Acf 504 - Definition of the Dataset

Definition of the Dataset

The dataset used in this report is derived from Thomson ONE Banker. The spreadsheet in Appendix contains the daily price of the TESCO and the FTSE All Share index during the period from 1 December 2014 to 30 November 2015. Each closing price includes 254 observations. We obtain 253 daily returns of the TESCO and 253 daily returns of FTSE index after calculating daily simple returns by using the following formula.

r_t=(p_t-p_(t-1))/p_(t-1)

The Capital Asset Pricing Model (CAPM)

Before calculating the annualized standard deviation of daily stock returns and index returns, assuming that the expected return on the index is equal to the average of simple index returns, the expected return on the index equals to -0.002%. Since the number of sample of daily index returns is 253, we calculate the annualized expected return on the index as below.

(〖(1-0.002%)〗^253-1)=-0.606%

The following formula is used to calculate the sample standard deviation:

S=√(1/(253-1) ∑_(i=1)^253▒(x_i-x ̅ )^2 )

By using Excel function of STDEV.S, the sample standard deviation of daily index returns and of daily stock returns are 1.01% and 2.05% respectively. After multiplying by√253, the annualized sample standard deviation of daily index returns (S_(r_FTSE )) and of daily stock returns (S_(r_Tesco )) are 16.06% and 32.59%, respectively. The correlation of daily returns between the FTSE index and the TESCO share is equal to 0.64448, which can be calculated by using Excel function of CORREL. Also, we can get the covariance between the FTSE index’s daily return and the TESCO share’s daily return by using the correlation formula (Corr(r_FTSE,r_Tesco)=ρsm=(Cov(r_FTSE,r_Tesco))/(S_(r_FTSE ) S_(r_Tesco ) )). Thus, the covariance is 0.03372.

In order to calculate the expected return on the stock, we use the capital asset pricing model (CAPM).

E(R_s )=R_f+β*(E(R_m )-R_f )=3%+1.31*5%=9.54%

The beta coefficient (β) is 1.31 which is equal to the covariance divided by the variance of daily index returns. A beta of 1.31 indicates that the security's price is 31% more volatile than the market. We could use the riskless interest rate (3%), the equity market premium (5%), and the beta (1.31) to get the expected return on the TESCO’s stock, which is 9.54%.

Minimum-Variance Hedging Strategy

Assuming that the initial wealth on 30 November 2015 is W_1 =£100,000, all the wealth are invested in the stock of TESCO. The investment horizon is one year and the wealth on 30 November 2016 is denoted by W_2. We also assume that the forward contract on the stock of TESCO is available and that the forward price for the 30 November 2016 is equal to future value of the spot price on 30 November 2015. Therefore, we can calculate forward price by following formula:

F_1=S_1 e^(r*t)=167.2e^(0.03*1)=172.29

where F_1 is the forward price for the 30 November 2016 and S_1 is the stock price on 30 November 2015.

The payoff of the wealth on 30 November 2016, W_2, is

W_2=S_2 Q_A+(F_1-F_2