This problem set has two parts. Part 1 deals with stock portfolio hedges.  These situations would be handled with stock index futures contracts.  Part 2 deals with bond portfolio hedges.  These can be handled with a variety of hedging techniques such as duration-based hedging, conversion factor weighting, or other means of constructing hedge ratios with bond characteristics.

Finance 410 Exam 2 Problems

Winter 2020

Dr. Belcher

This problem set has two parts. Part 1 deals with stock portfolio hedges.  These situations would be handled with stock index futures contracts.  Part 2 deals with bond portfolio hedges.  These can be handled with a variety of hedging techniques such as duration-based hedging, conversion factor weighting, or other means of constructing hedge ratios with bond characteristics.

The assignment will begin on Tuesday, March 31 and end on Friday April 3 at 5 PM EDT. Good luck!

Part 1: Stock Portfolio Hedging

For each problem, follow the instructions to evaluate your price expectations, construct your hedge, and evaluate its performance.

1. A large mutual fund holds 100,000 shares of Lowe’s common stock, which is currently trading at $87/share with a beta of 1.25. The DJIA E-mini futures contract trades at $5 times the index, which for the June contract is at 21,636.

1. The fund managers are worried about a major slowdown in construction spending, which could hurt Lowe’s. Construct a hedge position (short or long) on the basis of this fear. Compute N* = β S/F = optimal number of contracts for the hedge. Round up to the nearest whole contract.
2. In June, their fears are realized. Lowe’s has underperformed the market, closing at $82 while the index is at 22,320.  Calculate the change in their portfolio holdings and the change in their futures position. Now compute the net change in their position (portfolio change + futures change). Was their strategy successful?

2. An equity portfolio manager rarely is fully invested in the fund, but will have some funds in cash. Unfortunately, this creates what is called a “cash drag” on the portfolio due to the low returns on cash funds.  One way to deal with this is called “neutralizing cash”.  It involves using stock index futures to “synthetically” raise the equity position of the portfolio to overcome the cash drag. A “synthetic” financial instrument is one that artificially mimics another financial product but in a different way. It “copies” the other instrument but is structured differently.

The portfolio currently has an asset value of $100 million.  95% of it is invested in a stock portfolio that has an average beta = 1.10.  The remaining 5% is in a cash fund.  In a six-month period, the broad market (S&P) rises by 11.50% while the cash fund rises by 2.5%.

1. Based on the portfolio weights, compute the portfolio weighted average return over the six-month period. Compare this return to the broad market return. How much did the portfolio underperform the market?
2. One way to add returns is to “synthetically” add stock exposure with stock index futures. We want to have a synthetic portfolio that has 100% stock exposure, so we need to “add” 5% of the portfolio value in stock index futures:

N* = optimal number of contracts = (additional portfolio size in dollars/size of futures contract in dollars) X portfolio beta

The current index futures price is 1100 and the contract size is $250 times the index.  Based on these parameters, compute N*.

1. This is different than a hedge in that we want the additional stock exposure, so we would take a long position in futures. The chosen contract will mature three months from today.
2. In three months, the following changes have taken place: The S&P 500 has gone from 1120 to 1150 and the contract matures, so convergence takes place. Based on these parameters, analyze the performance of the futures position. How much portfolio value did the “extra” equity exposure add?

3. A corporate takeover bid is often pursued in stages as the acquiring firm seeks a controlling interest in the acquisition. A company, company A, has identified company B as an acquisition target.  B’s stock is currently trading at $26.50 per share.  If word leaks, then the stock price will likely be driven up, increasing the cost of the acquisition.  The firm therefore wants to hedge against this possibility.
4. The company wants to buy 100,000 shares on January 1. Company B’s stock currently has a beta of 0.9.  March contracts on the S&P 500 are trading at 2541.7, with a multiplier of $250 times the index price.   Based on this, construct an optimal hedge using the March S&P contract.
5. On December 17, B’s stock is trading at $28.25 and the March futures price is 2658.50. Calculate the additional cost of the shares as well as the gain/loss on the futures position.  Was the hedge successful?

