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Worldwide stress on low carbon economy and reducing aggregate CO2 emission levels exposed fossil fuel GenCos to carbon risk associated with prices of carbon permits needed to be environmentally compliant. This risk is substantial for fossil fuel GenCos aiming to maximize profit. This paper addresses a power portfolio optimization approach for a fossil fuel GenCo to maximize profit and minimize risk of volatile input costs and output revenue. Carbon price risk along with fuel and electricity price risk with correlation between all revenue and cost side markets has been considered for portfolio selection using Markowitz mean variance theory. A realistic case study on Nordpool market illustrate that carbon price uncertainty considerations alter trading decision of GenCo in electricity market for efficient risk management. Correlated revenue and cost side markets provides better tradeoff in terms of profit and risk for same risk averse level for GenCo. Under strong correlation of electricity and carbon market a higher allocation in spot market provides risk protection. The carbon price risk impact is prominent for high emission GenCos.