Leland,O'Brien and Rubinstein (Who Invented Portfolio Insurance)came Up with a Product

question 75

Essay

Leland,O'Brien and Rubinstein (who invented portfolio insurance)came up with a product called "supershares." The product works as follows.It starts with two conventional funds: an index fund owning stocks in the S&P 500 and a money-market fund.
The index fund is divided into two securities.One of those securities is called a "dividend share" and gives the holder the right to all dividends paid during three years and all price appreciation up to 25% during those three years.The other security is called an "appreciation share" and gives the holder the right to all price appreciation above 25% during those three years.
The money-market fund is also divided into two securities.One of those securities is called a "money market income supershare" and the other security is called a "protection supershare".The money market supershare gives the holder the right to all interest income during three years.At the end of those three years,the holder may also get back some or all of the principal value,depending on how well the stock market performs.For every 1% that the S&P 500 has fallen below its current level,the principal value payable to the holder of a money market supershare is reduced by 1% and is instead paid to the holder of a protection supershare (which also has a three-year lifetime).
Assume that the current level of the S&P 500 index is 277,that the standard deviation of the index is 25%,and that the average dividend yield on the index is 4%.Also assume that the current six-month T-bill rate is 8% (which is also the rate on the money-market account)and that money-market fund securities are in units of $100.
(Hints: Remember that the value of the dividend share plus the appreciation share equals the current level of the S&P 500 index and that the value of the money market income supershare plus the protection supershare equals the value of the money market fund.Also,you can adjust for dividends in the Black-Scholes formula by subtracting the dividend yield from the riskless rate and then using this adjusted rate instead of the riskless rate in the formula.)
a. Estimate the value of the appreciation share.
b. Estimate the value of the dividend share.
c. Estimate the value of the protection supershare.
d. Estimate the value of the money market income supershare.

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