Pricing the "guarantee" in a guaranteed return equity fund
Team Latte
July 16, 2006

A fund manager was recently contemplating to sell a simple, absolute return vanilla equity fund of 5 year maturity that was linked to a basket of stocks that very closely mimicked the Hang Seng Index. He also wanted to add a guarantee feature so that the fund would guarantee a certain minimum return on the fund to the investors. The minimum return was decided to be 5% which was the 10-yr US Treasury rate. This meant that over the entire term, which was five years, the fund will return at least 5% annually (compounded) to the investors. This was to be guaranteed by the fund manager, i.e. the bank which was issuing the fund.

The fund manager wanted to charge a premium (cost) of 1.5% per year over and above the usual charges of management fee, administration costs, etc. for providing this guarantee. Was this a fair estimate for the guarantee? Let us see

The guaranteed return on the fund was 5%. The dividend yield on Hang Seng index is roughly 3.15%, and this can be safely used as a proxy for the dividend yield on the baske of stocks that made up the fund. Therefore, since dividends will return 3.15% per annum the capital gains on the basket of stocks must provide 1.85% per annum to match the guaranteed rate of 5% per annum. The current level of Hang Seng index was 15,500 and using a growth rate of 1.85% per annum the forecast level of the index at the end of 5 years should be:

Therefore, this should be the level of the index after 5 years for the fund to return at least 5% per annum return to the investors.

Thus the guarantee that a return of 5% per annum will be generated in the next five years on an index that is currently at 15,500 and has a dividend yield of 3.15% is equivalent to the right to sell the index for 17,002 in 5 years. In other words, this guarantee is nothing but a put option on the index with a strike of 17,002.

If we assume the volatility of Hang Seng Index (this is a very critical parameter and great care should be taken to estimate the value of the volatility) of 20% then the price of the put, using BSM, turns out to be 15.11%

Therefore, on an annualized basis the cost of the guarantee turned out to be 3.02%, far above the figure of 1.5% per year that the fund manager was contemplating to add. If the fund manager charged 1.5% per annum to the investors then he would be selling the put option on Hang Seng at a price far below the fair price of the put and would be absorbing the balance of the cost from his own pocket. He would be taking a risk but then he may be assuming that this is a calculated risk to take since the general sentiment in the market is one of optimism and a stock market is expected to move northwards in the coming years.

Reference: A very good book for Algorithmic trading strategies is Optimal Trading Strategies by Robert Kissell and Morton Glantz (American Management Association) where many of the above strategies are discussed in great detail .

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