I have already done a, just not sure if it\'s right. A fund manager has a portfo

Question

I have already done a, just not sure if it's right.

A fund manager has a portfolio worth $50 million with a beta of 1.35. The manager is concerned about the performance of the market over the next three months and plans to use four-month Mini S&P 500 futures contract to hedge the risk. The current level of the index is 1,560, the risk-free rate is 0.60% per annum, and the dividend yield on the index is 1.7% per annum. The current four-month futures price is 1,555. One futures contract covers $50 times the index.

Solution:

Number of contracts to hedge = 1.35*$50000000/1560/250=173.07

Thus, rounding to the nearest whole number, the investor should short 173 contracts to eliminate exposure to the market.

Explanation / Answer

Though you were on the right track, your answer to 1a is incorrect. Let's work it out step by step:

Notional to hedge (you were correct): $50M * 1.35 = $67.5

Since S&P is a broad sector ETF we can treat it as nearly equal to the market itself. This means that we need to buy $67.5 M worth of S&P minis.

One S&P mini covers 50 * Index = $50 * 1560 = $78k of exposure. Therefore the number of contracts we need to buy is $50M / $78k = 641.025 contracts. In short 641 contracts.

(Im not sure why you divided by an extra 5).

Solution to 1b) Assuming beta for the portfolio remains the same (which is very rare), there will be no profit or less on the notional (ignoring rounding error of 0.025 contracts above).

However, we would have made money due to interest rate vs dividend yield of the future. Per Mini Contract, he would make 1600 * 50 * (1.7% - 0.6%) * 3/12 (in case 1) = $220. Therefore for 641 contracts he would have made $141k.

Similarly if the level was 1700 he would have made $149.8k

This is not much money compared to the notional at hand. Also assuming his portfolio's beta doesnt move and that div yield > interest rate yield.

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