ECO00042M Topics in Financial Econometrics 2022-3
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ECO00042M
MSc Degree Examinations 2022-3
Economics
Topics in FinanciaI Econometrics
SECTION A:
This section consists of three questions and you are required to answer only two out of three questions. {50 Marks}.
A1. To analyse the determinants of bilateral trade lows amongst the 14 EU member countries (Austria, Belgium-Luxemburg, Denmark, Finland, France, Germany, Greece, lreland, ltaly, Netherlands, portugal, spain, sweden, United kingdom), using annual data over 1960-2001 (42 years), serlenga and shin (2007) consider the panel data gravity model:
yit = β1(、)x1,it + β2(、)x2,it + T1(、)z1i + T2(、)z2i + Eit , i = 1, ..., N, t = 1, ..., T (1)
with two-way error components:
Eit = ai + θt +uit (2)
where yit is a scalar dependent variable (the bilateral trade lows), x1,it and x2,it are k1 根1 and k2 根1 vectors of time-varying regressors, z1i and z2i are L1 根1 and L2 根1 vectors of time-invariant regressors.
we assume that unobserved individual efects, ai , unobserved time efects, θt and idiosyn- cratic disturbances, uit follow:
ai … iid(, σ a(2)); θt … iid(0, σθ(2)); uit … iid(0, σu(2)); E(aiuit ) = 0; E(θtuit ) = 0; E(ai θt ) = 0 for all i, t. (3)
(a) we further assume that
E(θt |x1,it ) = 0; E(θt |x2,it ) 0; E(θt |z1i ) = 0; E(θt |z2i ) 0 (5)
Describe an estimation procedure which can consistently estimate β1 and β2 as well as T1 and T2 . {10 Marks}
(b) Anderson and van wincoop (2003) propose to include multilateral resistance terms that capture the fact that bilateral trade lows depend on bilateral barriers as well as trade barriers across all trading partners. To address this important issue, we now allow the error components to follow the multi-factor structure:
Eit = ai + Ψi(、)θt + uit (6)
where θt is an r 根 1 vector of unobserved common factors, which are correlated with
the regressors, and Ψi is the r 根 1 vector of heterogeneous loading coeicients. Discuss the implications of (6). {5 Marks}
(c) Given large T and large N, describe how to consistently estimate β1 and β2 as well as
T1 and T2 in the model (1) with (6). {10 Marks}
A2. Consider the CAPM regression model:
yt = a + βxt +Et , t = 1, ..., T, (7)
where yt isa dependent variable (excess return on an individual portfolio), xt is the regressor (excess return on the market index), a and β are the intercept and slope parameter, and Et … iidN(0, σ2 ) is the idiosyncratic error. All excess returns are expressed in % per annum.
(a) some Us studies ind that inancially distressed irms have low, not high, average returns, suggesting that the equity market has not properly priced distress risk. This inding is called ‘the distress anomaly,. To investigate this issue in the Uk, we employ the data for Uk public companies trading on the London stock Exchange over the period January 1998- December 2007 (a total of 120 observations), run the CAPM regression for the excess returns on the long-short portfolios that go long in portfolio 1 (constructed as the 10% of stocks with the lowest default risk) and short-sell portfolio 2 (constructed as the 10% of stocks with the highest default risk), and obtain the OLs estimation results:
yt = 1 - 19(.7)xt with R2 = .116
where the igures in (.) are standard errors and R2 is the multiple correlation coef- icient. Discuss the inancial implications of these estimation results, and evaluate whether or not the Uk data provide evidence in favour of the distress anomaly. {7 Marks}
(b) Describe what is meant by ”the value premium.” Then, discuss and compare the alternative explanations of the value premium provided by the fundamental-based and the sentiment-based theories. {8 Marks}
(c) There has been a large anomaly literature where irm-speciic characteristics such as past returns, book-to-market ratios and size help explain cross sectional returns, which contradicts the prediction of CAPM. ln this regard, derive the Fama and French (1993) three-factor model. Describe how to test its validity using the Fama-MacBeth (1973, FM) two-pass regression approach. {10 Marks}
A3. (a) we have itted a RiskMetrics model to the log daily returns for lBM over the period July 1962 - September 1997 as follows:
rt = at , at = σtEt , t = 1, ..., 9190
σt(2)= 0.94σt2-1 + (1 - 0.94)at(2)-1
From the itted model, we have r9190 = 0.04 and σ(换)9(2)190 = 0.001. At the 1% and 5% quantiles, evaluate the forecasts of the daily value-at-risk (vaR) on a ε1,000,000 long position at 1 and 10 day horizons, where the one-sided 1% and 5% quantile of a standard normal distribution is -2.33 and -1.65. Then, discuss the weakness of this approach. {8 Marks}
(b) Suppose that we have a sample of n return series, T1 , ..., Tn . The sample a quantile, denoted q(a), can be found as:
换(q) (a) = arg min Ln (q)
where
Ln (q) = [a - I {Ti < q}] [ri -q]
and I {A} is an indicator function equal to unity if the event A is true, and 0 otherwise. Show that 教(q)(a) is the sample quantile. Discuss briely the relative advantages and disadvantages of the quantile estimation approach. {8 Marks}
(c) Consider two possible investments, A and B, which have the loss proile shown in the table below.
|
s1 |
s2 |
s3 |
p(si ) |
0.03 |
0.03 |
0.94 |
A |
1000 |
0 |
0 |
B |
0 |
1000 |
0 |
where three diferent scenarios S1 , S2 and S3 are associated with probabilities p(Si ) for i = 1, 2, 3. using this example show that vaR fails the subadditivity condition such that disaggregated risk management does not work using this measure. {9 Marks}
SECTlON B:
This section consists of two questions and you are required to answer BOTH questions. {50 Marks}.
B1. (a) Discuss why the parametric GARCH model tends to underestimate vaR. Then, de- scribe an alternative approach which can improve the vaR evaluation in terms of backtesting. {13 Marks}
(b) Describe how to estimate the time-varying optimal hedge ratio by combining the bi- variate error correction model and the dynamic conditional correlation GARCH model. Explain why this joint approach is more likely to be efective in reducing the variance of the hedging portfolio relative to the naive hedging. {12 Marks}
B2. (a) Consider an ARCH(1) process, εt . Assuming that the 4th moment of εt is inite, derive the unconditional 4th moment of εt , namely E (εt(4)), and the unconditional kurtosis of εt , deined by E (εt(4)) / {Ⅴ ar (εt )}2 . Comment on your indings in terms of the tail behavior of εt . {7 Marks}
(b) Describe the GARCH(1,1) process. what stylised features of inancial data could be modelled using a GARCH(1,1) process? Then, derive the h-step ahead forecast conditional on the information set at T, and comment on your indings. {8 Marks}
(c) Describe two important extensions to the GARCH model by describing the GJR GARCH-M model in detail. what additional characteristics of inancial data might they be able to capture? {10- Marks}
2023-08-08