# ECN1008 ASSIGNMENT ONE

• Answer BOTH QUESTIONS 1 and 2
• Questions have multiple parts. ANSWER ALL PARTS
• Q1 and Q2 are both worth 50 marks. The marks are broken down at the end of each question part.
• Read the ‘Help’ sections at the end of the questions carefully.
• The hand-in date is on or before 19 APRIL 2021, 12pm.
• Coursework should be submitted ONLINE to the ECN1008 portal page on or before the date specified. Please upload a single document in either MS Word or PDF form.  Do not upload Excel files.
• Late work will result in a maximum score of 40% if submitted within 24hrs of the deadline, zero marks thereafter (assuming no valid extenuating circumstances are claimed).
• Coursework will be marked within 4 working weeks of the due date and feedback will be provided via the student portal.

ASSESSMENT CRITERIA

Marks will be awarded according to the following main criteria:

• Directly addressing the questions raised by the essay  Logical structure of answer.
• Critical interpretation of material/data.
• Appropriate use and interpretation of diagrams, data and quantitative techniques  Clarity of explanation – fluency of written exposition, grammar and correct spelling  Clarity/accuracy of presentation of data.
• Demonstrated knowledge of relevant material/literature with proper citation of sources and full details in the Bibliography

# QUESTION 1 BETTING MARKETS (50 marks)

A researcher has estimated a statistical model that prices the odds of Premier League match outcomes.  These outcomes are either: that the team playing at their home ground wins the game (H); the match is a draw (D); or that the away team wins (A).  The probabilities of these outcomes are defined as p(H), p(D) and p(A) respectively.  The algebraic equations for calculating the probabilities are as follows:

p(H) = 1/ (1 + R1 + R2)                                   (1)

p(D) = R1 * p(H)                 (2) p(A) = R2 * p(H)                 (3)

Where R1 is the ratio of p(D)/p(H) and R2 is the ratio of p(A)/p(H)

Using historical data from the 2018/19 season, the researcher estimates that

 R1 = exp (-1.2-0.5*HP +1.1*AP) (4) R2= exp (-1.1-0.9*HP + 1.4*AP) (5)

where

HP is the average points-per-game to-date achieved by the team playing at home AP is the average points-per-game to-date achieved by the team playing away from home exp (…) denotes the exponential function

As an example, suppose for a given fixture, the home team has currently achieved an average of 0.6 points per game (HP = 0.6) and the team playing away has achieved 2.1 points (AP = 2.1), then the probabilities of the match outcomes of the game between the two are calculated as

 R1 = exp ( -1.2 – 0.5 * 0.6 + 1.1 * 2.1) = 2.248 R2 = exp ( -1.1 – 0.9 * 0.6 + 1.4 * 2.1) = 3.669 P(H) = 1/ (1+2.248 + 3.669) = 0.144 P(D) = 2.248 * 0.144 = 0.325 P(A) = 3.669 * 0.144 = 0.53

These results imply, for example, that the home team has a 14.4% chance of winning the game, and fair odds on the home team winning are therefore 1/0.144= 6.92 (£5.92 profit per £1 bet)

ANSWER EACH OF THE FOLLOWING QUESTION PARTS

1. Use equations (1) to (5) to price the betting odds of the home team winning, the match ending in a draw, and the away team winning in any 5 upcoming Premier Fixtures. Show your workings clearly, including how you calculate HP and AP in each fixture. (15 marks)
2. Compare these odds to the odds offered by any bookmaker (e.g. BET365) and thereby, for each match, identify any betting option(s) that the model considers to be favourable in relation to the bookmaker odds (e. identify any ‘value bets’). Briefly explain your betting recommendation in each case. (15 marks)
3. If betting markets are efficient in any form, explain why this researcher’s model is unlikely to ‘beat the bookmaker’ and yield a profit over time. (20 marks)

HELP

For part 1a, the points per game can be found from any internet site showing the current state of the Premier League, BBC Sport has such a table.  Remember it should be points per game achieved directly before the matches you have chosen are played.  Take the total points currently achieved (usually this is the final column in such a table) and divide by the total number of games played – e.g as of 24 February 2021, Liverpool had played 25 games in total and had achieved 40 points – their value for HP or AP on 24 Feb would therefore have been 40/25=1.60.  When you make your calculations you should use the most recent data available.

Your calculated odds will be in decimal form.  You should be able to get decimal odds from visiting any bookmaker’s website (e.g. BET365).  Some bookmakers may display odds in fractional form but there should be a settings option on their website to display as decimal.  If you can’t find this option and need to translate fractional to decimal odds this can be achieved by subtracting the denominator from the numerator and dividing by the denominator.  e.g. fractional odds of 9/2 are (9-2)/2 = 7/2 = 3.50

Represent your analysis for part 1b in a manner similar to that of the table on Slide 14 of Lecture 7.  Provide a sentence or two explaining the betting recommendation for each fixture (probably at most this will be 200 words).

To answer part 1c of the question, you firstly need to define what is meant by market efficiency and the different forms of efficiency.  You need to think about the circumstances under which the model estimated would contain superior information to the prices set by the bookmaker, thereby providing more accurate betting odds, and whether this is at all likely.  You should provide academic references to support your answer.   As a guide, you should perhaps be looking to write around 400 words for this part.  There is no maximum word limit.

# QUESTION 2   DEAL OR NO DEAL (50 marks)

1. Consider the game show ‘Deal or No Deal’. Explain what, in theory, the Banker’s strategy should be in offering a deal to a risk averse contestant.  Show how it may be rational for a risk averse contestant to accept an offer that is less than the expected value of the remaining boxes.  Use a diagram or diagrams to illustrate your answer. (35 marks)
2. Using at least one example from an actual game, assess whether the Banker behaves according to theory by calculating the expected value of the remaining boxes at point of the Banker’s Offer and comparing it to the Offer made. (15 marks)

HELP

For part 2a you can find a diagrammatic analysis of the Deal or No Deal in Lecture 2.  You should attempt to use and explain that analysis in your own words.  500 words should be a reasonable guideline for answering this part of the question.

For part 2b you should be able to find suitable past episodes of DoND on the internet (e.g. YouTube).  If you have several examples you will have better evidence to assess the Banker’s behaviour.