# PM - Using multifactor Model EOC question

Hi,

Could someone please help me understand the EOC question number 9 in Reading 44, I thought the answer was B but as per the curriculum the answer is C and I am unable to comprehend this, help me please?

Expected Return

Factor Sensitivity

A

0.02

0.5

B

0.04

1.5

C

0.03

0.9

The arbitrage opportunity identified by Zapata can be exploited with:

A Strategy 1: Buy $50,000 Fund A and $50,000 Fund B; sell short $100,000 Fund C.

B Strategy 2: Buy $60,000 Fund A and $40,000 Fund B; sell short $100,000 Fund C.

C Strategy 3: Sell short $60,000 of Fund A and $40,000 of Fund B; buy $100,000 Fund C

-> to my understanding, Fund A and B will have 60 % and 40 % weights which gives this portfolio return of 2.8% ( buy A and B)

->and Fund C expected return is 3% ( sell Fund C).

Am I missing something here?

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Hi,

Given the factor sensitivities (risk factors) fund C is in relation to the funds A and B underpriced.

For example, if you wanna have the same expected return E(R) as fund C combining funds A and B you would purchase 50% of each with E(R)

_{A+B }= 3% and a combined factor sensitivity of 1.0. (Note, this is higher by 0.1 than the factor sensitivity of fund C)Hence, you want to exploit this mispricing by an

going long fund C while shorting a combination of funds A and B. (arbitrage strategy“Buy low, sell high”)1. Sell short $60,000 of fund A and $40,000 of fund B: E(R)

_{A+B }= -2.8% // Factor sensitivity_{A+B}= -0.92. Go long $100,000 fund C: E(R)

_{C }= +3.0% // Factor sensitivity_{A+B}= +0.93. Net position portfolio: E(R)

_{P }= +0.2% // Factor sensitivity_{P}= 0.0You earn a riskless return of 0.2%. This

because you are are simultaneously long and short the same risk-factor at an equal level - that is you hedged away the risk.return is riskless (=arbitrage)Regards,

Oscar

The objective is to create a portfolio whose sensitivity to the factor is zero, and which makes a positive profit.

Simplify the complicated side; don't complify the simplicated side.

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