Orb Trust (Orb) has historically leaned toward a passive management style of its portfolios. The only model that Orb’s senior management has promoted in the past is the capital asset pricing model (CAPM). Now Orb’s management has asked one of its analysts, Kevin McCracken, CFA, to investigate the use of the arbitrage pricing theory (APT) model.McCracken believes that a two-factor APT model is adequate, where the factors are the sensitivity to changes in real GDP and changes in inflation. McCracken has concluded that the factor risk premium for real GDP is 8% while the factor risk premium for inflation is 2%. He estimates for Orb’s High Growth Fund that the sensitivities to these two factors are 1.25 and 1.5, respectively. Using his APT results, he computes the equilibrium expected return of the fund. For comparison purposes, he then uses fundamental analysis to compute the actually expected return of Orb’s High Growth Fund. McCracken finds that the two estimates of the Orb High Growth Fund’s expected return are equal.McCracken asks a fellow analyst, Sue Kwon, to provide an estimate of the expected return of Orb’s Large Cap Fund based on fundamental analysis. Kwon, who manages the fund, says that the expected return is 8.5% above the risk-free rate. McCracken then applies the APT model to the Large Cap Fund. He finds that the sensitivities to real GDP and inflation are .75 and 1.25, respectively.McCracken’s manager at Orb, Jay Stiles, asks McCracken to construct a portfolio that has a unit sensitivity to real GDP growth but is not affected by inflation. McCracken is confident in his APT estimates for the High Growth Fund and the Large Cap Fund. He then computes the sensitivities for a third fund, Orb’s Utility Fund, which has sensitivities equal to 1.0 and 2.0, respectively. McCracken will use his APT results for these three funds to accomplish the task of creating a portfolio with a unit exposure to real GDP and no exposure to inflation. He calls the fund the “GDP Fund.” Stiles says such a GDP Fund would be good for clients who are retirees who live off the steady income of their investments. McCracken does not agree with Stiles, but says that the fund would be a good choice if upcoming supply side macroeconomic policies of the government are successful.If the GDP Fund is constructed from the other three funds, which of the following would be its weight in the Utility Fund? (a) −2.2; (b) −3.2; or (c) .3.

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Asked Mar 8, 2020
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Orb Trust (Orb) has historically leaned toward a passive management style of its portfolios.
The only model that Orb’s senior management has promoted in the past is the capital asset pricing model (CAPM). Now Orb’s management has asked one of its analysts, Kevin McCracken, CFA, to investigate the use of the arbitrage pricing theory (APT) model.
McCracken believes that a two-factor APT model is adequate, where the factors are the sensitivity to changes in real GDP and changes in inflation. McCracken has concluded that
the factor risk premium for real GDP is 8% while the factor risk premium for inflation is 2%.
He estimates for Orb’s High Growth Fund that the sensitivities to these two factors are 1.25 and 1.5, respectively. Using his APT results, he computes the equilibrium expected return of the fund. For comparison purposes, he then uses fundamental analysis to compute the actually expected
return of Orb’s High Growth Fund. McCracken finds that the two estimates of the Orb High Growth Fund’s expected return are equal.
McCracken asks a fellow analyst, Sue Kwon, to provide an estimate of the expected return of Orb’s Large Cap Fund based on fundamental analysis. Kwon, who manages the fund, says that the expected return is 8.5% above the risk-free rate. McCracken then applies the APT model to the Large Cap Fund. He finds that the sensitivities to real GDP and inflation are .75 and 1.25, respectively.
McCracken’s manager at Orb, Jay Stiles, asks McCracken to construct a portfolio that has a unit sensitivity to real GDP growth but is not affected by inflation. McCracken is confident in
his APT estimates for the High Growth Fund and the Large Cap Fund. He then computes the sensitivities for a third fund, Orb’s Utility Fund, which has sensitivities equal to 1.0 and 2.0,
respectively. McCracken will use his APT results for these three funds to accomplish the task of creating a portfolio with a unit exposure to real GDP and no exposure to inflation. He calls the fund the “GDP Fund.” Stiles says such a GDP Fund would be good for clients who are retirees who live off the steady income of their investments. McCracken does not agree with Stiles, but says that the fund would be a good choice if upcoming supply side macroeconomic policies of the government are successful.

If the GDP Fund is constructed from the other three funds, which of the following would be its weight in the Utility Fund? (a) −2.2; (b) −3.2; or (c) .3.

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Expert Answer

Step 1

The question is based on the concept of fund performance and factor to impact it with three different funds structure as High Growth Fund, Large Cap Fund and Utility Fund

Step 2

In order to construct a GDP fund, we should eliminate inflation factor. The three different equation will be formed with different variables of High Growth Fund(X), Large Cap Fund(Y) and Utility Fund (Z)

  1.   three equations with the GDP sensitivity of all three funds will equal 1 as  the first equation, inflation sensitivity of all funds  will equal 0 as the second equation and the sum of all fund weights must equal 1 as the third equation.

Finance homework question answer, step 2, image 1

    2. Solving the above equations as

  • Equation 2 – 2* equation 1 , will get

Finance homework question answer, step 2, image 2

  •    Equation 1- Equation 3, will get

Finance homework question answer, step 2, image 3

  • Thus, the above equation

Finance homework question answer, step 2, image 4 can be rewritten as

Finance homework question answer, step 2, image 5

  • Putting the value in equation 3 ,

  Finance homework question answer, step 2, image 6

...

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