A portfolio manager with a South African equity portfolio of R100 million is concerned that the market will decline within the next 3 months. The portfolio beta is 2.5 and the risk-free rate is 6% per annum (annually compounded) (NACA). Table 1A and Table 1B contain market data as at 1 January 2021 and 1 April 2021 respectively.

Table 1A: Market data available as at 1 January 2021:

Spot All Share Index level 67,250

Futures price All Share Index 68,800

Contract size R10 per index point

Delivery date 1 June 2021 Dividend yield on index 3% per annum (annually compounded) (NACA)

Table 1B: Market data available as at 1 April 2021:

Spot All Share Index level 52,101

Futures price All Share Index 52,200

Contract size R10 per index point

Delivery date 1 June 2021

Dividend yield on index 3% per annum (annually compounded) (NACA)

Required:

1.1 On 1 January 2021, calculate the number of contracts and what the position of the trade should be to eliminate all systematic risk in the portfolio. (1)

1.2 On 1 January 2021, the portfolio manager also wants to stress test two scenarios with respect to the portfolio. Calculate the number of contracts and the position of the trade to: 1.2.1 reduce the portfolio beta to 0.8. (1)

1.2.2 increase the portfolio beta to 2.7. (1)

1.3 With reference to 1.2, explain what the portfolio managers expectations are with respect to market changes when a) reducing the beta and b) increasing the beta. (1)

1.4 On 1 January 2021 the portfolio manager entered into the June futures contract to eliminate all systematic risk in the portfolio. On 1 April 2021 he decides to close out his futures position. 1.4.1

Explain how the portfolio manager will close out his futures position. (1)

1.4.2 Calculate the expected return on the portfolio for the three month period. (1)

1.4.3 Calculate the expected value of the portfolio including the hedge. (2)

1.4.4 Give two reasons why the portfolio manager can justify hedging the portfolio. (1)

1.4.5 Calculate the basis at the time the hedge is entered into (1 January 2021) and the basis when the hedge is closed out (1 April 2021) and indicate if the basis has strengthened or weakened. (1.5)

1.4.6 Explain how the change in the basis from (1 January 2021) to (1 April 2021) has impacted the portfolio manager in terms of the hedge. Calculate the net price of the short hedge using the basis.

(1.5) 1.5 Use the information in Table 1A relating to the market data for the All Share Index available as at 1 January 2021.

1.5.1 Determine what the theoretical price of the June futures contract should be. (2)

1.5.2 Given the answer in 1.5.1, determine whether an arbitrage opportunity exists. If there is, describe the steps you would take to take advantage of this opportunity on 1 January 2021. (no calculations are required, just describe the steps).