You are managing a portfolio of equities for a pension scheme. The portfolio is actively managed with a benchmark of the FTSE All-Share Index, and its current value is £120 million. The scheme has decided it wishes to disinvest from this portfolio as quickly as possible, but selling all of the

Question

You are managing a portfolio of equities for a pension scheme. The portfolio is actively managed with a benchmark of the FTSE All-Share Index, and its current value is £120 million. The scheme has decided it wishes to disinvest from this portfolio as quickly as possible, but selling all of the equities could cause a fall in the price of some of the assets. You therefore decide to sell futures on the FTSE 100 Index to hedge price movements in your portfolio. The size of each FTSE 100 futures contract is £10 per point. The current FTSE 100 index value is 6,000. The volatility of the FTSE 100 Index, on which the future is based, is 15% per annum; the beta of the portfolio relative to the FTSE 100 index is 1.2. Calculate the number of contacts required to hedge this position.

Accepted Answer

Using Equation (16.8), the portfolio size, Y , is £120,000,000. The notional value of a futures contract, X, is the index value, 6,000, multiplied by the change in value for a one-point move, £10. This gives a current notional contract value of £60,000. Combining these with a value of 1.2 for $\beta_Y$ gives:

$N_h=\beta _Y\frac{Y}{X}=1.2\frac{120000000}{60000}=2400.$ (16.9)

[latex]N_h=\beta _Y\frac{Y}{X}=1.2\frac{120000000}{60000}=2400.[/latex] (16.9)

Question 16.1: You are managing a portfolio of equities for a pension schem...