1. Long/short HedgeFund with Long Bias:150/50
A hedge fund has a capital of $100 million and invests in a long/short strategy on the U.S. equity
Market, with a long bias. It follows a 150/50 strategy, meaning 150% long and 50% short. Shares
can be borrowed from a primary broker. The primary broker accepts that securities be deposited
instead of cash. For any million of securities borrowed, the broker requires that 2 million of any
securities be deposited as collateral (for example you can borrow 10 million worth of security A
and deposit 20 million worth of security B). No additional costs are charged to borrow the shares.
The hedge fund has drawn up a list of shares regarded as undervalued (list U) and a list of
shares regarded as overvalued (list O). The hedge fund expects that shares in list U will
outperform the U.S. index by 3 percent over the year, while shares in list O will underperform the
U.S. index by 3 percent over the year.
a. What specific investment actions would you suggest?
b. Assume that the U.S. market goes up by 5% and that the expectations on shares U & O
materialize (alpha of + 3% and – 3%). Assume a zero interest rate. What is the return?
a. What specific investment actions would you suggest?
b. Assume that the U.S . Market goes up by 5% and that the expectations on shares U&O
materialize (alphaof+3%and- 3%).Assume a zero interest rate. What is the return?
c. Given the primary dealer requirement (For any million of securities borrowed, the broker requires that 2 millions of any securities be deposited as collateral), what is the maximum short position that you can take? [What I mean is could you become a170/70,
200/100 or 250/150 long/short hedge fund?].What is then the hedge fund return under the previous scenario?
2. Guaranteed Note with Equity Participation
You are a banker considering the issuance of a guaranteed note with stock index participation for a client. The current yield curve is flat at 4 percent for all maturities. Two-year at-the- money calls trade at 10 percent of the index value. You are hesitant about the terms to set in the structured note.
a. Your supervisor asks you to compute the “fair” participation rate that would be feasible
for a maturity of two years and a coupon rate of 0 percent, assuming the parvalueis
b. Explain the relationship between the amount of the guaranteed coupon and the participation rate that can be offered.
3. Optimal Hedge Ratio
A British investor holds a portfolio of British stocks. The market value of the portfolio is £20 million, with a β of 1.5 relative to the FTSE index. In November, the spot value of the FTSE index is 4,000. The dividend yield and pound interest rates are all equal to 4% (flat yield curve).
a. The investor fears a drop in the British stock market. The size of FTSE stock index contracts is ten pounds times the FTSE index. There are futures contracts quoted with December delivery. Calculate the futures price of the index.
b. How many contracts should you buy or sell to hedge the British stockmarket risk?
4. Impact of Execution Costs
You are an aggressive asset manager investing in Hong Kong stocks.Your highly-publicized investment objective is to provide clients with a performance equal to the return on the Hang Seng index plus 3%.You turn over the portfolio once a year to take advantage of tactical opportunities. You go through various brokers and they charge an average commission of
0.25 % that includes some stamp and VAT tax. A typical bid-ask spread forther at her illiquid securities that you specialize in is in the order of 1% for transactions of 1,000 shares or less. For transactions of more than 1,000 shares, brokers do not quote bid-ask spreads but try to execute the order at the best available price. Because you have become a large player on these securities, you are afraid that some of your transactions move the market price, especially your large transactions of smaller companies.For large orders(1,000 shares or more), you noticed that you have to buy (re:sell) well above (re:below) the previous market price; the difference is anaverage 1.5%.
• Over the year, the Hang Seng index went up by 10%. What should be your gross return to deliver on your promise?Assume that half your transactions (in market valu eterms)are for orders of less than 1,000shares, and half your transactions are for large orders (over 1,000shares).
5. Performance Calculation
A client has €1 million invested in European equity at the start of the quarter. After 1 month the portfolio value is €1.2 million and the client who needs cash withdraws € 300,000. At the end of the quarter the portfolio is worth €800,000. Over the quarter the European equity index, used as benchmark, gained 15%.
a. What are the rates of returns using the various methods outlined in the text? (No need to do the IRR calculations. Just write the equation to be solved.)
b. Which rate should you use to evaluate the performance of the manager relative to its benchmark?
6. Currency Risk Management
Today is April1st and you’re American. You hold €1million worth of European securities. You fear a depreciation of the euro. The spot exchange rate S is 1.25$ per € or 0.80 € per $. The forward rate maturing July 1 is also 1.25 $ per € or0.80 € per $. Currency options on the euro are traded in Chicago. The your options on 1 euro, maturing July 1 and whose prices (premium and strike) are given in U.S. cents in the following table:
120 5.5 0.5
125 1.9 2.0
•If you hedge using a forward contract, the bank requires no deposit.
