There are two well–diversified portfolios in the economy, portfolio A and portfolio B. Portfolio A has...

There are two well–diversified portfolios in the economy, portfolio A and portfolio B. Portfolio A has beta of 1.5 and expected return of 14%, while portfolio B has beta 0.9 and expected return of 11.4%. If the expected return on the market is 12% and risk–free rate is 6%, is there an arbitrage opportunity? If so, show your arbitrage strategy.

Expert Solution

CAPM Formula = Required Rate of Return = Risk Free Rate + Beta * (Market Return - Risk Free Rate)

Portfolio A:

Required Rate of Return = Risk Free Rate + Beta * (Market Return - Risk Free Rate)

Required Rate of Return = 6% + 1.50 * (12% - 6%)

Required Rate of Return = 15%

Expected Return of Portfolio A = 14%

Expected return of portfolio A is less than required rate of return calculated as per CAPM. it means the stock is overpriced. so arbitrage is possible . The strategy would be short sell portfolio A

Portfolio B:

Required Rate of Return = Risk Free Rate + Beta * (Market Return - Risk Free Rate)

Required Rate of Return = 6% + 0.90 * (12% - 6%)

Required Rate of Return = 11.40%

Expected Return of Portfolio A = 11.40%

Expected return of portfolio A is equal to required rate of return calculated as per CAPM. it means the stock at par with CAPM. so arbitrage is not possible thus there will be no strategy.

jeff jeffy answered 3 months ago

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