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Individual Assignment 1 - ECON5069

Question 1

In a representative agent model with time separable CRRA preferences, under the assumption of log normal and homoskedastic consumption and equity returns, the equity risk premium can be written as:

Et[rt+1 − r] = ycoU(Δc, r) −                   (1)

where rt+1 is log (gross) real equity return, r is log (gross) real risk free return, y is the relative risk aversion parameter, Δc is real per capita consumption growth and Gr(2) is the variance of real risky log returns.

You are provided a dataset called ukdata.csv. This dataset contains quarterly observation spanning the time period 1985Q1-2016Q4. Description of each column in the csv file are given below:

date - Time period covering 32 years in a quarterly frequency between 1985Q1 until 2016Q4. consexp - Nominal consumption expenditure in millions of pounds (£).

pop - Total active population in the UK, units are number of persons.

ftse100_price - FTSE 100 Index stock price in pounds (£), current price.

tb3m - 3 months US Treasury Bill Annual Returns, expressed in % points.

infl - Quarterly Inflation in consumer prices, defined as log difference in the consumer price index from the previous quarter, expressed in % units.

All variables are in quarterly frequency and there are no missing observations.

1.1 Interpret eq. (1) and describe the equity premium puzzle. Use the dataset to quantify the extent of this puzzle in quarterly UK data. You can approximate time t expectations with sample means; covariance and variances with sample covariance and variance, respectively. The 3 month TBill can be considered as the risk free asset. Use quarterly rates of all variables in your calculations. [40%]

1.2 The consumption based asset pricing literature has responded to the equity premium puzzle in several ways. Elaborate on any three of these approaches in not more than 700 words[60%]

Note: In answering 1,1, you should tabulate and comment on the values of the mean, standard deviation and first order auto-correlation of equity return, risk free return and consumption growth, respectively. You are expected to refer and cite journal articles in answering 1.2.