• If you buy options, you make the simplifying assumption that you can purchase options by borrowing at a zero interest rate.
•You assume that your securities will keep exactly the same value on July1.
a. You decide to hedge. What will be the dollar value of your portfolio on July 1?
b. You decide to insure your portfolio using currency options. Do you need to buy/sell calls €/puts€?
c. Assume that you use options with a strike of 125 U.S cents. How many € options do you need to insure your portfolio?
d. Same question with options with a strike of120?
e. Simulate the results of your hedge and insurance with the two options if the spot exchange rate on July 1 is equal to 1.00 $ per €, 1.25 $ per €, and 1.50 $ per €. Fill the following table with the value of the portfolio in euros:
Portfolio Value in dollars on July 1:
Portfolio Hedge Options125 Options120
S = 1.00$per€ 1,000,000
S = 1.25$per€ 1,250,000
S = 1.50$per€ 1,500,000
f. Whatis the best choice if you think that the chances of the depreciation of the € are very
7. Asset Liability Management: Insurance Company
The balance sheet of TATA insurance company is given below, in millions of dollars.
InvestmentPortfolio 200 NetEquity 20
OtherAssets20 Various Obligations 200
Total 220 Total 220
The various obligations are calculated as the present value (market value) of expected future claims discounted at the proper market interest rate. The duration of the claims is 10.
The investment portfolio is madeup of 50 in stocks and 150 in bonds. The duration of the bond portfolio is 8.
Other assets have a fixed value.
Remember what the duration (D) of a bond is: When the interest rate goes up by X, the bond value loses D times X. For example a bond port folio with a duration of 5 will go down by 50 basis points (0.5%) if the interest rate goes up by 10 basis points. If the portfolio value is $100, it will go down by $0.5=5 0.1%$100.
Assume thatthestock marketgoesdownby15%andthatinterestrates movesdownby1.0%. What isthe newNetEquityofTATA insurancecompany?
8. Example of TaxAdjustment
A U.S. investor buys100 shares of Heineken listed in Amsterdam for 40 euros. She goes through a U.S. broker, and the current exchange rate is 1 euro=1.1 U.S .dollars . Her total cost is $4,400, or $44 per share of Heineken (40× 1.1$per €). Three months later, a gross dividend of € 2 is paid (15 percent with holding tax), and she decides to sell the Heineken shares. Each share is now worth 38 euros, and the current exchange rate is 1 euro = 1.2 U.S. dollars because the euro has sharply risen against the dollar. The same exchange rate applied on the dividend payment date. There is a tax treaty between the US and Netherlands.
a. What are the cash flows received in U.S.dollars?
b. Assume that her personal U.S. tax rate is 20% on both capital gain and in come. What is the net rate of return?
9. Cross-holding Adjustments–An Example
Four companies belong to a group and a relisted on a stock exchange. The cross-holdings of these companies are as follows.
•Company A owns 30% of Company Band 10% of Company C.
•Company B owns 20% of Company C.
•Company C owns 10% of Company A, 20% of Company B, and30% of Company D.
• Company D owns 20% of company B.
Each company has a market capitalization of $100 billion.You wish to adjust forcross-holding to reflect the weights of these companies in a market-capitalization weighted index.
a. What adjustments would you make in the market capitalization of each company to reflect the free float?
b. What would be the total adjusted market capitalization of the four companies?
10.Asset Allocation and Regret Theory
Assume that there is NO exchange rate risk. You are managing an equityMPF in Hong Kong and wonder about your global asset allocation.You believe that foreign markets will out perform HK, but nothing is sure.You do a mean variance optimization and find that you should allocate 80% abroad. You know that the theory of the CAPM tells you to allocate according to market capitalization weights; hence you should invest more than 95% in non-HongKong equity. On the other hand you observed the standard of MPF in Hong Kong is only to invest 40% abroad (average overall equity MPFs). Note ,that there is no RIGHT answer. Please consider that you are writing a short memo to your investment committee.
a. In the absence of specific expectations about returns in HongKong or abroad, what would regret theory suggest as global asset allocation?
b. Given all the information above,what will you choose as a percentage of asset allocation and why?
c. You decide to forget about regret and simply try to obtain the best risk-adjusted return.
Actually your own expectation is quite bullish about China and Hong Kong but you know that any forecast is uncertain. But you expect Hong Kong to out perform the rest of the world by some 2% (12% instead of 10%).HongKong sigma is 20% while that of the MSCI World index (excluding Hong Kong) is only 15% with a correlation of 0.5.You desire that the volatility (sigma) of your portfolio be no more than15%. How would you determine the optimal allocation between HK and the rest of the world?