on the risk-free asset at time t (UK govt three (3) months Treasury bill price)
R_(m,t)= return on the market portfolio at time t (FTSE 100 Index)
α_i and β_i are the coefficients to be estimated.
Your task for the month is to produce a report detailing the time series pattern, return analysis and forecast of a stock that is a constituent of the FTSE 100 index (refer to list of FTSE 100 firms). The main body of your report should be structured based on the following sections.
Time Series Analysis
Stock Returns Analysis
Forecasting
Below are detailed requirements for each component of your report.
PART ONE: TIME SERIES ANALYSIS
Produce a time-series graph of the monthly price series for (i) the selected stocks, (ii) the risk-free asset and (iii) the market portfolio, for the past 15 years.
Provide a description of the patterns observed for your series plots, that is, whether you observe a trend, season, cycle, structural break, random walk or a combination of them).
Identify an economic/fundamental reason for the patterns observed in each of the series analysed above.
[20 marks]
PART TWO: STOCK RETURNS ANALYSIS
Estimate a monthly return series for your chosen stock (R_(i,t)), the risk-free asset (r_(f )), the market portfolio.
Due to the desirable properties of logarithm transformation, the following log-return formula is to be used for calculating the return series:
R_t=ln(P_t/P_(t-1) ) ×100
where, Rt is the return on asset i at time t, P_t is the price of the asset at time t, P_(t-1) the price of asset at time t-1, ln is the natural logarithm and R_it is the return on stock i.
Plot a time-series graph of all the return series estimated and comment on how their pattern differ from that of the price series in part one.
Estimate a static linear regression of the monthly return series using equation (1).
Interpret the coefficients of your regression and comment on their statistical significance.
Comment on how the presence of autocorrelation is likely to affect your analysis of the result above.
[40 marks]
PART THREE: FORECASTING
You are expected to provide forecasts of your chosen stock. These forecasts will inform the trading division on their buy and sell decisions.
Produce a forecast of the monthly price and return series of your chosen stock for the last 3 years using (i) the moving average method, (ii) exponential smoothing method and (iii) the regression estimates from your previous section.
Compute the mean square error (MSE) and mean absolute percentage error (MAPE) for all the three forecasting methods and comment on the accuracy of your forecasts.
[30 marks]