FIN30200: Estimation Capital Asset Price Model (CAPM) and testing hypotheses second part about estimation and selection ARIMA models: Econometrics of Financial Markets Assignment, UCD

This assignment is composed of two parts. The first part is about the estimation of the Capital Asset Price Model (CAPM) and testing hypotheses. The second part is about the estimation and selection of ARIMA models.

You have to return a PDF file with answers to all questions, reporting tables with results, plots, and in Appendix, you should add PYTHON codes. Remember to add your name and your ID number on the first page! There is no word count or page limitations.

PART 1 – CAPM

A fundamental idea of modern finance is that an investor needs a financial incentive to take a risk. In other words, the expected return on a risky investment, R, must exceed the return on a safe, or risk-free, investment, Rf . Thus the expected excess return, R − Rf, on a risky investment, like owning stock in a company, should be positive.

At first, it might seem like the risk of a stock should be measured by its variance. Much of that risk, however, can be reduced by holding other stock in a ”portfolio” (i.e. by diversifying your financial holdings). This means that the right way to measure the risk of a stock is not by its variance but rather by its covariance with the market.

The Capital Asset Pricing Model (CAPM) formalizes this idea. According to this model, the expected excess return on an asset is proportional to the expected excess return on a portfolio of all available assets (”the market portfolio”). The CAPM says:

where Rit is the expected return of the firm j, Rf t measures the expected of return of a risk-free asset during period t (the Federal Funds Rate, FFR), and Rmt is the expected return on the market portfolio t (SP500).

According to the CAPM, a stock with a β < 1 has less risk than the market portfolio and therefore has a lower expected excess return than the market portfolio.

Meanwhile, a stock with β > 1 is riskier than the market portfolio and thus commands a higher expected excess return. For more details see Brooks, pages 134 and 648.

The purpose of this assignment is to use the CAPM model to cryptocurrencies (as reference, see Shen, Urquhart, and Wang, 2020, Finance Research Letters.

The model they use is a little different. Please use the standard CAPM model in your assignment.).

a) Using https://finance.yahoo.com/cryptocurrencies, download the prices of 10 cryptocurrencies from September 2015 (or the oldest release) to August 2021 (in historical data). Transform them adequately to have log return x 100 (rt=ln(Pt/Pt−1)x 100). Using a dataset maintained by Federal Reserve of St. Louis
download SP500 and risk-free interest rate (FFR) for the same sample period.

b) Transform SP500 in order to have a growth return (taking the logarithmic first difference and multiplying it by 100).

c) Estimate model 1) on the overall sample. Report results and comment statistical indicators. Check if residuals are normally distributed, serially correlated, and/or heteroscedastic. Comment the results.

d) Re-estimate point c) using robust standard errors. Did something change? Comment.

e) For each cryptocurrency, test the null hypothesis that α = 0 against alternative hypothesis α 6= 0, using a significance level of 95%. Would rejection of this null hypothesis imply that the CAPM has been invalidated? Comment.

f) Split your sample into two parts. Repeat point c). Do you have the same results? Comment

g) Repeat point c) without including the constant. Do you have the same results? Comment.

PART 2 – ARIMA

Using FRED St. Louis dataset (https://fred.stlouisfed.org/), download a macroeconomic series. Select monthly or quarterly frequency and extract the series from January 1995 until today.

a) Report the plot of the series. Comment.

b) Report the correlogram of the series. Comment.

c) Is the series stationary? Comment.

d) Transform adequately the series.

e) Estimate several ARIMA models according to correlogram, model diagnostic (significance, tests on residuals, and information criteria). Comment.

f) Compare the estimated models. Which is the best one? Comment.