QUESTIONS
1) The purpose of this exercise is to train you to do performance measurement and evaluation from raw data. The spreadsheet HW3_Q1 has monthly (end of month) data for an investment fund. The fund invests in two stocks, Sears and AIG. The first four columns have the date, the cashflows from clients, and the number of shares purchased/sold by the fund. Assume that client flows and stock purchases/sales are at the end of each month, and dividend payments reflect the number of stocks held at the end of the previous month). The other columns have the prices and dividends per share of Sears and AIG, and a Total Return Index for the Russell 3000.
a) Calculate how much ($) the fund has at each point in time.
Hint: Start by creating the number of Sears and AIG shares owned at each point in time. Then calculate the amount of cash held at each point in time, taking into account client flows, dividend receipts, and stocks purchases/sales.
Then add the value of stock positions to the amount of cash held to find the total amount at each point in time.
b) What is the dollar-weighted average return of the fund? (monthly and annualized)
c) What is the time-weighted average return of the fund? (monthly and annualized)
d) What is the Sharpe Ratio of fund (monthly and annualized)? What is the CAPM alpha of the fund (monthly and annualized). Assume the risk-free rate is equal to zero throughout the entire period, and that the Russell 3000 index is the Market Portfolio.
e) What is the Information Ratio of the fund? (monthly and annualized). Assume the Russell 3000 is the benchmark.
f) What is the Maximum Draw Down of the fund?
g) Are fund managers doing a good job?
2) The purpose of this exercise is to train risk-adjusting returns using real world data. In portfolio123, create a custom universe of Russell 3000 stocks (Prussell3000) with non-missing ProjPECurFY and ProjPENextFY (PE ratios based on earnings forecasts for current and next fiscal year) and a rating system based on the formula:
0.5*(1/ProjPECurFY)+0.5*(1/ProjPENextFY)
Check the performance of the ranking in the custom Universe using 10 buckets, MAX time period, rebalancing every 3 months, minimum price equal to 3, All Sectors, Long, 0.0 Slippage, and Russell 3000 with dividends benchmark.
a) Check the performance of this ranking system in the MAX time period using OUTPUT=Annualized Returns. Make sure that attractive, cheap stocks are located on the buckets to the right. Download results to an Excel spreadsheet. Copy-paste the graph.
b) Same as item a) but using OUTPUT=Performance Graph. Download results to an Excel spreadsheet. Copy-paste the graph. Calculate period-by-period returns for each of the 10 buckets and the benchmark using the item b) results you downloaded. Note each period (but the last) has 91 days. Calculate both the arithmetic average return and the time-weighted return/geometric average (for a 91 day period).
Annualize both returns, considering that a year has 365 days. Using these calculations, answer:
i) Does portfolio123 use time-weighed/geometric averages or arithmetic averages when you choose OUTPUT=Annualized Returns?
ii) Does the "Volatility Drag" formula relating time-weighted/geometric averages to arithmetic averages work in this case?
c) Evaluate the performance of the top bucket portfolio (cheapest, most attractive stocks). You will need the risk-free rate each period. Use the time series of risk-free rate 91-day returns from the HW2_risk-free Excel spreadsheet on Blackboard.
i) Calculate the Sharpe Ratio of the top bucket and the Sharpe Ratio of the Russell 3000 with dividends (91-day and annualized).
ii) Calculate the CAPM alpha of the top bucket, using the Russell 3000 with dividends as the Market Portfolio. (91-day and annualized)
iii) Calculate the 91-day Information Ratio of the top bucket, using the Russell 3000 with dividends as the benchmark. (91-day and annualized)
iv) Find the maximum drawdown of the top bucket and maximum drawdown of the Russell 3000 with dividends. Calculate the volatility of the top bucket and the Russell 3000 (91-day and annualized). Calculate the CAPM beta of the top bucket.
Given the risk calculations above, discuss whether the top bucket appears to be a good investment portfolio.
d) This exercise shows that even a small position in the top bucket portfolio leads to performance improvement relative to holding a portfolio with the risk-free asset and the Market Portfolio. Calculate the 91-day Sharpe Ratio of a portfolio that has 20% in the risk-free asset (earning the risk-free rate), 70% in the Russell 3000 with dividends, and 10% in the top bucket portfolio. The portfolio is rebalanced to keep these proportions throughout. How does the Sharpe Ratio of this portfolio compare to the Sharpe Ratio of the Russell 3000 with dividends?
Hint: create a new column with the returns of the 70%-10%-20% portfolio
3) The purpose of this exercise is to train you to subject claims about stock market returns to rigorous data testing.
Your friend is a big fan of megacap stocks (the top 100 or so stocks in terms of market cap). He claims that megacaps have outperformed other stocks over the last 15 years or so. Use portfolio123 to test this claim. Make sure to test the claim both on a risk-unadjusted basis and on a risk-adjusted basis (using Sharpe Ratios). Use the risk-free returns from the HW2_risk-free spreadsheet.
4) i) Why do professional equity managers report time-weighted as opposed to dollar-weighted returns?
ii) Under which two conditions will time-weighted returns be very different from dollar-weighted returns?
5) Mr. Smith is a busy entrepreneur. A financial advisor decides where to invest Mr. Smith's stock portfolio worth several million dollars. After a few years, Mr. Smith hires two consultants to independently evaluate the performance of his stock portfolio. These consultants were given daily data on the total dollar value of portfolio, as well as the data on the episodic infusions of cash from Mr. Smith. "I can't trust these guys", says Mr. Smith. "It is true they found the same time-weighted and dollar-weighted returns, but the risk-adjustment calculations don't match." Consultant 1 reports that Mr. Smith's stock portfolio had an annual Sharpe Ratio of 0.43, and while "a broad stock market index" had an
annual Sharpe Ratio of 0.40. He also found an annualized CAPM alpha of 0.54% per year. In contrast, Consultant 2 reports annualized Sharpe Ratios of 0.38 and 0.39 for Mr. Smith's portfolio and for a "broad stock market index", respectively, and an annualized CAPM alpha of -0.21%. Is it possible that both consultants have correct calculations?
Explain in detail.
6) Mr. Newton Burt claims risk-adjustment is easy because "Once you have all the data in a spreadsheet, it is very easy to calculate Sharpe Ratios, CAPM alphas, Information Ratios, and Max DD." Is it possible that Mr. New B. is both right and wrong at the same time? Discuss.