You are the Investment Analyst at FH Capital, a boutique investment firm. You are tasked to create an equity fund and analyse its return and risk (volatility) characteristics.
The terms of reference are detailed below.
PART ONE: CONSTRUCTING THE EQUITY FUND
(i)Construct an equity fund “FH Equity Fund” composed of 10 to 15 equities listed on the New York Stock Exchange and/or NASDAQ.
(ii)Your stock picking should be underpinned by a sound investment strategy (such as growth,value, index, dividend growth, contrarian investing strategy etc.)
(iii)Briefly discuss your investment strategy and support it with economic theory and references.
(iv)Collect the daily price series for the equities in your fund from January 2010 to December 2020 and estimate the daily return series for the fund.
(v)Assign equal weights to all the equities in your portfolio and set the rebalance at monthly.
For instance, if you have 12 stocks, the weight of each stock will be 1/12 = 0.083]
PART TWO: STOCK RETURN PREDICTABILITY
UNIVARIATE TIME SERIES MODELS
Using the daily returns of the fund for the period 1 January 2014 to 31 December 2017:
(i)Estimate an appropriate Autoregressive Moving Average (ARMA) for the daily return series of your fund.
(ii)Discuss the diagnostic results (residual analysis) of the ARMA model results.
(iii)Produce an out-of-sample forecast for the next two years(1 January 2018 to 31 December 2019).
(iv)Compare your forecasts to the return series for the forecast window, using the following measures:
- Mean Square Error (MSE)
- Root Mean Square Error (RMSE), and
- Mean Absolute Percentage Error (MAPE).
EXPONENTIAL SMOOTHING & TECHNICAL ANALYSIS
(i)Estimate an appropriate exponential smoothing (ETS) model for the daily price series for the period 1 January 2014 to 31 December 2017. Your model should incorporate a trend term and a dampening factor if required.
(ii)Produce an out-of-sample forecast for the last two years (1 January 2018 – 31 December 2019) and discuss the forecasts’ accuracy measures.
(iii)Construct a moving average convergence divergence (MACD) for the daily price series of any two stocks in your fund and the S&P 500 Index for the period 1 January 2014 to 31 December 2018. Set the parameters for the MACD at; 𝒔𝒔 = 𝟖𝟖, 𝒍𝒍 = 𝟑𝟑𝟑𝟑 and 𝒌𝒌 = 𝟗𝟗 .
(iv)Analyse the predictability of the price series’ trend and momentum from the MACD plots and highlight when the chart correctly predicts (or misses) the trend and momentum in the series. [15 MARKS]
DISCUSSION OF RESULTS
With reference to your ARMA/ETS and technical analysis, discuss the predictability of stock prices.
Relate your discussion to the notion that financial markets are informationally efficient. [10 MARKS]
[TOTAL 40 MARKS]
PART THREE: VOLATILITY MODELLING WITH GARCH
In addition to the return on the fund, it is important to understand how volatile the fund is relative to the market.
(i)Using the daily returns (in percentages) from 1 January 2014 to 31 December 2018,estimate the GARCH (1, 1) and the GJR GARCH (1, 1) process for;
- The S&P 500 index
- The equity fund you formed in Part 1
- Any two (2) stocks from the equity fund in Part 1.
(ii)Plot your volatility estimates and summarise the coefficients from your GARCH (1, 1) and GJR GARCH (1,1) models in an appropriate table and comment upon the results. [6 MARKS]
(iii)What do the results for GARCH (1, 1) suggest about the riskiness of your fund and stocks relative to the market portfolio? Discuss. [7 MARKS]
(iv)Using the GJR GARCH (1,1) results, discuss whether your volatility estimates are symmetrical or not. Is this result in line with the economic theory of investor reaction to good and bad news? [7 MARKS]
[TOTAL 20 MARKS]
PART FOUR: VECTOR AUTOREGRESSIVE MODELS/COINTEGRATION
CHOOSE ONLY ONE QUESTION FROM THIS SECTION
QUESTION ONE: VECTOR AUTOREGRESSIVE MODELS(VAR)
Using the relevant quarterly series from January 2010 to December 2020:
(i)Estimate a vector autoregressive model (VAR) using the following series.
- The equity fund’s return series (from Part One)
- Real Gross Domestic Product [GDPC1]
- Industrial Output [INDPRO]
- Consumer price index [USACPIALLMINMEI]
- Federal fund effective rate [FEDFUNDS]
- Yield spreads (difference between the US 3 months T-Bill and 10-Year Treasury Constant Maturity Rate) [T10Y3M]
- SP 500 Index [^GSPC]
Note: the labels in the square bracket [ ] are the variable names in the Federal Reserve Economic Database (FRED), except for SP500 which is the variable in Yahoo Finance.
(ii)Report the following results using appropriate tables and charts:
- Granger causality between your fund’s return and all the variables in the model [ignoring all other causality results]
- Impulse response function from all other factors to your fund’s return series [ignoring all other impulse response function results].
(iii)Discuss the Granger causality results and impulse response function on the fund return series only. [10 MARKS]
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