FBE 555: Investments
Spring 2025
Problem Set 1
To carry out this problem set, you will need a computer running Microsoft Excel. You can use data from https://www.nasdaq.com/market-activity/quotes/historical and compute returns for Question 5 based on Close/Last prices ignoring dividends. You can also consult the guidelines described in the attached file Getting_Data.pdf.
This problem set is due by 1:59pm PT on Wednesday, February 12, 2025. Your solutions should be in the form of a single Excel file with each question answered in a separate sheet. You can make use of the template provided separately. Make sure to include the names of all people in your team somewhere obvious inside the file. Submit the file on Brightspace. It is all team members’ responsibility that the problem set is submitted on time. It is sufficient if one of the team members makes a submission.
Question 1
You deposited $100,000 in a margin account and proceeded to buy $150,000 of stockin GRPN. There is a 30% maintenance margin required by your broker.
If the price of GRPN falls by 60%, how much cash will your broker require you to send if you are to keep him from selling your positions? What if GRPN falls by 30%? By what percent does GRPN have to fall before you will receive a margin call?
If GRPN falls by 60% and you are unable to send any additional cash, what is the minimum fraction of your holdings in GRPN that your broker will liquidate?
Question 2
Suppose you have $50,000 in cash in your brokerage account. You then short sell 20 sharesofTSLA, currently priced at $1500 per share. What is the dollar gain or loss on your portfolio, over the next year,if TSLA falls to $1250 per share?
What would have been the gain or loss on your portfolio had you bought (using margin) 50 shares of TSLA instead?
For both parts of the question, assume that the interest rate for borrowing and lending is 1% per year.
Question 3
Without relying on published NAV figures, but using data from the ETF’s own website, compute the net asset value (on aper share basis) of the VanEck Vectors Semiconductor ETF (ticker symbolSMH). Specify clearly the date on which this calculation was made. Compare this value with the contemporaneous market price per share of SMH.
Question 4
Assume that the market price of SMH was $1 higher than the value that you actually observed. If you were the manager of a large hedge fund, would you see this as a profitable trading opportunity? What would you expect as a rate of return on that trade? What would you do if the price of SMH was $1 lower?
Question 5
Download the last 10 years of daily returns on three assets:
1. One S&P 500 Index ETF
2. One stock that is in the Dow Jones Industrial Average
3. One stock with a market capitalization of $100 million or less.
Compute the mean and standard deviation of each. Assess whether any of the assets displays return behavior. that is inconsistent with the normal distribution.
Question 6
Assume that the number of shares outstanding in the two stocks from question 5 has not changed over the last ten years. Compute the returns on equal weighted and value weighted portfolios of the two stocks (not the ETF). The return on an equal weighted portfolio is just the 50/50 average of the returns of the two stocks. The return on the value weighted portfolio is w1 R1 + w2 R2, where Ri is the return on stock i and wi is the market capitalization of stock i divided by the sum of the market capitalizations of both stocks.
What are the correlations between each of the stocks and the value weighted portfolio? What are the correlations with the equal weighted portfolio? Why do you think that some correlations are higher than others?