Skip to content

FRM Part I · FRM Exam Part I · The Arbitrage Pricing Theory and Multifactor Models of Risk and Return

A fund's returns follow a two-factor model: R = alpha + 0.8 F1 + 1.5 F2 + e. The fund is worth USD 200 million. The manager hedges both factors using two tradable factor-mimicking portfolios, each with unit exposure to its own factor and zero exposure to the other. What hedge positions in the mimicking portfolios leave the fund with zero exposure to both factors?

Short USD 160 million of the first factor portfolio and short USD 300 million of the second. Each hedge notional is the factor beta times the fund value (0.8 x 200 and 1.5 x 200), and both are short because the fund's exposures are positive.

  1. AShort USD 160 million of F1 portfolio and short USD 300 million of F2 portfolioCorrect
  2. BShort USD 200 million of each portfolio
  3. CShort USD 250 million of F1 portfolio and short USD 133.3 million of F2 portfolio
  4. DShort USD 160 million of F1 portfolio and long USD 300 million of F2 portfolio

Explanation

Hedge notional equals exposure times value for each factor: 0.8 x 200 = 160 and 1.5 x 200 = 300, both short to offset positive exposures. Dividing 200 by the betas gives the third option's figures, which is wrong. Going long F2 would double the exposure.

Did you get it right without looking?

One question tells you little. A timed set on The Arbitrage Pricing Theory and Multifactor Models of Risk and Return shows your real accuracy, how long you take and where you lose marks.

Practise The Arbitrage Pricing Theory and Multifactor Models of Risk and ReturnFree diagnostic mock

More The Arbitrage Pricing Theory and Multifactor Models of Risk and Return questions