Part 2: Bond Portfolio Hedging

Follow the same steps as in Part 1.  Evaluate your price or interest rate expectations, construct your hedge, then evaluate its performance.

4. There are a number of ways to construct bond hedge ratios. One way to write a duration-based hedge ratio is as follows:

Hedge Ratio = CF_ctd X (P_b X D_b)     where

(P_f X D_f )

CF = conversion factor for CTD bond

P_b = price of bond portfolio as percentage of par

D_b = duration of bond portfolio

P_f = price of futures contract as percentage of 100%

D_f = duration of CTD bond for futures contract

A bond portfolio manager holds a bond portfolio with a face value of $8 million that is currently worth a market value of $8.25 million.  The manager is concerned about future rising interest rates and so decides to hedge with a T-Bond futures contract.  The cheapest to deliver bonds have an 8 1/8% coupon and a projected duration at maturity of 12 years.  Their conversion factor is 1.125 and at their current price the futures price is 98-02.  The current duration of the bond portfolio is 5.25 years.

1. Based on the above data, compute the optimal hedge ratio.
2. Based on the interest rate expectations, should they take a short or long position?
3. The optimal number of contracts to hedge with is given by:

Number of contracts = HR X (Portfolio current market value/current value of futures contract)

Where each futures contract is for $100,000 face value of bonds.

Based on this, compute the optimal number of futures contracts to hold.

1. The closing futures contract price is 89-00. Based on this, how did the futures position perform?

5. A bond fund currently holds a bond portfolio with a face value of $10 million. The current market value of the portfolio is only 92.2% of face, however.  The fund’s managers anticipate a rise in bond yields (interest rates) in the near future, so they desire a T-bond hedging strategy to protect themselves.

1. Given their rate expectations, should they short or go long in T-bond futures? Explain.
2. The risk managers use $100,000 face value T-bond contracts. If they use a 1-1(naïve) hedge ratio between cash and futures positions, how many contracts should they use?
3. The deliverable bonds are 10 ¾% with a conversion factor of 1.2922. If accrued interest is zero, what cash amount would be transacted per contract if the quoted futures price is 76-31?
4. At close, the market value of the bond portfolio is now 90.2% of face. The cash amount transacted per contract is .97458 times the face value of the futures contract.  Calculate the loss in the bond portfolio’s market value versus the change in value of the hedge.
5. Did the hedge work?  Explain.

6. On February 24 a company decides to issue $5 million face value in new bonds on May 24.  They desire to issue them at their current coupon rate of 13.76%. They will be priced at par value with a 20-year maturity and duration of 7.22 years.  However, if rates rise while due diligence is occurring, the market will factor that into the bonds’ value, resulting in less funds being raised. To deal with this, they decide to hedge the issue.

11. June futures contracts are trading at 68-11.
12. The CTD bond underlying the futures contract has a yield of 13.60% and a projected duration of 7.83 years.
13. The optimal number of contracts is given by:

N* = (P_b X D_b) (1+YTM_ctd)    where

(P_f X D_f ) (1+YTM_b)

P_b = dollar value of bond portfolio at par

D_b = duration of bond portfolio

P_f = dollar value of one futures contract at current price

D_f = duration of CTD bond for futures contract

YTM_ctd = Yield to Maturity of CTD bond

YTM_b = Yield to Maturity of the portfolio

Face value of TBond futures contract = $100,000

1. Should they take a short or long position and why? Compute N* for the hedge.
2. On May 24 the bonds are issued and the futures position closed out. The yield on comparable bonds is now 15.25%, so the bonds are issued at a 13.76 coupon but at a price of 90.74638/100 face.  Compute the new value of the portfolio and how much it lost in value because of the rate change.
3. The futures price at close is now 60-25. Compute the gain on the futures position based on this and N*.
4. Compute the performance of the hedge. Did the hedged portfolio gain or lose value?