The promoter of the film venture offers a new investment designed to attract reluctant investors. One unit of this new investment has a payoff of three times the original investment if the venture is highly successful, and it refunds the original investment otherwise. Assuming that the other three investment alternatives described in Example 11.6 are also available, what is the price of this money-back guaranteed investment?

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Example 11.6 (Residual rights) While pondering the possibility of investing in the film venture of the previous example, our investor discovers that it is also possible to invest in film residuals, which have a large payoff if the film is highly successful. Each dollar invested in residual rights produces $6 if the venture has high success and zero in the other two cases. Now what should the investor do? He must solve the portfolio optimization problem again with this new informa- tion. There are now three securities; the original film venture, the risk-free alternative, and residual rights. He will purchase these in amounts 01, 02, and 03, respectively. The necessary equations are .9 301 +1.202 +603 .36 + 301 +1.202+603 .4 + = 01 +1.202 .48 .36 + = 1.8 01 +1.202 1.202 301 +1.202+603 =. In addition there is the wealth constraint 01 +02+03 = W. These equations have solution =-1.0W, 02 = 1.5W, 03= .5W, and x = 1/W. In other words, the investor should short the ordinary film venture by an amount equal to his total wealth in order to invest in the other two alternatives.