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# R10.P1.T1.BODIE_CH10_Portfoloio_Arbitrage_SML

##### Active Member
Need some help understanding the breakdown of the Arbitrage Portfolio....   How is the Beta of the Portfolio .5 , the Return 7% and the Excess Rate 3%...?          #### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @gargi.adhikari I borrowed that example directly from Bodie (i am not very original! ). I hope I spoke to this, but the arbitrage portfolio = 50% security A + 50% the riskfree asset. It's β = 50%*1.0 + 50%*0 = 0.50, because the risk-free asset has a beta of zero, right? (it's correlation with the market factor is zero, so its beta is also zero). Similarly, the expected return = 50%*10% + 50% *4.0% = +7.0%. This is the achievement of an arbitrage opportunity in the single-factor world because we have Security C and the Portfolio (security A + Rf free rate) that have the same beta but different returns, so we can short Security C and buy the Portfolio with neutral net beta yet +1.0% return. I hope that answers it! Thanks,

##### Active Member
@David Harper CFA FRM Thanks so much for the clarification on this - very clear now     .....One lingering question on this....did we choose the 50 %-50% weightage of the Security A & the Risk Free Asset for some specific reason..?

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
@gargi.adhikari if you look at the SML, security C is below the line so it is mispriced and we can arbitrage if we buy the portfolio on the line (vertically above it) with the same beta, which is 0.50. So its because (C) has beta of 0.5 and we want an "efficient" portfolio with beta = 0.5. The easiest way to achieve this is mix in 50% Rf with Security (A). Thanks,