Reference no: EM132170494

Part A - Short selling and capital -

Suppose that you are the manager of a dedicated short bias hedge fund with an NAV of $100M. You sell short 10 stocks, with a short position of $20M for each of them. Specifically, you borrow the shares through your broker and sell the shares. You must pass the shortsell proceeds as cash collateral as well as a 20% additional margin requirement. The positions are hedged by buying 8 stocks of $20M each. Your broker also finances the long positions and also requires a 20% margin on those.

a) What is the current minimum margin requirement? Correspondingly, what is the current level of free cash? What is the current balance sheet for the hedge fund?

b) If the margin requirement for long and short positions changed to 30%, would the current positions remain sustainable? If not, how much would they need to be scaled back?

c) Suppose that margin requirements remain at 20% and over the next year. Further, the overall stock market performs strongly, yielding a return of around 25% for major stock indices. The short positions increase in value by 10% and the long positions by 25%. The risk-free return is 4%, including on your brokerage account and your margin loans (no financing spread).

• What is the NAV at the end of the year?
• What is the percentage return of the hedge fund (ignoring transaction costs and other costs)?
• Did the hedge fund perform well? Specifically, how what was the hedge fund's alpha with respect to the market (assuming that all stocks have a beta of 1)?

d) Suppose instead that the stocks that you shortsell are on special such that the short proceeds earn a return of 0% instead of 4%. (The additional 20% margin cash for short positions earn the normal risk free rate.) Under this scenario, what is the return over the year?

Part B -

I) In problems 1-7, you back test an equity strategy called industry momentum. The idea is to buy industries on the rise, and short declining industries. The accompanying Excel spreadsheet has returns on 30 industry portfolios, the risk free return, and the market return. You can do the problem set using Excel or any other program of your choice.

1. Starting in 1927/07, for each industry and each month, compute the (arithmetic) average return over the previous 12 month for that industry (not including the month itself). Then for each month, rank the industries based on their past average return (hint: Excel has a function called "RANK(cell,range,1)"). Compute each industry's average rank (1=lowest past average return, etc.).

Which industry has the lowest average rank and which has the highest?

What is the average rank of these lowest and highest industries?

Plot of the rank of Autos industry over time.

Are the top industries stable or moving around a lot? I.e., is industry momentum a long-term bet on a few industries or a very dynamic strategy? Do you expect high or low turnover from this strategy?

2. Winner portfolio. Let the "winner industries" be the 15 industries with the highest past 12-month returns. For each month after 1927/07, compute the average return of the winner industries. I.e., compute the return on a portfolio of winner industries. (Hint: There are many ways of doing it. In Excel, an easy way is to use the function IF inside the function AVERAGE: ' = AVERAGE (IF( rank-range >= 16, return-range, "") )', but then you must hit control-shift-enter to execute (this is called an array formula). Another way is to do this in two steps: (1) For each industry, report the return if it is a top industry and a blank otherwise, IF(rank>= 16, return, ""). (2) Take the average of these numbers.)

• What is the average monthly return on this winner portfolio in excess of the risk free return?
• What is the standard deviation of its monthly excess returns?
• What is its monthly Sharpe ratio?
• What is its annualized Sharpe ratio?

3. Loser portfolio. Compute the return of a portfolio of "loser industries," the 15 industries with the worst past returns.

• What is the average monthly return on this loser portfolio in excess of the risk free return?
• What is the standard deviation of its monthly excess returns?
• What is its monthly Sharpe ratio?
• What is its annualized Sharpe ratio?
• What is the annualized Sharpe ratio of the overall market index?

4. Long-short ind-mom. Compute the return of a portfolio of that goes long $1 of winner industries and short $1 of loser industries each month. This is already an excess return. (To understand this, note that if you first compute the winner's and loser's excess returns over Rf and then subtract one from the other, then the risk-free rates will cancel.) Regress this monthly ind-mom excess return on the excess return of the market. (In Excel, you can use the function LINEST.)

• What is its annualized Sharpe ratio?
• What is the market beta and the t-statistic of the market beta?
• What is the monthly alpha and the t-statistic of the alpha?
• What is the annualized alpha (12 times monthly alpha)?
• Comment on these numbers.

5. Cumulative return. Compute the cumulative return of (a) the winner portfolio, (b) the loser portfolio, (c) the long/short ind-mom portfolio, and (d) the market. (Remember to use total returns, not excess returns, i.e., add the risk free return to the returns that are excess returns.) Plot these cumulative returns on a log-scale.

6. Ind-mom loss. Industry momentum had a big loss in 3 consecutive months in 2009. Which months? How did the market do those months? What do you think happened?

7. Suppose you buy the top N winner industries and shortsell the worst N loser industries, where N is some number. Above we consider the top/bottom half, so we had N=15, but the strategy might work better for a smaller N. A smaller N concentrates the portfolio is more extreme winners/losers, which might perform better, at the expense of less diversification. What has been the best N historically?

II) In problems 8-12, you have to explore the potential profits on trading twin stocks. The accompanying Excel sheet contain the stock price and the return index at close of 16 stocks, corresponding to two share classes for the following eight companies: A.P. Moller-Maersk (Denmark), Industrivärden, Investor, Svenska Handelsbanken and Volvo (Sweden), Volkswagen (Germany), Hyundai Motors (Korea) and Store Enso (Finland). All these shares pay dividends and you can assume that two stocks in the same pair pay the same dividend2 on the same day. Stock prices have been adjusted for splits, but not for dividends and other corporate actions, whereas you can think of the return index as a stock price adjusted for dividends and other corporate actions (i.e. with reinvested dividends etc.).

8. Pair correlation. First calculate the daily returns for each stock. Then calculate the correlation between daily returns for the stocks in the each pair. Make a bar plot of the correlations.

9. Pair co-movement. Adjust all the return indices to 100 on the September 8, 2004. Plot the return indices for stocks in the same pair together and assess whether you think there may be an arbitrage strategy. Do you see any unusual or surprising patterns?

10. Spreads. Calculate and plot the relative spread between the stock prices in the same pair (i.e., one price divided by the other minus 1) and assess whether you think there may be an arbitrage strategy. Do you see any unusual or surprising patterns?

11. Pairs trading based on absolute prices. Implement the following strategy: At close on the last day of each year, take a self-financing position in each pair where you go long the stock with the lowest price and short the one with the highest price. The initial value of each long position should be $1 and, similarly, the initial value of each short position should be $1. Hold the position for a year and rebalance again at close on the last day of the year.

a) Why might this strategy be profitable? Hint: What happens if the share price is unchanged from rebalancing to rebalancing?

b) Calculate the yearly excess return per pair, the SR, and test whether the yearly excess returns are statistically significant from zero (under the assumption that returns are independent and normally distributed).

c) Same as question b for a portfolio consisting of all eight pairs, equally weighted.

d) Which costs would you incur if you were to implement this strategy in practice?

12. Pairs trading based on "unusual" price spreads: mean-reversion. Consider the following alternative strategy: Put on a trade whenever the spread (relative price difference) between the stocks in a pair is "unusual" relative to the recent historical value of this spread. Specifically, at such times, go long $1 of the stock that is currently cheap (relative to what it "usually" is) and shortsell $1 of the stock which is currently expensive. Each day, either rebalance back to $1 long and $1 short or, when the spread again is "usual," close the position. The strategy can be implemented in many ways, for instance, you can do the following for each pair on each day.

Attachment:- Assignment Files.rar