Machine learning in Finance
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Adam Smith Business School Subject of Accounting & Finance Degree of MFin International Finance, MSc International Financial Analysis, MSc International Corporate Finance and Banking Degree Exam Data Science and Machine learning in Finance
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Students should answer ALL questions from both sections.
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Section A: Multiple Choice Questions
You must answer ALL questions from this section.
This section includes questions 1-5 (each question carries an equal weighting of 3% in the Final Exam). Questions and information related to Section A are provided separately via the course Moodle page. Section A overall weight in the Final Exam is 15%. Please refer to the course Moodle page, under Section: Degree Exam (ACCFIN5246_1D) to complete Section A.
Section B: Long-Answer Questions
You must answer ALL questions from this section.
Question 6
Discuss the bias-variance trade off and explain why over-fitting may lead to a higher mean- squared-error (MSE).
TOTAL: 20%
(Maximum word count: 200)
Question 7
Consider the following dataset with quarterly observations ( = 1,… ,N and N = 7) collecting information about an individual companys operations where Rating is an ordered categorical variable demonstrating the quality the companys outstanding bond to external debtholders such that ratings {A, B, C}, represent the highest to lowest quality, respectively, and that Sales is recorded in monetary units, ROA is the return-on-assets (in percentage points) and CTA is the cash-to-total assets ratio. To implement analytics, assign ratings to numerical values {(A : 5), (B : 4), (C : 3)}, and let { 1 ,, 2 ,, 3 ,} denote characteristics {Sales, ROA, CTA}, respectively; and answer the following parts:
7.1 Suppose data from an additional quarter become available such that the sample exhibited in the table below is extended to N + 1 appearing as {Sales = 5,200, ROA = 2%, CTA = 12.5%}, noting that rating is not yet issued.
Let = (^) ^1 = 1 , denote the average of each characteristic ,. Provide a formal expression to quantify how much averages change when the additional observation is added to the dataset. (10%) 7.2 Propose a model to predict Rating based on two of the available three predictors {Sales, ROA, CTA} and explain the justification behind this proposal. Discuss whether this specification can establish a one-directional relationship to the outcome variable. (10%) TOTAL 20% (Maximum word count: 200) Question 8 Consider a dataset comprising an outcome variable and two predictors 1 , and 2 , for = 1 ,…, N where N denotes the number of observations in the dataset and let =[ (^1) 1 1 . 2 2 ] denote an N4 array of characteristics, (^1) is a column vector of ones representing the constant term according to the following model:
= 0 + 1 1 ,+ 2 1 ,. 2 ,+ 3 2 ,+ (1)
8.1 Suppose the OLS estimation methodology provides the values for 0 , 1 , 2 and 3 based on the data. Provide an expression for the partial effect of the conditional expectation
with respect to the first predictor 1 , given by
[|] 1. How can this partial^ effect be interpreted across the dataset?
(10%)
8.2 Set up the Sum of Squared Residual (SSR) for the Ridge problem based on the provided specification and derive the first-order-conditions.
(15%)
TOTAL: 25%
(Maximum word count: 200)
6 END OF PAPER
Question 9
Consider the following linear specification with + 1 predictors (denoted by
=[ (^1) 1 2 … ]), where is the outcome of interest and = 1 ,…,:
= 0 + ,
= 1
+ (2)
where ~(), and () is a general-form probability density function and that is a m- dimensional vector of parameters that together with (.) fully characterise the distribution of the error term. Suppose that the error terms are independent across all instances for = 1 ,…, such that the likelihood function (,{,}) can be arranged as the product of marginal probability density functions.
9.1 Suppose all of the predictors are linearly independent. Explain the implications of the indexes associated with the dataset and the model: (,,) for the estimation of parameters of interest for = 0 ,…,. Your answer should discuss three possible cases that compare the three indexes: (i) <+ 1 <, (ii) + 1 <<, (iii) <<+ 1.
( 10 %)
9.2 Suppose some of the predictors (at least two and at most 1 ) are linearly dependent. Discuss the implications of the existence of the linear dependences for the maximum likelihood estimation, in particular, discuss whether a maximum likelihood estimator can be obtained when <+ 1 <.
(10%)
TOTAL: 20%
(Maximum word count: 200)
END OF PAPER
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