Question

A German investor holds a portfolio of British stocks. The market value of the portfolio is £20 million, with a ß of 1.5 relative to the FTSE index. In November, the spot value of the FTSE index is 4,000. The dividend yield, euro interest rates, and pound interest rates are all equal to 4% (flat yield curves). The German investor fears a drop in the British stock market (but not in the British pound). The size of FTSE stock index contracts is 10 pounds times the FTSE index. There are futures contracts quoted with December delivery. Calculate (cell formulas or algebra) the futures price of the index and explain your answer. b. How many contracts should you buy or sell to hedge the British stock market risk? Calculate (cell formulas or algebra) & explain your answer. You believe that the capital asset pricing model (CAPM) applies to British stocks. The expected stock market return is 10%. What is the expected return on this portfolio before and after hedging? Calculate (cell formulas or algebra) & explain your answer.

Answer 1

a.

The futures price is computed using the following formula :-

Futures Price = Spot Price × (1 + Risk-Free Interest Rate – Income Yield or Dividend Yield)

For computing the FTSE futures price, the risk-free interest rate will be taken as the Pound Interest Rate

Pound Interest Rate = 4%

Dividend Yield = 4%

Therefore,

Futures Price = Spot Price * (1 + 0.04 – 0.04)

Futures Price = 4,000 * 1 = 4,000

b.

To find out number of contracts required to buy or sell, we will use the following formula :-

(Target Beta - Portfolio beta) / (Beta of futures contract) * (Current Value of Portfolio / Price of the Futures Contract * Contract Multipler or lot size of futures contract)

Contract size = 10

To completely hedge the stock market risk, target beta should be set equal to 0

No of contracts = ( 0 - 1.5) / 1 * ( 20,000,000 / 4,000 * 10 ) = 750 contracts

Hence, we should sell 750 contracts to completely hedge the stock market risk

c.

Expected return before hedging :-

Beta of the portfolio before hedging = 1.5

4% + (10% - 4%) * 1.5 = 13%

Expected return after hedging :-

Beta of the portfolio after hedging = 0

Hence, expected return

= 4% + (10% - 4%) * 0 = 4%