Cooperative investment in a multi-period portfolio optimisation.
In this paper I develop a cooperative investment scheme in a multi-period portfolio optimisation. I suggest that agents can invest their joint capital in a common portfolio, and then divide the resulting outcome according to their risk-reward preferences. I prove that with this strategy all agents can achieve lower risk with the same expected profit, or greater expected profit with the same level of risk, compared to an optimal individual investment strategy. I define the strategy for an investor in a case of individual and cooperative investment, where the portfolio contains one risk-free asset and n risky securities in a single period, then I generalise the strategies into one risk-free asset and n risky securities for cooperative investment in a multi-period. I develop a dynamic programming algorithm to find the optimal time-consistent cooperative trading strategy, and construct the corresponding efficient frontier. The results are implemented and illustrated for components of the S&P 100 Index, for which the scenario tree for future returns was constructed using historical data simulation. In addition, I provide an example that is slightly modified from Grechuk and Zabarankin (2015) and seeks to show that if several agents have different risk preferences, they can reduce their investment risk using cooperation. This paper develops a technique for determining the optimal cooperative investment strategy in both one-period and multi-period portfolio optimisation frameworks. The key benefit from cooperation is that investors use different utility functions, and therefore can act as insurers for each other.
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