PART A

Question 1

This question is to be completed in the “TVM” worksheet. Your answers should be entered into this worksheet and a Word document, as appropriate. Clearly label your answers.

You wish to accumulate a sum of cash equal to the year of your birthday, followed by the value of the first letter of your first name and surname. In other words, if you are Andrew Benn and you were born in 1996, you wish to accumulate $199 612.

Assume the interest rate is 4.xy% where x is the integer of the average of the last three digits of your student ID and y is the integer of the standard deviation of the last three digits of your student ID. In other words, if your ID ends with the numbers 123, then x = 2 and y = 1, so the interest rate is 4.21%. The interest rate is a continuously compounding annual rate.

The length of time you will invest your cash is equal to z where z is the product of the 2nd letters of your first name and surname. If your first name starts from A to M, then you will be investing for z quarters, otherwise you are investing for z half-years.

Your job is to determine how much you need to have today in order to reach that goal.

a.) How much will you be needing to accumulate?

b.) What is the annual interest rate?

c.) How long will you invest the cash for?

d.) What is the amount you will need to invest today to achieve your goal, giving your answer correct to the nearest cent?

e.) How much would you need to deposit at the start of each month in order to meet your goal? (Research how an annuity is calculated with continuously compounding interest rates).

Reflection

This problem assumes the rate of return is constant over the investment period. To what extent is this realistic in this current market conditions? If one seeks to reach their goals using risky investments, how much additional risk will they need to take?

Question 2

This question is to be completed in the “Markets” worksheet. Use the data in the “StockIndices” worksheet to answer the following questions.

The low interest rate environment created by the central banks has led to more volatile stock markets, with markets rising to higher levels yet followed by sharper corrections. You have been provided with four different periods of the end of day index levels for the S&P 500, the ASX 200 Composite and the Sensex 50. The four periods are:

29th June 2007 to 31st March 2009 (the subprime crisis)

1 st December 2017 to 28th February 2018 (the February “taper tantrum” following the December 2017 rate rise by the Federal Reserve)

30th November 2018 to 31st January 2019 (the 2018 Christmas correction, again largely driven by the Federal Reserve raising rates in December 2018)

1 st January 2020 to 2nd March 2020 (the fastest market decline arising from fears over the coronavirus outbreak)

We are interested in understanding the extent in which the markets can fall from their record highs to the near-term lows and how long it takes. This will provide an indicator as to how volatile the markets are as time passes.

a.) Perform an analysis of the returns for each of the indices over the four periods. Your output should contain the descriptive statistics, the price history, the QQ plot and the number of observations that exceed three standard deviations from the mean. Clearly label your output.

b.) Identify, using appropriate Excel functions, for the dates and levels of the maximum and minimum price levels for each index for the four periods. Present your answers in a clearly labelled table. (Hint: You may wish to use the VLOOKUP function, swap the price levels to make it on the left-hand side and the date on the right-hand side of the array table.)

c.) Calculate the size of the negative returns from the maximum to the minimum for each of the indices over the four periods, giving your answer as a % correct to 2 decimal places.

d.) Calculate the standard deviation of the daily returns for the ten days before and after the minimum levels. Present your answers in a table as a % correct to 2 decimal places.

Reflection

Consider the impact of the low interest rate environment created by the central banks since late 2008 on the broader asset markets. While the stock markets have risen over this period and the global economy appears to be “stronger” if stock price levels are used as an indicator, consider how the market volatility has changed. How will this impact on savings, borrowing and risk management?

Question 3

Refer to the “BinModel” worksheet when you are attempting this question. You should provide your answers in the “BinOption” worksheet.

You are working in a commodities trading firm and a client seeks your assistance to estimate the price of an option to help her manage her exposure. If you are enrolled in Group 1, your client will be wanting to purchase a call option and if you are enrolled in Group 2, your client will be wanting to purchase a put option.

The current price of the option is determined by sum of the 4th, 5th, 0th and 12th value of your student ID. So, if your ID is BBASEP16M012, then the price of the option is 19 + 5 + 0 + 2 = $24. The exercise price of the option is equal to the current price plus the difference between the day of your birthday minus the month of your birthday. So, if you are born on 4th August, then the exercise price is $ (24 +( 4 – 8)) = $20.

The option will have a life equal to the last digit of the product of the value of the 2nd letter of your surname and the 11th value of your student ID. Where your result is less than 3, add 4 to your result. So, if your surname is NGUYEN and your student ID is BBAJAN17S134, then the option life will be equal to 7 x 3 = 21, or 1. But since this is less than 3, then add 4, so the length of the option life will be 5 time steps.

The length of each time step for the option will be in months if your birthday is in January to March, quarters if it is in April to June, half-years if it is in July to September and weeks if it is in October to December.

The underlying asset price volatility is the first and last digits of your year of birth. So, if you are born in 1997, the asset price volatility is 17% p.a.

The risk-free rate is currently 3.5% p.a.

The probability of the asset increasing in price is the 0.56.

a.) Enter the correct inputs into the binomial option model.

b.) Use the formulae for the size of each period’s increase and decrease in the underlying asset price to fill the rows labelled “Up Step Increase” and “Down Step Decrease”.

c.) Use an appropriate formula to calculate the risk-neutral probability for calculating the option price using the risk-neutral pricing approach.

d.) What is the premium of the option, giving your answer correct to the nearest cent?

e.) Include in your output to bring into the examination room the Derivative Payoff, Replicating Portfolio and Risk-Neutral Pricing tables.

Reflection

The model estimates the option premium using the risk-neutral approach. However, what is the role of real-world price movements on the option value? Furthermore, if one wants to actually replicate the option using risk-free bonds and the underlying stock, how would they do it and what are the risks? Consider also the context of the current market environment as created by central bank policies and investor behaviour resulting from them.