# 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 arbitrage strategy going long fund C while shorting a combination of funds A and B. (“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 = -0.9
2. Go long \$100,000 fund C: E(R) C = +3.0% // Factor sensitivity A+B = +0.9
3. Net position portfolio: E(R) P = +0.2% // Factor sensitivity P = 0.0

You earn a riskless return of 0.2%. This return is riskless (=arbitrage) because you are are simultaneously long and short the same risk-factor at an equal level - that is you hedged away the risk.

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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