Market timing is generally viewed as the ability of the fund manager to profitably move from one asset class to another. The original Jensen technique to calculate alpha, whether from the market model or from multi-factor models, does not
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distinguish between market timing and fund manager skill in security selection (Moneta, 2015). Skilled fund managers, in addition to trying to select the most under- priced stocks given the risk objective of the fund, can also increase returns by timing the market based on their expectations of future market movements. Clark (2013) posits that fund managers can exhibit market timing skills by switching into defensive, low beta stocks in bear markets and aggressive, high beta shares in bull markets. If fund managers can successfully time the market, then returns to the fund will be high in bull markets due to investment in aggressive stocks and still relatively high in bear markets due to switching to defensive stocks.
Various performance measurement models endeavour to distinguish security selection capability from market timing ability, or the ability to forecast the market returns. Although alpha ordinarily measures both, market-timing models were developed to distinguish between these two aspects of performance. The two most common tests for market timing used in the literature are those of Treynor and Mazuy (1966) and Henrikson and Merton (1981). These have been used extensively in recent studies like those of DeAngelo et al. (2010), Kostakis et al. (2011) and Bolton et al. (2013). However, it has been noted that most fund managers are not able to successfully time the markets, and thus, such actions may have dire consequences since investors are now exposed to a higher level of risk per unit of return than they were willing to take initially (Qian and Shi, 2010).
2.6.1 The Treynor-Mazuy Model
The Treynor and Mazuy (1966) test of market timing imposes a quadratic term in the factor model to capture market timing and is famously referred to as the Treynor- Mazuy model. Numerous studies on market timing ability, such as Patton (2009), Kostakis et al. (2011) and Hoffman (2012), normally boost standard factor model regressions with a term that captures the convexity of fund returns derived from market timing. In the single factor model the quadratic term attempts to capture the nonlinear relation between excess fund returns and excess market returns. With regard to the Treynor-Mazuy model, the sign on the estimated coefficient of the quadratic term, and whether it is statistically different from zero, captures market- timing ability. Kostakis et al. (2011) asserts that if the market timing coefficient is significantly positive then it represents a convex, upward sloping regression line and
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indicates a confirmation of successful market timing by the portfolio manager. Thus, the coefficient will be positive if the manager raises beta upon acquiring a positive signal about the market. The hypothesis of no timing ability suggests that the coefficient ‘Ƴ’ on the quadratic term is zero or negative. The model is expressed as follows;
𝑅𝑖𝑡 = 𝛼𝑖 + 𝛽1𝑖(𝑅𝑀𝑡− 𝑅𝑓𝑡) + Ƴ(𝑅𝑀𝑡− 𝑅𝑓𝑡)2+ 𝜀𝑖𝑡 (9)
Where the formula follows the same format as the CAPM model, with the only exception being the addition of the squared market risk premium term preceded by the coefficient ‘Ƴ’ for market timing.
2.6.2 Henrikson - Merton Model
Henrikson and Merton (1981) developed an identical model (popularly known as the Henrikson-Merton model) of market timing by capturing the convex association between the return of a successful market timer's portfolio and the market return.
However, their model allows the portfolio's beta (risk) to oscillate between two levels conditional on the size of the market's excess return.
The Henrikson-Merton model tests for market timing ability using a similar regression to the Treynor-Mazuy model, with the only difference in the quadratic term being a + sign for the superscript instead of the 2 for the squared term. This term represents the maximum eigenvalue between zero and the market risk premium, and, thus, if its coefficient (δ) is significantly positive then it indicates evidence of successful market timing by the fund manager (Bodnaruk et al., 2015). The model is expressed as follows;
𝑅𝑖𝑡 = 𝛼𝑖 + 𝛽1𝑖(𝑅𝑀𝑡− 𝑅𝑓𝑡) + 𝛿(𝑅𝑀𝑡− 𝑅𝑓𝑡)++ 𝜀𝑖𝑡 (10)
Where (𝑅𝑀𝑡− 𝑅𝑓𝑡)+ = Max (0,𝑅𝑀𝑡− 𝑅𝑓𝑡) (11)
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In essence, both market timing methods try to capture the non-linearity of fund managers performing better than expected in bull markets and not performing as bad as expected in bear markets. Expression (11) above can also be written as (𝑅𝑀𝑡− 𝑅𝑓𝑡)+ = (𝑅𝑀𝑡− 𝑅𝑓𝑡)𝐷 where D is a dummy variable that is equal to 1 when (𝑅𝑀𝑡− 𝑅𝑓𝑡) positive and 0 otherwise. The magnitude of 𝛿 computes the disparity between the target betas, and will be positive for a portfolio manager that successfully times the market.
In other words, Henrikson and Merton (1981) advocates that the beta of the portfolio takes only 2 values. If the excess return on the market is positive, (𝑅𝑀𝑡− 𝑅𝑓𝑡)+ will be 1, otherwise it will be zero. Hence the beta of the portfolio is 𝛽1𝑖+ 𝛿 in bull markets and 𝛽1𝑖 in bear markets from equation (10).
A large body of evidence such as Blitz et al. (2012), Clark (2013) and Philippon (2015), exists which corroborates the EMH in reference tests of the market timing capability of portfolio managers. Accordingly, literature has it on record that future market movements are implicitly uncertain and, thus, investors who do not precisely forecast the market would face grave consequences (Malhotra, 2012).