  Portfolio managers often evaluate performance relative to benchmark, usually
taken to be the Standard & Poor 500 stock index fund. This relative portfolio
wealth is defined as the absolute portfolio wealth divided by wealth from
investing in the benchmark (including reinvested dividends). The classic Merton
problem for portfolio optimization considers absolute portfolio wealth. We
combine absolute and relative wealth in our new utility function. We also
consider the case of multiple benchmarks. To both absolute and relative wealth,
we apply power utility functions, possibly with different exponents. We obtain
an explicit solution and compare it to the classic Merton solution. We apply
our results to the Capital Asset Pricing Model setting.
