Quantitative Methods in Finance

FIN 617

Quantitative Methods in Finance

Quiz 5 November 20, 2020 Name: ________________________

Quiz 5

The quiz is open book, open notes, open computer. Answer each question providing detailed explanations of your answers, including any intermediate steps and the formulas/concepts used. Quizzes may be submitted to the Quiz 5 Submission folder in D2L as .docx, .pdf, or .xlsx. You may use different formats for different questions if you wish. Please submit your quiz file(s) using the naming convention “FIN 617 FQ 2020 Quiz 5 <last name> <first name>”. If you submit an Excel file, please document your formulas with text comments. Formulas embedded in cells will not count as showing your work. Also, if you submit an Excel file, please use a separate tab for each question and copy the text of the question into that tab at the top.

1. (16 points) Using quarterly average CPI index data from March 1980 through March 2020, you calculate the quarter over quarter change in the CPI index and estimate an AR(1) model for the series of changes in the quarterly CPI index:

Regression statistics		Autocorrelations of the Residual
R-squared	0.065771		Lag 1	-0.041804
SEE	0.006621		Lag 2	-0.023911
Observations	159		Lag 3	0.215020
			Lag 4	0.071199
	Coefficient	Std Error
Intercept	0.005391	0.000761
Lag 1	0.248092	0.074623

a. Calculate the t-statistics for the regression coefficients and the residual autocorrelations

b. Are the regression coefficients for the intercept and/or lag 1 significant at the level?

c. Does this data series exhibit seasonality?

d. Are the residuals serially correlated?

e. Is this model properly specified? Why or why not?

2. (10 points) Assume that the following one-factor macroeconomic model describes the expected return for portfolios: Also assume that all investors agree on the expected returns and factor sensitivity of the three highly diversified Portfolios A, B, and C given in the following table:

Portfolio	Expected Return	Factor Sensitivity
A	0.09	0.50
B	0.13	0.75
C	0.17	1.50

If the model and the table are both correct, determine whether or not an arbitrage opportunity exists. If not, why not? If so, explain how to exploit it.

3. (10 points) An investment firm uses the Carhart-Fama-French Model to track the performance of the portfolio managers in the firm. In 2019, the risk-free rate of return was 2.2% and the return on the S&P 500 (a proxy for the total market) was 28.9%. An actively managed large cap portfolio earned 32.8%, while the benchmark portfolio it was compared to earned 31.2%. The betas for the benchmark portfolio and the actively managed portfolio are:

	Betas
Risk Factor	benchmark portfolio	managed portfolio	factor return
Market risk (RMRF)	1.00	1.05	?
Small cap stocks (SMB)	-0.50	-0.70	-5.90%
Value stocks (HML)	0.20	0.40	-6.35%
Momentum stocks (WML)	0.10	0.20	6.44%

a. What is the active return on the managed portfolio?

b. What is the factor return for market risk (RMRF)?

c. What proportion of the active return is due to the market risk tilt?

d. What proportion of the active return is due to the large cap stocks tilt (the tilt away from small cap stocks)?

e. What proportion of the active return is due to the value stocks tilt?

f. What proportion of the active return is due to the momentum stocks tilt?

g. What proportion of the active return is due to the manager’s selection of individual stocks?

a. (5 points) Define the following terms:

a. Factor risk premium

b. Unit root

c. Random walk with drift

d. Standardized beta

e. ARCH

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Professor Edwalds Quiz 5 Fall 2020