- A cocoa merchant currently has a cocoa inventory worth approximately $10 million at current spot of $1840 per metric ton.Cocoa futures trade on the Coffee, Cocoa and Sugar Exchange with contract size equal to 10 metric tons.Current price for a May contract is $1630 per metric ton.She would like to hedge with a minimum variance hedge ratio, so she calculates some statistics.The standard deviation of returns for her inventory is .27.The measured volatility of the futures contract price is .33.The correlation between the spot cocoa and futures contract price is .85.
- 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.

- Compute the current number of metric tons in inventory based on the current price. Calculate the minimum variance hedge ratio and optimal number of contracts to hedge with.
- Should she go short or long with her position?Explain.
- If the May contract closes at $1725 and convergence occurs, calculate the gains/losses on the hedged position.Was the hedge successful?Explain.

The portfolio currently has an asset value of $500 million.95% of it is invested in a stock portfolio that has an average beta = 1.0.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%.

a. Based on the portfolio weights, compute the portfolio weighted average over the six month period.Compare this return to the broad market return.How much did the portfolio underperform the market? Weighted average is the sum of component weight times component return.

b. 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. So we want to add 5% in portfolio value.

The current index futures price is 1200 and the contract size is $250 times the index.Based on these parameters, compute N*.

c. 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.

d. In three months, the following changes have taken place: The S&P 500 has gone from 1120 to 1220 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?

- Portfolio 1 consists of a 1-year discount (zero-coupon) bond with a face value of $2000 and a 10 year discount (zero-coupon) bond with a face value of $6000.Portfolio 2 consists of a 5.95 year discount bond with a face value of $5000.The current yield on all bonds is 10 per cent per annum.

- Show that both portfolios have the same duration. Compute the weights of each bond in Portfolio 1(weight=bond market value/portfolio value) and compute the weighted average duration. Remember market vale us the present value of all cash flows, discounted at 10%. Use continuous compounding.
- Show that the percentage change in portfolio value for a 0.1% increase in yield is the same for both portfolios. (Re-discount the bonds with the higher rate of 10.1%)
- Find the percentage change in portfolio values for a 5% increase in yields. (Same as b, new rate 10%+5%)
- A large mutual fund holds 100,000 shares of Alphabet (Google) common stock, which is currently trading at $1,202/share with a beta of 1.15.The CME Group E Mini Dow futures contract trades at $5 times the index, which for the June contract is at 25,542.

- The fund managers are worried about the volatility of the tech stocks in their portfolio, so they want to hedge.Construct a hedge position (short or long) on the basis of this fear.
- In June, their fears are realized.Alphabet has underperformed the market, closing at $1175 while the index is at 26,056.Calculate the performance of the hedge by computing the change in the portfolio position and the change in the futures position.Was it successful?Explain.