PM - Using multifactor Model EOC question


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?


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® as fund C combining funds A and B you would purchase 50% of each with E® 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® A+B = -2.8% // Factor sensitivity A+B = -0.9 2. Go long $100,000 fund C: E® C = +3.0% // Factor sensitivity A+B = +0.9 3. Net position portfolio: E® 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.