ECO349 - Assignment 2 Evaluating Stock Market Indicies and Cryptocurrencies as Currency
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ECO349 - Assignment 2
February 7, 2024
Evaluating Stock Market Indicies and Cryptocurrencies as Currency
1 Crypto-Assets and Evaluating the Quantity Theory
1.1 Pick a crypto currency
1. Pick a cryptocurrency asset available to trade on the IB platform which you think has the best chance of replacing a domestic currency.
2. Briefly describe how the supply of this crypto-currency is issued, and why the issuer argues that the asset has value / and why you find their argument convincing or not.
1.2 Evaluate the history of this crypto-currency
1. Lookup the ticker of your chosen cryptocurrency on https://messari.io/, download 5 years of historical data, make sure to include these 10 columns: Date, Price (Close), Real Volume, Circulating Supply, New Issuance, Hash Rate, Average Difficulty, Active Addresses Count, Total Fees, Transaction Trans- fers, Reddit Subscribers
2. Compute the daily return and add as a new column to the data set
3. Save the raw data sheet 2 of your excel file, with sheet name given by the crypto ticker
4. Compute the following summary statistics
• Average of each variable
• Standard deviation of each variable
• Correlation between return and each of the other variables
5. Try to map these variables to objects in the quantity theory of money
6. How do the summary statistics compare with the predictions / assumptions of the quantity theory of money?
1.3 Trade on your conviction and form a $200,000 portfolio with the following characteristics
1. Take a long or short position of this asset between $10,000 and $100,000, depending on whether you think it will appreciate or depreciate in value.
2. Open two cross-currency swaps, one between CAD and USD, the other between any two other major currencies.
1.4 Record your trades in excel sheet 1, and monitor the portfolio while your position is open.
1.5 After at least 3 business days, close your position, compute your profits and explain what seemed to be the biggest news driver in price movements if any
2 ETFs, stock market indicies and playing with options
Use excel sheet 3 to record the contract details and IB trading activity for this question
1. Take a $10K long position on the S&P500 stock market index via an Exchange Traded Fund (ETF) ticker SPY.
2. Record three call and put option prices of this ETF each which are ’in-the-money”, “at-the-money” and ’out of the money” (i.e. option strike price below, at and above the current price) and have the same expiry.
3. Take a pair of the option prices seem consistent with the theoretical put-call parity relationship? Explain why or why not you would expect this relationship to hold with the options you are holding.
4. Record also a mini-SPX put and call option contract via ticker XSP which most closely resembles the one you just examined above (note these are also option contracts on the SPY ETF). How does the price of the two contracts compare with the ones you just looked at above? What explains the differences in the prices?
5. Suppose you believe the stock market is going to be very volatile over the next 3 months, but trade at an expected level 5% higher than the current price, construct an option portfolio which will pay off in such scenario. Obtain the relevant option contracts on IB (ignore the long SPY stock you are also holding)
6. Draw and label the payoff diagram based on the traded option contract
7. Hold this portfolio open for at least three business, then close the position. Compute and record the profits (losses) from this option trade over this time horizon
3 (Theory Exercise) Introducing Crypto-Assets to an Economy
Consider the same OLG money model from lecture with uy (c) = uo (c) = 5c0.5 but where instead of money there is a crypto-asset with time t supply At , MyCoin. It has initial supply A0 and grows at constant rate a and has economic cost ga which is paid from the young’s labour income y. Assume the old initially own (are endowed with) this asset. Let Qt be the price of this crypto-asset.
1. Mathematically describe the consumption/savings optimization problem of generation t young person. Clearly specify the choice variables, the constraints and the objective.
2. What is/are the market clearing condition(s) for this economy? Describe what they mean in words. Use your answer to define a stationary equilibrium in this economy.
3. Assume a stationary equilibrium. Give an equation characterizing the demand for MyCoin.
4. Denote z the real (consumption) value of the crypto-currency. A) Use market clearing to express z in terms of Q, A and N. B) Re-express your equation from Question 3 in terms of z and solve for z to give the equilibrium real demand for MyCoin.
5. Solve for the stationary equilibrium consumption allocations for the young and old generations. Who is better off with a higher growth of the crypto-currency supply?
6. Suppose at time zero the old generation had both a stock of fiat money, M0 and crypto A0 , with M0 < A0 , which asset would you predict the time-0 old generation to choose? Would your answer differ if it were the young generation that could choose?
7. Look back at the data you downloaded of your crypto asset in Problem 1. Is there any data there that you could use to help put numbers on g, a, and A0 in the model? Identify them if possible and give a one-two sentence explanation for the mapping. If not, say what other data you would choose. Do you think in reality g matters?
8. Think back to the other models discussed in the class, could we have used them to think about the introduction of a crypto-currency to Canada? Why or why not?
4 (Theory Exercise) Portfolio Choice in a Risky World
Consider a representative household with utility over two periods,t and t+1 of u(ct , ct+1) = u(ct )+βu(ct+1) where u(c) = c − gc2
The household has employment based endowment et = 1, et+1 = 0 and access to assets:
• discount bonds Bt from t, t+1 at price PtB which yields 2 units of t + 1 consumption
• shares Mt in the stock market index for PtM which yield D
∼ N(1, 0.01) t + 1 consumption
There is a fixed net supply of discount bondsB(¯) = 0, aggregate stock market index M(¯) = 1 .
1. Describe the representative household’s budget constraints and portfolio problem.
2. Describe the market clearing conditions.
3. Define a competitive market equilibrium in this setting.
4. Solve the household’s optimal demand for bonds and stocks.
5. Give two equations which pin down equilibrium prices of the assets.
6. Compute the equilibrium return of the stock market index, the bond return, and the equity risk pre- mium.
7. Determine the impact of increasing γ on the equity risk premium. Explain in your own words the intuition for the result.
8. (harder) Suppose now regulators allow households to invest not just in the aggregate stock market index but in one firm included in the aggregate stock market index, with (i) that firm’s shares given by St(i) and price Pt(i) with dividends Dt(i)+1 ∼ N(1, .02), (ii) the firm comprising 25% of the aggregate stock market index and (iii) the performance of this firm is independent (/ uncorrelated) of the performance of the remaining firms in the index. Note aggregate consumption is not changed from before.
• What is the correlation between this stock and the aggregate stock market index?
• Use your earlier results to give an expression pinning down this individual stock’s equilibrium price.
• How does the return of this stock compare to the return of the market index? Give intuition for the result
• Is this consistent with CAPM? If so, give expressions or otherwise link the components of CAPM e.g. βi and ϵi to what you found here. If not, explain the inconsistency.
2024-02-25