LOS j: Discuss and compare macroeconomic factor models, fundamental factor models, and statistical factor models.
Orb Trust (Orb) has historically leaned towards 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 model (APT).
McCracken has determined that a two-factor APT model is adequate where the factors are the sensitivity to changes in real GDP and changes in inflation. McCracken’s analysis has led him to the conclusion that the factor risk premium for real GDP is 8 percent while the factor risk premium for inflation is 2 percent. 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 expected return of the fund. For comparison purposes, he then uses fundamental analysis to also compute the 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 upon fundamental analysis. Kwon, who manages the fund, says that the expected return is 8.5 percent 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 0.75 and 1.25 respectively.
Kwon wants to learn more about the APT and discusses McCracken’s results with him. McCracken says “the APT model is a variation of the CAPM.” Kwon comments that “extending the CAPM to an APT framework must require additional assumptions.”
Craig Newland joins the conversation. Newland says that the APT really is just another ad hoc multifactor model. All a researcher needs to do to compose an APT model, according to Newland, is to find a few macroeconomic factors that are correlated with stock returns and do a simple linear regression for each asset. McCracken says that it really is not that easy. For one thing, according to McCracken, the coefficients in the APT have a different interpretation from that of a basic multifactor model.
McCracken’s manager at Orb, Jay Stiles, asks McCracken to compose 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 says that the fund would be a good choice if upcoming supply-side macroeconomic policies of the government are successful.
McCracken’s estimate of the expected return of Orb’s High Growth Fund would be:
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the risk-free rate plus 10%. | |
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the risk-free rate plus 13%. | |
The formula is: expected return = RF + 0.08 × 1.25 + 0.02 × 1.5 = RF + 13% (Study Session 18, LOS 66.j)
With respect to McCracken’s APT model estimate of Orb’s Large Cap Fund and the information Kwon provides, an arbitrage profit could:
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be earned by buying the High Growth Fund and selling short the Large Cap Fund. | |
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be earned by buying the Large Cap Fund and selling short the High Growth Fund. | |
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Based on the sensitivities to real GDP and inflation of 0.75 and 1.25, McCracken would calculate the expected return for the Orb Large Cap Fund to be:
expected return = RF + 0.08 × 0.75 + 0.02 × 1.25 = RF + 8.5%
Therefore, Kwon’s fundamental analysis estimate is congruent with McCracken’s APT estimate. If we assume that both Kwon’s and McCracken’s estimates of the return of Orb’s High Growth Fund are accurate, then no arbitrage profit is possible. Had Kwon provided an estimate of the Orb Large Cap Fund’s expected return that was less than 8.5 percent, for example, then we would consider selling that fund short and purchasing the High Growth Fund with the proceeds. (Study Session 18, LOS 66.l)
With respect to McCracken and Kwon’s comments concerning the relationship of the APT to the CAPM:
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both McCracken and Kwon are wrong. | |
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Kwon is correct and McCracken is wrong. | |
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McCracken is correct and Kwon is wrong. | |
McCracken is correct in saying the APT is a variation of the CAPM. Both the APT and the CAPM are equilibrium asset-pricing models. For example, both models assume there are no arbitrage opportunities available. The APT requires fewer (not more) assumptions, however, e.g., the APT does not assume all investors will hold the same portfolio and have the same expectations. (Study Session 18, LOS 66.n)
In the conversation between Newland and McCracken concerning the relationship of multifactor models in general and the APT:
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Newland was correct and McCracken was wrong. | |
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McCracken was correct and Newland was wrong. | |
The APT is a special case of a multifactor model. Two of the most important distinguishing characteristics are that the coefficients in the APT are not simply regression coefficients from a regression of returns over time on some factors that have been selected ad hoc. In the APT the coefficients are premiums for an asset’s exposure to certain types of risk. Their values represent a no-arbitrage condition, which is an important assumption in the APT that a general multifactor model does not require. (Study Session 18, LOS 66.j)
The GDP Fund composed from the other three funds would have a weight in Utility Fund equal to:
In order to eliminate inflation, the following three equations must be solved simultaneously, where the GDP sensitivity will equal 1 in the first equation, inflation sensitivity will equal 0 in the second equation and the sum of the weights must equal 1 in the third equation.
1. 1.25wx + 0.75wy + 1.0wz = 1
2. 1.5wx+ 1.25wy + 2.0wz = 0
3. wx + wy + wz = 1
Here, “x” represents Orb’s “High Growth Fund”, “y” represents “Large Cap Fund” and “z” represents “Utility Fund.” By multiplying equation 1 by 2.0 and subtracting equation 2 from the result, McCracken will get wx + 0.25wy = 2. McCracken can also subtract equation 3 from equation 1 and get 0.25wx – 0.25wy = 0. This means wx = wy. Thus, the equation wx + 0.25wy = 2 becomes 1.25wy = 2 and wy = wx = 1.6. It follows from any of the other equations that wz = -2.2.
(Study Session 18, LOS 66.j)
With respect to the comments of Stiles and McCracken concerning for whom the GDP Fund would be appropriate:
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McCracken was correct and Stiles was wrong. | |
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Stiles was correct and McCracken was wrong. | |
Since retirees living off a steady income would be hurt by inflation, this portfolio would not be appropriate for them. Retirees would want a portfolio whose return is positively correlated with inflation, to preserve value, and less correlated with the variable growth of GDP. Thus, the fund would not be appropriate for retirees and Stiles is wrong. McCracken is correct in that supply side macroeconomic policies are generally designed to increase output at a minimum of inflationary pressure. Increased output would mean higher GDP, which in turn would increase returns of a fund positively correlated with GDP. (Study Session 18, LOS 66.j)
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发表于 2010-4-14 15:47
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